JP2010206581A - Topology generation system, method, network topology design system, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To allow appropriate network topology design according to a degree of importance in subjective evaluation by a designer. <P>SOLUTION: At an input part 101, condition information, which contains a total link length of network, an average hop length weighed with a traffic ratio, and an average value of traffic amount ratio the connectivity of which is lost when single link failure is input from an input device and stored in a memory device. At a candidate topology set generating part 100, the condition information is read out of the memory device and a candidate topology set is generated within a predetermined time. At an output part 103, the candidate topology set generated by the candidate topology set generating part 100 is output through an output device. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a topology configuration technique in a network, and more particularly to a technique suitable for efficiently selecting a plurality of topology candidates and enabling efficient design of the network topology.

  The physical topology design of how to configure the physical network topology is an important issue for telecommunications carriers and ISPs (Internet Service Provide) that manage and operate physical resources of networks such as optical fibers and routers. It is.

  The physical topology is a factor that determines the facility costs of nodes and links, network management / maintenance costs, reliability against failures, and the like. The physical topology affects the link load and the packet route, and is one factor that determines user quality such as transmission delay quality and throughput.

  For the user, it is desirable to avoid congestion at the transit node and to reduce the transmission delay so that the total route distance is short. From the viewpoint of utilization efficiency and reliability of transmission resources, it is desirable to avoid traffic concentration on a specific link and to distribute the traffic load to all links as much as possible.

  Also, if the number of installed nodes and links is reduced in order to reduce equipment costs and management / maintenance costs, there is a possibility that the load will be concentrated on a specific link, and connectivity between nodes will be lost in the event of a link or node failure. Possibility increases and reliability decreases.

  As described above, when designing a network topology, it is necessary to simultaneously consider a plurality of evaluation measures that are different in units such as the degree of traffic distribution, the average path length, the network cost, and the reliability, and that are mutually contradictory. is there.

  AHP (Analytic Hierarchy Process) is known as a technique for making a rational decision making considering a plurality of evaluation scales at the same time. In AHP, related elements are grasped by a hierarchical structure, and qualitative measures such as importance of an evaluation measure are quantified by a paired comparison to enable rational decision making.

  Therefore, the inventor of the present application proposes a technique in which AHP is applied to network topology evaluation in Patent Document 1. In this technique, by using AHP, an appropriate network topology design corresponding to the importance of a designer's subjective evaluation scale can be achieved as follows.

  Usually, there are three types of elements in decision making: “Problem P”, “Evaluation Scale V”, and “Alternative A”. In AHP, these elements are grasped in a hierarchical structure as shown in FIG.

However, elements that are related to each other are connected by a straight line (only a part is shown in FIG. 1 for the sake of convenience), and the evaluation scale V can have a plurality of hierarchical structures (V ¹ , V ² ,...). is there. FIG. 1 shows a two-layer structure.

The Strength of association between elements a (weight) calculated, and finally, to derive the score S _i of each alternative A _i.

  When calculating the weight for the problem P of the evaluation scale V, there is no quantitative evaluation value from the beginning, and it is necessary to quantify it by some method. In AHP, as will be described below, quantification is made by comparing a pair of importance levels among all elements for element sets belonging to the same hierarchy.

First, the element _{X i} and element _{X j} belonging to the hierarchy c, and the values shown in FIG. 2, sets the relative importance _{a ij} for the element _{X j} elements _{X i.} When the original weight _{w i} of the element _{X i,} the original weight of the element _{X j} and _{w j, ideally} satisfy the relationship of _{a ij = w i / w j} .

When a paired comparison matrix having importance a _ij as an element is A and a vector w having an element weight w _i as an element is multiplied from the right side of the matrix A, Aw = nw is established. However, n is the number of elements. Therefore, the weight vector is an eigenvector of the matrix A, and n is an eigenvalue (maximum eigenvalue).

Actually, since it is difficult to perform a pairwise comparison with perfect consistency, it is necessary to determine the consistency of the matrix A. That is, assuming that the maximum eigenvalue of the matrix A is λ _max , λ _max ≧ n. Therefore, the degree of matching C.I defined by the formula "CI. = ([Lambda] _max- n) / (n-1)". I. Is used to determine consistency.

More consistency increases, the maximum eigenvalue lambda _max of the matrix A is decreased, when completely consistent is taken, since the maximum eigenvalue lambda _{max = n} matrix A, the matching degree C. I. Is smaller, the consistency is higher. I. If it is 0.1 or less, it is considered as passing.

Let w _ij ^c be the weight of element i in layer c with respect to element j in layer c-1. Of Hierarchical c-1 element and a set of elements that element _V ^{i c} hierarchy c is related to the [Phi _i ^c, the score _S ^{i c} to the problem P elements _V ^{i c} hierarchy c, the number of the next 1 It can be calculated from the formula of

In the hierarchy 1, the weight of each element for the problem P becomes the score S _i ¹ as it is.

Hereinafter, the hierarchical c = 2,3, ... order can be calculated score _S ^{i c} of, ultimately, to obtain a score _{S i} of each alternative _{A i.} The alternative with the highest score is the best option.

When such AHP is applied to the topology design in the network, the problem P to be solved (in this case, “optimal network selection”) is evaluated in the top hierarchy (hierarchy 0), and the central hierarchy (hierarchy 1) is evaluated. measure V _i is, and candidate topology lined bottom (Tier 2).

  The score (weight) for the problem P of the hierarchy 1 (evaluation scale) can be obtained by paired comparison. Further, the score (weight) for each element (evaluation scale) of hierarchy 1 of hierarchy 2 (candidate topology) does not need to be evaluated by pairwise comparison when the evaluation scale has a quantitative evaluation value.

AHP highly evaluates elements with high scores. Therefore, when each evaluation measure is so good that it takes a small value, the reciprocal of the value V _ij of the evaluation measure j of the candidate topology i is set to X _ij (X _ij = 1 / V _ij ), and the reciprocal X _ij Based on this, the weight is calculated.

The weight w _ij ² of the element of the layer 2 needs to satisfy the normalization condition “Σ _{i = 1} ^N2 (w _ij ² ) = 1” (N ₂ is the number of elements of the layer 2). Since the value obtained by simply normalizing X _ij among all candidates is regarded as the weight, the weight w _ij ² of the element in the layer ² is “w _ij ² = X _ij / Σ _{k = 1} ^N2 (X _kj )”.

However, since the number of network topology candidates becomes very large, the denominator becomes large, and the difference in the value of X _ij between the candidates is a much smaller value than the score difference between the evaluation measures. As a result, there is a strong tendency to select a candidate whose evaluation scale that is simply regarded as important is good, and values of other evaluation scales are hardly considered.

In order to solve this problem, the inventor of the present application has previously proposed that a value obtained by normalizing a value Y _ij obtained by linearly transforming X _ij is used as a weight instead of using the value X _{ij of the} evaluation scale itself. That is, a and b are arbitrary real numbers, and Y _ij = a (X _ij + b). In this case, the weight w _ij ² is expressed by the following equation (2).

To normalize the weights _{w ij} ² becomes independent of the real number a. Here, a value obtained by multiplying the minimum value among all candidates of the evaluation scale value X _ij by “−1” is set to b (b = −min) so that all weights take values of 0 (zero) or more. _i {X _ij }).

By performing linear transformation in this way, it is possible to widen the difference in weight between candidates, and in particular, it is possible to greatly reduce the weight for a candidate with a large evaluation value (small X _ij ). It is possible to avoid the problem of erroneously evaluating a topology including a very bad evaluation measure.

  However, when performing network topology (network topology) evaluation using AHP, it is necessary to generate a “candidate topology set” to be evaluated in advance. Hereinafter, generation of such a “candidate topology set” will be described.

  Consider nodes and links as generalized components of the network (NW). The position of the node and the AC traffic matrix between the nodes are given, and it is possible to install links between all the nodes.

  That is, assuming that the number of nodes is N, the number L of places where links can be installed is “L = N (N−1) / 2”. However, it is assumed that the installation link is bidirectional, and traffic flows in both directions between the nodes at both ends.

The link installation locations of these L present, because the candidate topology is generated by selecting a portion for installing the link, the total number of possible configurations candidate topology becomes 2 ^L.

  In general, the problem of outputting all candidates satisfying a certain condition without duplication is called an “enumeration problem”, and the “division method” described below is conventionally known as one of the enumeration algorithms.

  The division method is an enumeration method that divides a solution set of a problem and recursively solves each as a child problem, and when the number of solutions included in the child problem becomes the only one as a result of repeated division, the solution is obtained. Is output.

Therefore, in order to apply the division method, it is necessary to solve the problem recursively. Regarding the above-described candidate topologies, numbers 1 to L are arbitrarily assigned to each of the L link installable positions, and each link installable position is expressed as “l ₁ , l ₂ ,..., L _L ”. To do.

If a binary variable that defines “1” when installing a link at the link installation position l _e and “0” when not installing it is defined as x _e , it is arbitrary using an L-dimensional vector X having x _e as an element. Can be represented.

For each of the links can be installed position l _e, partly when decided whether installation of the link, recursively child issues a combination of the presence or absence of installation of the link to the solution set for the remaining links installable position l _e It is possible to divide the network into the network topology enumeration.

  In the division method, when it can be determined that the child problem generated by the division does not have a solution that satisfies the condition, the division of the child problem is interrupted and returned to reduce the calculation time.

  Therefore, in order to shorten the calculation time, it is necessary to be able to determine that there is no solution that satisfies the condition for a child problem including a plurality of candidates. This means that in a child problem including a plurality of solutions, it is necessary to determine that all candidates do not satisfy the condition C without determining whether each of the candidate topology sets satisfies the condition C.

  However, since the solution set that satisfies the condition C does not have monotonicity, the calculation time cannot be reduced only by the condition C.

  Therefore, the inventor of the present application proposes a technique for newly providing a constraint upper limit value D in the total link length in Japanese Patent Application No. 2008-170359. In this technique, if the total link length exceeds the upper limit limit D within the range in which the presence or absence of the link is already determined, all candidate topologies included in this child problem must be the upper limit of the total link length. Therefore, it is not necessary to perform subsequent division processing, and a reduction in calculation time can be expected.

  However, even with this technique, it may not be possible to generate network topology candidates within a realistic time for a large-scale network.

  Hereinafter, such a case will be described using the node arrangement of 36 commercial ISP backbone NWs disclosed on the CAIDA Web page.

  FIG. 3 summarizes the number N of nodes, the number M of links, the average node order Ar, and the maximum node order Max of these 36 NWs.

To link distance d _e of each link can be installed position e to the linear distance between nodes. Further, the exchange traffic ratio r _ij between nodes (the ratio of the traffic volume originating from node i and arriving at node j to the traffic volume of the entire NW) is set to the product of the population ratios of the nodes at both ends.

That is, if the population of the node k is U _k , the total population is U, and the population ratio of the node k is r _k (= U _k / U), then “r _ij = r _i r _j ”.

Assuming that the shortest hop route by OSPF (Open Shortest Path First) is set as the packet transfer route, the total link length is considered as the _first evaluation measure V ₁ for evaluating each candidate topology (V ₁ = Σ _eεE (d _e )) As the second evaluation measure V ₂ , consider the average hop length (hop count) ε weighted by the traffic amount ratio (V ₂ = ε = Σ _{i, jεV} (r _ij h _ij )). However, V and E are a set of nodes and links, respectively, and h _ij is the shortest hop length (number of hops) between the nodes i and j.

Further, SLF link e with upper NW: when the set of node pairs that loss at connectivity and _{P e} (Single Link Failure, single link failure only assume one link fail simultaneously), connected at SLF The average value ξ of the traffic amount ratio at which the connectivity is lost is defined by the following equation (3), and the average value ξ of the traffic amount ratio at which the connectivity is lost at the SLF is used as the third evaluation measure.

  FIG. 4A shows a result of plotting the average value ξ of the traffic amount ratio at which connectivity is lost during SLF in each of the 36 NWs shown in FIG. Connectivity is completely maintained during SLF among 36 NWs (ξ = 0). Only 7 NWs are connected to a small proportion of traffic, although the ratio is less than 2% in most NWs. It can be confirmed that sex is lost on average.

  Moreover, four of the seven NWs are small-scale NWs with a node number N of less than 10, and many NWs, particularly medium-sized or larger NWs, rarely have NWs that can maintain complete connectivity during SLF. .

  This seems to be because, in order to construct an NW at a realistic cost, there must be a certain degree of nodes of degree 1 connected to only one node.

The candidate topology enumeration method using division method, by providing the restriction upper limit D on the total link length V _1, is to shorten the required calculation time, to set to what extent the value of D becomes a problem. For example, as the constraint upper limit D is set smaller, the required calculation time is shortened, but the generated candidate topologies are limited to a small number having a smaller constraint upper limit D.

  When selecting an appropriate topology using AHP, the wider the range of values of each evaluation scale of the candidate topology to be evaluated, the more flexible evaluation can be performed, and it is desirable that the constraint upper limit D is larger.

Therefore, in order to confirm how much the total link length is in the actual NW, in FIG. 4B, the total link length of each NW 36 in FIG. The results of plotting the values divided by the total link length _Dmax when a link is installed at the position (full mesh) against the number N of nodes are shown.

  When the number N of nodes is small, it is possible to install links at all possible installation positions in a full mesh shape. In fact, some of the small-scale NWs have a shape close to a full mesh.

  However, as the number of nodes N increases, the number of link installable positions increases explosively. As the number of nodes N increases, the total link length in an actual NW is compared with the total link length in the case of a full mesh. Much smaller.

Therefore, the upper limit D / D _max of the total link length ratio is set to “1” for N <10 NW, so that the topology of the total link length in the actual NW is included in the candidates. “0.2” for NW with N <30, “0.07” for NW with 30 ≦ N <40, “0.03” with NW for 40 ≦ N <60, 60 For NW of ≦ N, set to “0.02” roughly. In FIG. 4B, the set D / D _max value is also shown.

  G (x) is defined as the sum of the x link lengths when x are selected in order from the shortest distance from the link installable position of L (= N (N−1) / 2), and G (x) ≦ Let x ′ be the maximum value of x that satisfies D.

Even when links are installed at all of these x ′ link installation possible positions, the constraint condition V ₁ ≦ D is satisfied, and therefore, for each of x ′, generated from a combination of cases where a link is not installed or not. All of the 2 ^{x ′} topologies to be satisfied satisfy the upper bound on the total link length.

Actually, there are many topologies that satisfy V ₁ ≦ D among the topologies in which links are installed at positions other than x ′ where links can be installed. Therefore, the number of candidate topologies to be enumerated is 2 ^{× ′.} Although it becomes much larger, in order to grasp the dimension of the required calculation time when a candidate topology is generated using a division method for a large-scale NW, here, at least 2 ^{x ′ that} needs to be listed is necessary. Evaluate the time required to generate individual topologies.

FIG. 5A shows the maximum value x ′ of the link installable position x satisfying “total link length G (x) ≦ constraint upper limit D” in 36 NWs shown in FIG. The result plotted against is shown. As the number N of nodes increases, the number of link installable positions having a short distance with respect to the full mesh total link length _Dmax of the link installable positions increases.

Therefore, the larger the number of nodes N is, the smaller the ratio of the constraint upper limit D of the total link length V to D _max is. However, as the number of nodes N increases, the total link length G (x) ≦ the constraint upper limit D is satisfied. The maximum value x ′ of the link installable position x increases rapidly.

Since the required calculation time depends on the constraint condition and the evaluation scale to be considered, here, it is a process specific to the division method, and the link installation state vector X for 2 ^{x ′} topologies is always obtained by recursive calculation. Evaluate only the time required to generate.

  Actually, since the time required for determining the constraint condition and calculating the evaluation scale is added, the actual required calculation time is much longer than the calculation time evaluated here.

  The maximum value x ′ of the link installable position x satisfying the total link length G (x) ≦ constraint upper limit D on a PC (personal computer) equipped with two 3 GHz CPUs (Central Processing Units) and 8 GB memory. Calculation for the case of = 28 took about 41 seconds.

FIG. 5B shows the result of plotting the value of “41 × 2 ^x′−28 ”, which is the lower limit of the theoretical required calculation time, against the number N of nodes. However, the four NW node number N ≧ 74, are omitted for the lower limit of the required calculation time exceeds ^{10 100.}

In an NW where the number of nodes N is about 10 or more, even when a practical upper limit is set for the total link length and the division method is used, in a realistic time of about 3 hours (10 ⁴ seconds), the candidate topology It is confirmed that the set cannot be generated.

  As described above, AHP is a technique for comprehensively evaluating each candidate in consideration of a plurality of evaluation scales when a plurality of candidates are given. There is no provision for technology.

  In addition, the division method is a technique for outputting all candidate solutions satisfying a certain condition without duplication by recursive processing. However, since all candidate solutions satisfying the condition are output, the candidate candidates satisfying those conditions are output. If the number is enormous, candidates cannot be generated in a realistic time even using the division method.

JP 2006-353926 A

  The problems to be solved are, for example, (1) that the generation technique of candidates to be evaluated in AHP is not disclosed in the conventional technique, and (2) candidates that satisfy the conditions in the division method. In the case where the number of nodes is enormous, the candidate topology cannot be generated in a realistic time.

  The object of the present invention is to solve the problems of the prior art, to generate a candidate topology in a realistic time even for a large-scale NW, and to improve the performance of a system that performs network topology design using the generated candidate topology. It is to improve.

  In order to achieve the above object, the present invention does not enumerate all solution candidates that satisfy the conditions, but efficiently generates only solution candidates that seem to have desirable properties. Specifically, the total link length, the average hop length (number of hops) weighted by the traffic ratio, and the average value of the traffic volume ratio at which connectivity is lost when a single link failure (SLF) occurs. First, a topology that satisfies the connectivity between all nodes, which is the minimum requirement required for the network, is generated, and connectivity is maintained for this generated topology during a single link failure (SLF). A topology with a minimum number of links added is generated as a basic topology so that the level to be the same level as the current network, and further, for this basic topology, the maximum link length variation is maximized. A minimum number of link installation positions are selected so that various topology candidates are generated.

  According to the present invention, a set of candidate topologies can be generated in a realistic time for a large-scale network, and the performance of a system that performs topology design in the large-scale network using the generated candidate topologies is improved. Can be made.

It is explanatory drawing which shows the hierarchical structure example of AHP. It is explanatory drawing which shows the example of the coincidence comparison value applied by AHP. It is explanatory drawing which shows the specific example of the basic characteristic of each network used for evaluation of this invention. It is explanatory drawing which shows the specific example of the average value of the loss-of-connectivity traffic amount ratio at the time of SLF corresponding to the number of nodes, and a total link length ratio. It is explanatory drawing which shows the specific example of the minimum of the link installation possible number corresponding to the number of nodes, and the minimum of theoretical required calculation time. It is a block diagram which shows the structural example of the system which concerns on this invention. It is an explanatory diagram showing a specific example of a calculation time required to obtain the topology T _b number of component links of the topology T _b corresponding to the number of nodes. It is explanatory drawing which shows the 1st evaluation result example of the system of this example. It is explanatory drawing which shows the 2nd evaluation result example of the system of this example. It is a flowchart which shows the process example of the system which concerns on this invention.

  Hereinafter, embodiments for carrying out the present invention will be described with reference to the drawings. FIG. 6 shows a configuration example of a system for generating a topology according to the present invention. This system has a computer configuration including a CPU (Central Processing Unit), a main memory, and the like, and is connected via an optical disk drive device or the like. After the program and data recorded in a storage medium such as a CD-ROM are installed in the external storage device, the function of each processing unit is executed by reading the program and data from the external storage device into the main memory and processing them by the CPU.

  In the system of this example, candidate topology set generation unit 100 and input unit 101 (“node information, traffic ratio information, number of link installation location candidates, input unit” in the figure) are used as each processing unit that executes programmed computer processing. Description) and an output unit 106 (described as “candidate topology output unit” in the figure).

  The input unit 101 is an all-in-one network in the processing target network that is input online, for example, via an external storage medium or a network by an operator's input operation using an input device such as a keyboard or a mouse (not shown). Input condition information such as node position information, traffic volume ratio between nodes, average connection control loss traffic volume ratio requirement ξ 'at the time of single link failure (SLF), number of link installation location candidates x, Store in a storage device (not shown).

  The candidate topology set generation unit 100 reads out the condition information from the storage device, and uses this condition information to perform a process according to the present invention, that is, a realistic time on the condition of ensuring connectivity between all nodes at normal time. A candidate topology set is generated in

  The output unit 106 displays the candidate topology set generated by the candidate topology set generation unit 100 on a display device such as a CRT (Cathode Ray Tube) or an LCD (Liquid Crystal Display), prints it with a printer, or stores it. Output processing such as recording on a medium or transmitting to another online computer device or the like is performed.

  The candidate topology set generation unit 100 includes a minimum tree generation unit 102, a permanent link addition unit 103, a link installation candidate position selection unit 104, and a candidate topology generation unit 105 as functions for executing programmed computer processing.

  With such a configuration, in the system of this example, the position of all nodes is given, and when it is possible to install a link between arbitrary nodes, it is necessary to ensure connectivity between all nodes in a normal state. A candidate topology set is generated in a realistic time.

In this example, three are evaluated: the total link length V ₁ , the average hop length (number of hops) V ₂ weighted by the traffic ratio, and the average value ξ ′ of the traffic volume ratio at which connectivity is lost when a single link failure occurs. A candidate topology is generated using the scale.

  At this time, for a given link cost, there is always connectivity between all nodes in the normal state, and the link installable position that constitutes the minimum tree that is the topology that minimizes the total sum of all link costs is always in place. Establish a link. A value obtained by dividing the link distance by the traffic amount ratio between nodes is used as the link cost.

  In addition, the average loss-of-connectivity traffic ratio at the time of a single link failure in a topology in which only one link is installed for each link installation possible position not included in the minimum tree with respect to the generated minimum tree And repeats the process of installing a link at the link installable position where this value is the minimum until the average loss-of-connectivity traffic ratio at the time of a single link failure is less than or equal to the arbitrarily given value. Links are always installed at all link installation positions added to the tree.

In addition, for each of the link installable positions not included in the generated topology, the average hop length (number of hops) weighted by the traffic volume of the topology in which only one link is installed is calculated. The process of selecting the minimum link installation possible position as the link installation candidate position is repeated by an arbitrarily given number x. Further, in consideration of the case where a link is not installed for each of the selected x link installable positions, 2 ^x topologies that can be configured in combination are generated as candidates.

  Hereinafter, such processing operation will be described in more detail. In FIG. 6, in this example, the input unit 101 inputs the position of all nodes and the traffic volume ratio between nodes, the required level ξ ′ of the average connectivity loss traffic volume ratio during SLF, and the link installation location candidate number x. To do.

  For example, the coordinate data such as (123, 45) where the geographical coordinates where each node exists is, for example, as the node position, and the traffic amount ratio between the nodes 3, 4 is 0.003 as the traffic amount ratio between the nodes, for example. In addition, for example, “ξ ′ = 0.05” is used as the required level ξ ′ of the average connectivity loss traffic rate ratio during SLF, and “x = 5” is used as the input parameter for the link installation location candidate number x, for example. Entered.

  The minimum tree generation unit 102 generates a minimum tree for the network using each input parameter, and the permanent link addition unit 103 determines, based on the generated generation tree, that the average loss-of-connectivity traffic ratio during SLF is Select a permanent link to be added to meet the constraint limits.

  The link installation candidate position selection unit 104 selects a link installation candidate position at a position where the effect of reducing the weighted average hop length (hop count) is high, and the candidate topology generation unit 105 generates a set of configurable candidate topologies. To do. The output unit 106 outputs the generated candidate topology set.

  The data format of the candidate topology is “1” when a link is set for each link installable position, and “0” when it is not set, for all x link installable positions. Link installation information vector (eg: (0, 0, 1, 0, 1, 1, 0, 1, 0)) and values of each evaluation scale (eg: 100.56, 1.43, 0. 003), the topology data is output to each candidate.

  The minimum tree generation unit 102 of the present example generates a minimum tree using the Prime algorithm (prim method: minimum spanning tree problem). In this algorithm, one node is first selected at random, and a link is set between the selected node and the node having the smallest link cost. Then, repeat the process of adding links one by one to the position where the link cost is minimum between any node belonging to the obtained subtree and any node other than the subtree until all nodes are included in the tree To do.

  The permanent link adding unit 103 calculates an average connectivity loss traffic amount ratio ξ at the time of SLF for a topology in which only one link is added to each link installation position selected by the minimum tree generation unit 102. Then, only one link is added to the link installable position where the calculated ratio ξ is minimized. This process is repeated until ξ ≦ ξ ′ is satisfied.

In the initial state, the link installation candidate position selection unit 104 sets the set E _c of x link installation possible positions as an empty set, is selected by the minimum tree generation unit 102, and is added by the permanent link addition unit 103. The average hop length (the number of hops) ε weighted by the traffic amount ratio when only one link is added to each of the links is calculated, and the link installable position e _{1 at which the} weighted average hop length ε is minimized. the, to add to the set E _c of the link can be installed position.

Further, the link installation candidate position selection unit 104 further adds a traffic amount ratio when only one link is added to each of the remaining link installation possible positions with respect to the topology in which the link installation possible position e ₁ is added. Then, the average hop length ε weighted in (1) is calculated, and the link installable position e ₂ that minimizes ε is added to the set E _c .

The same process is repeated x times arbitrarily given. As a result, a candidate topology set that minimizes the minimum value of the weighted average hop length (V ₂ ) is generated on the condition that “x” link installable positions are added, and a link installable position set E _c is obtained. be able to.

The candidate topology generation unit 105 generates candidate topology data for all combinations of cases where a link is installed for each of the obtained link installation possible position sets E _c and cases where the link is not installed.

  Hereinafter, details of the enumeration procedure of such network topology candidates according to the present invention by the candidate topology set generation unit 100 in FIG. 6 will be described with reference to FIG. The description will be made in the order of [select link permanent location] by the minimum tree generation unit 102 and permanent link addition unit 103, and [select link candidate location] by the link installation candidate position selection unit 104 and candidate topology generation unit 105.

[Selection of permanent link location]
The topology in which the sum of link costs is minimized while satisfying the connectivity between all nodes when given the cost of each link is known as the minimum spanning tree (MST) and is the minimum based on the greedy method. Known as tree generation methods are the Kruskal and Prim algorithms.

  In the candidate topology set generation unit 100 of this example, a minimum tree is generated using the Prime algorithm (step S101).

  In this algorithm, one node is first selected at random, and a link is set between the selected node and a node having the smallest link cost. Then, a process for adding links one by one at a position where the link cost is minimum between any node belonging to the obtained subtree and any node other than the subtree is included in the tree. Repeat until.

By using this algorithm, _a topology Ta composed of N−1 links can be obtained in O (N ³ ) polynomial time. Here, “d _ij / r _ij ” that is the reciprocal of s _ij is used as the link cost.

Thus the topology T _a obtained is satisfied connectivity between all nodes in a normal state, no consideration is given connectivity during SLF. Therefore, the average connectivity loss traffic ratio xi] at SLF is 36 actual to be a less than or equal to the respective ratios xi] xi] 'in NW, consider adding the minimum number of links in the topology T _a.

First, T _b = T _a is set (step S102), and an average connectivity loss traffic amount ratio ξ in a topology in which only one link is added to each link installable position not included in the topology T _b is set. calculated, processing the calculated xi] to add the minimum and AnTome link installable located topology T _b (step S103), the calculated xi] exceeds demanding xi] 'is one of the evaluation criteria set in advance (Step S104).

That is, only one link is added to each link installable position of “all link installable locations L−x _a ” excluding “x _a = N−1” books included in the topology T _a . The average connectivity loss traffic amount ratio ξ is calculated for the topology, and only one link is added to the link installable position where the ξ is minimized. Such a process is repeated until “ξ ≦ ξ ′” is satisfied, and the obtained topology is defined as T _b .

FIG. 7A shows the result of plotting the number of links x _b of the topology T _b obtained in 36 NWs in this way against the number of nodes N. FIGS. 7 (a) as shown in, but the value of x _a required for construction of minimum spanning trees are shown by a solid line, that must be added to meet the average connectivity loss traffic amount ratio ξ at SLF link number is less than about 30% of x _a, it is confirmed that sufficiently reduces the ξ by simply adding a few links.

FIG. 7B shows a result of plotting the total time t _b required to obtain the topology T _a and the topology T _b in each NW against the number N of nodes. However, in three NWs with the number N of nodes of 5 or 6, the required calculation time is very short and it is not possible to measure, so it is omitted.

Since the amount of calculation required to configure topology T _b from topology T _a is O (x _a x _b N ⁴ ), the amount of calculation required to configure topology T _b from topology T _{a as} node N increases. t _b increases rapidly. Nevertheless, if the node N is not more than about 100, in a realistic time of about several 10 minutes, it is possible to configure the topology T _b.

[Selection of candidate links]
In all candidate topology generated, the link installation position of x _b present constituting the topology T _b, always placed the link. That is, the candidate topologies to be generated are limited to those in which links are installed at these _xb positions.

When the topology T _b is configured, since the link cost “d _ij / r _ij = 1 / s _ij ” is small, links are installed only in as few places as possible. the total link length V ₁ of the of the scales is that good topology is generated.

Further, the generated topology is limited to the average connectivity loss traffic amount ratio ξ that is equal to or less than the actual NW value, and therefore the average connectivity loss traffic at the time of SLF among the above three evaluation measures. good topology is generated also for the amount ratio V _3.

However, no consideration is given to weighted average hop length V ₂ is a leaving rating scale. Hereinafter, a procedure for selecting a candidate topology considering such weighted average hop length V ₂ will be described.

Generally, as the number of links to be installed increases, the diversity of paths between nodes increases, and the weighted average hop length V ₂ decreases. Therefore, it can be said that the topology T _{b in} which the number of installed links is suppressed is a topology having a relatively large weighted average hop length V ₂ among the configurable topologies. Therefore, it is considered to generate a candidate topology set having diversity in the weighted average hop length V ₂ by additionally installing links from the topology T _b .

Here, the number of links set position to allow additional links for topology T _b and x, the set of links can be installed position of x present and E _c.

Since a candidate topology is generated by all combinations of installing links at arbitrary positions in the link installation possible position set E _c , 2 ^x candidates having links are always included in the link positions constituting the topology T _b. A topology set T _d is generated.

  As the number of links x allowed to be added increases, the diversity of candidate topologies increases and a more flexible topology design becomes possible, but the time required for generating candidate topologies explosively increases.

As the number of links is added to the topology T _b , the weighted average hop length V ₂ monotonously decreases. Therefore, the maximum value of the weighted average hop length V ₂ in the generated candidate topology is the topology T _b itself. weighted average hop length ε next, become independent of the set E _c of the link can be installed position.

On the other hand, the minimum value of the average hop length V ₂ depends on the set E _c of the link installable position, as the minimum value of the average hop length V ₂ is small, a high diversity of the average hop length V _2, excellent It can be said that it is a candidate topology set.

Therefore, a small number of link addition as possible, so that the minimum value of the average hop length V ₂ in the candidate topology set generated is small, it is desirable to select a set E _c of the link can be installed position.

  Here, the generation method by the greedy method shown below is considered.

In the initial state, the set _{E c} of the link can be installed position an empty set (step S105). And, except for x _b book links constituting the topology T _b for each of the links can be installed position of "all the links can be installed location number L-x _b", when you add a link only one weighting The average hop length ε is calculated, the link installable position e ₁ that minimizes ε is added to the link installable position set E _c , and the link installable position e ₁ is further added to the topology T _b. For each of the remaining “Lx _b −1” link installable positions, a weighted average hop length ε is calculated when only one link is added. The process of adding the link installable position e ₂ having the minimum length ε to the link installable position set E _c (step S106) is repeated x times arbitrarily given (step S107).

As a result, a link installable position set E _c that generates a candidate topology set that minimizes the minimum value of the average hop length V ₂ can be obtained under the condition that x link installable positions are added.

  Hereinafter, the “evaluation result” of the system of this example will be described with reference to FIG.

Topology average hop length V ₂ becomes minimum, in case of a full mesh was placed a link to all the links can be installed position of L present, "0" through the hop length of traffic destination nodes are the same node (zero ), The routed hop length of all the tracks with different departure and arrival nodes is “1”. The minimum value ε _min of the weighted average hop length ε is “ε _min = 1−Σ _{n = 1} ^N ( r _ii ) ".

FIG. 8 shows link normalized positions obtained by dividing the minimum value of the average hop length V _{2 by} the minimum achievable value ε _min in the generated topology set for every 36 NWs. The result plotted against the set value (number) of x is shown.

FIG. 8A shows the results of 18 NWs with a node number N of less than 27, and FIG. 8B shows the results of 18 NWs with a node number N of 27 or more. However, in the number of nodes N is 74 or more four NW, the time required for generation of links can be installed position set E _c has aborted the evaluation at the time of more than 1 hour, results in a small area of the link can be installed position x Only shows.

As shown in FIG. 8 (a), (b) , the horizontal axis is logarithmic, the vertical axis in the linear graph, with the increase of the link installable position x, substantially linearly, mean hop length V ₂ is reduced . Therefore, in the small region of the link installable position x, but the minimum value of the rapid average hop length V ₂ with increasing x decreases, the link can be installed in a large area at a position x, the minimum value of the average hop length V ₂ It can be confirmed that decreases gradually and reaches the minimum value ε _min .

Therefore, even if the link installation possible position x is set to a small value, it can be expected to obtain a topology set T _d having a relatively small average hop length V ₂ and various candidates.

For one topology, since the amount of computation required to calculate the average hop length ε were weighting is O (N ^3), the time t _c required for generating the link installable position set E _c 'O (XLN ³ ) = O (xN ⁵ ) ”.

Further, when 2 ^x candidate topology sets T _d are generated using the obtained topology set T _b and the link installable position set E _c , three evaluation measure values are set for each candidate topology. It is necessary to calculate.

That is, O (x) for the total link length V ₁ , O (N ³ ) for the average hop length V ₂ , and O ((x ₂ + x) for the average loss-of-connectivity traffic ratio V ₃ during SLF. N ² ) is required for each calculation. Here, if it is regarded as the following equation ( ⁴ ), a calculation amount of about O (N ³ ) is required for each candidate topology.

Therefore, the time t _d required to generate 2 ^x candidate topologies from the topology set T _b and the link installable position set E _c is O (2 ^x N ³ ). FIG. 9 shows the relationship between the time t _d required to generate such 2 ^x candidate topologies and the number of nodes.

In FIG. 9A, the result of plotting the time t _c required to generate the link installable position set E _c in each NW of 36 when the number of additional links x = 20 is plotted against the number N of nodes. Is shown.

FIG. 9B also shows the result of plotting the time t _d required to generate the candidate topology set T _d against the number N of nodes when the number of additional links x = 20. . However, the three NWs with 5 or 6 nodes are omitted because the required calculation time is too short to be measured.

Using these results and the result of the time t _b required to generate the candidate topology set shown in FIG. 7B, the MST (minimum tree) generation is performed for any number of link installation candidate positions x. It estimates an estimate tau of total required computation time leading to the generation of candidate topology formula _{"τ = t b + (x /} 20) × t c +2 x-20 t d ".

The approximate value τ of the total required calculation time increases as the number of link installation candidate positions x increases, but the maximum number of link installation candidate positions x satisfying τ ≦ τ _max with respect to the actual allowable calculation time τ _max . Let x _max be the value.

FIG. 9C shows the result of plotting the maximum value x _{max of the} number of link installation candidate positions of each NW when τ _max = 3600 seconds is set against the number N of nodes. However, the network "GG" of the node number N = 126, shown in Figure 3, the candidate topology set T _b already only at time t _b required for generation of, because it was in excess of realistic acceptable computation time tau _max rating Not applicable.

As shown in FIG. 9C, when the number of nodes N is less than about 10, the maximum value x _{max of the} number of link installation candidate positions is “x _max = number of places where all links can be installed L−x _b ”. All link installable positions can be candidates, but in an NW with the number of nodes N of about 10 or more, the link installable positions are limited, and the allowable maximum number gradually increases as the number of nodes N increases. Decrease.

In FIG. 9 (d), the was a "link installation candidate position number x" = "maximum value x _max link installation candidate position number satisfying estimate tau ≦ realistic acceptable computation time tau _max of the total required computation time" A value obtained by dividing the maximum value and the minimum value of the weighted average hop length V ₂ in the candidate topology set generated at times by the minimum value ε _min of the weighted average hop length is normalized with respect to the number N of nodes. The plotted results are shown.

As shown in FIG. 9 (c), with an increase in the number of nodes N, the candidate topology sets that can be obtained in real time, the minimum value of the weighted average hop length V ₂ increases gradually. When the number of nodes N is less than about 30, the lower limit that can be achieved is about 40% or less, and when the number of nodes N is about 30 to 60, about 50% is increased, and the number of nodes N is about 60 to 100. In NW, it is about 60% to 80% increase.

Further, the candidate topology resulting set, the range width is the difference between the minimum and maximum values of the weighted average hop length V _2, in the NW the number N is equal to or greater than about 20 nodes, compared to the case of enumerating all candidates It can be confirmed that it is roughly halved.

To summarize the above evaluation, by using the candidate topology generation technique in this example, for an NW (network) where the number of nodes N is less than about 20, candidates at the same time as enumerating all candidates are listed. Although the generation of topology, for number of nodes N is about 20 to 100 NW, although range width weighted average hop length V ₂ becomes about half the total listed candidate in a realistic time A topology can be generated. However, it is difficult to generate a candidate topology in a realistic time for an NW having the number of nodes N of about 100 or more even if this method is used.

  As described above with reference to FIGS. 1 to 10, the candidate topology generation technique of this example does not enumerate all solution candidates that satisfy the conditions, but only the solution candidates that seem to have desirable properties. Generate efficiently.

  That is, the evaluation measures are the total link length, the average hop length weighted by the traffic ratio, and the average value of the traffic volume ratio at which the connectivity is lost at the time of single link failure (SLF). A topology with the lowest link cost that satisfies the connectivity between all nodes, which is the minimum requirement for the network, is generated, and connectivity is predetermined for this generated topology in the event of a single link failure (SLF). A topology (basic topology) with a minimum number of links added to maintain the same level (for example, the same level as that of the current network). In order to generate various topology candidates so that the link length variation is maximized, the minimum number of link installation positions is selected, that is, It generates a topology obtained by adding the number of links that are predefined for diversity path selection between over de increases, and outputs the topology candidate topology and stearyl.

  More specifically, the system for generating a candidate topology in this example generates a network topology by programmed computer processing, and a candidate topology set as a processing unit that executes the processing of the programmed computer. A generation unit 100, an input unit 101, and an output unit 103 are provided. In the input unit 101, an average hop length inputted from an input device and weighted by a traffic ratio and a single link failure are connected. The condition information including the average value of the traffic volume ratio that loses the characteristics is input and stored in the storage device, and the candidate topology set generation unit 100 reads the condition information from the storage device, and the candidate topology set within a predetermined time. In the output unit 103, the candidate topology set generation unit 100 generates Via the output device topology set.

  Further, the candidate topology set generation unit 100 includes a minimum tree generation unit 102. The condition information stored in the storage device by the input unit 101 includes a link cost input from the input device. Generates a minimum tree, which is a topology that minimizes the total sum of all link costs, on condition that the connectivity between all nodes during normal operation is ensured, and identifies the nodes that make up the generated minimum tree as possible link installation positions. The candidate topology set generation unit 100 generates a candidate topology set in which links are installed at the link installation possible positions specified by the minimum tree generation unit 102.

  As the link cost, a value obtained by dividing the link distance by the traffic amount ratio between the nodes is used.

  In addition, the candidate topology set generation unit 100 includes a permanent link addition unit 103. In the permanent link addition unit 103, each node not included as a link installation possible position in the minimum tree generated by the minimum tree generation unit 102 is included. On the other hand, for the topology with only one link installed, calculate the average loss of traffic volume ratio at the time of single link failure, specify the node with the smallest calculated ratio as the link installable position, and install the link The candidate topology set generation unit 100 repeats the above processing until the ratio falls below a predetermined value, and the candidate topology set generation unit 100 sets the candidate topology set in which links are set at all link installation possible positions specified by the permanent link addition unit 103. Is generated.

  Further, the candidate topology set generation unit 100 includes a link installation candidate position selection 104. In the link installation candidate position selection 104, each of arbitrary nodes not included as the link installation possible positions specified by the permanent link addition unit 103 is included. On the other hand, the process of calculating the average hop length weighted by the traffic amount of the topology in which only one link is installed, and selecting the link installation possible position where the calculated average hop length is the minimum as the link installation candidate position, The candidate topology set generation unit 100 generates a candidate topology set in which links are installed at all link installation possible positions selected by the link installation candidate position selection unit 104 by repeating a predetermined number x of links.

The candidate topology set generation unit 100 includes a candidate topology generation unit 105. For each of the x link installation possible positions selected by the link installation candidate position selection unit 104 in the candidate topology generation unit 105, a link is provided. 2 ^× topologies that can be configured as a combination of the case where the case is installed and the case where it is not set are generated as candidates.

  In this way, in this example, the total link length, the average hop length weighted by the traffic ratio, and the average value of the traffic volume ratio at which connectivity is lost at the time of single link failure (SLF) are By using it as an evaluation measure, a set of candidate topologies can be generated in a realistic time for a large-scale network.

  In addition, this invention is not limited to the example demonstrated using FIGS. 1-10, In the range which does not deviate from the summary, various changes are possible. For example, in this example, the description is limited to a technique for generating a set of candidate topologies. However, by using the candidate topology set generated by this technique in a network topology design system using, for example, AHP, A high performance network topology design system can be constructed.

  100: candidate topology set generation unit, 101: input unit, 102: minimum tree generation unit, 103: permanent link addition unit, 104: link installation candidate position selection, 105: candidate topology generation unit, 106: output unit

Claims (10)

A system for generating a topology in a network in which positions of all nodes are given and links can be set between arbitrary nodes by programmed computer processing,
As a means of executing programmed computer processing,
A first means for generating a topology having a minimum link cost that satisfies connectivity between all nodes in the network;
A second means for generating a topology with a minimum number of links added so that connectivity at the time of a single link failure is maintained at a predetermined level with respect to the topology generated by the first means;
And a third means for generating a topology in which a predetermined number of links are added to the topology generated by the second means so as to increase the diversity of path selection between nodes. Candidate topology generation system. By programmed computer processing
A system for generating a network topology,
As a means of executing programmed computer processing,
A storage device that inputs condition information including an average hop length weighted by the total link length of the network and a traffic ratio, and an average value of a traffic volume ratio at which connectivity is lost when a single link fails, input from an input device Input means for storing
Candidate topology set generation means for reading the condition information from the storage device and generating a candidate topology set within a predetermined time;
A topology generation system comprising: output means for outputting the candidate topology set generated by the candidate topology set generation means via an output device. The topology generation system according to claim 2,
Including link cost as the above condition information,
The candidate topology set generation means includes:
A minimum tree that generates a minimum tree, which is a topology that minimizes the total sum of all link costs, on the condition that connectivity between all nodes during normal operation is secured, and that identifies the nodes that make up the generated minimum tree as link installation positions Comprising generating means,
A topology generation system for generating a candidate topology set in which links are installed at positions where link establishment is possible specified by the minimum tree generation means. The topology generation system according to claim 3,
A topology generation system using a value obtained by dividing a link distance by a traffic amount ratio between the nodes as the link cost. A topology generation system according to claim 3 or 4, wherein:
The candidate topology set generation means includes:
Average connectivity loss traffic ratio at the time of a single link failure in a topology in which only one link is installed for each node not included as the link installation possible position in the minimum tree generated by the minimum tree generation means And a permanent link adding unit that repeats the process of specifying a node having the smallest calculated ratio as a link installable position and installing a link until the ratio falls below a predetermined value. ,
A topology generation system, characterized in that a candidate topology set is generated in which links are also installed at all link installation positions specified by the permanent link addition means. The topology generation system according to claim 5,
The candidate topology set generation means includes:
Calculate the average hop length weighted by the traffic amount of the topology in which only one link is installed for each of the arbitrary nodes that are not included as the link installation possible positions specified by the permanent link addition means,
Link installation candidate position selection means for repeating the process of selecting the link installation possible position where the calculated average hop length is minimum as the link installation candidate position by a predetermined number x of links,
A topology generation system for generating a candidate topology set in which links are installed at all link installation possible positions selected by the link installation candidate position selection means. The topology generation system according to claim 6,
The candidate topology set generation means includes:
Candidate topologies that generate 2 ^x topologies that can be configured as a combination of cases where links are not installed and cases where links are not installed for each of the x link installable positions selected by the link installation candidate position selection means. A topology generation system comprising generation means. By programmed computer processing
A system topology generation method for generating a network topology,
As an execution procedure by programmed computer processing,
A topology generation method comprising a processing procedure executed by each means in the topology generation system according to claim 1.   The program for functioning a computer as each means in the topology generation system in any one of Claims 1-7. By programmed computer processing
A system for designing a network topology,
As a means of performing programmed computer processing,
Each means in the topology generation system according to any one of claims 1 to 7,
A network topology design system, wherein the topology of the network is designed using each topology included in the candidate topology set output by the output means.

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