JP4845858B2 - Network topology / link capacity design processing method, system and program - Google Patents

Description

  The present invention relates to a network topology and link capacity design technology in the Internet and the like, and in particular, in a network topology design problem, an arbitrary link usage rate can be arbitrarily set in consideration of detour traffic occurring at the time of a single link failure. The present invention relates to a technique for obtaining an optimal network topology and link capacity by minimizing the total cost under the constraint that it is kept below a predetermined upper limit value.

  The Internet does not manage the state of individual flows in the network, and routing processing is performed based only on received addresses. Within a single AS (Autonomous System) managed by each ISP (Internet Services Provider), packets are forwarded on a route that minimizes the sum of link weights fixedly set by OSPF (Open Shortest Path First). .

  In addition, since the transmission host autonomously determines the transfer rate without performing flow admission control, link congestion may occur in principle. For this reason, in order to maintain appropriate communication quality, designing and managing the network so that the utilization rate of all links constituting the network is below an appropriate level is one of the main issues of the ISP.

  The link usage rate is determined by the design bandwidth of each link and the amount of traffic flowing. However, the amount of traffic always changes due to changes in the amount of AC traffic demand and changes in the route due to various failures. For this reason, many traffic engineering (TE) studies have been made to dynamically set a route through which a packet flows so as to actively use a link having a low utilization rate and to distribute a link load.

  For example, if MPLS (Multi-Protocol Label Switching) is used, a path can be explicitly set between a pair of arrival and departure nodes. Non-Patent Document 1 proposes a design technique for leveling between a plurality of paths where traffic between each arrival / departure node can be installed. In Non-Patent Documents 2 and 3, the link load is the entire network. A technique for setting a fixed link weight of OSPF so as to be leveled has been proposed.

  In addition, OSPF calculates a detour route autonomously at the time of a link or node failure. For example, in Non-Patent Document 4, paying attention to detour traffic generated at the time of a failure, link load is reduced in some failure patterns. It is considered to prepare each OSPF link weight pattern so as to be well distributed.

  In these technologies, a static AC matrix assumed in advance (the traffic amount for each pair of incoming and outgoing nodes is represented as a matrix, and the elements of i rows and j columns become the traffic amount from node i to node j. ”,“ Demand matrix ”,“ traffic exchange ”, etc.), the route is optimized. For example, in Non-Patent Documents 5 and 6, packets are dynamically generated based on the link usage rate measured in real time. It is also being considered to optimize the route of the flow.

  When such TE is used, the link load can be leveled, and when the AC matrix changes dynamically (Non-Patent Documents 5 and 6) or when detour traffic occurs due to a link node failure ( Non-patent document 4) also makes it possible to minimize the occurrence of congestion by effectively utilizing network resources.

  However, the link utilization rate depends not only on the AC matrix and path, but also on the network topology and link capacity.

  In the above-described TE, it is assumed that the network topology and link capacity are given as known ones. On the other hand, network topology and link capacity are major factors that determine network construction costs and operation costs, and have a great influence on ISP management.

  Accordingly, the ISP can freely design the topology and link capacity of the network operated by itself, and it is important to appropriately design these in order to keep good communication quality at a low cost.

  In addition, when a route is dynamically set by TE, the number of links (number of hops) that pass through increases as compared with a route determined by OSPF using static link weights.

  Therefore, it is desirable to set a route by OSPF using static link weights without using TE from the viewpoint of suppressing the consumption of network resources.

  Further, assuming that OSPF is used as a routing protocol type (routing method), a link capacity design method necessary for maintaining communication quality at or above a prescribed value has been studied in Non-Patent Document 7, for example, It is assumed that the network topology is given without being designed.

  Hereinafter, an appropriate design of the network topology and link capacity, which is important for maintaining good communication quality at a low cost when the ISP itself operates the network, will be described.

  The network topology affects various evaluation measures such as network cost, transmission delay, load distribution degree, and reliability. For this reason, when evaluating and designing a network topology, it is necessary to evaluate the optimality by simultaneously considering these multiple evaluation measures.

  For example, Non-Patent Documents 8 and 9 by the inventors of the present application describe a technique for evaluating a network topology using DEA (Data Environment Analysis) or AHP (Analytical Hierarchy Process) capable of simultaneously considering multiple evaluation measures. ing.

  Further, the utilization factor of each link is determined when an AC matrix is given and the topology, link capacity, and route are determined. Therefore, by introducing constraints on quality measures related to the usage rate of each link such as the user experience quality such as transmission delay and load distribution, an integer programming problem that optimizes a single evaluation measure called total cost Become.

  In other words, network topology, link capacity, and route are simultaneously optimized to minimize total cost for constraints related to node location, AC matrix, and link utilization (or packet transfer delay and design link capacity). Problem. This is described in Non-Patent Document 10, for example.

  Many approaches for solving the topology design problem as an integer programming problem have already been studied. For example, in Non-Patent Documents 11 and 12, a discrete optimization problem that minimizes the total link cost is heuristically determined by the “Branch hand bound method” under the constraint that the delay time between nodes is kept below a specified upper limit value. The technology to solve the same problem, starting with a state where many links are installed, repeat the work of removing links one by one until the improvement of the solution is no longer seen in order of improvement of the solution Solving techniques are being studied.

  However, failures are not considered in these topology design techniques. For example, as described in Non-Patent Document 13, a topology design technique that takes into account faults is a discrete optimum that minimizes the total link cost, with the constraint that there are more than a specified number of disjoint paths between nodes. As a constraint condition, the link cost can be reduced with the technology that heuristically solves the optimization problem by local search and the maintenance of connectivity between all nodes even in the case of any single node failure as described in Non-Patent Document 14. Technologies that solve heuristics such as tab search and genetic algorithms are being studied to minimize the sum.

  However, these technologies consider only the connectivity at the time of failure, and there is no research that considers keeping the quality within the specified level even for detour traffic occurring at the time of failure.

D. Mitra and K.M. Ramakrishna, “A Case Study of Multiservice Multiplicity Traffic Engineering Design,” IEEE Globecom 99. B. Fortz and M.M. Thorup, “Internet Traffic Engineering by Optimizing OSPF Weights,” IEEE Infocom 2000. B. Fortz and M.M. Thorup, “Robust optimization of OSPF / IS-IS weights,” INOC 2003. A. Kvalbein, A.M. F. Hansen, T .; Cicic, S.M. Gessing, and O.G. Lysne, “Fast IP Network Recovery Multiple Routing Configurations,” IEEE Infocom 2006. A. Elwalid, C.I. Jin, S.J. Low, and I.D. Widjaja, “MATE: MPLS Adaptive Traffic Engineering,” IEEE Infocom 2001. S. Kandula, D.C. Katabi, B.A. Davie, and A.D. Charny, “Walking the Tigtrope: Responsive Yet Stable Traffic Engineering,” ACM SIGCOMM 2005. M.M. Menth, R.M. Martin, J.M. Charzinski, “Capacity Overprovisioning for Networks with Reliance Requirements,” ACM SIGCOMM 2006. N. Kamiyama, “Network Topology Designing Data Environment Analysis,” IEEE Globecom 2007. ¥ bibitem {Kamiyama2} Noriaki Kamiyama, Daisuke Sato, “Network topology design using AHP,” IEICE Tech. M.M. Gerla and L. Kleinrock, “On the Topological Design of Distributed Computer Networks,” IEEE Trans. Communications, COM-25, 1, pp. 48-60, 1977. N. G. Chattopadhyay, T .; W. Morgan, and A.M. Raghuram, “An Innovative Technology for Backbone Network Design,” IEEE Trans. System, Man, and Cybernetics, 19, 5, 1989. A. Gersht and R.M. Weimayer, “Joint Optimization of Data Network Design and Facility Selection,” IEEE J. Selec. Areas, Commun. , 8, 9, pp. 1667-1681, 1990. K. Steiglitz, P.M. Weiner, and D.W. J. et al. Kleitman, “The Design of Minimum-Cost Survivable Networks,” IEEE Trans. Circuit Theory, CT-16, 4, pp. 455-460, 1969. E. C. G. Wille, M.C. Mellia, E .; Leonardi, and M.M. A. Marsan, “Topological Design of Survivable IP Networks Using Metaheuristic Approaches,“ Lecture Notes in Computer Science, Springer. 191-206, 2005.

  The problem to be solved is that the conventional technology considers only connectivity at the time of failure, and does not consider keeping the quality within the specified level even for detour traffic occurring at the time of failure. is there.

  An object of the present invention is to solve these problems of the prior art and to enable the design of network topology and link capacity in consideration of the quality for detour traffic at the time of a single link failure.

  In order to achieve the above object, in the present invention, when a node position, a traffic AC matrix, and a routing protocol type (routing method) are given in order to perform a network topology and link capacity design process, The total network cost is minimized by restricting the usage rate of any given link to below the specified value γ. At this time, when the number of links L and an arbitrarily determined real number parameter ε taking a value in the range of 0 to 1, the normal amount of traffic occurs in the descending order of k = εL links. Considering the detour traffic to be performed, it is a constraint that the link usage rate is suppressed to γ or less, and that connectivity between all nodes is maintained even in the case of a single failure of each of the remaining Lk links. . Also, start from a state where links are set between all nodes, and repeat the task of preferentially deleting the link cost divided by the amount of traffic flowing under normal conditions from the large link until the total network cost can no longer be improved. To do. Furthermore, when an arbitrary link is deleted, the calculation time is reduced by recalculating the route only for the path passing through the deleted link.

  According to the present invention, when data including at least a node position, an AC traffic matrix between nodes, a route setting method (routing protocol type), and a specified upper limit of a link usage rate is given, It is possible to design an optimal network topology and link capacity within the constraint that the link usage rate is kept below a specified upper limit while taking into account detour traffic caused by a single link failure.

  The best mode for carrying out the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing a configuration example of a system for designing a network topology and a link capacity according to the present invention. The system in FIG. 1 includes a CPU (Central Processing Unit), a main memory, a display device, The computer is composed of an input device and an external storage device. After the program and data recorded in a storage medium such as a CD-ROM are installed in the external storage device via an optical disk drive device, etc., the external storage device The function of each processing unit is executed by reading into the memory and processing by the CPU.

  In other words, the system for designing the topology and link capacity of the network of this example has an input processing device (“note information, AC matrix, route setting method, constraint input device” in the figure) as programmed computer processing execution means. Description) 101, a design processing device (described as “network topology / link capacity design device”) 102, and an output processing device (described as “optimal topology / optimum link capacity output device”) 103.

  The input processing device 101 performs an input operation from a keyboard or reading from a file, and the position of the node, the traffic demand amount between nodes (AC matrix), the route setting method (routing protocol type), the specified upper limit value γ of the link usage rate, and the detour Data such as the link number ratio ε or the like to be considered for traffic is captured, input and stored in the storage device, and the design processing device 102 reads the data input from the input processing device 101 from the storage device, and these data Is used to calculate the optimum network topology and link capacity, and the output processing apparatus 103 outputs the optimum topology and optimum link capacity calculated by the input processing apparatus 101 to a CRT screen, a storage device, or the like.

  In this example, in order to avoid link congestion in this example, the topology and link capacity of the network that minimizes the total cost under the constraint that the link utilization rate is below a given level. The design value of is calculated. More specifically, data including at least a node position, a traffic AC matrix, a routing protocol type (routing method), and a value γ that defines an upper limit of the usage rate of an arbitrary link at normal time is input as a constraint condition. In order to calculate the network topology and the link capacity that suppresses the usage rate of each link in the normal state to a specified value γ or less and minimizes the total network cost by the programmed computer device. As an apparatus processing execution means, an input processing apparatus 101 and a design processing apparatus 102 are provided. The input processing apparatus 101 includes a number L of links to be installed between all nodes in addition to a constraint condition and a predetermined link. The design processing device 102 inputs the number k (<L) and writes it to the storage device. Network topology and link capacity that reads information consisting of the number of links k from the storage device, uses the read information to keep the usage rate of each link normal or below the specified value γ, and minimizes the total network cost As a constraint condition, it is limited to the top k links with a large traffic volume, and the connectivity between all nodes is maintained even when the remaining Lk links have a single failure. The network topology and link capacity are calculated in consideration of the detour traffic associated with the single link failure of each link.

  Although the traffic AC matrix changes constantly, physical equipment is designed on a long-term time scale of several months or more, and therefore it is usually necessary to design based on a static AC matrix. Since the AC matrix shows periodic fluctuations such as days and weeks, it may be designed based on, for example, the traffic volume during the busy hour.

  Even when OSPF using static link weights is used, the route through which traffic flows changes due to unintended failures of links and nodes, and failures occur on various links on a daily basis (see “A. Markopoulou, (See G. Inanaccon, S. Battercharya, C. Chuah, and C. Diot, “Characterization of Failures in an IP Backbone,” when using the rate of the link when using IEEE Infocom.) Need to be considered.

  In the IP backbone, about 70% of unintended failures except for those caused by maintenance are single link failures (see “A. Markopoulou, G. Inanaccone, S. Bhattacharya, C. Chuah, and C. Diot, "Characterization of Failures in an IP Backbone," IEEE Infocom 2004. ") In this example, the link usage rate is suppressed to a specified value or less in consideration of the detour traffic occurring at the time of a single link failure.

  Also, in this example, we analyze the network topology designed using this design technology for the US and Japanese backbones, and what kind of link is the excess bandwidth designed to accommodate detour traffic due to failures. Analyze how many are prepared.

  In this example, the backbone is designed for a network closed to a single ISP. By using wavelength multiplexing technology (DWDM), the transmission capacity of the link can be dramatically improved (“R. Ramamimi and K. N. Sivarajan,“ Optical Networks, 200 Ac. In many cases, IP backbones already use DWDM for transmission links installed between routers.

  Also in this example, the link is assumed to be a network composed of optical cores wavelength-multiplexed by DWDM. Further, OSPF is assumed as a routing protocol type (routing method). Failure recovery using SONET / SDH (Synchronous Optical Network / Synchronous Digital Hierarchy) is fast but expensive, and in recent years, there are many ISPs that perform failure recovery in the IP layer (“F. Giroire, A. Nucci, Taft, and C. Diot, “Increasing the Robustness of IP Backbones in the Absence of Optical Level Protection,” IEEE Infocom 2003. ”.

  Therefore, in this example, SONET / SDH is not used, and it is assumed that a bypass route is set by OSPF in the IP layer when a failure occurs. In this case, there is a problem that it takes time until the detour route becomes stable. Recently, FRR (Fast ReRoute) which is dealt with by calculating an alternative route in advance has been studied (“A. Atlas, et al., “Basic specification for IP fast-route: loop-free alternate,” Internet draft, draft-ietf-rtgwg-ipfrr-spec-base-01. It is assumed that a bypass route is set only by OSPF.

  The network topology and link capacity design processing technology that takes into account detour traffic at the time of a link failure according to this example will be described in detail below.

  In order for ISPs to continue to provide users with stable quality while avoiding link congestion, it is practically sufficient to design and operate a network with the goal of keeping the utilization rate of each link below a rough specified value. It seems to be.

That is, if the usage rate of a link installed between node i and node j (hereinafter referred to as “e _ij ”) is u _ij, and the specified upper limit of the link usage rate is γ, an arbitrary link is installed. A constraint is that u _ij ≦ γ is satisfied for the set i, j.

The link capacity (number of design wavelengths in the optical network) of the link e _ij is x _ij, and x _ij = 0 when no link is installed. The link is bi-directional, and x _ji = x _ij .

  Further, assume that the AC matrix is D, the traffic demand amount from node s to node d is Dsd, and traffic demand amount Dds = traffic demand amount Dsd. That is, it is assumed that the AC matrix (AC matrix) is symmetrical, and a packet from node d to node s goes through the same node and link in the reverse direction as a packet from node s to node d. However, the design method of this example shown below can be easily extended even when the AC matrix is asymmetric and the link is unidirectional.

Hereinafter, given the link usage rate constraint (the upper limit γ of the link usage rate), the geographical location of the node, and the AC matrix D, the network topology and the link are aimed at minimizing the cost C of the entire network. A process of designing the capacity (design wavelength number x _ij ) will be described.

  “L. Li, D. Alderson, W. Willinger, and J. Doyle,“ A First-Principles Approach to Understand the the Internet's Router-Level. We examine the network topology and analyze that the main factor that determines the topology is the constraint determined by "cost" and "router processing capability".

  However, the pace of “router processing capability” has been increasing rapidly. Currently, routers having processing capability of 1.28 Tbps are used as described in “Cisco systems, http://www.cisco.com.”, For example. In this example, it is assumed that the router processing capacity constraint is not considered.

  First, the cost C of the entire network will be described below.

The network cost C is the sum of the node cost and the link cost. In this example, for simplicity, it is assumed that the cost per router port is C _ep and that the required number of router ports are prepared at both ends of the link. Consider node cost in link cost.

  The link cost is modeled below. In this example, since the wavelength division multiplexing link between routers by DWDM is assumed, the link cost is composed of civil engineering infrastructure cost, optical core cost, and optical device cost.

The civil engineering infrastructure cost is a cost for laying a clay pipe for accommodating an optical fiber, and a cost for borrowing a clay pipe from a railway company, a power company, a local government, etc. that possess the clay pipe, and the cost per km is C _cd .

Further, the cost per 1 km of the optical fiber is C _fb . Since there is a restriction on the number of wavelengths that can be multiplexed on one optical fiber, if the upper limit of the number of wavelengths that can be multiplexed is W, the number of optical fibers shown in the following equation 1 is laid on the link e _ij . There is a need.

  In addition, in order to perform DWDM transmission, a wavelength multiplexing / demultiplexing device that performs wavelength multiplexing and demultiplexing at both ends of a link, an optical amplifier that amplifies an attenuated optical signal, crosstalk (signal leakage), and ASE ( A repeater that repairs a deteriorated optical pulse by amplified spontaneous emission (PMD) or polarization mode dispersion (PMD) is required (see “R. Ramaswami and K. N. Sivarajan,“ Optical m. ).

Since the cost of the wavelength demultiplexing device is approximately proportional to the number of wavelengths, the cost per wavelength is assumed to be C _md here. Further, the cost of one optical amplifier is C _ap . Assuming that the cost of one transponder (relay device) is C _tp , optical pulse shaping needs to be performed after conversion into an electrical signal, so the cost required for one repeater is (C _tp + 2C _md ) x _ij .

Accordingly, the cost c _ij (d _ij , x _ij ) of the link e _ij having the distance “d _ij ” and the design wavelength number (design link capacity) “x _ij ” is expressed by the following equation.

c _ij (d _ij , x _ij ) = C _cd d _ij + {α (d _ij ) + β (d _ij ) W} y _ij + α (d _ij ) δ _ij (z _ij ) + β (d _ij ) z _ij .

However, in the above formula, “y _ij ” is the number of optical cores multiplexed with the upper limit of W wavelengths, and “z _ij ” is the remaining 1 in which the number of wavelengths less than W is multiplexed. This is the number of multiplexed wavelengths in the optical fiber of the book, and is represented by the following equation (2).

Further, the "δ _{ij (z ij)",} when _{"z ij} ≧ 1" in the "δ _{ij (z ij)} = 1", when the _{"z ij} = 0", "δ _{ij (z ij)} = 1" Is defined as a function.

Furthermore, “α (d _ij )” is a term that depends only on the distance in the cost required for one optical core, and “β (d _ij )” is proportional to the number of design wavelengths (design link capacity). Which is given by the following equation (3).

However, in the above formula 3, “Δ _ap ” and “Δ _rp ” are the installation intervals of the optical amplifier and the repeater, respectively.

  Next, the “design algorithm” will be described.

  First, we formulate network topology and link capacity design problems.

Let T be a network topology arbitrarily designed for a given node set, and E be a set of edges (links) included in the network topology T. A network topology obtained by removing an arbitrary link e _ij included in the set E from the network topology T is represented by the following equation (4).

  It is assumed that the path through which a packet flows between the respective arrival and departure nodes is set by OSPF using a fixed link weight.

As described in “Modeling Link Cost” above, the link cost depends on the distance (d _ij ) and the number of design wavelengths (link capacity x _ij ), but the distance (d _ij ) is independent of the design amount. In this example, the link distance _dij is used as the link weight because it is easy to use as a fixed weight.

The total cost C is expressed by the following equation 5 using the above-mentioned “cost c _ij (d _ij , x _ij ) of the link e _ij having the distance“ d _ij ”and the design wavelength number“ x _ij ”. can get.

With respect to the network topology T and the AC matrix D, the traffic amount indicated by the following expression 6 that flows through the link e _ij included in the link set E at the normal time is as shown in the following expression 7.

However, “P _sd (T)” in _Equation 7 is a set of links through which the traffic from the source node s to the destination node d in the network topology T passes.

Further, when the same AC matrix D is given in the network topology represented by the following equation (8), an arbitrary link e _ij included in the edge set represented by the following equation (9) in the network topology is represented. Assuming that the amount of traffic flowing is indicated by the following symbol 10, the relational expression shown in the following equation 11 is obtained.

  In order to keep the usage rate of each link below the specified upper limit γ even in the event of any single link failure, the maximum defined by the following equation 13 is used for each link of the set E (see the following equation 12). Assuming the traffic volume, it is sufficient that the following expression 14 is satisfied. However, B in Formula 14 is a wavelength transmission band.

  Assuming that the number of links included in the set E is L, when the link capacity is designed in consideration of the detour traffic caused by a single link failure for all L links, the traffic volume ( It is expected that a very large band is over-designed as compared with (see Equation 6).

  Therefore, it is considered that the links to be considered for link failure are not limited to all L links, but are limited to k links given by Equation 15 below. However, ε in Equation 15 is a design parameter that takes a value in the range of 0 ≦ ε ≦ 1.

  The higher the amount of traffic that flows through each link during normal operation (see Equation 6), the greater the amount of detour traffic that occurs during a failure, so the top k links with the larger amount of traffic that flows through each link during normal operation (see Equation 6). Consider detour traffic only for.

  However, considering that maintaining the connectivity between all nodes even in the case of any single link failure is considered as a constraint, whether or not an isolated node occurs in the case of a single failure for the remaining Lk links. Judgment is made.

From the above, the network topology and link capacity design problem of this example (determination problem of the number of design wavelengths x _ij ) can be expressed as an integer programming problem shown in the following Expression 16.

  However, the maximum traffic amount defined for the links limited to the top k in the constraint equation of Formula 16 is expressed by Formula 17 below.

  In the above equation 17, E (k) is a set of k links with the largest amount of traffic that normally flows (see equation 6) among the links included in the set E.

Further, the value shown in the following equation 18 in the constraint equation of the above equation 17 is the sum of the link weights of the link set shown in the following equation 19, and E ^(L−k) in the constraint equation of the above equation 16 is the set. This is a link set obtained by excluding k links that consider detour traffic from E.

  However, this kind of integer programming problem is an NP-hard problem (the number of solutions that satisfy the conditions is enormous and it is difficult to find the best solution in a realistic time), and the exact optimal solution in polynomial time. It is known that the above cannot be obtained (see the above-mentioned “Non-Patent Document 10”).

  For this reason, various heuristics such as “local search”, “tab search”, “genetic algorithm”, and “annealing method” are available so that an approximate optimal solution can be obtained in a realistic calculation time even for large-scale problems. A solution has been developed (see “Yasuura Yanagiura, Toshihide Ibaraki,“ Combinatorial Optimization, ”Asakura Shoten, 2004.).

  In general, each approximate solution method is compatible with the problem, and there is no general-purpose excellent solution method. Therefore, in this example, we do not enter into detailed evaluation of the approximate solution method, and the basic method of the approximate algorithm along with the local search method One of them is “greedy arithmetic”.

  This “greedy calculation method” is a method that starts from an initial state and repeats correction of a solution that seems to have the largest improvement in the objective function value until no improvement in the objective function value is observed.

  In this example, an approach is used in which the links are removed one by one, starting from a state in which links are set in a full mesh between all nodes (see Non-Patent Document 12 above).

  According to this method, by removing a link, the traffic that has passed through that link goes to another link, but the route with the lowest cost is always selected. The amount increases. As the cost decreases by removing the link with respect to this cost increase, the effect of improving the total cost by removing the link can be expected.

  Therefore, a link with a high link cost and a small traffic volume, that is, a link with a large value shown in the following equation 20 is preferentially removed.

  The network topology and link capacity design algorithm according to the present invention using such “greedy calculation method” will be described below with reference to FIG. FIG. 8 is a flowchart showing an example of network topology / link capacity design processing operation according to the present invention by the system shown in FIG.

  (1) First, an initial setting process is performed (step S801). That is, links are installed between all the nodes, and the maximum traffic volume defined for the top k links (see formula 6 below) with a large traffic volume (refer to formula 6) flowing through each link in the normal state from the above-described equation (17). And the total cost C of the network is calculated from the above equation (5).

(2) Next, a link evaluation value is calculated (step S802). That is, the evaluation values a _ij of the links e _ij represented by the following formula 22 are calculated for all links, and sorted in descending order of the evaluation values a _ij . Also, j = 1.

(3) Further, the total cost after the link removal is calculated (step S803). That is, for topology evaluation value a _ij is to remove large link e _{i'j 'in} j-th link e _ij (see number 23 below), from the above equation number 17, flows to each link in the normal The maximum traffic amount defined for the top k links having the largest traffic volume (see Equation 6) is calculated, and the total cost C of the network is calculated from the above equation (5). Further, whether or not connectivity between all the nodes is maintained is checked even when each of the links included in the set E ^(Lk) is removed.

(4) Then, it is determined whether to remove the link (step S804). That is, when the total cost C is reduced and connectivity between all nodes is maintained even in the case of a single failure of an arbitrary link (see the following equation 24) included in the set E ^(Lk) Then, the process proceeds to the above-described “(2) link evaluation value calculation” process. Otherwise, “j” is incremented by “1” without removing the corresponding link, and “(3) after link removal” is performed. To “total cost calculation”. If “j = L”, the process ends.

  In the system of this example, the CPU sequentially reads the program stored in the hard disk device or the like and executes computer processing, and stores the data generated in each processing in the storage device such as the main memory. This operation is realized by sequentially reading out the stored data and using it in the following process.

  That is, the input processing device 101 inputs, as a constraint, data including at least a node position, a traffic AC matrix, a routing protocol type, and a value γ that defines the upper limit of the usage rate of an arbitrary link in a normal state. The design processing device 102 executes the first procedure for writing to the storage device, and the design processing device 102 uses the second procedure for reading the constraint condition from the storage device and the read constraint condition for each link installed between all nodes. Then, the third procedure for calculating the cost of the link and the maximum traffic amount that suppresses the usage rate of the link to the specified value γ or less and writing it in the storage device, and the cost of each link calculated in the third procedure are calculated. Add and calculate the total cost that is the cost of the entire network and write it to the storage device, and the cost of each link calculated in the third procedure is normal for the link The fifth procedure that calculates the value divided by the amount of traffic that flows from time to time as the evaluation value of the link, sorts and writes it to the storage device, and removes the link with the highest evaluation value of each link sorted in the fifth procedure For each of the remaining links, the above-mentioned cost and maximum traffic amount calculation and writing to the storage device are added, and the link cost calculated in this sixth procedure is added to remove the link. A seventh procedure for calculating the total cost of the entire network and writing it to the storage device, whether the total cost calculated in the seventh procedure is less than the total cost calculated in the fourth procedure, and An eighth procedure for determining whether connectivity between all nodes is maintained even in the event of a single failure of each of the remaining links, and the eighth procedure reduces the total cost and Connectivity between If the link is removed, the total cost is not reduced by the ninth procedure that repeats the processing from the fifth procedure described above and the eighth procedure described above, or between all nodes. If it is determined that the connectivity is not maintained, the link having the next highest evaluation value calculated in the above-described fourth procedure is removed without removing the link, and the process from the sixth procedure is repeated. Ten procedures and an eleventh procedure for ending the repetitive processing from the sixth procedure according to the tenth procedure with a predetermined number of links are executed.

Note that, in the above-mentioned “(3) Total cost calculation after link removal” process (step S801 in FIG. 8), the traffic affected by the route by removing the link e _{i′j ′} is the link e _{i ′} It is inefficient to recalculate routes for all incoming and outgoing node pairs only through _{j ′} .

Therefore, in this example, for each link e _ij , the route is recalculated only for the affected departure / arriving node pair by managing the set of departure / arriving node pairs via the link e _ij .

  Similarly, when calculating the amount of detour traffic at the time of a single link failure, a detour route is calculated only for a pair of arrival and departure nodes via the link where the failure has occurred.

  In addition, the “determination of connectivity maintenance” in the “(3) total cost calculation after link removal” process obtains the path cost when the Dijkstra method is applied as a finite value between any departure and arrival nodes. Depending on whether or not.

That is, assuming that the number of nodes is N, the amount of computation of the Dijkstra method is O (N ² ). Since the initial state starts with a complete graph, there are O (N ² ) links at an early point of the algorithm, but the number of incoming / outgoing node pairs passing through each link is the total number of pairs N (N−1) / Much smaller than 2. Therefore, the amount of calculation in the “(3) Total cost calculation after link removal” processing is approximately O (N ⁴ ). Therefore, the total amount of calculation is about O (N ⁶ ).

Hereinafter, numerical evaluation results based on the network topology and link capacity design of this example will be described. Here, the distance d _ij between the nodes is a linear distance (Euclidean distance) between the node i and the node j, a specified upper limit γ of the link usage rate is 0.7, and an upper limit of the number of multiplexed wavelengths of the optical core It is assumed that W = 60, wavelength transmission band B = 10 Gbps, optical amplifier installation interval Δ _ap = 80 km, and repeater installation interval Δ _rp = 2000 km.

All costs are considered as relative values, and the current price is taken into consideration, and “cost C _fb = 0.1 km per optical fiber core”, “cost C _ap = 240 for one optical amplifier”, “transponder 1 The unit cost C _tp = 75 ”,“ cost per router port C _ep = 40 ”, and“ cost per wavelength C _md = 3.3 ”are set.

However, the civil infrastructure cost is not considered because it depends heavily on geographical factors and contract form and is difficult to set appropriately (C _cd = 0).

  In addition, the evaluation was conducted on “Abilene”, which is the backbone of the Internet 2 where universities and companies from all over the United States participate. “Abilene” is composed of 11 nodes arranged in the United States.

  The node position uses public information (see “Abilene topology and traffic dataset. Http://www.cs.utexas.edu/˜yzhang/research/AbileneTM/”). In addition, the AC matrix is similarly distributed so as to be proportional to the actually measured values so that the total traffic amount becomes V.

  However, since the total traffic volume in the United States as of the end of 2006 was 1.39 to 2.47 Tbps ("Minnesota Internet Traffic Studies (MINTS). Http://www.dtc.umn.edu/mints/home. html ”) and the total traffic volume V = 1 Tbps and 10 Tbps, respectively.

  Here, the influence of the ratio ε of the number of links k considering the detour traffic at the time of a single failure to the total number of links L on various performances is evaluated.

  FIG. 2 is an explanatory diagram showing a design example of the network topology by the system in FIG. 1. In FIG. 2, 3 is the ratio ε of the number k of links to the total number L of links k considering the detour traffic at the time of a single failure. For each of the values, the designed network topology is shown.

  First, in the case of “total traffic amount V = 1 Tbps”, when looking at (a) to (c) in FIG. 2, when the ratio ε = 0 (without considering detour traffic at all), it is shown in FIG. Thus, the link with the maximum traffic flow at normal time was (2, 5), and the link with the next largest flow rate was (4, 5).

  When the ratio ε is set to a small value, only detour traffic at the time of failure of a specific link having a large traffic flow rate is considered. When the ratio ε = 0, these links are part of a large loop, and when a failure occurs in these links, the detour traffic passes through many links, which is inefficient.

  Therefore, for example, when the ratio ε = 0.1, as shown in FIG. 2 (b), links (3, 5) for efficiently bypassing the detour traffic at the time of failure of these links are added. Can be confirmed.

  On the other hand, when the ratio ε is large and close to “1”, as a result of considering detour traffic at the time of a single link failure for a large number of links, as shown in FIG. It can be confirmed that the network topology is a combination of loops that can efficiently accommodate the detour traffic of the network with a common link.

Further, if the excess design bandwidth Ex (e _ij ) is defined as the excess design bandwidth Ex (e _ij ), which is obtained by subtracting the amount of traffic flowing during normal operation from the design link capacity of the link e _ij , The excessive design band Ex (e _ij ) of the links (1, 11) and (1, 5) is prominent and large.

  This is because the total number of links is L = 14, the number of links k = 2 considering the detour traffic at the time of a single failure, and the upper two links with the large amount of normally flowing traffic (see the above-mentioned equations 6 and 7). This is because (5, 8) and (8, 11) form the same loop as these links.

  In “Abilene”, cities with a large population are concentrated on the east coast, and links with a large amount of traffic flowing normally (see the above-mentioned equations 6 and 7) tend to concentrate in a specific area. In such a case, if the ratio ε is set to be small, there is a tendency that links over-designing the band tend to concentrate in such areas.

  FIG. 3 is an explanatory diagram of an example in which the link usage rate at the normal time of each link is plotted in descending order, and when the ratio ε = 0, the usage rate of all links is the specified upper limit γ (= 0.7). However, when the ratio ε = 0.1, the utilization rate of a small number of links is greatly reduced, and when the ratio ε is greater than 0.4, the variation in link utilization rate is large. It can be confirmed that there is a wide distribution from a value close to the specified upper limit γ (= 0.7) to a small value.

  On the other hand, in the case of “total traffic volume V = 10 Tbps”, the AC traffic volume is larger than that in the case of V = 1 Tbps, and even if the traffic is not aggregated between a plurality of grounds, it is sufficient compared with the wavelength band. Therefore, as shown in FIGS. 2D to 2F, direct links are installed for a large number of grounds.

  Next, in order to confirm how much different network topologies are designed according to the difference in the ratio ε, the degree of coincidence η (A, B) between the two topologies A and B is expressed as “η ( A, B) = n (A∩B) / n (A∪B) ”. However, “n (A∩B)” and “n (A∪B)” are the number of links of a product set and a union of links included in topology A and topology B, respectively.

  FIG. 4 is an explanatory diagram illustrating an example of the degree of coincidence between two topologies. In FIG. 4A, the degree of coincidence with the design topology T (ε = 0) at the ratio ε = 0, and in FIG. 4B, the design topology T (ε = 1) at the ratio ε = 1. Are shown for ε respectively.

  4A, the degree of coincidence with the design topology T (ε = 0) decreases as the ratio ε increases, whereas in FIG. 4B, the design increases as the ratio ε increases. The degree of coincidence with the topology T (ε = 1) increases.

  In FIG. 4B, the degree of coincidence with the design topology T (ε = 1) is as high as about 70% or more regardless of the value of the ratio ε. Therefore, it can be said that the influence of the ratio ε on the shape of the designed topology is small as a whole.

FIG. 5 is an explanatory diagram showing the correspondence between the number of links in the topology designed by the system in FIG. 1 and the average value of the designed link capacity and the ratio of the number of links considering the detour traffic at the time of a single failure to the total number of links. Yes, the number L of links in the design topology and the average value of the design link capacity x _ij are shown with respect to the ratio ε.

  As shown in FIG. 4, the ratio ε of the number of links considering the detour traffic at the time of a single failure to the total number of links has little influence on the design topology. The number L does not change much.

  On the other hand, as the ratio ε increases, the average design link capacity increases in order to consider detour traffic of a larger number of single link failure patterns. However, in the region where the ratio ε is larger than the middle level, the design link capacity hardly changes even if the ratio ε is increased.

As shown in FIG. 5C, this tendency can also be confirmed from the characteristic of the average excess design bandwidth (average value of Ex (e _ij ) over all links) with respect to the ratio ε. If the link capacity is designed in consideration of the detour traffic at the time of a link failure of about half the amount of traffic during normal operation (see Equation 6 above), much of the detour traffic that occurs when the remaining link fails. The reason is that it can be absorbed.

  As a result, as shown in FIG. 5D, in the region where the ratio ε is medium or higher, the total cost hardly increases as the ratio ε increases.

  Next, the characteristics at the time of a single link failure will be considered using FIG. FIG. 6 is an explanatory diagram showing a plot example of the link usage rate at the time of a single link failure. In FIG. 6A, the usage rate of each link in all (L) single link failure patterns. FIG. 6B shows an example in which the maximum utilization rate in the L single link failure patterns is plotted in descending order for each link.

  Here, only the result of the total traffic volume V = 10 Tbps is shown. In FIG. 6A, when the ratio ε is “0” or “0.1”, detour traffic due to an unexpected link failure is shown. Thus, the average utilization of many links exceeds the specified upper limit γ = 0.7.

  In particular, as shown in FIG. 6B, it can be confirmed that the maximum link utilization rate of a small number of links becomes very high. In particular, the failure utilization rate of the link (7, 9) having the highest maximum utilization rate is prominently high, but the normal traffic volume of this link is the smallest among all links, and the ratio ε is set to “0”. The excessive design band when “0.1” is also minimized.

  As described above, it is not sufficient to consider the detour traffic at the time of failure by limiting to only a small number of links having a large traffic amount at normal time (see the above-described Expression 6).

  FIG. 7 is an explanatory diagram showing a plot example with respect to the ratio between the average value and the maximum value of the link utilization rate over all links at the time of a single link failure. In FIG. 7A, all single link failure patterns are shown. The average value and the maximum value of the link utilization rate over all the links are plotted against the ratio ε, and in FIG. 7B, the link utilization rate is the specified value γ = 0 when a single link failure occurs. The ratio of the traffic volume via the link exceeding .7 to the total traffic volume V is shown.

  As shown in FIG. 7A, it can be confirmed that as the ratio ε increases, the traffic amount that exceeds the specified upper limit and passes through the link in a congested state decreases exponentially.

  Further, as shown in FIG. 7B, the larger the traffic amount V, the larger the value of k (the number of upper links having a larger traffic amount (see the above-mentioned equation 6)) for the same ratio ε. The excess ratio will be low.

  When the ratio ε is lower than medium, a ratio of traffic that cannot be ignored at the time of a single link failure passes through the congestion link. Therefore, it is desirable to set the ratio ε to be medium or higher. In order to always satisfy the specified upper limit of the link utilization rate for all traffic, it is necessary to set the ratio ε to a value close to “1”, but in the region where the ratio ε is medium or higher, as described above. Even if the ratio ε is increased, the total cost hardly increases.

  From the above, it can be concluded that the ratio ε = 1 should be set.

  As described above with reference to FIGS. 1 to 8, in this example, the upper limit of the node position, the traffic AC matrix, the routing protocol type (routing method), and the usage rate of any link at normal time is set. Data that includes at least the specified value γ is input as a constraint, and the network usage that minimizes the total network cost while keeping the usage rate of each link under normal conditions below the specified value γ by a programmed computer device. In order to calculate the topology and the link capacity, the processing unit of the programmed computer device includes an input processing device 101 and a design processing device 102. The input processing device 101 includes all nodes in addition to the constraint conditions. The number of links L installed between them and the predetermined number of links k (<L) are input and written to the storage device, and the design processing device The device 102 reads out information consisting of the constraint condition, the number of links L, and the number of links k from the storage device, and uses the read information to suppress the usage rate of each link under normal conditions to a predetermined value γ or less, and When calculating the network topology and link capacity to minimize the network cost, it is limited to the top k links with a large traffic volume, and all nodes are connected even when a single failure occurs in each of the Lk links. The network topology and the link capacity are calculated in consideration of the detour traffic accompanying the single link failure of each link, under the condition that the performance is maintained.

  In addition, the design processing device 102 starts calculating the network topology and the link capacity from a state where links are installed between all nodes, and preferentially removes from a link having a large value obtained by dividing the link cost by the amount of traffic flowing under normal conditions. This process is repeated until there is no improvement in the total network cost.

  More specifically, the design processing apparatus 102 reads the constraint condition from the storage device, and uses the read constraint condition, and for each link installed between all nodes, the link cost and the link usage rate. Calculate the maximum traffic volume that keeps the value below the specified value γ and write it to the storage device, add the calculated cost of each link to calculate the total cost of the entire network, write it to the storage device, and calculate The value obtained by dividing the cost of each link by the amount of traffic that normally flows to the link is calculated as the evaluation value of the link, sorted, written to the storage device, and the link with the highest evaluation value of each sorted link is removed. For each remaining link, calculate the cost and maximum traffic volume, write to the storage device, and add the calculated cost for each link. Calculate the total cost of the entire network after removing the link and write it to the storage device, whether this calculated total cost is less than the previously calculated total cost, and each single failure of each remaining link Sometimes it is determined whether connectivity between all nodes is maintained, and if it is determined that the total cost is reduced and connectivity between all nodes is maintained, the link is removed and the above If the process from the link evaluation value calculation procedure is repeated and it is determined that the total cost does not decrease or connectivity between all nodes is not maintained, the link is not removed and the evaluation value is the next highest The link is removed, the calculation of the maximum traffic and cost for the remaining links is repeated, and this repetition process is terminated with a predetermined number of links.

  Further, when the link is removed (deleted), the design processing apparatus 102 recalculates the route only for the path that passes through the removed (deleted) link, thereby reducing the calculation time.

  In addition, the design processing apparatus 102 determines whether to maintain connectivity based on whether or not the cost of the route when the Dijkstra method is applied can be obtained as a finite value between any nodes between arrivals and departures.

  Thus, in this example, a detour caused by an arbitrary single link failure is given when the position of the node, the AC traffic matrix between nodes, the route setting method, and the specified upper limit of the link usage rate are given. Optimal network topology and link capacity can be designed within the constraint that the link usage rate is kept below a specified upper limit while taking traffic into consideration.

  In addition, this invention is not limited to the example demonstrated using FIGS. 1-8, In the range which does not deviate from the summary, various changes are possible. For example, in this example, an optical network has been described as an example, but the present invention is not limited to this.

  In this example, only a single link is considered, but it can also be applied to cases where a single node failure is considered. In this case, it is assumed that a failure has occurred in all the links connected to each node, and detour traffic at the time of each node failure is considered simultaneously when calculating the maximum traffic volume of each link.

  Further, regarding the configuration of the computer device of this example, a computer configuration without a keyboard or optical disk drive device may be employed. In this example, an optical disk is used as a recording medium. However, an FD (Flexible Disk) or the like may be used as a recording medium. As for the program installation, the program may be downloaded and installed via a network via a communication device.

It is a block diagram which shows the structural example of the system which designs the topology of a network and link capacity | capacitance based on this invention. It is explanatory drawing which shows the example of a network topology design by the system in FIG. It is explanatory drawing of the example which plotted the link usage rate at the time of the normal of each link in order with a big value. It is explanatory drawing which shows the example of a coincidence degree of two topologies. FIG. 2 is an explanatory diagram illustrating a correspondence relationship between the average number of links and the design link capacity of the topology designed by the system in FIG. 1 and the ratio of the number of links considering the detour traffic at the time of a single failure to the total number of links. It is explanatory drawing which shows the example of a plot of the link utilization rate at the time of a single link failure. It is explanatory drawing which shows the example of a plot with respect to the ratio of the average value of the link utilization rate over all the links at the time of a single link failure, and the maximum value. 2 is a flowchart showing an example of network topology and link capacity design processing operation according to the present invention by the system in FIG.

Explanation of symbols

  101: input processing device (note information, AC matrix, route setting method, constraint input device), 102: design processing device (network topology / link capacity design device), 103: output processing device (optimum topology / optimum link capacity output) apparatus).

Claims (9)

Data including at least a value γ that defines the upper limit of the usage rate of any link in the normal state, the node position, the traffic AC matrix, the routing protocol type, and the normality is input by the programmed computer device. A network topology / link capacity design processing method for calculating a network topology and a link capacity that suppresses the usage rate of each link to the specified value γ or less and minimizes the total network cost,
As a processing execution means of a programmed computer device, it comprises an input processing means and a design processing means,
The input processing means executes a first procedure for inputting the number of links L installed between all the nodes and a predetermined number of links k (<L) and writing them to the storage device in addition to the above-mentioned constraints. ,
The design processing means is
The information including the constraint condition, the number of links L, and the number k of links is read from the storage device, and the maximum traffic volume of each link is calculated using the read information. When calculating the network topology and link capacity that minimizes the total network cost and the usage rate of each link at the time of one failure is limited to the above specified value γ, it is limited to the top k links with large traffic volume, In addition, the above network topology considering the detour traffic accompanying the single link failure of each link, with the constraint that the connectivity between all nodes is maintained even in the case of a single failure of the remaining Lk links, A network topology / link capacity design processing method characterized by executing a second procedure for calculating a link capacity.

A network topology / link capacity design processing method according to claim 1,
The design processing means in the second procedure,
The above network topology and link capacity calculation starts from a state where links are installed between all nodes, and the process of preferentially removing from the link with a large value obtained by dividing the link cost by the amount of traffic that flows normally is the total network cost. A network topology / link capacity design processing method, characterized by iterating until no improvement is observed. A network topology / link capacity design processing method according to claim 1 or 2,
The design processing means is
It is considered that all links connected to each node have failed for a single node failure, and detour traffic at each node failure is considered at the same time when calculating the maximum traffic volume of each link. Network topology and link capacity design processing method. A method of designing a network topology and link capacity by a programmed computer device,
As a processing execution means of a programmed computer device, it comprises an input processing means and a design processing means,
The input processing means inputs, as a constraint, data including at least a node position, a traffic AC matrix, a routing protocol type, and a value γ that defines an upper limit of the usage rate of an arbitrary link in a normal state to a storage device. Perform the first step of writing,
The design processing means includes a second procedure for reading the constraint condition from the storage device;
Using the read constraints, for each link installed between all nodes, the cost of the link and the maximum traffic amount that keeps the link usage rate below the specified value γ are calculated and stored in the storage device. A third procedure for writing;
A fourth procedure in which the cost of each link calculated in the third procedure is added to calculate the total cost, which is the cost of the entire network, and is written in the storage device;
A fifth procedure in which a value obtained by dividing the cost of each link calculated in the third procedure by the amount of traffic normally flowing in the link is calculated as an evaluation value of the link, sorted, and written to the storage device;
6 procedures for calculating the cost and the maximum traffic amount and writing to the storage device for each remaining link from which the link having the largest evaluation value of the links sorted in the fifth procedure is removed; ,
A seventh procedure for calculating the total cost of the entire network after adding the cost of each link calculated in the sixth procedure and removing the link and writing it to the storage device;
Whether or not the total cost calculated in the seventh procedure is lower than the total cost calculated in the fourth procedure, and the connectivity between all the nodes even in the single failure of each of the remaining links An eighth procedure for determining whether or not to be maintained;
If it is determined in the eighth procedure that the total cost is reduced and connectivity between all nodes is maintained, the link is removed and the processing from the fifth procedure is repeated. Procedure and
If it is determined in the eighth procedure that the total cost does not decrease or connectivity between all nodes is not maintained, the evaluation value calculated in the fourth procedure without removing the link is A tenth procedure that removes the large link and repeats the process from the sixth procedure;
A network topology / link capacity setting processing method, wherein the iterative process from the sixth procedure according to the tenth procedure is executed with an eleventh procedure for ending with a predetermined number of links. A network topology and link capacity design processing method according to any one of claims 2 to 4,
The design processing means is
A network topology / link capacity design processing method characterized by executing a procedure of recalculating a route only for a path passing through a deleted link when the link is removed. A network topology and link capacity design processing method according to any one of claims 1 to 5,
The design processing means is
The network topology / link capacity design process characterized in that the determination of the maintenance of the connectivity is made based on whether or not the cost of the route when the Dijkstra method is applied is obtained as a finite value between any nodes between arrival and departure Method. A network topology / link capacity design processing method according to any one of claims 1 to 6,
The network consists of an optical network,
A network topology / link capacity design processing method, wherein the link capacity is the number of wavelengths. Data including at least a value γ that defines the upper limit of the usage rate of any link in the normal state, the node position, the traffic AC matrix, the routing protocol type, and the normality is input by the programmed computer device. A network topology / link capacity design processing system for calculating a network topology and a link capacity that suppresses the usage rate of each link to the specified value γ or less and minimizes the total network cost,
As a means of performing programmed computer processing,
A network topology / link capacity design processing system comprising processing means for executing each procedure in the network topology / link capacity design processing method according to claim 1.   The program for making a computer perform each procedure in the network topology link capacity | capacitance design processing method in any one of Claims 1-7.

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