JP2000022750A - Communication network design circuit, its method, and storage medium recording program and read by machine - Google Patents

Abstract

PROBLEM TO BE SOLVED: To design a link capacity and a node capacity of a communication network on the premises that a traffic demand is fluctuated. SOLUTION: In order to represent fluctuation in a traffic pattern, a demand is given as a random variable. In order to handle a capacity according to the probability distribution as a mathematical programming problem, a satisfaction sale definition equation generating means 102 that defines a satisfaction degree for a request capacity of a demand pair and an expected value lower limit constraint generating means 103 that decides a lower limit of the expected value of the satisfaction degree are provided. Moreover, an optimizing reference generating means 101 that generates an object function to minimize the cost, and a path flow storage constraint generating means 104, a link allocation constraint generating means 105 and a node allocation constraint generating means 106 that generate constraint equations to obtain a link capacity and a node capacity are provided. In addition, an optimizing means 107 is provided to solve the mathematical programming problems generated by each means above.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a communication network design circuit, a communication network design method, and a recording medium on which a communication network design program is recorded, and more particularly to a communication network design method that copes with demand fluctuations and network failures.

[0002]

2. Description of the Related Art Conventionally, in this type of communication network design method, there is a method of designing path and link capacities using a linear programming method for a given specific demand. For this method, see `` Restoration
Strategies and Spare Capacity Requirements in Self
-Healing ATM Networks '' (Yijun Xiong and Lorne Mas
on, Infocom'97, April 1997). Here, the linear programming refers to a method of handling a problem of finding an extreme value of a linear objective function under the conditions of a system of linear equations and inequalities.

FIG. 31 is a block diagram showing an example of a conventional communication network design method. In this design method, a path for each demand is set for each failure state so that communication can be maintained even when an assumed link failure occurs, and the capacity of the link is designed so that these paths can be accommodated when a failure occurs.

As inputs, a network topology, a demand, a link cost coefficient, and an assumed failure state are given. When this input is given, the optimization criterion creating unit 3001 creates an objective function for minimizing costs related to links. Further, the path accommodation condition creating unit 3002 creates a constraint expression that the sum of the capacities allocated to the path candidates is equal to the required capacity of the demand.

[0005] The link accommodation condition creating means 3003 creates a constraint expression that the capacity of the link is larger than the sum of the capacities flowing in the paths passing through each link in each state. Subsequently, the optimization unit 3004 solves the linear programming problem created by the optimization criterion creation unit 3001, the path accommodation condition creation unit 3002, and the link accommodation condition creation unit 3003, and determines the path and link capacity. Note that the linear programming problem generally refers to a problem of maximizing or minimizing an objective function expressed by a linear expression under constraints expressed by some linear equations or inequalities.

[0006]

The above-described conventional communication network design method has a problem that "optimal design is performed only for a given deterministic demand pattern". Here, the demand pattern represents a set of demands required between all nodes.

Since a given deterministic demand pattern is optimized using a mathematical programming method, an optimal network which minimizes the cost is designed while ensuring that the demand pattern can be accommodated. Therefore,
There is no guarantee for a pattern different from the demand pattern.

However, in an actual communication network, a demand pattern differs depending on a time zone, a day of the week, a season, and the like, and changes depending on an event or the like. Even if the season, day of the week, and time are the same, it is unlikely that the demand pattern will be exactly the same. Furthermore, demand patterns may change significantly due to the spread of new communication services and the introduction of new technologies. In a conventional telephone network-centered network, demand can be predicted to some extent, but in recent multimedia networks, demand prediction has become extremely difficult.

An object of the present invention is to solve the above-mentioned problems and to design a communication network capable of accommodating the traffic even if the demand pattern changes to some extent.

[0010]

In order to cope with various demand patterns, the required capacity of a demand pair is given as following a probability distribution. Then, in order to treat the required capacity according to the probability distribution as a mathematical programming problem, a satisfaction definition formula creating means (102 in FIG. 1) for defining the degree of satisfaction with the required capacity of the demand pair, and an expectation for defining a lower limit of the expected value of the satisfaction. Value lower limit creating means (103 in FIG. 1). Satisfaction definition formula creation means (2002 in FIG. 20) for defining the degree of satisfaction of the demand capacity of the demand pair, and optimization criterion creation means (2002 in FIG. 20) for creating an objective function for maximizing the expected value of satisfaction.
2001) and cost upper limit constraint creation means (2003 in FIG. 20) for defining the upper limit of the cost.

[0011]

The satisfaction degree definition formula creating means defines the satisfaction degree for each scenario which is one realization of the required capacity value of each demand pair. Further, the expected value lower limit constraint creating means obtains the expected value of the degree of satisfaction and gives the lower limit.

[0012] The satisfaction definition formula creating means defines satisfaction for each scenario which is one realization of the required capacity value of each demand pair. Create an objective function that maximizes

[0013]

DESCRIPTION OF THE PREFERRED EMBODIMENTS A first embodiment of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram showing a configuration example of a communication network design circuit according to the first embodiment of the present invention. Optimization criterion creating means 101, satisfaction definition formula creating means
102, expected value lower limit constraint creating means 103, path flow storage constraint creating means 104, link accommodation constraint creating means 105, node accommodation constraint creating means 106, and optimizing means 107.

FIG. 2 shows an example of a network designed in the first embodiment of the present invention. The network comprises nodes 201 to 205 and links 206 to 212. A set of nodes having a traffic demand is called a demand pair, and the capacity of the traffic demand is called a required capacity. The required capacity flows from one node of the demand pair as a start point and the other node as an end point as a flow on a path composed of arbitrary continuous nodes and links. For example, in FIG. 2, a demand pair is formed by a node 201 and a node 203, and the required capacity of this demand pair flows through any of the paths 213 to 217. Further, the link has a link capacity to accommodate the path flow, and the node has a node capacity to accommodate the path flow and the link capacity.

Next, symbols used in the description of the first embodiment will be described.

First, random variables relating to the required capacity of the demand pair and variables relating to the path will be described. Demand @ ap
Is defined as a random variable v _p . V1 _, v2 _,
.. _, The entire sample space of v _P is defined as Ω. The element ω of Ω represents one realization of the value of the required capacity of each demand pair, in other words, it can be called a scenario. Element ω
For example, a day of the week, a time zone, or the like can be considered. In the following description, ω is called a scenario. Since v _p is a function of the scenario ω∈Ω, it is expressed as v _p (ω) to clearly show this relationship.

Subsequently, the path candidate of the demand pair p is set to i _p
Is defined. In FIG. 2, the paths 213 to 217 correspond to the path candidates. In the first embodiment variable representing the flow flowing through the path candidate i _p it is expressed as a function c _ip (omega) of Omega∈omega. The symbols including v _p (ω) _and c _ip (ω) just described are summarized below.

N: Node set. Each element is represented by n. L: Link set. Each element is represented by l. L (n): a set of links passing through node n. P: a set of demand pairs. Each element is represented by p. P (n): a set of demand pairs starting or ending at node n. P (ω): probability of occurrence of event ω. I _p : a set of path candidates for the demand pair p. Each element is i _p
Expressed by I _p ^(l) : a set of path candidates of the demand pair p passing through the link l. · Ω: request capacity v ₁ of demand _pair, v _{2, ...,} v sample space _{that P} is defined. Each element is represented as ω. W _l : cost coefficient of link l Ε: cost coefficient of the node. Λ: Capacity of one link unit. • ν: capacity of one node unit. V _p (ω): Required capacity of demand pair p. Random variable. Α: Lower limit of expected value of satisfaction. · C _ip (ω): Under scenario omega, flow allocated to path candidate i _p demand pairs p. variable. F _p (ω): the total flow of the demand pair p flowing in the path in the scenario ω. D _l : number of units assigned to link l variable. E _n : the number of units assigned to node n. variable.

FIG. 3 is a flowchart showing a communication network designing method according to the first embodiment of the present invention, and FIG. 4 shows a detailed processing example of the communication network designing method according to the first embodiment of the present invention. It is a flowchart. The processing shown in FIGS. 3 and 4 is realized by each means of the communication network design circuit according to the first embodiment of the present invention executing a program recorded in a control memory (not shown). Can use a floppy disk or a ROM (read only memory).

First, as input data, a network topology, a required capacity of a demand pair (probability variable), a path candidate of each demand pair, a cost coefficient of a link / node, and a lower limit of an expected value of satisfaction are given.

The optimization criterion creating means 101 creates an objective function shown in the following equation (1) based on the given data (FIG. 3).
Step 301 of FIG. 4 and Step 401 of FIG. 4).

[0023]

(Equation 1)

Equation (1) means minimizing the cost for the link and the cost for the node.

The satisfaction degree definition expression creating means 102 creates the following constraint expressions (2) and (3) for defining the satisfaction level (steps in FIG. 3).
302, step 402 in FIG. 4). First, the satisfaction degree θ _p (ω) for each demand pair in each scenario is defined.

[0026]

(Equation 2)

[0027]

(Equation 3)

Equations (2) and (3) are synonymous with the following equation (4).

[0029]

(Equation 4)

Subsequently, the degree of satisfaction of each scenario θ ^min (ω)
Is defined as in the following equation (5).

[0031]

(Equation 5)

The expected value lower limit constraint creating means 103 creates the following constraint equation (6) for defining the lower limit of the expected value of the degree of satisfaction obtained through all scenarios (step 303 in FIG. 3 and step 403 in FIG. 4).

[0033]

(Equation 6)

The path flow storage constraint creation means 104 creates the following constraint equation (7) for distributing the total path flow to the paths for each demand pair in all scenarios (steps 304 and 4 in FIG. 3). Step 404).

[0035]

(Equation 7)

The link accommodation constraint creating means 105 creates the following constraint equation (8) for accommodating the path flow in the link (step 305 in FIG. 3 and step 405 in FIG. 4).

[0037]

(Equation 8)

The node accommodation constraint creating means 106 creates the following constraint equation (9) for accommodating the path flow and the terminal capacity of the link in the node (step 306 in FIG. 3 and step 406 in FIG. 4).

[0039]

(Equation 9)

The objective function (1) and constraint equations (2), (3), (5),
Mathematical programming problems are composed of (6), (7), (8) and (9). The optimizing means 107 solves this mathematical programming problem to obtain the capacity of each link and the capacity of the node (step 307 in FIG. 3).
Step 407 in FIG. 4).

FIG. 5 is a flowchart showing a detailed processing example of the communication network designing method according to the second embodiment of the present invention. A second embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG.
Each means of the communication network design circuit according to the embodiment is realized by executing a program recorded in a control memory (not shown), and the control memory may be a floppy disk, a ROM (read only memory), or the like. .

Here, the configuration of the second embodiment is the same as that of the first embodiment of the present invention, and the symbols used in the description of this embodiment are the same as those of the first embodiment. is there.

In the present embodiment, the operation of each means other than the satisfaction degree definition expression creating means 102 and the expected lower limit constraint creation means 103 is the same as that of the first embodiment, so that the description is omitted, and the satisfaction degree definition expression is omitted. Only the creation means 102 and the expected value lower limit constraint creation means 103 will be described.

The satisfaction degree definition expression creating means 102 creates the following constraint expressions (10) and (11) for defining the satisfaction degree (step 502 in FIG. 5).

[0045]

(Equation 10)

[0046]

[Equation 11]

Equations (10) and (11) are synonymous with the following equation (12).

[0048]

(Equation 12)

The expected value lower limit constraint creating means 103 sets the lower limit of the expected value of the degree of satisfaction for each demand pair by the following constraint expression (13)
Is created (step 503 in FIG. 5).

[0050]

(Equation 13)

FIG. 6 is a flowchart showing a detailed processing example of the communication network designing method according to the third embodiment of the present invention. The third embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG. 6 is realized when each unit of the communication network design circuit according to the third embodiment of the present invention executes a program recorded in a control memory (not shown), and the control memory is a floppy disk. Or a ROM (Read Only Memory).

Here, the configuration of the third embodiment is the same as that of the first embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the first embodiment except that δ is used for satisfaction. This is the same as the first embodiment. δ will be described later.

In this embodiment, the operation of each means other than the satisfaction degree definition expression creating means 102 and the expectation lower limit constraint creation means 103 is the same as that of the first embodiment, so that the explanation is omitted, and the satisfaction degree definition expression Only the creation means 102 and the expected value lower limit constraint creation means 103 will be described.

The satisfaction definition expression creating means 102 creates the following constraint expressions (14) and (15) for defining the satisfaction (Step 602 in FIG. 6). First, the degree of satisfaction δ _p (ω) for each demand pair in each scenario is defined.

[0055]

[Equation 14]

[0056]

(Equation 15)

Equations (14) and (15) have the same meaning as equation (16).

[0058]

(Equation 16)

Subsequently, the degree of satisfaction δ ^min (ω) of each scenario
Is defined as shown in the following equation (17).

[0060]

[Equation 17]

The expected value lower limit constraint creating means 103 creates the following constraint equation that defines the lower limit of the expected value of the degree of satisfaction obtained through all scenarios (step 603 in FIG. 6).

[0062]

(Equation 18)

FIG. 7 is a flowchart showing a detailed processing form of the communication network designing method according to the fourth embodiment of the present invention. Referring to FIG. 7, the fourth embodiment of the present invention will be described.
An embodiment will be described. Note that the processing shown in FIG. 7 is realized when each unit of the communication network design circuit according to the fourth embodiment of the present invention executes a program recorded in a control memory (not shown), and the control memory is a floppy disk. Or a ROM (Read Only Memory).

Here, the configuration of the fourth embodiment is the same as that of the first embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the third embodiment. is there.

In the present embodiment, the operation of each means other than the satisfaction degree definition expression creating means 102 and the expected lower limit constraint creation means 103 is the same as that of the third embodiment, so that the explanation is omitted, and the satisfaction degree definition expression Only the creation means 102 and the expected value lower limit constraint creation means 103 will be described.

The satisfaction degree definition equation creating means 102 creates the following constraint equation defining the satisfaction level (step 702 in FIG. 7). First, satisfaction δ _p for each demand pair in each scenario
(Ω) is defined.

[0067]

[Equation 19]

[0068]

(Equation 20)

Equations (19) and (20) have the same meaning as equation (21).

[0070]

(Equation 21)

The expected value lower limit constraint creating means 103 creates the following constraint expression (22) for defining the lower limit of the expected value of the degree of satisfaction of each demand pair (step 703 in FIG. 7).

[0072]

(Equation 22)

FIG. 8 is a flowchart showing a detailed processing example of the communication network designing method according to the fifth embodiment of the present invention. The fifth embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG. 8 is realized when each unit of the communication network design circuit according to the fifth embodiment of the present invention executes a program recorded in a control memory (not shown). Or a ROM (Read Only Memory).

Here, the configuration of the fifth embodiment is the same as that of the first embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the first embodiment except for the following symbols. This is the same as the embodiment.

[0075] · c _ip: define a variable representing the flow flowing through the path candidate i _p as variable c _ip that is independent of Omega∈omega.

In the present embodiment, the operations of the respective units except for the path flow storage constraint creation unit 104 and the link accommodation constraint creation unit 105 are the same as those of the first embodiment, so that the explanation is omitted, and the path flow storage constraint creation unit 104 Only the link accommodation restriction creating means 105 will be described.

The path flow storage constraint creating means 104 creates the following constraint expression (23) for distributing the total path flows to path candidates independent of the scenario for each demand pair in all scenarios (see FIG. 8). Step 804).

[0078]

(Equation 23)

The link accommodation constraint creating means 105 creates the following constraint equation (24) for accommodating the path flow in the link (step 805 in FIG. 8).

[0080]

(Equation 24)

FIG. 9 is a flowchart showing a detailed processing example of the communication network designing method according to the sixth embodiment of the present invention. The sixth embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG. 9 is realized by each unit of the communication network design circuit according to the sixth embodiment of the present invention executing a program recorded in a control memory (not shown). Or a ROM (Read Only Memory).

Here, the configuration of the sixth embodiment is the same as that of the first embodiment of the present invention, except for the path flow storage constraint creating means 104 and the link accommodation constraint creating means 105 in this embodiment. The operations of the respective units are the same as those in the second embodiment, and a description thereof will be omitted, and only the path flow storage constraint creating unit 104 and the link accommodation constraint creating unit 105 will be described.

The path flow storage constraint creating means 104 creates the following constraint formula (25) for distributing the total path flows to path candidates independent of the scenario for each demand pair in all scenarios (step in FIG. 9). 904).

[0084]

(Equation 25)

The link accommodation constraint creating means 105 creates the following constraint equation (26) for accommodating the path flow in the link (step 905 in FIG. 9).

[0086]

(Equation 26)

FIG. 10 is a flowchart showing a detailed processing example of the communication network designing method according to the seventh embodiment of the present invention. The seventh embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG. 10 is realized when each unit of the communication network design circuit according to the seventh embodiment of the present invention executes a program recorded in a control memory (not shown). Or a ROM (Read Only Memory).

Here, the configuration of the seventh embodiment is similar to that of the first embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the third embodiment except for the following symbols. This is the same as the embodiment.

[0089] · c _ip: define a variable representing the flow flowing through the path candidate i _p as variable c _ip that is independent of Omega∈omega.

In the present embodiment, the operation of each unit except for the path flow storage constraint creation unit 104 and the link accommodation constraint creation unit 105 is the same as that of the third embodiment, and therefore the explanation is omitted, and the path flow storage constraint creation unit 104 Only the link accommodation restriction creating means 105 will be described.

The path flow storage constraint creating means 104 creates the following constraint equation (27) for distributing the total of path flows to path candidates independent of the scenario for each demand pair in all scenarios (see FIG. 10). (Step 1004)
.

[0092]

[Equation 27]

The link accommodation constraint creating means 105 creates the following constraint equation (28) for accommodating a path flow in a link.
(Step 1005 in FIG. 10).

[0094]

[Equation 28]

FIG. 11 is a flowchart showing a detailed processing form of the communication network designing method according to the eighth embodiment of the present invention. Referring to FIG. 11, the eighth embodiment of the present invention will be described.
An embodiment will be described. Note that the processing shown in FIG. 11 is realized by each unit of the communication network design circuit according to the eighth embodiment of the present invention executing a program recorded in a control memory (not shown). Or a ROM (Read Only Memory).

Here, the configuration of the eighth embodiment is the same as that of the first embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the fourth embodiment except for the following symbols. This is the same as the embodiment.

[0097] · c _ip: define a variable representing the flow flowing through the path candidate i _p as variable c _ip that is independent of Omega∈omega.

In the present embodiment, the operation of each unit except for the path flow storage constraint creation unit 104 and the link accommodation constraint creation unit 105 is the same as that of the fourth embodiment, so that the explanation is omitted, and the path flow storage constraint creation unit 104 Only the link accommodation restriction creating means 105 will be described.

The path flow storage constraint creating means 104 creates the following constraint equation (29) for distributing the total path flows to the path candidates independent of the scenario for each demand pair in all the scenarios (FIG. 11). (Step 1104)
.

[0100]

(Equation 29)

The link accommodation constraint creating means 105 creates the following constraint equation (30) for accommodating the path flow in the link (step 1105 in FIG. 11).

[0102]

[Equation 30]

FIG. 12 is a flowchart showing a detailed processing example of the communication network designing method according to the ninth embodiment of the present invention. The ninth embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG. 12 is realized by each unit of the communication network design circuit according to the ninth embodiment of the present invention executing a program recorded in a control memory (not shown). Or a ROM (Read Only Memory).

Here, the configuration of the ninth embodiment is the same as that of the first embodiment of the present invention. Next, symbols used in the description of the ninth embodiment will be described.

First, random variables relating to the required capacity of the demand pair and variables relating to the path will be described. The request capacity of Demandopea p is defined as a random variable v _p. Also, v _1,
The entire sample space of v _2, ... _, v _P is defined as Ω. Ω element ω
Represents one realization of the value of the required capacity of each demand pair, and in other words, can be called a scenario. The element ω may be, for example, a day of the week, a time zone, or the like. In the following description, ω is called a scenario. Since v _p is a function of the scenario ω∈Ω, it is expressed as v _p (ω) to clearly show this relationship.

Further, a state (or network state) represented by whether each link on the network is faulty or normal is defined, and this is represented by the symbol ξ∈Ξ.

Subsequently, a path candidate ip of the demand pair _p is defined. Ninth variable representing the flow flowing through the path candidate i _p in the embodiment of ω∈Ω and ξ∈Ξ functions c _ip
(Ω _, ξ).

The v _p (ω) _and c _ip (ω described above)
_, ) are summarized below.

N: Node set. Each element is represented by n. L: Link set. Each element is represented by l. L (n): a set of links passing through node n. P: a set of demand pairs. Each element is represented by p. P (n): a set of demand pairs starting or ending at node n. P (ω): probability of occurrence of event ω. I _p : a set of path candidates for the demand pair p. Each element is i _p
Expressed by I _p ^(l) : a set of path candidates of the demand pair p passing through the link l. · Ω: request capacity v ₁ of the _demand, v _{2, ...,} v sample space _{that P} is defined. Each element is represented as ω.・ Ξ: Network state set. Each element is represented by ξ. W _l : cost coefficient of link l -Ε: cost factor of the node. Λ: capacity of one link unit. Ν: capacity of one node unit. T (lξ): a constant that takes 1 when the link 1 is normal in the state 1 and takes 0 when it has a failure. V _p (ω): Required capacity of demand pair p. Random variable. Α: The lower limit of the expected value of satisfaction. _{· C ip (ω, ξ)} : Scenario omega, flow allocated in the state xi] in path candidate i _p demand pairs p. variable. • f _P (ω): The total capacity of the demand pair p flowing in the path flow in the scenario ω. D _l : number of units assigned to link l variable. E _n : the number of units assigned to node n. variable.

First, as input data, the topology of the network, the required capacity (probability variable) of the demand pair, the path candidate of each demand pair, the cost coefficient of the link / node, the lower limit of the expected value of the degree of satisfaction, the assumed network state Gives.

The optimization criterion creating means 101 creates the following objective function (31) based on the given data (step 1201 in FIG. 12).

[0112]

(Equation 31)

The satisfaction definition expression creating means 102 creates the following constraint expressions (32) and (33) for defining the satisfaction (Step 1202 in FIG. 12). First, the satisfaction degree θ _p (ω) for each demand pair in each scenario is defined.

[0114]

(Equation 32)

[0115]

[Equation 33]

Equations (32) _and (33) are synonymous with the following equation (34).

[0117]

(Equation 34)

Subsequently, the satisfaction degree θ ^min (ω) of each scenario
Is defined.

[0119]

(Equation 35)

The expected value lower limit constraint creating means 103 creates the following constraint equation (36) for defining the lower limit of the expected value of the degree of satisfaction obtained through all scenarios (step 1203 in FIG. 12).

[0121]

[Equation 36]

The path flow storage constraint creating means 104 creates the following constraint equation (37) for distributing the total path flows to the path candidates for each demand pair in all scenarios and states (step 1204 in FIG. 12). ).

[0123]

(37)

The link accommodation constraint creating means 105 creates the following constraint equation (38) for accommodating the path flow in the link (step 1205 in FIG. 12).

[0125]

(38)

The node accommodation condition creating means 106 creates the following constraint expression (39) for accommodating the path flow and the link capacity in the node (step 1206 in FIG. 12).

[0127]

[Equation 39]

The objective function (31) and constraint equations (32), (33), (3
5), (36), (37), (38) and (39) constitute a mathematical programming problem. This is solved by the optimizing means 107 in this mathematical programming problem to obtain the capacity of each link and the capacity of the node (FIG. 12).
Step 1207).

FIG. 13 is a flowchart showing a detailed processing example of the communication network designing method according to the tenth embodiment of the present invention. The tenth embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG.
Each means of the communication network design circuit according to the tenth embodiment is realized by executing a program recorded in a control memory (not shown), and a floppy disk or a ROM (read only memory) or the like may be used as the control memory. it can.

Here, the configuration of the tenth embodiment is the same as that of the first embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the ninth embodiment. is there.

In the present embodiment, the operation of each means other than the satisfaction degree definition expression creating means 102 and the expected lower limit constraint creation means 103 is the same as that of the ninth embodiment, so that the description is omitted, and the satisfaction degree definition expression Only the creation means 102 and the expected value lower limit constraint creation means 103 will be described.

The satisfaction definition expression creating means 102 creates the following constraint expressions (40) and (41) for defining the satisfaction (Step 1302 in FIG. 13).

[0133]

(Equation 40)

[0134]

[Equation 41]

Equations (40) and (41) are synonymous with the following equation (42).

[0136]

(Equation 42)

The expected value lower limit constraint creating means 103 sets the lower limit of the expected value of the degree of satisfaction for each demand pair by the following constraint equation (43).
Is created (step 1303 in FIG. 13).

[0138]

[Equation 43]

FIG. 14 is a flowchart showing a detailed processing example of the communication network designing method according to the eleventh embodiment of the present invention. An eleventh embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG.
Each means of the communication network design circuit according to the eleventh embodiment is realized by executing a program recorded in a control memory (not shown), and a floppy disk or a ROM (read only memory) or the like may be used as the control memory. it can.

Here, the configuration of the eleventh embodiment is the same as that of the first embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the first embodiment except that δ is used for satisfaction. This is the same as the ninth embodiment. δ will be described later.

In this embodiment, the operation of each means other than the satisfaction degree definition expression creating means 102 and the expected lower limit constraint creation means 103 is the same as that of the ninth embodiment, so that the explanation is omitted, and the satisfaction degree definition expression Only the creation means 102 and the expected value lower limit constraint creation means 103 will be described.

The satisfaction definition expression creating means 102 creates the following constraint expressions (44) and (45) for defining the satisfaction (Step 1402 in FIG. 14). First, the degree of satisfaction δ _p (ω) for each demand pair in each scenario is defined.

[0143]

[Equation 44]

[0144]

[Equation 45]

Equations (44) and (45) are synonymous with the following equation (46).

[0146]

[Equation 46]

Subsequently, the degree of satisfaction of each scenario δ ^min (ω)
Is defined as shown in the following equation (47).

[0148]

[Equation 47]

The expected value lower limit constraint creating means 103 creates the following constraint equation (48) for defining the lower limit of the expected value of the degree of satisfaction obtained through all scenarios (step 1403 in FIG. 14).

[0150]

[Equation 48]

FIG. 15 is a flowchart showing a detailed process of the communication network designing method according to the twelfth embodiment of the present invention. Referring to FIG. 15, the twelfth embodiment of the present invention will be described.
An embodiment will be described. Note that the processing shown in FIG. 15 is realized by each unit of the communication network design circuit according to the twelfth embodiment of the present invention executing a program recorded in a control memory (not shown). Or a ROM (Read Only Memory).

Here, the configuration of the twelfth embodiment is the same as that of the first embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the first embodiment except that δ is used for satisfaction. This is the same as the ninth embodiment. δ will be described later.

In the present embodiment, the operation of each means other than the satisfaction degree definition expression creating means 102 and the expected lower limit constraint creation means 103 is the same as that of the ninth embodiment, so that the explanation is omitted, and the satisfaction degree definition expression Only the creation means 102 and the expected value lower limit constraint creation means 103 will be described.

The satisfaction definition formula creation means 102 creates the following constraint formula defining the satisfaction (step 1502 in FIG. 15). Satisfaction δ _p (ω) for each demand pair in each scenario
Is defined.

[0155]

[Equation 49]

[0156]

[Equation 50]

Equations (49) and (50) are synonymous with the following equation (51).

[0158]

(Equation 51)

The expected value lower limit constraint creating means 103 creates the following constraint formula (52) for defining the lower limit of the expected value of the degree of satisfaction obtained for all scenarios (step 1503 in FIG. 15).

[0160]

(Equation 52)

FIG. 16 is a flowchart showing a detailed processing example of the communication network designing method according to the thirteenth embodiment of the present invention. A thirteenth embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG.
Each means of the communication network design circuit according to the thirteenth embodiment is realized by executing a program recorded in a control memory (not shown), and a floppy disk or a ROM (read only memory) may be used as the control memory. it can. Here, the configuration of the thirteenth embodiment is the same as that of the first embodiment of the present invention.
This is the same as the embodiment. The symbols used in the description of this embodiment are the same as those in the ninth embodiment, except for the following symbols.

[0162] · c _ip (ξ): Flow assign the state xi] in path candidate i _p demand pairs p. variable.

In the present embodiment, the operation of each means except for the path flow storage constraint creation means 104 and the link accommodation constraint creation means 105 is the same as that of the ninth embodiment, so that the explanation is omitted, and the path flow storage constraint creation means 104 Only the link accommodation restriction creating means 105 will be described.

The path flow storage constraint creating means 104 creates the following constraint formula (53) for distributing the total path flows to the scenario-independent path candidates for each demand pair in all scenarios and states (FIG. 16 steps 1604).

[0165]

(Equation 53)

The link accommodation constraint creating means 105 creates the following constraint equation (54) for accommodating the path flow in the link (step 1605 in FIG. 16).

[0167]

(Equation 54)

FIG. 17 is a flowchart showing a detailed processing example of the communication network designing method according to the fourteenth embodiment of the present invention. The fourteenth embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG.
Each means of the communication network design circuit according to the fourteenth embodiment is realized by executing a program recorded in a control memory (not shown), and a floppy disk or a ROM (read only memory) may be used as the control memory. it can.

Here, the configuration of the fourteenth embodiment is the same as that of the first embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the tenth embodiment except for the following symbols. This is the same as the embodiment.

[0170] · c _ip (ξ): defined as a path candidate i-independent variable representing the flow ω∈Ω flow to _p variable c _ip (ξ).

In the present embodiment, the operations of the respective units except for the path flow storage constraint creation unit 104 and the link accommodation constraint creation unit 105 are the same as those of the tenth embodiment, so that the description is omitted, and the path flow storage constraint creation unit 104 Only the link accommodation restriction creating means 105 will be described.

In all scenarios and states, the path flow storage constraint creation means 104
The following constraint expression (55) for distributing the total path flows to the path candidates independent of the scenario is created (step 1704 in FIG. 17).

[0173]

[Equation 55]

The link accommodation constraint creating means 105 creates the following constraint equation (56) for accommodating the path flow in the link (step 1705 in FIG. 17).

[0175]

[Equation 56]

FIG. 18 is a flowchart showing a detailed processing example of the communication network designing method according to the fifteenth embodiment of the present invention. The fifteenth embodiment of the present invention will be described with reference to FIG. The processing shown in FIG.
Each means of the communication network design circuit according to the fifteenth embodiment is realized by executing a program recorded in a control memory (not shown), and a floppy disk or a ROM (read only memory) may be used as the control memory. it can.

Here, the configuration of the fifteenth embodiment is the same as that of the ninth embodiment of the present invention, and the symbols used in the description of the present embodiment are the eleventh except for the following symbols. This is the same as the embodiment.

[0178] · c _ip (ξ): defined as a path candidate i-independent variable representing the flow ω∈Ω flow to _p variable c _ip (ξ).

In the present embodiment, the operations of the respective units except for the path flow storage constraint creation unit 104 and the link accommodation constraint creation unit 105 are the same as those in the eleventh embodiment, so that the description is omitted, and the path flow storage constraint creation unit 104 Only the link accommodation restriction creating means 105 will be described.

In all scenarios and states, the path flow storage constraint creation means 104
The following constraint equation (57) for distributing the total path flows to the path candidates independent of the scenario is created (step 1804 in FIG. 18).

[0181]

[Equation 57]

The link accommodation constraint creating means 105 creates the following constraint equation (58) for accommodating the path flow in the link (
Step 1405 in FIG. 18).

[0183]

[Equation 58]

FIG. 19 is a flowchart showing a detailed processing form of the communication network designing method according to the sixteenth embodiment of the present invention. Referring to FIG. 19, the sixteenth embodiment of the present invention will be described.
An embodiment will be described. Note that the processing shown in FIG. 19 is realized by each means of the communication network design circuit according to the sixteenth embodiment of the present invention executing a program recorded in a control memory (not shown). Or a ROM (Read Only Memory).

Here, the configuration of the sixteenth embodiment is the same as that of the first embodiment of the present invention, and the symbols used in the description of the present embodiment are the twelfth except for the following symbols. This is the same as the embodiment.

[0186] · c _ip (ξ): defined as a path candidate i-independent variable representing the flow ω∈Ω flow to _p variable c _ip (ξ).

In the present embodiment, the operations of the respective units except for the path flow storage constraint creating unit 104 and the link accommodation constraint creating unit 105 are the same as those of the twelfth embodiment, so that the description is omitted, and the path flow storage constraint creating unit 104 Only the link accommodation restriction creating means 105 will be described.

The path flow storage constraint creating means 104 creates the following constraint formula (59) for distributing the total path flows to path candidates independent of the scenario for each demand pair in all scenarios and states (see FIG. 19 steps 1904).

[0189]

[Equation 59]

The link accommodation constraint creating means 105 creates the following constraint equation (60) for accommodating a path flow in a link (
Step 1905 in FIG. 19).

[0191]

[Equation 60]

A seventeenth embodiment of the present invention will be described. Figure
20 is a block diagram illustrating a configuration example of a communication network design circuit according to a seventeenth embodiment of the present invention. Optimization criterion creation means 2001, satisfaction definition formula creation means 2002, cost upper limit constraint creation means 2003, path flow storage constraint creation means 200
4. Consisting of link accommodation constraint creation means 2005, node accommodation constraint creation means 2006, and optimization means 2007.

Next, symbols used in the description of the seventeenth embodiment will be described.

First, random variables relating to the required capacity of the demand pair and variables relating to the paths will be described. The request capacity of Demandopea p is defined as a random variable v _p. Also, v1 _, v
The entire sample space of _2, ... _, V _P is defined as Ω. The element ω of Ω represents one realization of the value of the required capacity of each demand pair, in other words, it can be called a scenario. In addition,
In the following description, ω is called a scenario. v _{p is} also a scenario ω
Since it is a function of ∈Ω, v
expressed as _p (ω).

A path candidate of the demand pair _p is defined as ip. In the seventeenth embodiment variable representing the flow flowing through the path candidate i _p it is expressed as a function c _ip (omega) of Omega∈omega.

The symbols including v _p (ω) _and c _ip (ω) just described are summarized below.

N: Node set. Each element is represented by n. L: Link set. Each element is represented by l. L (n): a set of links passing through node n. P: a set of demand pairs. Each element is represented by p. P (n): a set of demand pairs starting or ending at node n. P (ω): probability of occurrence of event ω. I _p : a set of path candidates for the demand pair p. Each element is i _p
Expressed by I _p ^(l) : a set of path candidates of the demand pair p passing through the link l. · Ω: request capacity v ₁ of the _demand, v _{2, ...,} v sample space _{that P} is defined. Each element is represented as ω. Wl: link cost factor. Ε: cost coefficient of the node. Λ: capacity of one link unit. • ν: represents the capacity of one node unit. V _p (ω): Required capacity of demand pair p. Random variable.・ Β: Upper limit of cost. · C _ip (ω): flow allocated to path candidate i _p demand pairs p. variable. F _p (ω): the total flow of the demand pair p flowing in the path in the scenario ω. D _l : number of units assigned to link l variable. E _n : the number of units assigned to node n. variable.

FIG. 21 is a flowchart showing a communication network designing method according to the seventeenth embodiment of the present invention. FIG. 22 shows a detailed processing example of the communication network designing method according to the seventeenth embodiment of the present invention. It is a flowchart. Note that the processing shown in FIGS. 21 and 22 is realized by each unit of the communication network design circuit according to the seventeenth embodiment of the present invention executing a program recorded in a control memory (not shown). Can use a floppy disk or a ROM (read only memory).

First, as input data, a network topology, a required capacity (probability variable) of a demand pair, a path candidate of each demand pair, a cost coefficient of a link / node, and an upper limit of cost are given.

The optimization criterion creating means 2001 creates the following objective function (61) based on the given data (step 2101 in FIG. 21 and step 2201 in FIG. 22).

[0201]

[Equation 61]

Equation (61) means maximizing the expected value of satisfaction.

The satisfaction definition expression creating means 2002 creates the following constraint expressions (62) and (63) for defining the satisfaction (Step 2102 in FIG. 21 and Step 2202 in FIG. 22). First, the satisfaction degree θ _p (ω) for each demand pair in each scenario is defined.

[0204]

(Equation 62)

[0205]

[Equation 63]

Equations (62) and (63) are synonymous with the following equation (64).

[0207]

[Equation 64]

Subsequently, the degree of satisfaction of each scenario θ ^min (ω)
Is defined as in the following equation (65).

[0209]

[Equation 65]

The cost upper limit constraint creating means 2003 sets a constraint equation (66) for determining the upper limit value of the total cost of the link and the node.
(Step 2103 in FIG. 21 and Step 220 in FIG. 22)
3)

[0211]

[Equation 66]

The path flow storage constraint creating means 2004 creates the following constraint equation (67) for distributing the total path flows to the path candidates for each demand pair in all scenarios (step 2104 in FIG. 21, FIG. 22). Step 2104).

[0213]

[Equation 67]

The link accommodation constraint creating means 2005 creates the following constraint equation (68) for accommodating the path flow in the link (step 2105 in FIG. 21 and step 2205 in FIG. 22).

[0215]

[Equation 68]

The node accommodating condition creating means 2006 generates a constraint equation (69) for accommodating the path flow and the link capacity in the node.
(Step 2106 in FIG. 21 and Step 220 in FIG. 22)
6).

[0219]

[Equation 69]

The objective function (61) and constraint equations (62), (63), (6
5), (66), (67), (68) and (69) constitute a mathematical programming problem. The mathematical programming problem is solved by the optimization means 2007 to obtain the capacity of each link and the capacity of the node (FIG. 21).
Step 2107 of FIG. 22 and Step 2207 of FIG. 22).

FIG. 23 is a flowchart showing a detailed processing example of the communication network designing method according to the eighteenth embodiment of the present invention. The eighteenth embodiment of the present invention will be described with reference to FIG. Incidentally, the processing shown in FIG.
Each means of the communication network design circuit according to the eighteenth embodiment is realized by executing a program recorded in a control memory (not shown), and a floppy disk or a ROM (read only memory) may be used as the control memory. it can.

Here, the configuration of the eighteenth embodiment is the same as that of the seventeenth embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the seventeenth embodiment except that δ is used for satisfaction. This is the same as the seventeenth embodiment. δ will be described later.

In the present embodiment, the operation of each means other than the satisfaction degree definition formula creating means 2002 is the same as that of the seventeenth embodiment, so that the description will be omitted, and only the satisfaction degree definition formula creation means 2002 will be described.

The satisfaction definition expression creating means 2002 creates the following constraint expressions (70) and (71) for defining the satisfaction (Step 2302 in FIG. 23). First, the degree of satisfaction δ _p (ω) for each demand pair in each scenario is defined.

[0223]

[Equation 70]

[0224]

[Equation 71]

Equations (70) and (71) have the same meaning as equation (72).

[0226]

[Equation 72]

Subsequently, the degree of satisfaction of each scenario δ ^min (ω)
Is defined as in the following equation (73).

[0228]

[Equation 73]

FIG. 24 is a flowchart showing a detailed processing example of the communication network designing method according to the nineteenth embodiment of the present invention. The nineteenth embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG.
Each means of the communication network design circuit according to the embodiment is realized by executing a program recorded in a control memory (not shown), and the control memory may be a floppy disk, a ROM (read only memory), or the like. .

Here, the configuration of the nineteenth embodiment is the same as that of the seventeenth embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the seventeenth embodiment except for the following symbols. This is the same as the embodiment.

[0231] · c _ip: define a variable representing the flow flowing through the path candidate i _p as variable c _ip that is independent of Omega∈omega.

In this embodiment, the operation of each means except the path flow storage constraint creation means 2004 and the link accommodation constraint creation means 2005 is the same as that of the seventeenth embodiment, so that the explanation is omitted, and the path flow storage constraint creation means 2004 Only the link accommodation restriction creating means 2005 will be described.

The path flow storage constraint creating means 2004 creates the following constraint equation (74) for distributing the total path flows to path candidates independent of the scenario for each demand pair in all scenarios (step in FIG. 24). 2404).

[0234]

[Equation 74]

The link accommodation constraint creating means 2005 creates the following constraint equation (75) for accommodating the path flow in the link (
Step 2405 in FIG. 24).

[0236]

[Equation 75]

FIG. 25 is a flowchart showing a detailed processing example of the communication network designing method according to the twentieth embodiment of the present invention. The twentieth embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG.
Each means of the communication network design circuit according to the twentieth embodiment is realized by executing a program recorded in a control memory (not shown), and a floppy disk or a ROM (read only memory) may be used as the control memory. it can.

Here, the configuration of the twentieth embodiment is the same as that of the seventeenth embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the eighteenth embodiment except for the following symbols. This is the same as the embodiment.

[0239] · c _ip: to define a variable that represents the flow flowing through the path candidate i _p as a variable c _ip which does not depend on the ω∈Ω.

In the present embodiment, the operation of each means except the path flow storage constraint creation means 2004 and the link accommodation constraint creation means 2005 is the same as that of the eighteenth embodiment, so that the explanation is omitted, and the path flow storage constraint creation means 2004 Only the link accommodation restriction creating means 2005 will be described.

The path flow storage constraint creating means 2004 creates the following constraint equation (76) for distributing the total path flows to path candidates independent of the scenario for each demand pair in all scenarios (step in FIG. 25). 2504).

[0242]

[Equation 76]

The link accommodation constraint creating means 2005 creates the following constraint equation (77) for accommodating the path flow in the link (step 2505 in FIG. 25).

[0244]

[Equation 77]

FIG. 26 is a flowchart showing a detailed processing example of the communication network designing method according to the twenty-first embodiment of the present invention. The twenty-first embodiment of the present invention will be described with reference to FIG. The processing shown in FIG.
Each means of the communication network design circuit according to the twenty-first embodiment is realized by executing a program recorded in a control memory (not shown), and a floppy disk or a ROM (read only memory) may be used as the control memory. it can.

Here, the configuration of the twenty-first embodiment is the same as that of the seventeenth embodiment of the present invention.

Next, symbols used in the description of the twenty-first embodiment will be described.

First, random variables relating to the required capacity of the demand pair and variables relating to the paths will be described. The request capacity of Demandopea p is defined as a random variable v _p. Also, v1 _, v
The entire sample space of _2, ... _, V _P is defined as Ω. The element ω of Ω represents one realization of the value of the required capacity of each demand pair, in other words, it can be called a scenario. Element ω
For example, a day of the week, a time zone, or the like can be considered. In the following description, ω is called a scenario. Since v _p is a function of the scenario ω∈Ω, it is expressed as v _p (ω) to clearly show this relationship.

Further, a state (or network state) represented by whether each link on the network is faulty or normal is defined, and this is represented by the symbol ξ∈Ξ.

Subsequently, the path candidate of the demand pair p is set to i _p
Is defined. In the twenty-first embodiment, the path candidate _ip
Is expressed as a function c _ip (ω _, ξ) of ω∈Ω and ξ∈Ξ.

The above described v _p (ω) _, c _ip (ω
_, ) are summarized below.

N: Node set. Each element is represented by n. L: Link set. Each element is represented by l. L (n): a set of links passing through node n. P: a set of demand pairs. Each element is represented by p. P (n): a set of demand pairs starting or ending at node n. P (ω): probability of occurrence of event ω. I _p : a set of path candidates for the demand pair p. Each element is i _p
Expressed by I _p ^(l) : a set of path candidates of the demand pair p passing through the link l. · Ω: request capacity v ₁ of the _demand, v _{2, ...,} v sample space _{that P} is defined. Each element is represented as ω.・ Ξ: Network state set. Each element is represented by ξ. W _l : cost coefficient of link l -Ε: cost factor of the node. Λ: capacity of one link unit. Ν: capacity of one node unit. T (lξ): a constant that takes 1 when the link 1 is normal in the state 1 and takes 0 when it has a failure. V _p (ω): Required capacity of demand pair p. Random variable.・ Β: Upper limit of cost. _{· C ip (ω, ξ)} : Scenario omega, flow allocated in the state xi] in path candidate i _p demand pairs p. variable. F _p (ω): the total capacity of the demand pair p flowing in the path flow in the scenario ω. D _l : number of units assigned to link l variable. E _n : the number of units assigned to node n. variable.

FIG. 26 is a flowchart showing a communication network designing method according to the twenty-first embodiment of the present invention. FIG. 26 shows a detailed processing example of the communication network designing method according to the twenty-first embodiment of the present invention. It is a flowchart. 26. The processing shown in FIG. 26 is realized by each means of the communication network design circuit according to the twenty-first embodiment of the present invention executing a program recorded in a control memory (not shown). And ROM
(Read only memory) or the like can be used.

First, as input data, a network topology, a required capacity of a demand pair (probability variable), a path candidate of each demand pair, a cost coefficient of a link / node, an upper limit of cost, and an assumed network state are given. Optimization criterion creation means 20 based on given data
In 01, the following objective function is created (Step 2601 in FIG. 26)
.

[0255]

[Equation 78]

Equation (78) means maximizing the expected value of satisfaction.

The satisfaction degree definition equation creating means 2002 creates the following constraint equations (79) and (80) for defining the degree of satisfaction (step 2602 in FIG. 26). First, the satisfaction degree θ _p (ω) for each demand pair in each scenario is defined.

[0258]

[Expression 79]

[0259]

[Equation 80]

Equations (79) and (80) are synonymous with the following equation (81).

[0261]

[Equation 81]

Subsequently, the degree of satisfaction of each scenario θ ^min (ω)
Is defined as in the following equation (82).

[0263]

(Equation 82)

The cost upper limit constraint creating means 2003 generates a constraint expression (8
3) is created (step 2603 in FIG. 26).

[0265]

[Equation 83]

The path flow storage constraint creating means 2004 creates the following constraint expression (84) for distributing the total path flows to the path candidates for each demand pair in all scenarios and states (step 2604 in FIG. 26). ).

[0267]

[Equation 84]

The link accommodation constraint creating means 2005 creates the following constraint equation (85) for accommodating the path flow in the link (step 2605 in FIG. 26).

[0269]

[Equation 85]

The node accommodating condition creating means 2006 generates a constraint expression (8
6) is created (step 2606 in FIG. 26).

[0271]

[Equation 86]

The objective function (78) and the constraint equations (79), (80), (8
2), (83), (84), (85), and (86) constitute a mathematical programming problem. This is solved by the optimizing means 2007 in this mathematical programming problem to obtain the capacity of each link and the capacity of the node (FIG. 26).
Step 2607).

FIG. 27 is a flowchart showing a detailed processing example of the communication network designing method according to the twenty-second embodiment of the present invention. The twenty-second embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG.
Each means of the communication network design circuit according to the twenty-second embodiment is realized by executing a program recorded in a control memory (not shown), and a floppy disk or a ROM (read only memory) may be used as the control memory. it can.

Here, the configuration of the twenty-second embodiment is the same as that of the seventeenth embodiment of the present invention, and the symbols used in the description of the present embodiment are the same as those of the seventeenth embodiment except that δ is used for satisfaction. This is the same as the twenty-first embodiment. δ will be described later.

In this embodiment, the operation of each means other than the satisfaction degree definition expression creating means 2002 is the same as that of the twenty-first embodiment, so that the description is omitted, and only the satisfaction degree definition expression creation means 2002 will be described.

The satisfaction degree definition expression creating means 2002 creates the following constraint expressions (87) and (88) for defining the satisfaction degree (step 2702 in FIG. 27). First, the degree of satisfaction δ _p (ω) for each demand pair in each scenario is defined.

[0277]

[Equation 87]

[0278]

[Equation 88]

Equations (87) and (88) are synonymous with the following equation (89).

[0280]

[Equation 89]

Subsequently, the degree of satisfaction of each scenario δ ^min (ω)
Is defined as in the following equation (90).

[0282]

[Equation 90]

FIG. 28 is a flowchart showing a detailed processing example of the communication network designing method according to the twenty-third embodiment of the present invention. Note that the processing shown in FIG. 28 is realized by each unit of the communication network design circuit according to the twenty-third embodiment of the present invention executing a program recorded in a control memory (not shown). Or a ROM (Read Only Memory).

Here, the configuration of the twenty-third embodiment is the same as that of the seventeenth embodiment of the present invention. The symbols used in the description of this embodiment are the same as those in the twenty-first embodiment except for the following symbols.

[0285] · c _ip (ξ): Flow assign the state xi] in path candidate i _p demand pairs p. variable.

In the present embodiment, the operation of each means except the path flow storage constraint creation means 2004 and the link accommodation constraint creation means 2005 is the same as that of the twenty-first embodiment, so that the description is omitted, and the path flow storage constraint creation means 2004 Only the link accommodation restriction creating means 2005 will be described.

In all scenarios and states, the path flow storage constraint creation means 2004
The following constraint equation (91) for distributing the total path flows to the path candidates independent of the scenario is created (step 2804 in FIG. 28).

[0288]

[Equation 91]

The link accommodation constraint creating means 2005 creates the following constraint equation (92) for accommodating the path flow in the link (step 2805 in FIG. 28).

[0290]

(Equation 92)

FIG. 29 is a flowchart showing a detailed processing example of the communication network designing method according to the twenty-fourth embodiment of the present invention. The twenty-fourth embodiment of the present invention will be described with reference to FIG. Note that the processing shown in FIG.
Each means of the communication network design circuit according to the twenty-fourth embodiment is realized by executing a program recorded in a control memory (not shown), and a floppy disk or a ROM (read only memory) or the like may be used as the control memory. it can.

The structure of the twenty-fourth embodiment is the same as that of the seventeenth embodiment of the present invention. This is the same as the embodiment.

[0293] · c _ip (ξ): defined as a path candidate i-independent variable representing the flow ω∈Ω flow to _p variable c _ip (ξ).

In the present embodiment, the operation of each means except the path flow storage constraint creation means 2004 and the link accommodation constraint creation means 2005 is the same as that of the twenty-second embodiment, so that the description is omitted, and the path flow storage constraint creation means 2004 Only the link accommodation restriction creating means 2005 will be described.

The path flow storage constraint creating means 2004 creates the following constraint equation (93) for distributing the total path flows to the path candidates independent of the scenario (step 29 in FIG. 29).
04).

[0296]

[Equation 93]

The link accommodation constraint creating means 2005 creates the following constraint equation (94) for accommodating the path flow in the link (
Step 2905 in FIG. 29).

[0298]

[Equation 94]

FIG. 30 is a block diagram showing an example of a hardware configuration for realizing the communication network design circuit shown in FIGS. 1 and 20, and comprises a computer C and a recording medium K. The recording medium K is a disk, a semiconductor memory, or another recording medium, and stores a network design control program for operating the computer C as a communication network design circuit.

In the case where the communication network design circuit shown in FIG. 1 is realized, the network design control program recorded on the recording medium K is read by the computer C and controls the operation of the computer C so that the computer C operates. On C, the optimization criterion creating means 101, the satisfaction degree definition formula creating means 102, the expected value lower limit creating means 103
, A path flow storage constraint creation unit 104, a link accommodation constraint creation unit 105, a node accommodation constraint creation unit 106, and an optimization unit 107.

When the communication network design circuit shown in FIG. 20 is to be realized, the network design control program recorded on the recording medium K
By controlling the operation of the computer C, the optimization criterion creating means is provided on the computer C.
2001, a satisfaction definition formula creating means 2002, a cost upper limit constraint creating means 2003, a path flow storage constraint creating means 2004, a link accommodation constraint creating means 2005, a node accommodation constraint creating means 2006, and an optimizing means 2007 are realized.

[0302]

A first effect of the present invention is that a network can be designed that can accommodate a traffic pattern even if it changes to some extent and that can reduce the cost. The reason is to design a network that minimizes the cost after satisfying the expected value of the required degree of satisfaction with respect to the demand according to the probability distribution.

The second effect is that a network that is resistant to changes in traffic patterns can be designed while suppressing costs. The reason is to design a network that maximizes satisfaction within the upper limit of the required cost.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of a communication network design circuit according to a first embodiment of the present invention.

FIG. 2 is a diagram illustrating an example of a network designed in the first embodiment of the present invention.

FIG. 3 is a flowchart illustrating a network design method according to the first embodiment of the present invention.

FIG. 4 is a flowchart illustrating a detailed processing example of the network design method according to the first embodiment of the present invention.

FIG. 5 is a flowchart illustrating a detailed processing example of a network design method according to a second embodiment of the present invention;

FIG. 6 is a flowchart illustrating a detailed processing example of a network design method according to a third embodiment of the present invention.

FIG. 7 is a flowchart illustrating a detailed processing example of a network design method according to a fourth embodiment of the present invention;

FIG. 8 is a flowchart illustrating a detailed processing example of a network design method according to a fifth embodiment of the present invention.

FIG. 9 is a flowchart illustrating a detailed processing example of a network design method according to a sixth embodiment of the present invention;

FIG. 10 is a flowchart illustrating a detailed processing example of a network design method according to a seventh embodiment of the present invention;

FIG. 11 is a flowchart illustrating a detailed processing example of a network design method according to an eighth embodiment of the present invention;

FIG. 12 is a flowchart illustrating a detailed processing example of a network design method according to a ninth embodiment of the present invention;

FIG. 13 is a flowchart illustrating a detailed processing example of the network design method according to the tenth embodiment of the present invention;

FIG. 14 is a flowchart illustrating a detailed processing example of a network design method according to an eleventh embodiment of the present invention;

FIG. 15 is a flowchart illustrating a detailed processing example of a network design method according to a twelfth embodiment of the present invention.

FIG. 16 is a flowchart illustrating a detailed processing example of a network design method according to a thirteenth embodiment of the present invention;

FIG. 17 is a flowchart illustrating a detailed processing example of a network design method according to a fourteenth embodiment of the present invention;

FIG. 18 is a flowchart illustrating a detailed processing example of the network design method according to the fifteenth embodiment of the present invention;

FIG. 19 is a flowchart illustrating a detailed processing example of a network design method according to a sixteenth embodiment of the present invention;

FIG. 20 is a block diagram showing a configuration of a communication network design circuit according to a seventeenth embodiment of the present invention.

FIG. 21 is a flowchart illustrating a network design method according to a seventeenth embodiment of the present invention.

FIG. 22 is a flowchart illustrating a detailed processing example of a network design method according to a seventeenth embodiment of the present invention;

FIG. 23 is a flowchart illustrating a detailed processing example of the network design method according to the eighteenth embodiment of the present invention;

FIG. 24 is a flowchart illustrating a detailed processing example of the network design method according to the nineteenth embodiment of the present invention;

FIG. 25 is a flowchart illustrating a detailed processing example of a network design method according to a twentieth embodiment of the present invention;

FIG. 26 is a flowchart illustrating a detailed processing example of the network design method according to the twenty-first embodiment of the present invention;

FIG. 27 is a flowchart illustrating a detailed processing example of a network design method according to a twenty-second embodiment of the present invention.

FIG. 28 is a flowchart illustrating a detailed processing example of a network design method according to a twenty-third embodiment of the present invention.

FIG. 29 is a flowchart illustrating a detailed processing example of the network design method according to the twenty-fourth embodiment of the present invention;

FIG. 30 is a block diagram illustrating an example of a hardware configuration of a communication network design circuit.

FIG. 31 is a block diagram showing an example of a conventional network design method.

[Explanation of symbols]

 101… Optimization criterion creation means 102… Satisfaction definition formula creation means 103… Expected value lower limit constraint creation means 104… Path flow storage constraint creation means 105… Link accommodation constraint creation means 106… Node accommodation constraint creation means 107… Optimization means 201 ... 205 ... nodes 206 -213 ... links 214 -217 ... paths 2001 ... optimization criterion creation means 2002 ... satisfaction definition formula creation means 2003 ... cost upper limit constraint creation means 2004 ... path flow storage constraint creation means 2005 ... link accommodation constraint creation means 2006: Node accommodation constraint creation means 2007 ... Optimization means 3001 ... Optimization standard creation means 3002 ... Path accommodation condition creation means 3003 ... Link accommodation condition creation means 3004 ... Optimization means

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Claims (78)

[Claims] A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as a start point and the other node as an end point, the flow is passed as a flow on a path defined by any continuous nodes and links, and the link has a link capacity to accommodate the path flow. A communication network design circuit for designing a network having a node capacity for accommodating the path flow, wherein an optimization criterion creating means for creating an objective function for minimizing a cost related to the link and the node; And a constraint formula for defining the degree of satisfaction of the demand capacity of the demand pair following the probability distribution. Degree definition formula creating means, expected value lower limit constraint creating means for creating a constraint equation for determining a lower limit of the expected value of satisfaction, and a constraint equation for distributing the required capacity of the demand pair as a flow to a path. Path flow storage constraint creation means to be created; link accommodation constraint creation means to create a constraint equation for accommodating the path flow in the link; and node accommodation constraint creation to create a constraint equation for accommodating the path flow in the node. A communication network comprising: a means; and an optimizing means for determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint formula created by the respective means. Design circuit. 2. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by With one node as a start point and the other node as an end point, the flow is passed as a flow on a path defined by any continuous nodes and links, and the link has a link capacity to accommodate the path flow. A communication network design circuit for designing a network having a node capacity for accommodating the path flow, and an optimization criterion creating means for creating an objective function for minimizing costs related to the link and the node And one actual value of the required capacity value of each demand pair when the required capacity of each demand pair follows the probability distribution. In each of the scenarios, for each demand pair, take 1 if the sum of the path flows exceeds the required capacity, otherwise define a satisfaction level that is the value obtained by dividing the total of the path flows by the required capacity. Means for creating a constraint definition formula for defining a constraint that defines the minimum value of the degree of satisfaction in the scenario, and an expectation for creating a constraint that the expected value obtained from the minimum value of the satisfaction is equal to or greater than a previously requested value. Value lower limit constraint creation means, and in each scenario, for each demand pair, a path flow storage constraint creation means for creating a constraint equation for distributing the total path flow to each path, and in each scenario, a path flow through a link. Link accommodation constraint creation means for creating a constraint expression that the link capacity is greater than or equal to the sum, and in each scenario, a node Node accommodation constraint creating means for creating a constraint equation that the node capacity is greater than or equal to the sum of the capacity of the terminating path flow and link; and a mathematical programming problem composed of the objective function and the constraint equation created by the means. Optimizing means for determining the capacity of the link and the node by solving equation (1). 3. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and a required capacity of the demand pair is determined by the demand pair. With one node as a start point and the other node as an end point, the flow is passed as a flow on a path defined by any continuous nodes and links, and the link has a link capacity to accommodate the path flow. A communication network design circuit for designing a network having a node capacity for accommodating the path flow, and an optimization criterion creating means for creating an objective function for minimizing costs related to the link and the node And one actual value of the required capacity value of each demand pair when the required capacity of each demand pair follows the probability distribution. In each of the scenarios, for each demand pair, a constraint formula is defined that defines 1 if the sum of the path flows exceeds the required capacity, and otherwise takes the value obtained by dividing the total of the path flows by the required capacity. Means for creating a satisfaction degree definition formula to be created; and means for creating a lower limit of expected value constraint for creating a constraint expression that the expected value of the satisfaction level obtained for each demand pair is equal to or more than a previously requested value. A path flow storage constraint creating means for creating a constraint for distributing the total path flow to each path for each demand pair, and a constraint in each scenario that the link capacity is greater than or equal to the total path flow through the link Means for creating a link accommodation constraint that creates the Node accommodation constraint creating means for creating a constraint equation that the node capacity is greater than or equal to the sum of the above, and solving the mathematical programming problem composed of the objective function and the constraint equation created by the means, A communication network design circuit comprising: optimization means for determining a node capacity. 4. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as a start point and the other node as an end point, the flow is passed as a flow on a path defined by any continuous nodes and links, and the link has a link capacity to accommodate the path flow. A communication network design circuit for designing a network having a node capacity for accommodating the path flow, and an optimization criterion creating means for creating an objective function for minimizing costs related to the link and the node For each demand pair, 1 if the total path flow exceeds the required capacity in each scenario. If not, a satisfaction degree definition means for defining a satisfaction degree taking 0, and further creating a constraint equation defining a minimum value of the satisfaction degree in each scenario, and an expectation obtained from the minimum value of the satisfaction degree Expected value lower limit creating means for creating a constraint equation that the value is equal to or greater than a previously requested value, and in each scenario, create a constraint equation for distributing the total path flow to each path for each demand pair Path flow storage constraint creation means; link accommodation constraint creation means for creating a constraint formula that the link capacity is greater than or equal to the total path flow through the link in each scenario; path flow and link terminating at the node in each scenario Node accommodation constraint creating means for creating a constraint expression that the node capacity is greater than or equal to the total capacity of the nodes. Optimizing means for determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint equation created from a stage. 5. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as a start point and the other node as an end point, the flow is passed as a flow on a path defined by any continuous nodes and links, and the link has a link capacity to accommodate the path flow. A communication network design circuit for designing a network having a node capacity for accommodating the path flow, wherein an optimization criterion creating means for creating an objective function for minimizing a cost related to the link and the node; And one actual value of the required capacity value of each demand pair when the required capacity of each demand pair follows the probability distribution. In each of the scenarios, for each demand pair, if the total path flow exceeds the required capacity, take 1; otherwise, take the satisfaction level as 0. An expected value lower limit constraint creating means for creating a constraint expression that the expected value of the satisfaction obtained for each demand pair is equal to or more than a previously requested value, and in each scenario, Path flow preservation constraint creation means for creating a constraint equation for distributing the path to each path, and link accommodation constraint creation means for creating a constraint equation that the link capacity is greater than or equal to the total path flow through the link in each scenario. In each scenario, whether the node capacity is larger than the sum of the path flow and link capacity that terminates at the node, etc. A node accommodation constraint creating means for creating a constraint formula, and an optimization for determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint formula created by the means. And a communication network design circuit. 6. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as a start point and the other node as an end point, the flow is passed as a flow on a path defined by any continuous nodes and links, and the link has a link capacity to accommodate the path flow. A communication network design circuit for designing a network having a node capacity for accommodating the path flow, and an optimization criterion creating means for creating an objective function for minimizing costs related to the link and the node And one actual value of the required capacity value of each demand pair when the required capacity of each demand pair follows the probability distribution. In each of the scenarios, for each demand pair, take 1 if the sum of the path flows exceeds the required capacity, otherwise define a satisfaction level that is the value obtained by dividing the total of the path flows by the required capacity. Means for creating a constraint definition formula for defining a constraint that defines the minimum value of the degree of satisfaction in the scenario, and an expectation for creating a constraint that the expected value obtained from the minimum value of the satisfaction is equal to or greater than a previously requested value. Value lower limit constraint creating means, and in each scenario, for each demand pair, a path flow storage constraint creating means for creating a constraint formula for distributing the total path flow to each path independent of the scenario, and a link in each scenario. Link accommodation constraint creation means for creating a constraint expression that the link capacity is greater than or equal to the total path flow passing through In E, a node accommodation constraint creating means for creating a constraint formula that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node, and the objective function and the constraint formula created by the respective means Optimizing means for determining the capacity of the link and the node by solving a mathematical programming problem to be performed. 7. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as a start point and the other node as an end point, the flow is passed as a flow on a path defined by any continuous nodes and links, and the link has a link capacity to accommodate the path flow. A communication network design circuit for designing a network having a node capacity for accommodating the path flow, and an optimization criterion creating means for creating an objective function for minimizing costs related to the link and the node And one actual value of the required capacity value of each demand pair when the required capacity of each demand pair follows the probability distribution. In each of the scenarios, for each demand pair, a constraint formula is defined that defines 1 if the sum of the path flows exceeds the required capacity, and otherwise takes the value obtained by dividing the total of the path flows by the required capacity. Means for creating a satisfaction degree definition formula to be created; and means for creating a lower limit of expected value constraint for creating a constraint expression that the expected value of the satisfaction level obtained for each demand pair is equal to or more than a previously requested value. A path flow storage constraint creating means for creating a constraint formula for distributing the total path flow to each path independent of the scenario for each demand pair, and, in each scenario, whether the link capacity is larger than the total path flow through the link A link accommodation constraint creation means for creating a constraint expression of equality, and in each scenario, a path termination terminating at a node. Node accommodating constraint creating means for creating a constraint expression that the node capacity is greater than or equal to the sum of the link capacity and the link capacity, and solving a mathematical programming problem composed of the objective function and the constraint formula created by the means. Optimizing means for determining the capacity of the link and the node. 8. A demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, is provided with a required capacity, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as a start point and the other node as an end point, the flow is passed as a flow on a path defined by any continuous nodes and links, and the link has a link capacity to accommodate the path flow. A communication network design circuit for designing a network having a node capacity for accommodating the path flow, and an optimization criterion creating means for creating an objective function for minimizing costs related to the link and the node And one actual value of the required capacity value of each demand pair when the required capacity of each demand pair follows the probability distribution. In each of the following scenarios, for each demand pair, define a satisfaction level that takes 1 if the sum of the path flows exceeds the required capacity, otherwise takes 0, and further defines the minimum value of the satisfaction level in each scenario A satisfaction degree definition expression creating means for creating a constraint expression to perform; and an expected value lower limit constraint creation means for creating a constraint expression that an expected value obtained from the minimum value of the satisfaction degree is equal to or greater than a previously requested value In a scenario, for each demand pair, a path flow storage constraint creating means for creating a constraint formula for distributing the total path flow to each path independent of the scenario, and in each scenario, the link capacity is calculated from the total path flow passing through the link. A link accommodation constraint creating means for creating a constraint expression of greater or equal, and a path terminating at a node in each scenario Node accommodation constraint creating means for creating a constraint expression that the node capacity is greater than or equal to the sum of the row and link capacities; and solving a mathematical programming problem composed of the objective function and the constraint equation created by the means. Optimizing means for determining the capacity of the link and the node. 9. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as a start point and the other node as an end point, the flow is passed as a flow on a path defined by any continuous nodes and links, and the link has a link capacity to accommodate the path flow. A communication network design circuit for designing a network having a node capacity for accommodating the path flow, wherein an optimization criterion creating means for creating an objective function for minimizing a cost related to the link and the node; And one actual value of the required capacity value of each demand pair when the required capacity of each demand pair follows the probability distribution. In each of the scenarios, for each demand pair, if the total path flow exceeds the required capacity, take 1; otherwise, take the satisfaction level as 0. An expectation lower limit constraint creating means for creating a constraint expression that the expected value of the degree of satisfaction obtained for each demand pair is equal to or greater than a previously requested value; and in each scenario, the total of path flows for each demand pair. Flow preservation constraint creation means for creating a constraint expression for distributing the path to each path independent of the scenario, and link accommodation for creating a constraint expression that the link capacity is greater than or equal to the total path flow through the link in each scenario The constraint creation means and, in each scenario, the total capacity of the path flows and links terminating at the node. Node accommodation constraint creating means for creating a constraint equation that the load capacity is large or equal to each other, and solving the mathematical programming problem composed of the objective function and the constraint equation created by each of the means, thereby obtaining the link and node capacity. A communication network design circuit comprising: an optimization unit that determines 10. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. The link and the node And an optimization criterion creating means for creating an objective function for minimizing the cost related to each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution. For each demand pair, if the sum of the path flows exceeds the required capacity, take 1; otherwise, define the satisfaction that is the value obtained by dividing the total of the path flows by the required capacity, and further define the minimum of the satisfaction in each scenario. Means for creating a satisfaction definition expression for creating a constraint expression for defining a value; and an expectation obtained from the minimum value of the satisfaction. An expected value lower limit creating means for creating a constraint expression that is equal to or more than a predetermined value; and a demand in each scenario and a network state which is one realization of a state such as normal or failure of each link. Path flow storage constraint creation means for creating a constraint formula for distributing the total path flow to each path for each pair, and that the link capacity is greater than or equal to the total path flow through the link in each scenario and network condition Link accommodating constraint creating means for creating a constraint equation; and in each scenario, node accommodating constraint creating means for creating a constraint equation that the node capacity is greater than or equal to the sum of the path flows terminating at the node and the link capacity, The objective function and the constraint formula created by the means. Communication network design circuit; and a optimization means for determining the capacity of the links and nodes by solving the mathematical programming problem that. 11. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. The link and the node And an optimization criterion creating means for creating an objective function for minimizing the cost related to each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution. For each demand pair, if the sum of the path flows exceeds the required capacity, take 1; otherwise, create a constraint formula that defines the satisfaction level that is the value obtained by dividing the total of the path flows by the required capacity. Creating means, and that the expected value of the degree of satisfaction obtained for each demand pair is equal to or more than a previously requested value. Expected value lower limit constraint creation means for creating a contract formula; In each scenario, and in each of the states of the network, which is one realization of the state such as normal or failure of each link, the total of path flows is calculated for each demand pair for each path. Path flow preservation constraint creation means for creating a constraint formula for distributing to a link, and link accommodation constraint creation means for creating a constraint equation that the link capacity is greater than or equal to the sum of the path flows passing through the links in each scenario and network condition And, in each scenario, a node accommodation constraint creating means for creating a constraint expression that the node capacity is greater than or equal to the total capacity of the path flows and links terminating at the node; and the objective function and the objective function created by the means By solving a mathematical programming problem consisting of And the communication network design circuit, characterized in that it comprises a and optimization means for determining the capacitance of the node. 12. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and a required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. The link and the node And an optimization criterion creating means for creating an objective function for minimizing the cost related to each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution. For each demand pair, in each scenario, if the sum of the path flows exceeds the required capacity, take a value of 1; otherwise, define a satisfaction level of 0, and define a minimum value of the satisfaction level in each scenario. A satisfaction definition expression creating means for creating an expression; and an expected value obtained from the minimum value of the satisfaction is required in advance. An expected value lower limit constraint creating means for creating a constraint expression that is equal to or greater than the set value, in each scenario, and in each of the network states which are one realization of a state such as normal or failure of each link, for each demand pair, Path flow storage constraint creation means for creating a constraint equation for distributing the total path flow to each path, and creating a constraint equation that the link capacity is greater than or equal to the total path flow through the link in each scenario and network condition A link accommodation constraint creating unit that creates a constraint expression that, in each scenario, the node capacity is greater than or equal to the sum of the path flow terminating at the node and the link capacity, and a node accommodation constraint creating unit that is created by each of the means. Mathematical programming question composed of the objective function and the constraint equation Communication network design circuit; and a optimization means for determining the capacity of the links and nodes by solving. 13. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. The link and the node And an optimization criterion creating means for creating an objective function for minimizing the cost related to each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution. Satisfaction definition formula creation means for creating a constraint formula for defining a satisfaction level that takes 1 when the total of the path flows exceeds the required capacity for each demand pair and takes 0 otherwise, In addition, an expected value lower limit constraint is created by creating a constraint expression that the expected value of the satisfaction level is equal to or greater than a value required in advance. For each demand pair, create a constraint expression for distributing the total path flow to each path in each stage and in each state of the network, which is one realization of a state such as normal or failed state of each link. Path flow storage constraint creation means, and link accommodation constraint creation means for creating a constraint expression that the link capacity is greater than or equal to the total path flow passing through the link in each scenario and network state, In each scenario, terminate at a node Node accommodation constraint creating means for creating a constraint equation that the node capacity is greater than or equal to the sum of the path flows and link capacities to perform, and a mathematical programming problem composed of the objective function and the constraint equation created by the means. Optimization to determine the capacity of the link and node by solving Communication network design circuit; and a stage. 14. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. The link and the node And an optimization criterion creating means for creating an objective function for minimizing the cost related to each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution. For each demand pair, if the sum of the path flows exceeds the required capacity, take 1; otherwise, define the satisfaction that is the value obtained by dividing the total of the path flows by the required capacity, and further define the minimum of the satisfaction in each scenario. Means for creating a satisfaction definition expression for creating a constraint expression for defining a value; and an expectation obtained from the minimum value of the satisfaction. An expected value lower limit creating means for creating a constraint expression that is equal to or more than a predetermined value; and a demand in each scenario and a network state which is one realization of a state such as normal or failure of each link. Path flow storage constraint creation means for creating a constraint formula for distributing the total path flow to each path independent of the scenario for each pair; and in each network state, the link capacity is greater than or equal to the total path flow through the link Link accommodation constraint creation means for creating a constraint expression that: In each scenario, node accommodation constraint creation means for creating a constraint expression that the node capacity is greater than or equal to the sum of the capacity of the path flow terminated at the node and the link capacity; The objective function and the constraint expression created by each means Communication network design circuit; and a optimization means for determining the capacity of the links and nodes by solving the mathematical programming problem that is. 15. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. The link and the node And an optimization criterion creating means for creating an objective function for minimizing the cost related to each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution. For each demand pair, if the sum of the path flows exceeds the required capacity, take 1; otherwise, create a constraint formula that defines the satisfaction level that is the value obtained by dividing the total of the path flows by the required capacity. Creating means, and that the expected value of the degree of satisfaction obtained for each demand pair is equal to or more than a previously requested value. An expected value lower limit constraint creating means for creating a contract formula; and in each scenario, and in each of the network states which are one realization of a state such as a normal or failed state of each link, a total of path flows for each demand pair in a scenario. Path flow preservation constraint creation means for creating a constraint expression for distributing to each independent path; and link accommodation constraint for creating a constraint expression that the link capacity is greater than or equal to the total path flow through the link in each network state Creating means; in each scenario, a node accommodation constraint creating means for creating a constraint expression that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node; and the objective function created by each of the means Solve the mathematical programming problem consisting of Communication network design circuit; and a optimization means for determining the capacity of links and nodes. 16. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the demand capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. The link and the node And an optimization criterion creating means for creating an objective function for minimizing the cost related to each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution. For each demand pair, in each scenario, if the sum of the path flows exceeds the required capacity, take a value of 1; otherwise, define a satisfaction level of 0, and define a minimum value of the satisfaction level in each scenario. A satisfaction definition expression creating means for creating an expression; and an expected value obtained from the minimum value of the satisfaction is required in advance. An expected value lower limit constraint creating means for creating a constraint expression that is equal to or greater than a given value. Path flow storage constraint creation means for creating a constraint equation for distributing the total path flow to each path independent of a scenario, and a constraint equation that the link capacity is greater than or equal to the total path flow through the link in each network state A link accommodation constraint creating unit that creates a constraint expression that, in each scenario, the node capacity is greater than or equal to the total of the path flow terminating at the node and the link capacity, and a node accommodation constraint creating unit that creates Mathematics composed of the created objective function and the constraint equation Communication network design circuit; and a optimization means for determining the capacity of the links and nodes by solving the image problem. 17. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. The link and the node And an optimization criterion creating means for creating an objective function for minimizing the cost related to each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution. Satisfaction definition formula creation means for creating a constraint formula for defining a satisfaction level that takes 1 when the total of the path flows exceeds the required capacity for each demand pair and takes 0 otherwise, In addition, an expected value lower limit constraint is created by creating a constraint expression that the expected value of the satisfaction level is equal to or greater than a value required in advance. And a constraint for distributing the total path flow to each scenario-independent path for each demand pair in each scenario and in each state of the network, which is one realization of the state of normal or failed link. Path flow preservation constraint creation means for creating an equation; link accommodation constraint creation means for creating a constraint equation that the link capacity is greater than or equal to the total path flow through the link in each network state; and in each scenario, a node Node accommodation constraint creating means for creating a constraint expression that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link that terminates at Determine the capacity of the link and node by solving the problem Communication network design circuit; and a optimization unit. 18. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and a required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, the link has a link capacity for accommodating the path flow, and the node is a communication network design circuit for designing a network having the node capacity for accommodating the path flow, wherein an expected value of satisfaction is provided. An optimization criterion creating means for creating an objective function for maximizing, a satisfaction definition formula creating means for creating a constraint formula for defining a degree of satisfaction with the required capacity of the demand pair according to the probability distribution, and the link and A cost upper limit constraint creating unit that creates a constraint formula for defining an upper limit of cost for the node; a path flow storage constraint creating unit that creates a constraint formula for distributing the required capacity of the demand pair as a flow to a path; Link accommodation constraint creating means for creating a constraint equation for accommodating a path flow in the link; Node accommodating constraint creating means for creating a constraint equation for accommodating a flow in the node; and solving the mathematical programming problem composed of the objective function and the constraint equation created by each of the means, thereby forming the link and the node. And a optimizing means for determining the capacity of the communication network. 19. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow, wherein a minimum value of the satisfaction is provided. An optimization criterion creating means for creating an objective function for maximizing the expected value obtained from the above, and a scenario which is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution For each of the demand pairs, if the sum of the path flows exceeds the required capacity, take 1 if not, define the satisfaction that is the value obtained by dividing the total of the path flows by the required capacity otherwise, and define the satisfaction in each scenario. A satisfaction definition expression creating means for creating a constraint expression that defines a minimum value of the degree; Cost upper limit constraint creation means for creating a constraint expression that is equal to or less than the required value, and a path flow storage constraint for creating a constraint expression for distributing the total path flow to each path for each demand pair in each scenario Creation means; link accommodation constraint creation means for creating a constraint expression that the link capacity is greater than or equal to the total path flow through the link in each scenario; and, in each scenario, the path flow terminating at the node and the capacity of the link. Node accommodation constraint creation means for creating a constraint expression that the node capacity is greater than or equal to the sum; and the link and node by solving a mathematical programming problem composed of the objective function and the constraint expression created by the respective means Communication means comprising: optimization means for determining the capacity of a communication network Total circuit. 20. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the demand capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. An optimization criterion creating means for creating an objective function for maximizing the expected value obtained from the above, and a scenario which is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the constraints, for each demand pair, 1 is defined if the sum of the path flows exceeds the required capacity; otherwise, 0 is defined, and a constraint equation defining the minimum value of the satisfaction in each scenario is defined. Means for creating a satisfaction degree definition formula for creating a link, wherein a cost related to the link and the node is equal to or less than a predetermined value. A cost upper limit constraint creating means for creating an equation, a path flow storage constraint creating means for creating a constraint equation for distributing the total path flow to each path for each demand pair in each scenario, and a link in each scenario. Link accommodation constraint creating means for creating a constraint expression that the link capacity is greater than or equal to the sum of the path flows passing through, and in each scenario, the constraint that the node capacity is greater than or equal to the sum of the path flows terminating at the node and the link capacity A node accommodation constraint creating means for creating an equation, and an optimizing means for determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint equation created by each of the means. A communication network design circuit, comprising: 21. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is set to one of the demand pairs. With the start point of the node and the other node as the end point, the flow is passed as a flow on a path defined by any continuous nodes and links, and further, the link has a link capacity to accommodate the path flow, A node is a communication network design circuit for designing a network having a node capacity to accommodate the path flow, and an optimization criterion for creating an objective function for maximizing an expected value obtained from a minimum value of satisfaction. Creating means and one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution. In each of the narios, for each demand pair, we define 1 if the sum of the path flows is greater than the required capacity, otherwise define the satisfaction that is the value obtained by dividing the total of the path flows by the required capacity. Satisfaction definition expression creating means for creating a constraint expression that defines the minimum value of satisfaction, Cost upper limit constraint creating means for creating a constraint expression that the cost relating to the link and the node is equal to or less than a predetermined value, In each scenario, for each demand pair, a path flow storage constraint creating means for creating a constraint formula for distributing the total path flow to each path independent of the scenario, and in each scenario, link from the total path flow passing through the link. Link accommodating constraint creation means for creating a constraint formula that the capacity is large or equal, and each scenario A node accommodation constraint creating means for creating a constraint equation that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node; and the objective function and the constraint equation created by the respective means. Optimizing means for determining the capacity of the link and the node by solving a mathematical programming problem to be performed. 22. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. An optimization criterion creating means for creating an objective function for maximizing the expected value obtained from the above, and a scenario which is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the constraints, for each demand pair, 1 is defined if the sum of the path flows exceeds the required capacity; otherwise, 0 is defined, and a constraint equation defining the minimum value of the satisfaction in each scenario is defined. Means for creating a satisfaction degree definition formula for creating a link, wherein a cost related to the link and the node is equal to or less than a predetermined value. A cost upper limit constraint creating means for creating an equation; and a path flow storage constraint creating means for creating a constraint equation for distributing the total path flow to each path independent of the scenario for each demand pair in each scenario. Link accommodation constraint creating means for creating a constraint expression that the link capacity is greater than or equal to the total path flow through the links in the scenario; and in each scenario, the node capacity is greater than the sum of the path flows terminating at the node and the link capacity Node accommodation constraint creating means for creating a constraint expression that is equal to or equal to, optimally determining the capacity of the link and node by solving a mathematical programming problem composed of the objective function and the constraint equation created by the means And a communication network design circuit. 23. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow, wherein a minimum value of the satisfaction is provided. An optimization criterion creating means for creating an objective function for maximizing the expected value obtained from the above, and a scenario which is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution For each of the demand pairs, if the sum of the path flows exceeds the required capacity, take 1 if not, define the satisfaction that is the value obtained by dividing the total of the path flows by the required capacity otherwise, and define the satisfaction in each scenario. A satisfaction definition expression creating means for creating a constraint expression that defines a minimum value of the degree; Cost upper limit constraint creating means for creating a constraint expression that is equal to or less than a required value for each demand pair in each scenario and in a network state that is one realization of a state of normal or failure of each link. A path flow storage constraint creating means for creating a constraint equation for distributing the total path flow to each path; and a constraint equation that the link capacity is greater than or equal to the total path flow through the link in each scenario and network condition. A link accommodation constraint creating unit that creates a constraint expression that, in each scenario, the node capacity is greater than or equal to the total of the path flows terminating at the node and the link capacity, and a node accommodation constraint creating unit that creates Consists of the created objective function and the constraint equation Communication network design circuit; and a optimization means for determining the capacity of the links and nodes by solving the physical programming problem. 24. A demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, is provided with a required capacity, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. An optimization criterion creating means for creating an objective function for maximizing the expected value obtained from the above, and a scenario which is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the constraints, for each demand pair, 1 is defined if the sum of the path flows exceeds the required capacity; otherwise, 0 is defined, and a constraint equation defining the minimum value of the satisfaction in each scenario is defined. Means for creating a satisfaction degree definition formula for creating a link, wherein a cost related to the link and the node is equal to or less than a predetermined value. A cost upper limit constraint creating means for creating an equation, and in each scenario, and in each state of the network, which is one realization of a state such as a normal or failed state of each link, a total of path flows is distributed to each path for each demand pair. Path flow storage constraint creation means for creating a constraint formula for performing, and in each scenario and network state, link accommodation constraint creation means for creating a constraint equation that the link capacity is greater than or equal to the sum of the path flows passing through the link, In each scenario, a node accommodation constraint creating means for creating a constraint formula that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node; and the objective function and the constraint formula created by the respective means Solving the mathematical programming problem Communication network design circuit; and a optimization means for determining the volume of fine nodes. 25. A demand capacity, which is constituted by nodes and links connecting the nodes, is provided to a demand pair defined by an arbitrary set of nodes, and the required capacity of the demand pair is determined by the demand capacity of the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow, wherein a minimum value of the satisfaction is provided. An optimization criterion creating means for creating an objective function for maximizing the expected value obtained from the above, and a scenario which is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution For each of the demand pairs, if the sum of the path flows exceeds the required capacity, take 1 if not, define the satisfaction that is the value obtained by dividing the total of the path flows by the required capacity otherwise, and define the satisfaction in each scenario. A satisfaction definition expression creating means for creating a constraint expression that defines a minimum value of the degree; Cost upper limit constraint creating means for creating a constraint expression that is equal to or less than a required value for each demand pair in each scenario and in a network state that is one realization of a state of normal or failure of each link. A path flow storage constraint creating means for creating a constraint equation for distributing the total path flow to each path independent of the scenario; and a constraint equation in each scenario that the link capacity is greater than or equal to the total path flow through the link. A link accommodation constraint creating unit that creates a constraint expression that, in each scenario, the node capacity is greater than or equal to the total of the path flows terminating at the node and the link capacity, and a node accommodation constraint creating unit that creates Mathematics composed of the created objective function and the constraint equation Communication network design circuit; and a optimization means for determining the capacity of the links and nodes by solving the image problem. 26. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node is a communication network design circuit for designing a network having a node capacity for accommodating the path flow. An optimization criterion creating means for creating an objective function for maximizing the expected value obtained from the above, and a scenario which is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the constraints, for each demand pair, 1 is defined if the sum of the path flows exceeds the required capacity; otherwise, 0 is defined, and a constraint equation defining the minimum value of the satisfaction in each scenario is defined. Means for creating a satisfaction degree definition formula for creating a link, wherein a cost related to the link and the node is equal to or less than a predetermined value. Cost upper limit constraint creating means for creating an expression, and in each of the scenarios and the network state which is one realization of a state such as a normal or failed state of each link, the total of path flows does not depend on the scenario for each demand pair Path flow storage constraint creation means for creating a constraint formula for distributing to each path; and in each scenario, link accommodation constraint creation means for creating a constraint equation that the link capacity is greater than or equal to the total path flow through the link, In each scenario, a node accommodation constraint creating means for creating a constraint formula that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node; and the objective function and the constraint formula created by the respective means Solving the mathematical programming problem Communication network design circuit; and a optimization means for determining a capacity of over de. 27. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a node capacity for accommodating the path flow. Creating an objective function for minimizing the cost related to, and creating a constraint formula for defining a degree of satisfaction with the required capacity according to the probability distribution of the demand pair, and setting a lower limit of the expected value of the degree of satisfaction. Creating a constraint equation for determining the required capacity of the demand pair as a flow, and creating a constraint equation for accommodating the path flow in the link. Creating a constraint expression for accommodating the path flow in the node , The communication network design method characterized by comprising the steps of: determining the capacity of the links and nodes by solving the mathematical programming problem constituted by the objective function and the constraint equation created from each step. 28. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost associated with each demand pair, in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution In addition, if the total path flow exceeds the required capacity, take 1; otherwise, define the satisfaction level that is the value obtained by dividing the total path flow by the required capacity, and further define the minimum value of the satisfaction level in each scenario. Creating a constraint expression, and the expected value obtained from the minimum value of the satisfaction is less than or equal to a previously requested value. Creating a constraint expression for distributing the total path flow to each path for each demand pair in each scenario; and, in each scenario, creating a constraint expression for the path flow through the link. Creating a constraint equation that the link capacity is greater than or equal to the sum; and, in each scenario, creating a constraint equation that the node capacity is greater than or equal to the sum of the capacity of the path flow and link terminating at the node; Determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint formula created in each step. 29. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost associated with each demand pair, in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution Taking a value of 1 if the sum of the path flows exceeds the required capacity; otherwise, creating a constraint formula defining a degree of satisfaction that is obtained by dividing the total of the path flows by the required capacity; A step of creating a constraint expression that the expected value of the satisfaction level is equal to or greater than a previously requested value. Creating a constraint for distributing the total path flow to each path for each demand pair in each scenario; and in each scenario, the link capacity is greater than or equal to the total path flow through the link Creating a constraint expression; and, in each scenario, creating a constraint expression that the node capacity is greater than or equal to the sum of the path flow and link capacity terminating at the node; and the objective function created from each of the steps. And a step of determining a capacity of the link and the node by solving a mathematical programming problem composed of the constraint equation. 30. A demand capacity defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, is provided with a required capacity, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node The objective function for minimizing the cost for each demand pair, and for each demand pair, define a satisfaction level that takes 1 if the total path flow exceeds the required capacity and 0 otherwise. Creating a constraint formula defining a minimum value of satisfaction in each scenario; andcreating a constraint formula that an expected value obtained from the minimum value of satisfaction is equal to or greater than a previously requested value. In each scenario, a constraint for distributing the total path flow to each path for each demand pair Formulating the formula; and, in each scenario, formulating a constraint formula that the link capacity is greater than or equal to the sum of the path flows through the link; and, in each scenario, the sum of the path flows terminating at the node and the capacity of the link. Creating a constraint expression that the node capacity is larger or equal to the node capacity, and determining the capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint expression created in each step. And a communication network designing method. 31. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the demand capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost associated with each demand pair, in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution A step of creating a constraint formula that defines a degree of satisfaction that takes 1 when the sum of path flows exceeds the required capacity and takes 0 otherwise, and the expected value of the degree of satisfaction obtained for each demand pair is Creating a constraint that is greater than or equal to a previously required value; and Creating a constraint equation for distributing the total path flow to each path for each pair of nodes; and creating a constraint equation that the link capacity is greater than or equal to the total path flow through the link in each scenario; In each scenario, a step of creating a constraint equation that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node; and the objective function and the constraint equation created in each of the steps Determining the capacities of the links and nodes by solving a mathematical programming problem. 32. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost associated with each demand pair, in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution In addition, if the total path flow exceeds the required capacity, take 1; otherwise, define the satisfaction level that is the value obtained by dividing the total path flow by the required capacity, and further define the minimum value of the satisfaction level in each scenario. Creating a constraint expression, and the expected value obtained from the minimum value of the satisfaction is less than or equal to a previously requested value. Creating a constraint equation for distributing the total path flow to each path independent of the scenario for each demand pair in each scenario; and linking in each scenario Creating a constraint that the link capacity is greater than or equal to the sum of the path flows through the nodes, and, in each scenario, creating a constraint that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node And a step of determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint formula created in each of the steps. . 33. A demand capacity, which is constituted by nodes and links connecting the nodes, is provided to a demand pair defined by an arbitrary set of nodes, and the demand capacity of the demand pair is determined by the demand capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost associated with each demand pair, in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution Taking a value of 1 if the sum of the path flows exceeds the required capacity; otherwise, creating a constraint formula defining a degree of satisfaction that is obtained by dividing the total of the path flows by the required capacity; A step of creating a constraint expression that the expected value of the satisfaction level is equal to or greater than a previously requested value. And, in each scenario, for each demand pair, a step of creating a constraint formula for distributing the total path flow to each path independent of the scenario. In each scenario, the link capacity is calculated based on the total path flow through the link. Creating a constraint equation that is greater or equal to each other; and in each scenario, creating a constraint equation that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node. Determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint equation. 34. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a node capacity for accommodating the path flow. Creating an objective function for minimizing the cost associated with each demand pair, in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution Defining a satisfaction degree that takes 1 when the total of the path flows exceeds the required capacity, takes 0 otherwise, and creates a constraint expression that defines a minimum value of the satisfaction degree in each scenario; Step for creating a constraint expression that the expected value obtained from the minimum value of satisfaction is equal to or greater than the value requested in advance. And, in each scenario, for each demand pair, creating a constraint formula for distributing the total path flow to each path independent of the scenario. In each scenario, the link capacity is calculated from the total path flow through the link. Creating a constraint equation that is larger or equal to each other; and in each scenario, creating a constraint equation that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node. Determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint equation. 35. A demand capacity defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, is provided with a required capacity, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost associated with each demand pair, in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution A step of creating a constraint formula that defines a degree of satisfaction that takes 1 when the sum of path flows exceeds the required capacity and takes 0 otherwise, and the expected value of the degree of satisfaction obtained for each demand pair is Creating a constraint that is greater than or equal to a previously required value; and Creating a constraint for distributing the total path flow to each path independent of the scenario for each node pair, and creating a constraint that the link capacity is greater than or equal to the total path flow through the link in each scenario And, in each scenario, creating a constraint expression that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node; and the objective function and the constraint expression created from the above steps Determining the capacities of the links and nodes by solving a mathematical programming problem composed of: 36. A demand capacity defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, is provided with a required capacity, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost associated with each demand pair, in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution In addition, if the total path flow exceeds the required capacity, take 1; otherwise, define the satisfaction level that is the value obtained by dividing the total path flow by the required capacity, and further define the minimum value of the satisfaction level in each scenario. Creating a constraint expression, and the expected value obtained from the minimum value of the satisfaction is less than or equal to a previously requested value. And distributing the sum of path flows to each path for each demand pair in each scenario and in each state of the network, which is one realization of the state of normal or failed link. Creating a constraint expression for each of the scenarios, and for each scenario and network condition, creating a constraint expression that the link capacity is greater than or equal to the sum of the path flows through the link; and in each scenario, terminating at a node Creating a constraint equation that the node capacity is greater than or equal to the sum of the path flows and link capacities to perform; and solving the mathematical programming problem composed of the objective function and the constraint equation created from each of the steps. Determining the capacity of links and nodes. Communication network design method characterized by Rukoto. 37. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost associated with each demand pair, in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution Taking a value of 1 if the sum of the path flows exceeds the required capacity; otherwise, creating a constraint formula defining a degree of satisfaction that is obtained by dividing the total of the path flows by the required capacity; A step of creating a constraint expression that the expected value of the satisfaction level is equal to or greater than a previously requested value. Creating a constraint expression for distributing the total path flow to each path for each demand pair in each scenario and in each state of the network that is one realization of a state such as normal or failed state of each link And, in each scenario and the state of the network, creating a constraint equation that the link capacity is greater than or equal to the sum of the path flows through the link; and in each scenario, Creating a constraint equation that the node capacity is large or equal; and determining the link and node capacity by solving a mathematical programming problem composed of the objective function and the constraint equation created from each of the steps. And a communication network comprising: A total way. 38. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost of In each scenario, if the sum of the path flows exceeds the required capacity, take a value of 1; otherwise, take a value of 0, and define a constraint that defines a minimum value of satisfaction in each scenario. And the step, wherein the expected value obtained from the minimum value of the satisfaction level is equal to or more than a previously requested value. Creating a formula and distributing the sum of path flows to each path for each demand pair in each scenario and in each state of the network, which is one realization of a state such as normal or failed for each link. Creating a constraint equation; and, in each scenario and network condition, creating a constraint equation that the link capacity is greater than or equal to the sum of the path flows through the link; and, in each scenario, a path flow terminating at the node and Creating a constraint equation that the node capacity is greater than or equal to the sum of the link capacities; and solving the mathematical programming problem composed of the objective function and the constraint equation created from each of the steps, by linking the link and the node. Determining the capacity of the Communication network design method to. 39. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost of A step of creating a constraint formula that defines a degree of satisfaction that takes 1 when the sum of path flows exceeds the required capacity and takes 0 otherwise, and the expected value of the degree of satisfaction obtained for each demand pair is Creating a constraint expression that is greater than or equal to a previously required value; Creating a constraint for distributing the sum of path flows to each path for each demand pair in each of the network states, which is one realization of the state of normal or failed network; Creating a constraint that the link capacity is greater than or equal to the sum of the path flows through the link in the state; and in each scenario, the constraint that the node capacity is greater than or equal to the sum of the path flows terminating at the node and the capacity of the link. Creating a formula, and determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint formula created in each of the steps. Communication network design method. 40. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost associated with each demand pair, in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution In addition, if the total path flow exceeds the required capacity, take 1; otherwise, define the satisfaction level that is the value obtained by dividing the total path flow by the required capacity, and further define the minimum value of the satisfaction level in each scenario. Creating a constraint expression, and the expected value obtained from the minimum value of the satisfaction is less than or equal to a previously requested value. And creating a constraint expression that is: In each scenario, in each of the states of the network, one realization of the state of normal or failure of each link, for each demand pair, the sum of path flows does not depend on the scenario Creating a constraint for distributing to each path; and creating a constraint that the link capacity is greater than or equal to the sum of the path flows through the links in each network condition. Creating a constraint equation that the node capacity is greater than or equal to the sum of the capacity of the terminating path flow and link; and solving a mathematical programming problem composed of the objective function and the constraint equation created from each of the steps. Determining the capacity of the links and nodes; Communication network design method characterized in that it has. 41. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost associated with each demand pair, in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution Taking a value of 1 if the sum of the path flows exceeds the required capacity; otherwise, creating a constraint formula defining a degree of satisfaction that is obtained by dividing the total of the path flows by the required capacity; A step of creating a constraint expression that the expected value of the satisfaction level is equal to or greater than a previously requested value. And a constraint expression for distributing the total path flow to each scenario-independent path for each demand pair in each scenario and each state of the network, which is one realization of a state such as normal or failed state of each link. Creating a constraint that, for each network condition, the link capacity is greater than or equal to the sum of the path flows through the link; and in each scenario, the path flows terminating at the node and the capacity of the link. Creating a constraint equation that the node capacity is greater than or equal to the sum; and determining the link and node capacity by solving a mathematical programming problem composed of the objective function and the constraint equation created from each of the steps Communication network comprising the steps of: Over-click design method. 42. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost of In each scenario, if the sum of the path flows exceeds the required capacity, take a value of 1; otherwise, take a value of 0, and define a constraint that defines a minimum value of satisfaction in each scenario. And the step, wherein the expected value obtained from the minimum value of the satisfaction level is equal to or more than a previously requested value. In each of the scenarios and in each of the scenarios, and in each state of the network, which is one realization of the state of normal or failure of each link, for each demand pair, the sum of the path flows is added to each path independent of the scenario. Creating a constraint for distributing; and creating a constraint that, for each network condition, the link capacity is greater than or equal to the sum of the path flows through the link; and, in each scenario, terminating at a node. Creating a constraint equation that the node capacity is greater than or equal to the sum of the path flow and link capacity; and solving the mathematical programming problem composed of the objective function and the constraint equation created from each of the steps. And determining the capacity of the node Communication network design method characterized. 43. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the demand capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Furthermore, a communication network design method for designing a network having a node capacity to accommodate the path flow, wherein a link has a link capacity to accommodate the path flow, and the link and the node Creating an objective function for minimizing the cost of A step of creating a constraint formula that defines a degree of satisfaction that takes 1 when the sum of path flows exceeds the required capacity and takes 0 otherwise, and the expected value of the degree of satisfaction obtained for each demand pair is Creating a constraint expression that is greater than or equal to a previously required value; Creating a constraint for distributing the total path flow to each path independent of the scenario, for each demand pair, in each of the network states, which is one realization of the normal or failed state of the network; Creating a constraint that the link capacity is greater than or equal to the sum of the path flows through the link in the state of the network; And a step of determining the capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint equation created in each of the steps. Communication network design method. 44. A demand capacity defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, is provided with a required capacity. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Furthermore, a link has a link capacity for accommodating the path flow, and a node has a node capacity for accommodating the path flow. Creating an objective function for maximizing, and creating a constraint formula for defining the degree of satisfaction with the required capacity of the demand pair according to the probability distribution; and Creating a constraint formula for distributing the required capacity of the demand pair to the path as a flow, and creating a constraint formula for accommodating the path flow in the link, Creating a constraint expression for accommodating the path flow in the node; Determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint formula created in each step. 45. A demand capacity, which is constituted by nodes and links connecting the nodes, is provided to a demand pair defined by an arbitrary set of nodes, and the required capacity of the demand pair is determined by the demand capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link may have a link capacity for accommodating the path flow, and the node may have a node capacity for accommodating the path flow. Creating an objective function for maximizing the expected value obtained from the above, and in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution, For each demand pair, if the sum of the path flows exceeds the required capacity, take 1; otherwise, define the satisfaction that is the value obtained by dividing the total of the path flows by the required capacity, and further define the minimum value of the satisfaction in each scenario Creating a constraint expression defining the following: the cost of the link and the node is less than or equal to a previously required value A constraint formula for distributing the total path flow to each path for each demand pair in each scenario; and a sum of the path flows through the link in each scenario. Creating a constraint equation that the link capacity is greater or equal to each other; and in each scenario, creating a constraint equation that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node. Determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint formula created in the step. 46. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link may have a link capacity for accommodating the path flow, and the node may have a node capacity for accommodating the path flow. Creating an objective function for maximizing the expected value obtained from, and in each of the scenarios that is one realization of the value of the required capacity of each demand pair when the required capacity of each demand pair follows the probability distribution, For each demand pair, define a satisfaction level that takes 1 if the total of the path flows exceeds the required capacity, otherwise takes 0, and creates a constraint equation that defines the minimum value of the satisfaction level in each scenario. Creating a constraint expression that the cost related to the link and the node is equal to or less than a predetermined value. Creating a constraint formula for distributing the total path flow to each path for each demand pair in each scenario; and a constraint that the link capacity is greater than or equal to the total path flow through the link in each scenario. Creating an equation, in each scenario, creating a constraint equation that the node capacity is greater than or equal to the sum of the capacity of the path flow and link terminating at the node; and the objective function and the Determining a capacity of the link and the node by solving a mathematical programming problem formed by the constraint equation. 47. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the demand capacity of the demand pair is determined by With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link may have a link capacity for accommodating the path flow, and the node may have a node capacity for accommodating the path flow. Creating an objective function for maximizing the expected value obtained from the above, and in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution, For each demand pair, if the sum of the path flows exceeds the required capacity, take 1; otherwise, define the satisfaction that is the value obtained by dividing the total of the path flows by the required capacity, and further define the minimum value of the satisfaction in each scenario Creating a constraint expression defining the following: the cost of the link and the node is less than or equal to a previously required value Creating a constraint formula for distributing the total path flow to each path independent of the scenario for each demand pair in each scenario. Creating a constraint that the link capacity is greater than or equal to the sum of the passing path flows; and, in each scenario, creating a constraint equation that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node. And a step of determining a capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint equation created in each of the steps. 48. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link may have a link capacity for accommodating the path flow, and the node may have a node capacity for accommodating the path flow. Creating an objective function for maximizing the expected value obtained from, and in each of the scenarios that is one realization of the value of the required capacity of each demand pair when the required capacity of each demand pair follows the probability distribution, For each demand pair, define a satisfaction level that takes 1 if the total of the path flows exceeds the required capacity, otherwise takes 0, and creates a constraint equation that defines the minimum value of the satisfaction level in each scenario. Creating a constraint expression that the cost related to the link and the node is equal to or less than a predetermined value. In each scenario, for each demand pair, a step of creating a constraint formula for distributing the total path flow to each path independent of the scenario, and in each scenario, the link capacity is greater than the total path flow through the link Creating a constraint formula that equals or equals the node capacity greater than or equal to the sum of the capacity of the path flow and link terminating at the node in each scenario; and Determining the capacity of the link and the node by solving a mathematical programming problem composed of the objective function and the constraint equation. 49. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, a link may have a link capacity for accommodating the path flow, and the node may have a node capacity for accommodating the path flow. Creating an objective function for maximizing the expected value obtained from the above, and in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution, For each demand pair, if the sum of the path flows exceeds the required capacity, take 1; otherwise, define the satisfaction that is the value obtained by dividing the total of the path flows by the required capacity, and further define the minimum value of the satisfaction in each scenario Creating a constraint expression defining the following: the cost of the link and the node is less than or equal to a previously required value And distributing the total path flow to each path for each demand pair in each scenario and in each state of the network, which is one realization of the state of normal or failed link. Creating a constraint expression for each of the scenarios and network conditions, and creating a constraint expression that the link capacity is greater than or equal to the sum of the path flows through the link in each scenario and network condition. Creating a constraint equation that the node capacity is greater than or equal to the sum of the path flow and link capacity; and solving the mathematical programming problem composed of the objective function and the constraint equation created from each of the steps. And determining the capacity of the node Communication network design method characterized by and. 50. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, a link may have a link capacity for accommodating the path flow, and the node may have a node capacity for accommodating the path flow. Creating an objective function for maximizing the expected value obtained from, and in each of the scenarios that is one realization of the value of the required capacity of each demand pair when the required capacity of each demand pair follows the probability distribution, For each demand pair, define a satisfaction level that takes 1 if the total of the path flows exceeds the required capacity, otherwise takes 0, and creates a constraint equation that defines the minimum value of the satisfaction level in each scenario. Creating a constraint expression that the cost related to the link and the node is equal to or less than a predetermined value. Creating a constraint for distributing the sum of path flows to each path for each demand pair in each scenario and each state of the network that is one realization of a state such as normal or failed for each link; Creating a constraint that, for each scenario and network condition, the link capacity is greater than or equal to the sum of the path flows through the link; and in each scenario, the node is calculated from the sum of the path flows terminating at the node and the capacity of the link. Creating a constraint equation that the capacity is large or equal; and determining the capacity of the link and node by solving a mathematical programming problem composed of the objective function and the constraint equation created from each of the steps. Communication network configuration characterized by having Method. 51. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, a link may have a link capacity for accommodating the path flow, and the node may have a node capacity for accommodating the path flow. Creating an objective function for maximizing the expected value obtained from the above, and in each of the scenarios that is one realization of the required capacity value of each demand pair when the required capacity of each demand pair follows a probability distribution, For each demand pair, if the sum of the path flows exceeds the required capacity, take 1; otherwise, define the satisfaction that is the value obtained by dividing the total of the path flows by the required capacity, and further define the minimum value of the satisfaction in each scenario Creating a constraint expression defining the following: the cost of the link and the node is less than or equal to a previously required value In each scenario, and in each state of the network, which is one realization of a state such as normal or failure of each link, the sum of the path flows for each demand pair is independent of the scenario. Creating a constraint for distributing to the paths, and in each scenario creating a constraint that the link capacity is greater than or equal to the sum of the path flows through the links; and in each scenario, terminating at a node Creating a constraint equation that the node capacity is greater than or equal to the sum of the path flow and link capacity; and solving the mathematical programming problem composed of the objective function and the constraint equation created from each of the steps. And determining the capacity of the node Communication network design method characterized. 52. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link may have a link capacity for accommodating the path flow, and the node may have a node capacity for accommodating the path flow. Creating an objective function for maximizing the expected value obtained from, and in each of the scenarios that is one realization of the value of the required capacity of each demand pair when the required capacity of each demand pair follows the probability distribution, For each demand pair, define a satisfaction level that takes 1 if the total of the path flows exceeds the required capacity, otherwise takes 0, and creates a constraint equation that defines the minimum value of the satisfaction level in each scenario. Creating a constraint expression that the cost related to the link and the node is equal to or less than a predetermined value. In each scenario, and in each state of the network, which is one realization of a state such as normal or failed state of each link, for each demand pair, a constraint equation for distributing the total path flow to each path independent of the scenario is defined. Creating, and in each scenario, creating a constraint that the link capacity is greater than or equal to the sum of the path flows through the links; and in each scenario, the node is calculated from the sum of the path flows terminating at the node and the capacity of the links. Creating a constraint equation that the capacity is large or equal; and determining the capacity of the link and node by solving a mathematical programming problem composed of the objective function and the constraint equation created from each of the steps. Communication network design method characterized by having . 53. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, which is constituted by nodes and links connecting the nodes, and the required capacity of the demand pair is determined by the demand capacity of the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer for accommodating the path flow. And causing the computer to create an objective function for minimizing the cost related to the link and the node, and to create a constraint expression for defining a degree of satisfaction with the required capacity according to the probability distribution of the demand pair, A constraint formula for defining a lower limit of the expected value of the satisfaction is created, a constraint formula for distributing the required capacity of the demand pair as a flow to a path is created, and a constraint for accommodating the path flow in the link is created. Constraint for creating an expression and accommodating the path flow in the node Machine-readable recording that records a program for executing a process of determining the capacity of the link and the node by solving a mathematical programming problem composed of the created objective function and the constraint equation Medium. 54. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the realization scenarios, for each demand pair, define a satisfaction level that takes 1 if the total path flow exceeds the required capacity, and otherwise takes the value obtained by dividing the total path flow by the required capacity; and Create a constraint expression that defines the minimum value of the degree of satisfaction in each scenario, Create a constraint formula that the expected value obtained from the minimum value of satisfaction is equal to or greater than the value requested in advance.In each scenario, a constraint formula for distributing the total path flow to each path for each demand pair In each scenario, a constraint formula that the link capacity is greater than or equal to the total path flow through the link is created.In each scenario, the node capacity is greater than the sum of the path flow terminating at the node and the link capacity. A program for executing a process for determining the capacity of the link and the node by solving a mathematical programming problem composed of the created objective function and the constraint expression, A machine-readable recording medium. 55. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer for accommodating the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios to be realized, for each demand pair, if the total path flow exceeds the required capacity, take 1; otherwise, take the value obtained by dividing the total path flow by the required capacity. The expected value of the satisfaction obtained for each demand pair is calculated in advance. Create a constraint expression that is greater than or equal to the requested value, and in each scenario, create a constraint expression for distributing the total path flow to each path for each demand pair. In each scenario, a constraint formula that the node capacity is greater than or equal to the sum of the path flow and link capacity that terminate at the node is created. And a machine-readable recording medium storing a program for executing a process of determining a capacity of the link and the node by solving a mathematical programming problem constituted by the objective function and the constraint equation. 56. A demand capacity, which is constituted by a node and a link connecting the nodes, is provided to a demand pair defined by an arbitrary set of nodes, and the required capacity of the demand pair is determined by the demand capacity of the demand pair. With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer for accommodating the path flow. And causing the computer to create an objective function for minimizing costs for the links and the nodes, taking 1 for each demand pair if the total path flow exceeds the required capacity in each scenario, Otherwise, define a satisfaction level that takes 0, and further create a constraint expression that defines the minimum value of the satisfaction level in each scenario. If the expected value obtained from the minimum value of the satisfaction level is equal to or greater than a previously requested value, In each scenario, a constraint formula is created for each demand pair. Create a constraint formula for distributing the total flow to each path, and in each scenario, create a constraint formula that the link capacity is greater than or equal to the total path flow through the link.In each scenario, terminate at the node The constraint that the node capacity is greater than or equal to the sum of the path flows and link capacities to be performed is created, and the link and node capacities are solved by solving a mathematical programming problem composed of the created objective function and the constraint equation. And a machine-readable recording medium on which a program for executing a process for determining is stored. 57. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, which is constituted by nodes and links connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer for accommodating the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the realization scenarios, for each demand pair, a constraint formula is defined to define a satisfaction level that takes 1 if the total path flow exceeds the required capacity and 0 otherwise, and calculates for each demand pair A constraint expression that the expected value of the satisfaction level is equal to or greater than a value required in advance. In each scenario, a constraint formula for distributing the total path flow to each path is created for each demand pair, and in each scenario, the link capacity is greater than or equal to the total path flow through the link. In each scenario, a constraint expression that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node is created, and it is composed of the created objective function and the constraint expression. A machine-readable storage medium storing a program for executing a process for determining the capacity of the link and the node by solving a mathematical programming problem to be performed. 58. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the realization scenarios, for each demand pair, define a satisfaction level that takes 1 if the total path flow exceeds the required capacity, and otherwise takes the value obtained by dividing the total path flow by the required capacity; and Create a constraint expression that defines the minimum value of the degree of satisfaction in each scenario, Create a constraint formula that the expected value obtained from the minimum value of satisfaction is equal to or greater than the value required in advance, and in each scenario, distribute the total path flow to each path independent of the scenario for each demand pair In each scenario, a constraint formula that the link capacity is greater than or equal to the sum of the path flows through the links is created.In each scenario, the sum of the path flows terminating at the node and the link capacity is calculated. To execute a process of determining a capacity of the link and the node by solving a mathematical programming problem composed of the created objective function and the constraint equation, by creating a constraint equation that the node capacity is large or equal. A machine-readable recording medium that records a program. 59. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by With one node as the start point and the other node as the end point, it flows as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer for accommodating the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios to be realized, for each demand pair, if the total path flow exceeds the required capacity, take 1; otherwise, take the value obtained by dividing the total path flow by the required capacity. The expected value of the satisfaction obtained for each demand pair is calculated in advance. In each scenario, a constraint formula for distributing the total path flow to each path independent of the scenario is created for each scenario, and in each scenario, In each scenario, a constraint formula that the node capacity is greater than or equal to the sum of the path flows terminating at the node and the link capacity is created. A machine-readable recording medium storing a program for executing a process for determining a capacity of the link and the node by solving a mathematical programming problem formed by the created objective function and the constraint equation. 60. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios that are realizations, for each demand pair, define a satisfaction level that takes 1 if the sum of the path flows exceeds the required capacity, and takes 0 otherwise, and further defines the minimum value of the satisfaction level in each scenario. A constraint formula to be defined is created, and the expected value calculated from the minimum value of the satisfaction is predicted. In each scenario, a constraint expression for distributing the total path flow to each path independent of the scenario is created for each scenario. , Create a constraint formula that the link capacity is greater than or equal to the total path flow through the link, and in each scenario, create a constraint formula that the node capacity is greater than or equal to the sum of the path flow terminating at the node and the link capacity A machine-readable recording medium storing a program for executing a process of determining a capacity of the link and the node by solving a mathematical programming problem formed by the created objective function and the constraint equation. 61. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer for accommodating the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the realization scenarios, for each demand pair, a constraint formula is defined to define a satisfaction level that takes 1 if the total path flow exceeds the required capacity and 0 otherwise, and calculates for each demand pair A constraint expression that the expected value of the satisfaction level is equal to or greater than a value required in advance. In each scenario, a constraint formula for distributing the total path flow to each path independent of the scenario is created for each demand pair. In each scenario, the link capacity is calculated based on the total path flow through the link. In each scenario, a constraint formula is created in which the node capacity is equal to or greater than the sum of the capacity of the path flow and the link terminating at the node, and the created objective function and the A machine-readable storage medium storing a program for executing a process of determining the capacity of the link and the node by solving a mathematical programming problem composed of a constraint equation. 62. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the realization scenarios, for each demand pair, define a satisfaction level that takes 1 if the total path flow exceeds the required capacity, and otherwise takes the value obtained by dividing the total path flow by the required capacity; and Create a constraint expression that defines the minimum value of the degree of satisfaction in each scenario, A constraint formula is created in which the expected value obtained from the minimum value of the degree of satisfaction is equal to or more than a value requested in advance, and each scenario and one of the states such as normal or fault of each link are set.
In each of the two network states, a constraint expression for distributing the total path flow to each path is created for each demand pair. In each scenario and network state, the constraint expression is calculated based on the total path flow through the link. In each scenario, a constraint equation that the node capacity is greater than or equal to the sum of the path flow terminating at the node and the link capacity is created, and the created objective function And a machine-readable storage medium storing a program for executing a process of determining the capacity of the link and the node by solving a mathematical programming problem constituted by the constraint equation. 63. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer for accommodating the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios to be realized, for each demand pair, if the total path flow exceeds the required capacity, take 1; otherwise, take the value obtained by dividing the total path flow by the required capacity. The expected value of the satisfaction obtained for each demand pair is calculated in advance. Create a constraint expression that is greater than or equal to the required value. In each scenario, and in each of the network states, which is one realization of the state of normal or failed link, calculate the total path flow for each demand pair. Create a constraint expression to distribute to each path, and in each scenario and network condition, create a constraint expression that the link capacity is greater than or equal to the total path flow through the link.In each scenario, terminate at the node A constraint formula that the node capacity is greater than or equal to the sum of the path flows and the link capacities to perform, and solving the mathematical programming problem composed of the created objective function and the constraint formula, the link and node capacities Machine reading that records the program for executing the process that determines the A removable recording medium. 64. A demand capacity, which is composed of nodes and links connecting the nodes, is provided to a demand pair defined by an arbitrary set of nodes, and the demand capacity of the demand pair is determined by the demand capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios that are realizations, for each demand pair, a satisfaction level of 1 is defined if the total path flow exceeds the required capacity in each scenario, and a satisfaction level of 0 is otherwise defined. Create a constraint expression that defines the minimum value of In each scenario, and in each of the network states that are one realization of the state of normal or failure of each link, the demand equation is created. For each path, create a constraint formula for distributing the total path flow to each path, and in each scenario and network condition, create a constraint formula that the link capacity is greater than or equal to the total path flow through the link. In the above scenario, a constraint formula that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminated at the node is created, and the mathematical programming problem composed of the created objective function and the constraint formula is solved. For executing the processing for determining the capacity of the link and the node in A machine-readable recording medium on which a ram is recorded. 65. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer for accommodating the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the realization scenarios, for each demand pair, a constraint formula is defined to define a satisfaction level that takes 1 if the total path flow exceeds the required capacity and 0 otherwise, and calculates for each demand pair A constraint expression that the expected value of the satisfaction level is equal to or greater than a value required in advance. In each scenario and each state of the network, which is one realization of a state such as normal or failed state of each link, a constraint expression for distributing the total path flow to each path for each demand pair In each scenario and state of the network, a constraint formula is created in which the link capacity is greater than or equal to the sum of the path flows through the link. In each scenario, the node is calculated based on the sum of the path flows terminating at the node and the capacity of the link. A program for executing a process for determining a capacity of a link and a node by solving a mathematical programming problem composed of the created objective function and the constraint equation, by creating constraint equations that the capacity is large or equal. A machine-readable recording medium on which is recorded. 66. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the demand capacity of the demand pair is determined by the demand capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the realization scenarios, for each demand pair, define a satisfaction level that takes 1 if the total path flow exceeds the required capacity, and otherwise takes the value obtained by dividing the total path flow by the required capacity; and Create a constraint expression that defines the minimum value of the degree of satisfaction in each scenario, A constraint formula is created in which the expected value obtained from the minimum value of the degree of satisfaction is equal to or greater than a value requested in advance, and each scenario and each state of the network, which is one realization of a state such as normal or failure of each link, , A constraint formula is created for distributing the total path flow to each path independent of the scenario for each demand pair. In each network condition, the constraint that the link capacity is greater than or equal to the total path flow through the link In each scenario, a constraint expression that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link that terminates at the node is created, and the constraint function is composed of the created objective function and the constraint expression. Execute processing to determine the capacity of the link and node by solving a mathematical programming problem A machine-readable recording medium that stores a program for causing 67. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer for accommodating the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios to be realized, for each demand pair, if the total path flow exceeds the required capacity, take 1; otherwise, take the value obtained by dividing the total path flow by the required capacity. The expected value of the satisfaction obtained for each demand pair is calculated in advance. Create a constraint expression that is greater than or equal to the required value. In each scenario, and in each of the network states, which is one realization of the state of normal or failed link, calculate the total path flow for each demand pair. A constraint formula for distributing to each path independent of the scenario is created.In each network state, a constraint formula that the link capacity is greater than or equal to the total path flow through the link is created. A constraint formula that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at is created, and the link and the node are solved by solving a mathematical programming problem composed of the created objective function and the constraint formula. That records a program for executing the process of determining the capacity of A machine-readable recording medium. 68. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the realization scenarios, for each demand pair, for each demand pair, in each scenario, a satisfaction level of 1 is defined if the total path flow exceeds the required capacity, and a satisfaction level of 0 is defined otherwise. Create constraints that define the minimum value of satisfaction in each scenario. A constraint expression that an expected value obtained from the minimum value of the satisfaction level is equal to or more than a previously requested value is created, and each scenario and a state of a network which is one realization of a state such as a normal state or a failure state of each link. In each case, a constraint formula for distributing the total path flow to each path independent of the scenario is created for each demand pair, and in each network condition, the link capacity is greater than or equal to the total path flow through the link In each scenario, a constraint formula that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminating at the node is created, and it is composed of the created objective function and the constraint formula. Processing for determining the capacity of the link and node by solving the mathematical programming problem A machine-readable recording medium on which a program for executing processing is recorded. 69. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer for accommodating the path flow. And causing the computer to create an objective function for minimizing costs related to the link and the node, wherein one of the values of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the realization scenarios, for each demand pair, a constraint formula is defined to define a satisfaction level that takes 1 if the total path flow exceeds the required capacity and 0 otherwise, and calculates for each demand pair A constraint expression that the expected value of the satisfaction level is equal to or greater than a value required in advance. To distribute the total path flows to each path independent of the scenario for each demand pair in each scenario and in each state of the network, which is one realization of the state of normal or failed state of each link. In each network condition, a constraint formula that the link capacity is greater than or equal to the total path flow through the link is created. In each scenario, the sum of the path flows terminating at the node and the link capacity is calculated. In order to execute a process of determining a link and a node capacity by solving a mathematical programming problem composed of the created objective function and the constraint equation, by creating a constraint equation that the node capacity is larger or equal to the node function. A machine-readable recording medium on which the program of the above is recorded. 70. A demand capacity, which is constituted by nodes and links connecting the nodes, is provided to a demand pair defined by an arbitrary set of nodes, and the required capacity of the demand pair is determined by the demand capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for maximizing the expected value of satisfaction, to create a constraint formula for defining the degree of satisfaction with the required capacity of the demand pair according to the probability distribution, A constraint formula for defining an upper limit of the cost related to the node is created, a constraint formula for distributing the required capacity of the demand pair as a flow to a path is created, and a constraint formula for accommodating the path flow in the link is created. Create a constraint expression for accommodating the path flow in the node A machine-readable recording medium storing a program for executing a process of determining a capacity of the link and the node by solving a mathematical programming problem formed by the created objective function and the constraint equation. 71. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for maximizing the expected value obtained from the minimum value of the degree of satisfaction, the value of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios that are one of the realizations of the above, for each demand pair, the satisfaction level is defined as 1 if the total path flow exceeds the required capacity, otherwise, the satisfaction level is calculated by dividing the total path flow by the required capacity. In addition, a constraint formula that defines the minimum value of satisfaction in each scenario is created, and the link and the In each scenario, a constraint formula for distributing the total path flow to each path is created for each demand pair. In the above scenario, the constraint formula that the link capacity is greater than or equal to the sum of the path flows through the links is created. In each scenario, the constraint formula that the node capacity is greater than or equal to the sum of the path flows terminating at the node and the link capacity. Machine-readable recording that records a program for executing a process of determining the capacity of the link and the node by solving a mathematical programming problem composed of the created objective function and the constraint equation. Medium. 72. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for maximizing the expected value obtained from the minimum value of the degree of satisfaction, the value of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios, which are one realization of the above, for each demand pair, a satisfaction level of 1 is defined if the sum of the path flows exceeds the required capacity, otherwise, a satisfaction level of 0 is defined. A constraint formula that defines the minimum value is created, and costs for the link and the node are required in advance. In each scenario, create a constraint expression for distributing the total path flow to each path for each demand pair, and in each scenario, pass the link In each scenario, the constraint formula that the link capacity is greater than or equal to the sum of the path flows is created.In each scenario, the constraint formula that the node capacity is greater than or equal to the sum of the path flows and the link capacity that terminate at the node is created. A machine-readable storage medium storing a program for executing a process of determining the capacity of the link and the node by solving a mathematical programming problem formed by the objective function and the constraint equation. 73. A demand capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for maximizing the expected value obtained from the minimum value of the degree of satisfaction, the value of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios that are one of the realizations of the above, for each demand pair, the satisfaction level is defined as 1 if the total path flow exceeds the required capacity, otherwise, the satisfaction level is calculated by dividing the total path flow by the required capacity. In addition, a constraint formula that defines the minimum value of satisfaction in each scenario is created, and the link and the In each scenario, for each demand pair, a constraint expression for distributing the total path flow to each path independent of the scenario is created. In each scenario, create a constraint formula that the link capacity is greater than or equal to the total path flow through the link.In each scenario, check whether the node capacity is greater than the sum of the path flow terminating at the node and the link capacity. A machine which records a program for executing a process for determining a capacity of the link and the node by solving a mathematical programming problem composed of the created objective function and the generated constraint function by creating a constraint expression of equality A readable recording medium. 74. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for maximizing the expected value obtained from the minimum value of the degree of satisfaction, the value of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios, which are one realization of the above, for each demand pair, a satisfaction level of 1 is defined if the sum of the path flows exceeds the required capacity, otherwise, a satisfaction level of 0 is defined. A constraint formula that defines the minimum value is created, and costs for the link and the node are required in advance. In each scenario, a constraint expression for distributing the total path flow to each path independent of the scenario is created for each scenario, and in each scenario, In each scenario, a constraint formula that the node capacity is greater than or equal to the sum of the path flows terminating at the node and the link capacity is created. A machine-readable recording medium storing a program for executing a process for determining a capacity of the link and the node by solving a mathematical programming problem formed by the created objective function and the constraint equation. 75. A demand capacity, which is constituted by nodes and links connecting the nodes, is provided to a demand pair defined by an arbitrary set of nodes, and the required capacity of the demand pair is determined by the demand capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for maximizing the expected value obtained from the minimum value of the degree of satisfaction, the value of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios that are one of the realizations of the above, for each demand pair, the satisfaction level is defined as 1 if the total path flow exceeds the required capacity, otherwise, the satisfaction level is calculated by dividing the total path flow by the required capacity. In addition, a constraint formula that defines the minimum value of satisfaction in each scenario is created, and the link and the In each scenario, and in each state of the network, which is one realization of a state such as a normal state or a failure state of each link, a demand equation is created. For each path, create a constraint formula for distributing the total path flow to each path, and in each scenario and network condition, create a constraint formula that the link capacity is greater than or equal to the total path flow through the link. In the above scenario, a constraint formula that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminated at the node is created, and the mathematical programming problem composed of the created objective function and the constraint formula is solved. To execute the processing for determining the capacity of the link and the node. Machine-readable recording medium on which a program for recording is stored. 76. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for maximizing the expected value obtained from the minimum value of the degree of satisfaction, the value of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios, which are one realization of the above, for each demand pair, a satisfaction level of 1 is defined if the sum of the path flows exceeds the required capacity, otherwise, a satisfaction level of 0 is defined. A constraint formula that defines the minimum value is created, and costs for the link and the node are required in advance. In each scenario, and in each state of the network, which is one realization of the state such as normal or failure of each link, the total of the path flows is calculated for each demand pair in each scenario and each link. Create a constraint formula to distribute to each path, and in each scenario and network condition, create a constraint formula that the link capacity is greater than or equal to the total path flow through the link.In each scenario, terminate at the node A constraint formula that the node capacity is greater than or equal to the sum of the path flows and the link capacities to perform, and solving the mathematical programming problem composed of the created objective function and the constraint formula, the link and node capacities Machine reading a program for executing a process for determining Recording media. 77. A required capacity is provided to a demand pair defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, and the required capacity of the demand pair is determined by the required capacity of the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for maximizing the expected value obtained from the minimum value of the degree of satisfaction, the value of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios that are one of the realizations of the above, for each demand pair, the satisfaction level is defined as 1 if the total path flow exceeds the required capacity, otherwise, the satisfaction level is calculated by dividing the total path flow by the required capacity. In addition, a constraint formula that defines the minimum value of satisfaction in each scenario is created, and the link and the In each scenario, and in each state of the network, which is one realization of a state such as a normal state or a failure state of each link, a demand equation is created. For each scenario, create a constraint formula for distributing the total path flow to each path independent of the scenario, and in each scenario, create a constraint formula that the link capacity is greater than or equal to the total path flow through the link. In the above scenario, a constraint formula that the node capacity is greater than or equal to the sum of the capacity of the path flow and the link terminated at the node is created, and the mathematical programming problem composed of the created objective function and the constraint formula is solved. To execute a process for determining the capacity of the link and the node. A machine-readable recording medium that records a program. 78. A demand capacity defined by an arbitrary set of nodes, comprising a node and a link connecting the nodes, is provided with a required capacity, and the required capacity of the demand pair is determined by the demand pair. With one node as the start point and the other node as the end point, it is flowed as a flow on a path defined by any continuous nodes and links,
Further, a link has a link capacity for accommodating the path flow, and a node has a network medium for recording a network design control program for designing a network having a node capacity by a computer to accommodate the path flow. And causing the computer to create an objective function for maximizing the expected value obtained from the minimum value of the degree of satisfaction, the value of the required capacity of each demand pair when the required capacity of each demand pair follows a probability distribution In each of the scenarios, which are one realization of the above, for each demand pair, a satisfaction level of 1 is defined if the sum of the path flows exceeds the required capacity, otherwise, a satisfaction level of 0 is defined. A constraint formula that defines the minimum value is created, and costs for the link and the node are required in advance. In each scenario and each state of the network, which is one realization of the state such as normal or failed state of each link, the total of the path flows is calculated for each demand pair in each scenario and each link. Create a constraint expression for distributing to each path independent of the scenario, and in each scenario, create a constraint expression that the link capacity is greater than or equal to the total path flow through the link.In each scenario, terminate at the node A constraint formula that the node capacity is greater than or equal to the sum of the path flows and the link capacities to perform, and solving the mathematical programming problem composed of the created objective function and the constraint formula, the link and node capacities Machine readable recording the program for executing the process to determine the Recording media.