TWI393016B - Calculation Method of Network Reliability and Its System - Google Patents

Description

Network reliability calculation method and system thereof

The present invention relates to a network reliability computing system and method thereof, and more particularly to a method for calculating network reliability through a general generation function.

Currently, a network is a structure in which some components are connected to each other and have a functional relationship with each other. Some complex systems and project plans can be constructed as networks, and network characteristics can describe the performance of the systems or projects being built. Therefore, managers and consultants can analyze the networks to understand system value. In management science, network reliability is one of the most effective decision analysis tools and is closely related to today's society.

Many real systems, such as computer communication systems, power distribution systems, mobile phone networks, computer networks, transportation systems, and oil/gas production systems, often use network models for design validation and performance evaluation. Reliability is often one of the most important metrics in the tools used to evaluate these networks.

In a real network, there may be thousands of nodes and paths, so it is quite difficult to use algorithms to calculate the correct network reliability in a limited time. Moreover, the network is dynamic, that is, its characteristics (such as: bandwidth, speed, etc.) will quickly change with different times, even changing its state at the same time.

The general approach to network reliability calculations tends to focus on one-to-one network reliability analysis. The difficulty of calculating network reliability is significantly related to the size of its network. The computational complexity of network reliability is Non-deterministic Polynomial hard (NP-hard). According to the method used to transfer signals, reliability problems can be divided into two categories: Multistate-Arc Network (MAN) and Multistate-Node Network (MNN). In a multi-state arc network, each arc has a random variable with a non-negative integer value, and all signals in the network meet the conservation law. Conversely, the signals in the multi-state node network do not satisfy the conservation law.

Most of the conventional techniques use the Universal Generating Function (UGF) and the Universal Generating Function Method (UGFM) to evaluate the reliability of a multi-state arc network. For the one-to-many (point-to-multiple target points) network reliability calculation problem, the prior art can only perform reliability calculation for the Acyclic Multistate-Node Network (AMNN). However, in real-world applications, in order to provide redundancy or prevent overload, the actual application network is not a non-cyclic multi-state node network, that is, there must be a loop in the network.

From the above, a new calculation method and its system are needed to calculate the reliability of the multi-state arc network and solve the problem of network design and analysis.

In view of the above-mentioned problems of the prior art, the object of the present invention is to provide a method and system for calculating network reliability to solve the problem of network confirmation design and evaluation performance.

According to another object of the present invention, a method for calculating network reliability is provided, comprising the steps of: by using a general generation function processing unit, first setting a count value (i) to 2, and setting a starting point to [1], According to the calculation of u ([1]) and U ([1]). Next, the general generation function processing unit sets the point v to [i] and calculates u([i]) accordingly. Then, the general generation function processing unit calculates U([i]) according to u([i]) and U([i-1]), and simplifies it. The determination unit determines whether the count value (i) is smaller than the total number of nodes of the non-target point, and if not, the reliability calculation unit obtains the reliability coefficient r _J according to U([i]). Finally, the reliability calculation unit calculates the reliability function R _J reaching the J set according to the J set and r _J , and calculates the network reliability according to R _J .

Where [i] is the i-th order node. u([i]) is the general generation function of the i-th node. U([i]) is the general generation function of the i-th subnetwork, and U([1])=u([1]). V by the system node is connected to V _[i-1], does not belong to V among the nodes _[i-1] optionally a node, and _{V [i-1] = {} [1], [2] ,. ..,[i-1]}. The J set belongs to the set formed by the target points, and r _J is among U([i]), and the end point is the coefficient of all the items of the J set.

According to still another object of the present invention, a computing system for network reliability is provided, which may include: a storage unit, a general generation function processing unit, a reliability calculation unit, and a determination unit. The storage unit stores the network status and count value (i). The general generation function processing unit can calculate u([i]) and U([i]) according to the network state, the count value (i), the nodes v and U([i-1]), and U([ i]) After simplification, save it in the storage unit. The reliability calculation unit may separately calculate the reliability coefficient r _J according to the network state, U([i]) and the J set, and then separately calculate the reliability function R _J reaching the J set, and perform the network according to R _J Calculation of road reliability. The judging unit may judge whether the count value (i) is smaller than the total number of nodes of the non-target point in the network according to the network status and the count value (i), and if so, increment the count value (i) by 1 and notify the general generation function to process The unit continues processing, and if not, the reliability calculation unit is notified to perform network reliability calculation.

Wherein, in the general generation function processing unit, if the count value (i) is 1, the node v is the starting point, and if the count value (i) is not 1, the node v may be connected to V[ _i-1 ], and Any node that is not part of V[ _i-1 ], [i] is the i-th node, u([i]) is the general generation function of the i-th node, and U([i]) is the i-th order The subnet general generation function, and V[ _i-1 ]={[1], [2],...,[i-1]}.

Wherein, in the reliability calculation unit, the J set belongs to a set formed by the target points. r _J is the value of U([i]), and the end point is the coefficient of all the items of the J set.

As described above, the method and system for calculating network reliability according to the present invention may have one or more of the following advantages:

(1) It can solve the problem of network reliability calculation of one-to-many (one point to multiple target points) in a multi-state arc network with loops.

(2) The complex behavior of transmitting signals in the network between nodes is expressed by equations and calculated and analyzed by multiplication operators, which greatly simplifies the process of computational reliability and can efficiently perform network reliability. Calculation.

A description of some of the symbols will be set forth below to facilitate the description of the system and method of the present invention.

|●|: The number of elements in the ● collection.

V: A collection of all nodes in the network.

T: A collection of all target nodes in the network.

i: represents the count value (i).

[i]: A node representing the recursive procedure of the i-th generation into the general generation function method, which may be simply referred to as an i-th order node.

V _i : {1, 2, 3, ..., i}.

V _[i] :{[1], [2], [3],...,[i]}.

P _m:n Z ⁿ : probability of starting from the m node to the n node.

θ _m : a set of nodes that can be reached by the node m.

u([i]): the i-th node general generation function, .

: Multiplication operator, suitable for the calculation of general generation functions.

U([i]): the general generation function of the i-th subnetwork,

r _J : U([i]), the end point is the coefficient of all the items of the J set, called the reliability coefficient, wherein the J set belongs to the set formed by at least one target point.

R _J : the reliability function that reaches the J set, .

Please refer to FIG. 1 , which is a flowchart of a method for calculating network reliability according to the present invention. In the figure, the following steps are included: in step S101, by using the general generation function processing unit, the i value is first set to 2, the starting point is set to [1], and u([1]) and U([ 1]). In step S102, the generic function generation processing unit is connected to the V _[il], does not belong among the V _[il] the node and choose a node v, which is set to [I], and accordingly calculate u ([i]). In step S103, the general generation function processing unit calculates U([i]) from u([i]) and U([i-1]), and simplifies it. In step 104, the determining unit determines whether i is smaller than the total number of nodes of the non-target point, and if so, proceeds to step S108, increments the value of i by one, and repeats step S102; if not, proceeds to step S105, by way of reliability Calculate the unit and calculate the reliability coefficient r _J according to U([i]). In step S106, r _{J is} added to the total calculation, and the reliability function R _J reaching the J set can be calculated. In step S107, the reliability calculation unit performs network reliability calculation based on R _J and performs network design based on reliability.

Please refer to Figure 2, which is a schematic diagram of a network model. In the figure, the network G is composed of a network node set V={21, 22, 23, 24, 25} and an arc set E, which can be represented as G(V, E); wherein the first node 21 is a starting point. The fourth node 24 and the fifth node 25 are both target nodes. The calculation method of the network reliability of the present invention will be described below by taking the network model of FIG. 2 as an example.

To find all the reliability of the first node 21 from the starting point to the fourth node 24 and the fifth node 25 of the target node, please refer to the flow of FIG. 1 and the steps are as follows:

Step S101: Set i to 2 by the general generation function processing unit, and set the first node 21 to [1], and U([1])=u([1])=u(21)=P _1:2 Z ² +P _1:3 Z ³ +P _1:23 Z ²³ .

The step S102: General generating function processing unit connected to the V _[1], does not belong to V _[1] among the node and choose a node, such as the third node 23, and is set to [2], and u([2])=u(23)=P _3:Φ Z ^Φ +P _3:2 Z ² +P _3:4 Z ⁴ +P _3:24 Z ²⁴ .

Step S103: The general generation function processing unit calculates and simplifies U([2]) according to u([2]) and U([1]) as follows:

Step S104: The determination is made by the determination unit, and since i(=2) is less than 3 (=5-2), step S108 is performed.

Step S108: increment the value of i by 1, and proceed to step S102.

The step S102: General processing unit from generating function _[2] is connected to the V, does not belong to V _[2] among the node and choose a node as the second node 22, and is set to [3], and u([3])=u(22)=P _2:Φ Z ^Φ +P _2:3 Z ³ +P _2:5 Z ⁵ +P _2:35 Z ³⁵ .

Step S103: The general generation function processing unit calculates and simplifies U([3]) according to u([3]) and U([2]) as follows:

Step S104: The determination is made by the determination unit, and since i (=3) is not less than 3 (= 5-2), step S105 is performed.

Step S105: The reliability calculation unit respectively obtains the reliability coefficient r _J according to U([3]) as follows: r ₄ = P _{1: 3} P _{3: 4} + P _{1: 23} P _{3: 4} P _{2: Φ} + P _1:2 P _3:4 P _2:3 +P _1:3 P _3:24 P _2:Φ +P _1:23 P _3:4 P _2:3 +P _1:23 P _3:24 P _{2: Φ} ;r ₅ =P _1:3 P _3:2 P _2:5 +P _1:2 P _2:5 +P _1:2 P _3:Φ P _2:35 +P _1:23 P _3:Φ P _{2 :5} +P _1:23 P _3:Φ P _2:35 +P _1:2 3P _3:2 P _2:5 ; and r ₄₅ =P _1:3 P _3:24 P _2:5 +P _1:23 P _3:4 P _2:5 +P _1:2 P _3:4 P _2:35 +P _1:23 P _3:4 P _2:35 +P _1:23 P _3:24 P _2:5 .

Step S106: The reliability calculation unit adds the reliability coefficient r _J coefficients to the total operation, and obtains the reliability function R _J as follows:

R ₄ =r ₄ +r ₄₅ =(P _1:3 P _3:4 +P _1:23 P _3:4 P _2:Φ +P _1:2 P _3:4 P _2:3 +P _1:3 P _3:24 P _2:Φ +P _1:23 P _3:4 P _2:3 +P _1:23 P _3:24 P _2:Φ )+(P _1:3 P _3:24 P _2:5 +P _1:23 P _3:4 P _2:5 +P _1:2 P _3:4 P _2:35 +P _1:23 P _3:4 P _2:35 +P _1:23 P _3:24 P _2:5 )

R ₅ =r ₅ +r ₄₅ =(P _1:3 P _3:2 P _2:5 +P _1:2 P _2:5 +P _1:2 P _3:Φ P _2:35 +P _1:23 P _3:Φ P _2:5 +P _1:23 P _3:Φ P _2:35 +P _1:23 P _3:2 P _2:5 )+(P _1:3 P _3:24 P _2:5 +P _1:23 P _3:4 P _2:5 +P _1:2 P _3:4 P _2:35 +P _1:23 P _3:4 P _2:35 +P _1:23 P _3:24 P _2:5 )

R ₄₅ =r ₄₅ =(P _1:3 P _3:24 P _2:5 +P _1:23 P _3:4 P _2:5 +P _1:2 P _3:4 P _2:35 +P _1:23 P _3:4 P _2:35 +P _1:23 P _3:24 P _2:5 )

Step S107: The reliability calculation unit calculates the reliability of the network according to the reliability function R _J .

Next, please refer to FIG. 3, which is a schematic diagram of a network reliability calculation system of the present invention. In the figure, the network reliability calculation system may include a storage unit 31, a general generation function processing unit 32, a reliability calculation unit 33, and a determination unit 34. The storage unit 31 can store the network status 311 and the count value (i) 312. The general generation function processing unit 32 can calculate u([i]) and U([i]) according to the network state 311, the count value (i) 312, the nodes v, and U([i-1]), and After U([i]) is simplified, it is stored in the storage unit 31. The reliability calculation unit 33 may first calculate the reliability coefficient r _J according to the network state 311, U([i]) and the J set, and then separately calculate the reliability function R _J reaching the J set, and according to R _J Perform network reliability calculations. The determining unit 34 may determine, according to the network status 311 and the count value (i) 312, whether the count value (i) 312 is less than the total number of nodes of the non-target point in the network, and if so, increment the count value (i) 312 by one, and The notification general generation function processing unit 32 continues the processing, and if not, the notification reliability calculation unit 33 performs the calculation of the network reliability.

Wherein, in the general generation function processing unit 32, if the count value (i) 312 is 1, the node v is the starting point, and if the count value (i) 312 is not 1, the node v can be compared with V _[i-1] Connected, and does not belong to any node of V _[i-1] , [i] is the i-th node, u([i]) is the general generation function of the i-th node, U([i]) is The i-th sub-network general generation function, and V _[i-1] = {[1], [2], ..., [i-1]}.

Among them, in the reliability calculation unit 33, the J set belongs to a set formed by the target points. r _J is the value of U([i]), and the end point is the coefficient of all the items of the J set.

The network reliability model of the present invention will be described below by taking the network model of FIG. 2 as an example.

To find all the reliability from the first node 21 of the starting point to the fourth node 24 and the fifth node 25 of the target node, please refer to the system block diagram of Fig. 3, and the system processing is as follows: First, due to the count value (i) 312 is initially set to 1, and the general generation function processing unit 32 calculates U([1])=u([1])=u(21) according to the network state 311, the count value (i) 312, and the first node 21. =P _1:2 Z ² +P _1:3 Z ³ +P _1:23 Z ²³ , and it is simplified and stored in the storage unit 31.

Next, the determining unit 34 determines, according to the network state 311 and the count value (i) 312, that the value of the count value (i) 312 is smaller than the total number of nodes in the network that are not the end point, wherein the value of the count value (i) 312 is 1. The total number of nodes that are not at the end is 3. Next, the judging unit 34 first increments the value of the count value (i) 312 to 2, and then notifies the general generation function processing unit 32 to continue the processing.

Next, the general function of the processing unit 32 first by generating and V _[1] is connected to, does not belong to V _[1] Optionally a node among nodes, such as the third node 23, then according to the state of the web 311, the count value ( i), 3rd node 23 and U([1]), calculate u([2])=u(23)=P _3:Φ Z ^Φ +P _3:2 Z ² +P _3:4 Z ⁴ + P _3:24 Z ²⁴ , and calculate and simplify U([2]) as follows, and store the simplified U([2]) in the storage unit 31:

Next, the determining unit 34 determines, according to the network state 311 and the count value (i) 312, that the value of the count value (i) 312 is smaller than the total number of nodes in the network that are not the end point, wherein the value of the count value (i) 312 is 2, The total number of nodes that are not at the end is 3. Next, the judging unit 34 first increments the value of the count value (i) 312 to 3, and then notifies the general generation function processing unit 32 to continue the processing.

Next, the general generation function processing unit 32 is first connected to V _[2] , and any node that does not belong to V _[2] , such as the second node 22, according to the network state 311, the count value ( i), 2nd node 22 and U([2]), calculate u([3])=u(22)=P _2:Φ Z ^Φ +P _2:3 Z ³ +P _2:5 Z ⁵ + P _2:35 Z ³⁵ , and calculate and simplify U([2]) as follows, and store the simplified U([2]) in the storage unit 31:

Next, the determining unit 34 determines, according to the network state 311 and the count value (i) 312, that the value of the count value (i) 312 is not less than the total number of nodes in the network that are not the end point, wherein the value of the count value (i) 312 is 3. The total number of nodes that are not at the end is 3. Next, the judging unit 34 notifies the reliability calculating unit 33 of the calculation of the network reliability.

Finally, the reliability calculation unit 33 first calculates r _J according to the network state 311, U([3]), and J set as follows: r ₄ = P _{1: 3} P _{3: 4} + P _{1: 23} P _{3: 4} P _2:Φ +P _1:2 P _3:4 P _2:3 +P _1:3 P _3:24 P _2:Φ +P _1:23 P _3:4 P _2:3 +P _1:23 P _{3 :24} P _2:Φ ;r ₅ =P _1:3 P _3:2 P _2:5 +P _1:2 P _2:5 +P _1:2 P _3:Φ P _2:35 +P _1:23 P _{3: Φ} P _2:5 +P _1:23 P _3:Φ P _2:35 +P _1:23 P _3:2 P _2:5 ; and r ₄₅ =P _1:3 P _3:24 P _2:5 +P _1:23 P _3:4 P _2:5 +P _1:2 P _3:4 P _2:35 +P _1:23 P _3:4 P _2:35 +P _1:23 P _3:24 P _{2 :5} .

Then R & lt _J are calculated according to the arrival of the set of J R & lt reliability function _J as follows:

R ₄ =r ₄ +r ₄₅ =(P _1:3 P _3:4 +P _1:23 P _3:4 P _2:Φ +P _1:2 P _3:4 P _2:3 +P _1:3 P _3:24 P _2:Φ +P _1:23 P _3:4 P _2:3 +P _1:23 P _3:24 P _2:Φ )+(P _1:3 P _3:24 P _2:5 +P _1:23 P _3:4 P _2:5 +P _1:2 P _3:4 P _2:35 +P _1:23 P _3:4 P _2:35 +P _1:23 P _3:24 P _2:5 )

R ₅ =r ₅ +r ₄₅ =(P _1:3 P _3:2 P _2:5 +P _1:2 P _2:5 +P _1:2 P _3:Φ P _2:35 +P _1:23 P _3:Φ P _2:5 +P _1:23 P _3:Φ P _2:35 +P _1:23 P _3:2 P _2:5 )+(P _1:3 P _3:24 P _2:5 +P _1:23 P _3:4 P _2:5 +P _1:2 P _3:4 P _2:35 +P _1:23 P _3:4 P _2:35 +P _1:23 P _3:24 P _2:5 )

R ₄₅ =r ₄₅ =(P _1:3 P _3:24 P _2:5 +P _1:23 P _3:4 P _2:5 +P _1:2 P _3:4 P _2:35 +P _1:23 P _3:4 P _2:35 +P _1:23 P _3:24 P _2:5 )

And based on the reliability function R _J , the reliability of the network is calculated.

The above is intended to be illustrative only and not limiting. Any equivalent modifications or alterations to the spirit and scope of the invention are intended to be included in the scope of the appended claims.

S101-S108. . . step

twenty one. . . First network node

twenty two. . . 2nd network node

twenty three. . . Third network node

twenty four. . . 4th network node

25. . . 5th network node

31. . . Storage unit

311. . . Network status

312. . . Count value (i)

32. . . Generic generation function processing unit

33. . . Reliability calculation unit

as well as

34. . . Judging unit

Figure 1 is a flow chart of a method for calculating network reliability of the present invention;

Figure 2 is a schematic diagram of a network model;

Figure 3 is a schematic diagram of a computing system for network reliability of the present invention.

S101-S108. . . step

Claims (9)

A method for calculating network reliability is applicable to a network comprising a plurality of nodes and a plurality of arcs connecting the plurality of nodes, wherein the plurality of nodes include a point and at least one target point, the method The system comprises the following steps: (A) setting a count value (i) to 2 by a general generation function processing unit, and setting the starting point to [1], thereby calculating u([1]) and U ([J]), where [1] is the first-order node, u([1]) is the first-order node general-generation function, and U([1]) is the first-order sub-network general-generation function, and At this time, U([1])=u([1]); (B) the general generation function processing unit then sets a node v to [i], and accordingly calculates u([i]), where the node is connected by a line v V _[il], does not belong among the V _[il] optionally node a node, [i] is the i-th node, u ([i]) is the i-th common node Generate a function, and V[ _il ]={[1],[2],...,[i-1]}; (C) the general generation function processing unit according to u([i]) and U([i-1 ]), calculate U([i]), and simplify it, where U([i]) is the general generation function of the i-th sub-network; (D) judging the count value by a judgment unit (i) whether it is less than the total number of nodes of the non-target point, if not, proceed to step (E); (E) use a reliability calculation unit, and according to U([i]), respectively obtain the reliability coefficient r _J , Wherein, the J set belongs to a set formed by the at least one target point, r _J is a coefficient of U([i]), the end point is a coefficient of all the items of the J set; and (F) by the reliability calculation unit, And according to the J set and r _J , respectively calculate the reliability function R _J reaching the J set, and calculate the network reliability according to R _J . The method for calculating the network reliability according to claim 1, wherein in the step (D), if i is smaller than the total number of nodes of the non-target point, i is incremented by 1, and the step (B) is performed. The method for calculating network reliability as described in claim 2, wherein in the step (A) and the step (B), And _{wherein, P [i]: K Z} K by [i] node departure and arrival probability K nodes, [theta] _[i] by [i] starting set of all nodes reachable. The method for calculating the network reliability as described in claim 3, wherein in the step (C), And among them, For the multiplication operator, it is suitable for the calculation of the general generation function. The method for calculating the network reliability as described in claim 4, wherein in the step (F), And wherein the J set belongs to the set formed by the at least one target point. A network reliability computing system is applicable to a network, the network is configured by a plurality of nodes and a plurality of arcs, and the plurality of nodes include a point and at least one target point, and the method includes: a storage unit, The system is configured to store a network state of the network and a count value (i), wherein the count value (i) is initially set to 1; a general generation function processing unit according to the network status, The count value (i), a node v, and U([i-1]), calculate u([i]) and U([i]), and simplify U([i]) and store it In the storage unit, a reliability calculation unit calculates the reliability coefficient r _J according to the network state, U([i]) and the J set, and separately calculates the reliability function of the J set. R _J , and calculating the network reliability according to R _J ; and a judging unit determining whether the count value (i) is smaller than the non-target in the network according to the network state and the count value (i) The total number of nodes of the point, if yes, increment the count value (i) by 1, and notify the general generation function processing unit to continue processing, and if not, notify the reliable Calculation means calculates the reliability of the network; wherein the general processing unit generating function, if the counter value (i) is 1, the starting point for the system node v, if the counter value (i) is not 1, the node v is selected from a node connected to V _[i-1] and not belonging to V _[i-1] , [i] is an i-th node, u([i]) For the i-th node general generation function, U([i]) is the general generation function of the i-th sub-network, U([i-1]) is the general generation function of the i-th sub-network, and V _{[ I-1]} ={[1], [2],...,[i-1]}; further, in the reliability calculation unit, the J set belongs to a set formed by the at least one target point, and r _J Among U([i]), the end point is the coefficient of all the items of the J set. A computing system for network reliability as described in claim 6, wherein the general generating function processing unit And _{wherein, P [i]: K Z} K by [i] node departure and arrival probability K nodes, [theta] _[i] by [i] starting set of all nodes reachable. A computing system for network reliability as described in claim 7, wherein the general generating function processing unit And among them, For the multiplication operator, it is applied to the calculation of the general generation function, and U([1])=u([1]). A computing system for network reliability as described in claim 8, wherein the reliability calculating unit And wherein the J set belongs to the set formed by the at least one target point.