JP2006324959A - Apparatus, method and program for calculating failure frequency of communication network - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To quickly calculate failure frequency. <P>SOLUTION: A communication network failure frequency calculation apparatus for calculating failure frequency between nodes by using the normality probability and failure probability of respective links constituting a communication network comprises: a storage part for storing the normality probability of respective links which are previously provided and matrix data including the product of the normality probability and failure probability; a degeneration part for degenerating respective links between specified nodes; a matrix processing part for calculating the product of the normality probability and the failure probability of the degenerated links by using an expression obtained by substituting the stored matrix data for the normality probability in an expression to be used for the calculation of the operation rate of the links degenerated by the degeneration part; and a control part for outputting the product of the normal probability and the failure probability which is finally obtained by repeating degeneration and the calculation of the product of the normal probability and the failure probability as failure frequency between the specified nodes before link degeneration operation. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a technique for evaluating the reliability of a communication network, and in particular, to efficiently obtain a “failure frequency” that is an average number of times per unit time at which communication between a plurality of nodes is interrupted in a communication network. It relates to a suitable technique.

  The reliability of the communication network represents the degree or nature of the stable communication. The communication network is represented by points (nodes) and lines (links), points (nodes) represent communication devices (switches, multiplexers, etc.), and lines (links) represent line devices.

  The reliability of the communication network is specified by K nodes (2 ≦ K ≦ the total number of nodes constituting the communication network) (hereinafter referred to as “K node”, which corresponds to a particularly important large-scale exchange, etc.). Attention is paid to the evaluation (probability) that the K nodes can communicate with each other (operating rate), or the average number of occurrences per unit time (failure frequency) that the K nodes cannot communicate with each other.

  The operating rate is expressed as a probability that takes a value in the range of “0 to 1”. The failure frequency is expressed, for example, on a scale of how many times a year. Both availability and failure frequency are used as important reliability evaluation measures.

  Here, it is assumed that the node does not fail. Based on this assumption, the conventional technology for calculating the operation rate and failure frequency from the normality probability (probability of not having failed) and failure rate (reciprocal of the average time from repair to failure) of each link. As an efficient technique that is widely used, there is a degeneration method described in Non-Patent Document 1, for example.

  In Non-Patent Document 1, a specific method using the degeneration method for operating rate calculation is shown, but calculation of “fault frequency” is not described.

  Regarding the use of the degeneracy method for the calculation of “fault frequency”, for example, Non-Patent Document 5 merely suggests its applicability theoretically.

  Hereinafter, the degeneration method will be described with reference to FIGS.

  In the communication network configuration shown in FIG. 1, two K nodes (hereinafter, “black circle” in the figure represents a K node, “white circle” represents a node that is not a K node, and “double circle” represents which node. The degeneration method for calculating the operation rate will be described by taking as an example the case where the node is set).

  For the sake of explanation, the links are given numbers (1-3) as shown in the figure. Each link is identified below by this number (1-3). Further, the normal probability of each link i is Ai.

  Even if one of the links 1 and 2 fails, as long as the other is normal, there is no problem in ensuring communication between the K nodes. That is, if either link 1 or 2 is normal, communication can be secured. Such a relationship is called parallel.

  In this case, for the two links 1 and 2, even if the probability that either one of the links 1 or 2 is normal is replaced with one link given as the probability that the link is normal, the operation rate is equivalent in calculation. It is. That is, as shown in FIG. 2, the links 1 and 2 can be replaced with the links 4.

  Here, the probability “A4” that the link 4 is normal is “A4” where the probability that the link 1 is normal is “A1”, and the probability that the link 2 is normal is “A2”, “A4 = (A1 + A2) − (A1 × A2) ".

  Replacing the communication network with a simpler configuration without changing the operating rate between the K nodes in this way is called “degeneration”. In particular, as shown in FIG. 2, the operation of replacing the parallel link with one link is performed. This is called “parallel degeneration”.

  The communication network obtained by the degeneration in FIG. 2 is composed of the link 3 and the link 4, but these two links can ensure communication between the K nodes only when both are normal. Such a relationship is called a “series relationship”.

  Furthermore, even if the probability that both the link 3 and the link 4 are normal is replaced with the link given as the normal probability of the link, the links 3 and 4 are equivalent in calculating the reliability between the K nodes. is there. That is, as shown in FIG. 3, the links 3 and 4 can be replaced with the link 5 and represented.

  The probability “A5” that the link 5 is normal is obtained by an expression “A5 = A3 × A4”, where “A3” is the probability that the link 3 is normal and “A4” is the probability that the link 4 is normal. be able to. Such degeneration shown in FIG. 3 is referred to as “serial degeneration”.

  Eventually, the communication network in FIG. 1 can be replaced with one equivalent link in FIG. In this case, the operation rate is “A5” because it is the probability that the K node can communicate. That is, “operating rate = A5 = A3 × A4” is obtained from the serial degeneracy conversion formula in FIG.

  However, since “A4 = (A1 + A2) − (A1 × A2)” in the parallel degeneracy conversion formula in FIG. 2, the operation rate of the communication network in FIG. 1 is eventually “operation rate = A5 = A3 ×”. A4 = A3 × {(A1 + A2) − (A1 × A2)} ”.

  In this way, if the communication network is configured in series and in parallel, the operation rate can be obtained using degeneration.

  However, this technique is not sufficient as a calculation method. In other words, in the case of “serial degeneration” shown in FIG. 3, it is implicitly assumed that an intermediate node connecting two links in a serial configuration is not a K node (white circle).

  If this intermediate node is a K node, for example, in the case of FIG. 4, “serial degeneration” cannot be used. Hereinafter, it will be described that “serial degeneration” cannot be used in the communication network having the configuration shown in FIG.

  Assume that “serial degeneration” is applicable to the communication network having the configuration shown in FIG. First, when “serial degeneration” is applied to the links 41 and 42, the utilization rate = (A 1 × A 2) + A 3 − ( A1 × A2 × A3) ”, and then applying“ degeneration in series ”to the links 42 and 43, the fact that the link thus obtained is parallel to the link 1 can be used as“ operating rate ”. = (A2 * A3) + A1- (A2 * A3 * A1) ".

  These equations are not equal. In this way, although the same communication network is targeted, the calculation result of the operation rate cannot be different, so this is contradictory. This contradiction is caused by the fact that “serial degeneration” cannot be applied to the communication network having the configuration shown in FIG.

  This situation occurs because, in the case of FIG. 4, the disappearance of one of the K nodes due to “serial degeneration” changes the nature of the problem.

  In Non-Patent Document 1, even if the link has a serial structure, if the intermediate node is a K node, this is not called serial degeneration. In the example of FIG. 4, the intermediate node is connected. Since the number of links (hereinafter referred to as “order”) is “2”, it is generally impossible to apply degree 2 degeneration without changing the operating rate after calling it degree 2 degeneration. It is described that it is.

  However, the non-patent document 1 describes that this problem can be solved by using a correction coefficient Ω as a countermeasure. That is, even if the operating rate changes due to degree 2 degeneration, if a certain value Ω is added to the communication network to which order 2 degeneration is applied, the operation rate of the communication network before applying order 2 degeneration is obtained. Can do.

  For example, when a node of degree 2 is a K node and two nodes connected to the node of degree 2 (K node) are also K nodes (hereinafter referred to as “type 1”), degeneration is performed as follows: Follow the procedure.

Type 1 degree 2 reduction:
Procedure 1: Degeneration of order 2 is executed as shown in FIG.
Procedure 2: The normal probability (“A51 ′”) of the degenerated link 51 ′ is calculated by “A51 ′ = (A51 × A52) / {(A51 + A52) − (A51 × A52)}”. “A51” is the normal probability of the link 51, and “A52” is the normal probability of the link 52.
Procedure 3: “Ω = (A51 + A52) − (A51 × A52)”.
Procedure 4: The operation rate before the order 2 reduction is obtained by adding Ω to the communication network operation rate after the order 2 reduction.

  For example, when degree 2 degeneration is applied to the communication network in FIG. 4, the result is as shown in FIG. In this case, first, since the operation rate of the communication network after degeneration is a parallel configuration, assuming that the normal probability of the link 61 ′ is “A61 ′” and the normal probability of the link 63 is “A63”, “(A61 ′ + A63” )-(A61 ′ × A63) ”.

  Further, it is obtained as “A61 ′ = (A61 × A62) / {(A61 + A62) − (A61 × A62)}” by the order 2 reduction procedure. The correction coefficient Ω is “Ω = (A61 + A62) − (A61 × A62)”.

  In summary, the operation rate before the degree 2 reduction can be obtained by the following equation.

Occupancy rate = Ω × {(A61 ′ + A63) − (A61 ′ × A63)}
= {(A61 + A62)-(A61 * A62)} * [(A61 * A62) / {(A61 + A62)-(A61 * A62)} + A63]-[(A61 * A62) / {(A61 + A62-A61 * A62)} × A63]
= A61 * A62 + A63 (A61 + A62-A61 * A62) -A61 * A62 * A63
= A61 * A62 + A62 * A63 + A63 * A61-2 * A61 * A62 * A63

  In Non-Patent Document 1, the applicable types of degree 2 reduction are arranged into 8 types (types 1 to 8) shown in FIG. And a formula that gives a correction coefficient Ω (hereinafter referred to as a “correction coefficient formula”) are given as follows.

The type 1 degeneracy equation and correction coefficient equation are as follows.
A71 ′ = A71 × A72 / (A71 + A72−A71 × A72),
Ω = A71 + A72−A71 × A72

The degeneration formulas and correction coefficient formulas of types 2 to 4 are as follows: A71 ′ = δ / (α + δ),
A72 ′ = δ / (β + δ),
Ω = (α + δ) × (β + δ) / δ

  The parameters appearing in these equations are as follows for Type 2 and Type 3.

α = (1-A71) × A72 × (1-A73),
β = A71 × (1-A72) × (1-A73),
δ = A71 × A72 × A73 × {1+ (1-A71) / A71 + (1-A72) / A72 + (1-A73) / A73}

  The type 4 degeneracy equation and correction coefficient equation are as follows.

α = A71 × (1-A72) × (1-A73) × A74 + (1-A71) × A72 × A73 × (1-A74) + (1-A71) × A72 × (1-A73) × A74,
β = A71 × (1-A72) × A73 × (1-A74),
δ = A71 × A72 × A73 × A74 × {1+ (1-A71) / A71 + (1-A72) / A72 + (1-A73) / A73 + (1-A74) / A74}

  Degeneration formulas and correction coefficient formulas of types 5 to 8 (except in type 6 where the number of K nodes is 2) are as follows.

A71 ′ = γ / (α + γ),
A72 ′ = γ / (β + γ),
A73 ′ = γ / (δ + γ),
Ω = {(α + γ) × (β + γ) × (δ + γ)} / γ ²

  The parameters appearing in these equations are given for type 5 as follows:

α = (1-A71) × A72 × (1-A73) × A74,
β = A71 × (1-A72) × (1-A73) × A74 + (1-A71) × A72 × A73 × (1-A74),
δ = A71 × (1-A72) × A73 × (1-A74),
γ = A71 × A72 × A73 × A74 × {1+ (1-A71) / A71 + (1-A72) / A72 + (1-A73) / A73 + (1-A74) / A74}

  Type 6 is given as follows.

α = (1-A71) × A72 × A73 × (1-A74),
β = A71 × (1-A72) × A73 × (1-A74),
δ = A71 × A72 × (1-A73) × (1-A74),
γ = A71 × A72 × A73 × A74 × {1+ (1-A71) / A71 + (1-A72) / A72 + (1-A73) / A73 + (1-A74) / A74}

  For type 7, it is given as:

α = (1-A71) × A72 × A73 × (1-A74) × A75,
β = A71 × (1-A72) × A73 × {A74 × (1-A74) + (1-A74) × A75} + A72 × {(1-A71) × A73 × A74 × (1-A75) + A71 × ( 1-A73) × (1-A74) × A75},
δ = A71 × A72 × (1-A73) × A74 × (1-A75),
γ = A71 × A72 × A73 × A74 × A75 × {1+ (1-A71) / A71 + (1-A72) / A72 + (1-A73) / A73 + (1-A74) / A74 + (1-A75) / A75}

  For type 8, it is given as

α = (1-A71) × A72 × A73 × (1-A74) × A75,
β = A71 × (1-A72) × A73 × {(1-A74) × A75 × A76 + A74 × (1-A75) × A76 + A74 × A75 × (1-A76)} + A71 × A72 × (1-A73) × A76 × {A74 × (1-A75) + (1-A74) × A75} + (1-A71) × A72 × A73 × A74 × {(1-A75) × A76 + A75 × (1-A76)},
δ = A71 × A72 × (1-A73) × A74 × A75 × (1-A76),
γ = A71 × A72 × A73 × A74 × A75 × A76 × {1+ (1-A71) / A71 + (1-A72) / A72 + (1-A73) / A73 + (1-A74) / A74 + (1-A75) / A75 + (1-A76) / A76}

  The degeneracy formula and correction coefficient formula when the number of K nodes is 2 in type 6 are as follows.

A71 ′ = {A72 + A71 × (1−A72) × A73 × A74} / Ω,
Ω = A72 + A71 × (1-A72) × A73

  Further, in Non-Patent Document 2, as shown in FIG. 8, a node of degree 1 (when a node is connected to d links, d is called the order of that node) (hereinafter referred to as the order of the node) is reduced. , Referred to as “Degree-1 reduction” technology. This is done before performing another degeneration.

  If the node of degree 1 is not a K node, the availability factor does not change even if the link connected to that node is removed. If the node of degree 1 is a K node, a correction coefficient Ω composed of “Ω = Aj” is added to the operation rate of the communication network after the removal. Here, “j” is a link number connected to a node of degree 1.

  In the degeneration of FIG. 1, it can be easily understood that the link 3 can be removed originally by “order 1 degeneration”. Nevertheless, in the description of degeneration in FIG. 1, the example of “parallel degeneration” is shown first without using “order 1 degeneration” in order to make it easier to understand the introduction of degeneration. In actual calculation, the simplest degeneration, “Degeneration of degree 1”, is first performed. Hereinafter, it is assumed that degeneration is performed in this order.

  When the communication network has a serial structure, a parallel structure, and an order 1 structure due to these degenerations (parallel, serial, degree 2 reduction, order 1 reduction), the operating rate can be obtained. However, in other cases, for example, in the case of the configuration of the communication network shown in FIG. 9, it is not easy to obtain the operating rate only by the above-described degeneration.

  In such a case, for example, as described in Non-Patent Document 3 and Patent Document 1, a technique called delta-star conversion is used.

  For example, as shown in FIG. 10, this technique is a degenerate technique in which a triangular structure is replaced with a star-shaped structure. Strictly speaking, the delta-star conversion cannot accurately store the availability. In addition, by giving a certain correction coefficient, the operating rate before conversion cannot be accurately obtained from the operating rate after conversion. However, it is effective as an approximation method.

  The normal probabilities (A101 'to 103') of the links 101 'to 103' after conversion by the delta-star conversion are given by the following equations.

A101 ′ = (W1 × W2 × W3) ^1/2 / W1,
A102 ′ = (W1 × W2 × W3) ^1/2 / W2,
A103 ′ = (W1 × W2 × W3) ^1/2 / W3

  Here, W1, W2, and W3 are defined by the following equations.

W1 = A101 + A102 × A103−A101 × A102 × A103,
W2 = A102 + A103 × A101−A101 × A102 × A103,
W3 = A103 + A101 × A102−A101 × A102 × A103

  If the communication network cannot be transformed into one link using the degeneration method described above, a technique called a decomposition method is used. This technology disassembles the communication network into two communication networks in a certain way (the disassembled communication network is a little smaller in size), and calculates the pre-disassembly according to a certain formula from the operation rate of the disassembled communication network. This is a technique for calculating the operation rate of a communication network. The operation rate of the communication network after disassembly is obtained by degeneration. If it is not obtained by degeneration, further decomposition and degeneration may be repeated.

  The efficiency of this technique depends on the efficiency of the degeneration method used together. Therefore, the degeneration method is the basis of an efficient communication network operation rate calculation technique. Since details of the decomposition method are described in detail in Non-Patent Document 4, description thereof is omitted here.

  As described above, in these conventional techniques, the operation rate in the communication network can be calculated by the degeneration method. However, these conventional techniques do not disclose specific techniques used for evaluating the failure frequency.

  The failure frequency in the communication network cannot be obtained only by the normal probability of the link, but two parameters, the normal probability of the link and the link failure rate (reciprocal of the average time from recovery from failure to failure again). Is necessary, and the execution of the degeneration is complicated. For example, in Non-Patent Document 5, although the theoretical possibility is implied, the realistic procedure is unsolved. Met.

Japanese Patent Publication No. 7-71150 A. Satyaranayana, “A linear-time algorithm for computing K-terminal reliability in series-parallel networks”, SIAM J. Computing. Vol. 14, 1985, pp. 818-832 L.B.Page, J.E.Pellen, "A practical implementation of the factoring theorem for network reliability", IEEE Trans.Reliability, R-37, 1988, pp.259-267 S.D.Wang, C.H, Sun, “Transformatioin of star-delta & delta-star conversion reliability networks”, IEEE Trans.Reliability, R-45, 1996, pp.120-126 R.K.Wood, “Factoring algorithm for computing K-terminal network reliability,” IEEE Trans.Reliability vol. R-35, 1986, pp.269-278 Hayashi, Abe, “Algorithm conversion method from operation rate to failure frequency”, IEICE Technical Committee, CQ 2004, 2004, pp. 7-12

  The problem to be solved is that the conventional technique can only calculate the operation rate in the communication network by the degeneration method, and does not disclose a specific technique used for evaluating the failure frequency.

  In other words, the failure frequency in the communication network cannot be obtained only by the normal probability of the link, but is a normality probability of the link and a link failure rate (reciprocal of the average time from recovery from failure to failure again). Since two parameters are required and the two parameters are handled, the execution of degeneration is complicated. For example, in Non-Patent Document 5, a theoretical possibility is implied, but a realistic procedure is as follows: It was unsolved.

  The object of the present invention is to solve these problems of the prior art and to efficiently calculate the failure frequency.

  In order to achieve the above object, the present invention provides a specific configuration when a network configuration of a communication network includes nodes (points) and links (lines), and each link has a normal probability and a failure rate. Average number of times per unit time that communication between K nodes (2 ≦ K ≦ number of all nodes constituting the network) is interrupted (hereinafter referred to as failure frequency. On the other hand, the probability that communication between K nodes can be ensured is activated. In order to derive the communication network data and the reliability data of each link are input and stored in the physical medium as communication network data, the data representing the partial structure of the communication network is obtained. By executing a simple operation (degeneration), calculating the failure frequency related to the communication network data before simplification from the simplified network data obtained after the operation, and further repeating the reduction From the network data finally obtained Begin to calculate the fault frequency related to the inputted network data. At this time, the decrement communication network data and the correction coefficient are calculated from the communication network data of the degeneration network using a matrix form including link normal probability, 0, link failure frequency, and link normal probability. Execute. Further, focusing on the parallel structure of links and the number of links adjacent to each node (hereinafter referred to as the order), in the case of order 1, in the case of order 2, and in the case of order 2, a serial triangle The structure corresponding to the quadrangular and pentagon is discriminated and classified, and an operation procedure determined for each of the classified structures is executed. Further, when a degeneration is performed in which a node of degree 1 is discriminated and the node and a link adjacent to the node are deleted, a correction coefficient in a matrix format for calculating a failure frequency before the degeneration from communication network data after the degeneration Is calculated. Further, when the parallel structure is discriminated and the degeneracy in which two links of the parallel structure are replaced with one link is realized, the reliability data of the replaced link is determined in a matrix form. Further, by determining the node of degree 2, and searching for the order of the node connected to the node, and the order of the node connected to the node, and confirming the connection relation of the searched nodes, The link after degeneration when the partial structure corresponding to the square, quadrilateral, and pentagon is identified, and the partial structure corresponding to the series, quadrilateral, quadrilateral, and pentagon is replaced with a simpler structure. Reliability data is determined in a matrix format, and correction coefficients are determined in a matrix format. Further, by repeatedly applying the rewriting of the communication network data corresponding to the degeneration, the communication network data indicating the state in which the communication network data is finally made into one link is acquired, and the link of the link read from the communication network data is acquired. The failure frequency of the communication network is derived by obtaining the failure frequency of the communication network before degeneration from the failure frequency and normal probability.

  According to the present invention, an equation used in the degeneration method, which is a calculation method that has been used to calculate the operation rate of a conventional communication network, can be used as a failure frequency calculation by converting it in a matrix format. Since the degeneracy method is a very efficient method, the present invention makes it possible to calculate the failure frequency at a very high speed.

  The best mode for carrying out the present invention will be described below.

  In this example, unlike the calculation of the operation rate used in the conventional degeneration, it is assumed that the normal probability Ai and the failure rate λi are given to the link i in advance. Further, a matrix Mi represented by the following “Equation 1” is defined.

Then, the following processes (1) to (3) are executed in the degeneration of the operation rate described in the related art.
Process (1): The matrix Mi is made to correspond to each link i as a parameter.
Process (2): In all degenerations, the normal probability Ai in the link operation rate calculation formula and the correction coefficient formula is replaced with the matrix Mi.
Process (3): All sum / product quotients and powers are replaced with sum / product quotients and powers in the sense of a matrix. However, the operation Mi1 / Mj2 for dividing the matrix Mi1 by the matrix Mj2 means the product of the inverse matrix of Mi1 and Mj2.

  Specifically, the link utilization rate calculation formula and the correction coefficient formula in each degeneration are as follows. Note that α ′, β ′, γ ′, δ ′, and Ω ′ mean a matrix in the following expression.

For parallel degeneracy:
M1 ′ = M1 + M2−M1 × M2

In case of series:
M1 ′ = M1 × M2

For degree 2 reduction:
Type 1 is given by the following equation.
M1 ′ = M1 × M2 / (M1 + M2−M1 × M2),
Ω ′ = M1 + M2−M1 × M2

Types 2 to 4 are given by the following equations.
M1 ′ = δ ′ / (α ′ + δ ′),
M2 ′ = δ ′ / (β ′ + δ ′),
Ω ′ = (α ′ + δ ′) × (β ′ + δ ′) / δ ′

  The parameters appearing in these equations are given by the following equations for type 2 and type 3.

α ′ = (1-M1) × M2 × (1-M3),
β ′ = M1 × (1-M2) × (1-M3),
δ '= M1 * M2 * M3 * {1+ (1-M1) / M1 + (1-M2) / M2 + (1-M3) / M3}

For type 4, it is given by
α ′ = M1 × (1-M1) × (1-M3) × M4 + (1-M1) × M2 × M3 × (1-M4) + (1-M1) × M2 × (1-M3) × M4
β ′ = M1 × (1-M2) × M3 × (1-M4),
δ ′ = M1 × M2 × M3 × M4 × {1+ (1-M1) / M1 + (1-M2) / M2 + (1-M3) / M3 + (1-M4) / M4}

  Type 5 to type 8 (except in type 6 when the number of K nodes is 2) is as follows.

M1 ′ = γ / (α + γ),
M2 ′ = γ / (β + γ),
M3 ′ = γ / (δ + γ),
Ω = (α + γ) × (β + γ) × (δ + γ) / γ ²

The parameters appearing in these equations are given for type 5 as follows:
α ′ = (1-M1) × M2 × (1-M3) × M4
β ′ = M1 × (1-M2) × (1-M3) × M4 + (1-M1) × M2 × M3 × (1-M4),
δ ′ = M1 × (1-M2) × M3 × (1-M4),
γ ′ = M1 × M2 × M3 × M4 × {1+ (1-M1) / M1 + (1-M2) / M2 + (1-M3) / M3 + (1-M4) / M4},

Type 6 is given as follows.
α ′ = (1−M1) × M2 × M3 × (1-M4),
β ′ = M1 × (1-M2) × M3 × (1-M4),
δ ′ = M1 × M2 × (1-M3) × (1-M4),
γ ′ = M1 × M2 × M3 × M4 × {1+ (1-M1) / M1 + (1-M2) / M2 + (1-M3) / M3 + (1-M4) / M4}

For type 7, it is given as:
α ′ = (1−M1) × M2 × M3 × (1-M4) × M5
β ′ = M1 × (1-M2) × M3 × {M4 × (1-M5) + (1-M4) × M5} + M2 × {(1-M2) × M3 × M4 × (1-M5) + M1 × (1-M3) × (1-M4) × M5},
δ ′ = M1 × M2 × (1-M3) × M4 × (1-M5),
γ '= M1 * M2 * M3 * M4 * M5 * {1+ (1-M1) / M1 + (1-M2) / M2 + (1-M3) / M3 + (1-M4) / M4 + (1-M5) / M5 }

The type 8 is given as follows.
α ′ = (1−M1) × M2 × M3 × (1-M4) × M5
β '= M1 * (1-M2) * M3 * {(1-M4) * M5 * M6 + M4 * (1-M5) * M6 + M4 * M5 * (1-M6)} + M1 * M2 * {(1-M3) * M6 * {M4 * (1-M5) + (1-M4) * M5} + (1-M1) * M2 * M3 * M4 * {(1-M5) * M6 + M5 * (1-M6)},
δ ′ = M1 × M2 × (1-M3) × M4 × M5 × (1-M6),
γ ′ = M1 × M2 × M3 × M4 × M5 × M6 × {1+ (1-M1) / M1 + (1-M2) / M2 + (1-M3) / M3 + (1-M4) / M4 + (1-M5) / M5 + (1-M6) / M6}

For type 6 and the number of K nodes is 2, it is given as follows.
M1 ′ = {M2 + M1 × (1−M2) × M3 × M4} / Ω,
Ω ′ = M2 + M1 × (1−M2) × M3

For degree 1 reduction:
If the node of degree 1 is a K node, the correction coefficient Ω “Ω ′ = Mj” is given.

For delta-star conversion:
M1 ′ = (W′1 × W′2 × W′3) ^1/2 / W′1,
M2 ′ = (W′1 × W′2 × W′3) ^1/2 / W′2,
M3 ′ = (W′1 × W′2 × W′3) ^1/2 / W′3

Here, W′1, W′2, and W′3 are matrices defined by the following equations.
W′1 = M1 + M2 × M3−M1 × M2 × M3
W′2 = M2 + M3 × M1-MI × M2 × M3
W'3 = M3 + M1 * M2-M1 * M2 * M3

  For each degeneration, equations using specific matrix display instead of Mi are shown in Equations 2 to 13.

  If all the formulas appearing in the procedure for calculating the operating rate are replaced with the above formulas, a matrix of 2 rows and 2 columns can be obtained by the same degeneration procedure. The (2, 1) component of the obtained matrix is the communication network failure frequency.

For example, in the case of FIG. 4, based on the degeneration of FIG.
Occupancy rate = (A1 + A2-A1 * A2) * [A1 * A2 / (A1 + A2-A1 * A2) + A3- {A1 * A2 / (A1 + A2-A1 * A2)} * A3]
However, in the case of failure frequency, the following equation 14 is obtained.

The failure frequency of the communication network in this case is
Failure frequency = A1 × A2 × (λ1 + λ2) + A2 × A3 (λ2 + λ3) + A3 × A1 × (λ2 + λ3) −2 × A1 × A2 × A3 × (λ1 + λ2 + λ3)

  By the above processes (1), (2), and (3), it is shown that the (2, 1) component of the matrix of the degeneracy calculation result is the failure frequency of the communication network. Here, the fact described in Non-Patent Document 5 already known is applied.

  For the sake of explanation, the following definitions are introduced. Here, it is assumed that the total number of links in the communication network is N, and numbers 1, 2,..., N are assigned to the links.

Definition 1:
D is a mapping from the whole function X having A1, A2,..., An as variables to the whole function Y having A1, A2,..., An, λ1, λ2,. To do.

For any X element f, g,
D (Ai) = Ai × λi,
D (f + g) = D (f) + D (g),
D (f × g) = D (f) × g + fD (g)
Holds.

Definition 2:
ψ is a mapping from the entire function X having variables A1, A2,..., An to the entire matrix of 2 rows and 2 columns Z, and satisfies the condition expressed by the following equation (15).

  Non-Patent Document 5 described above shows the following properties.

Property 1: D and ψ exist.
Property 2: For any two elements f and g of X, the following operation is established.

ψ (f + g) = ψ (f) + ψ (g),
ψ (f−g) = ψ (f) −ψ (g),
ψ (f × g) = ψ (f) × ψ (g),
ψ (f / g) = ψ (f) / ψ (g)

  Here, “ψ (f) / ψ (g)” means the product of the matrix ψ (f) and “inverse matrix of ψ (g)”.

  Property 3: If f0 is a function representing the operation rate of the communication network, D (f0) is a function representing the failure frequency in the following equation (16).

  Even if the operation rate is determined by degeneration, it is merely the function f0 representing the operation rate obtained by repeating the calculation of the sum / difference product quotients of A1, A2,. It is an elementary mathematical fact that is required by repeated quotients.

  Therefore, as shown in the following equation 17, if Mi = ψ (Ai) (definitions 1 and 2 are used), the above processes (1) to (3) are applied to perform degeneration. From the property 2, it can be seen that the obtained function is the following formula 18.

Here, the processing (1) to (3) is posted again for easy understanding.
Process (1): The matrix Mi is made to correspond to each link i as a parameter.
Process (2): In all degenerations, normal probability Ai in the equation for obtaining the operation rate is replaced with Mi.
Process (3): All sum / difference products and power operations are replaced with sum / difference products and powers in the sense of a matrix.

  From the property 3, the (2,1) component of the obtained matrix represents the failure frequency.

  Embodiments of the present invention will be described below with reference to the drawings. FIG. 11 is a block diagram showing a configuration example of a communication network failure frequency calculation apparatus according to the present invention, and FIG. 12 shows a communication network to be subjected to communication network failure frequency calculation processing by the communication network failure frequency calculation apparatus in FIG. FIG. 13 is a block diagram illustrating a detailed configuration example of the degeneration unit in FIG. 11, and FIG. 14 is an explanatory diagram illustrating an operation example of degeneration of the communication network by the communication network failure frequency calculation apparatus in FIG. 15 is an explanatory diagram illustrating an example of a chain structure of a communication network to be degenerated by the communication network failure frequency calculation apparatus in FIG. 11, and FIG. 16 is an explanatory diagram illustrating a first data structure example stored in the storage unit in FIG. 17 is an explanatory diagram illustrating a second data structure example stored in the storage unit in FIG. 11. FIG. 18 is an explanatory diagram illustrating a third data structure example stored in the storage unit in FIG. In FIG. FIG. 20 is an explanatory diagram illustrating a fifth data structure example stored in the storage unit in FIG. 11, and FIG. 21 is a memory unit in FIG. It is explanatory drawing which shows the 6th data structure example.

  The communication network failure frequency calculation device in FIG. 11 has a computer configuration including a CPU (Central Processing Unit), a main storage device (main memory), a display device, an input device, an external storage device, a peripheral device, etc. After installing the program and data recorded in a storage medium such as a CD-ROM via the optical disk drive of the external storage device into the external storage device, each program is read from the external storage device into the main memory and processed by the CPU. The function of the department is executed.

  That is, the communication network failure frequency calculation apparatus in FIG. 11 performs degeneration processing on the storage unit 1104 and auxiliary storage unit 1103 that store data representing the shape of the communication network and data necessary for failure frequency calculation, and the data. Degeneration unit 1107, matrix processing unit 1106 for performing necessary matrix operations, input device 1101 including a keyboard and mouse, display display unit 1108, display memory 1109, output device 1102 including CRT, and data input / output processing A control unit 1105 that controls processing of each processing unit is included.

  First, the storage unit 1104 will be described, and further the processing function of the degeneration unit 1107 and the function of the control unit 1105 that controls the whole will be described.

  The structure of the data stored in the storage unit 1104 is shown in FIG. Each numerical value in FIG. 16 is a virtual value as an example. In FIG. 16, each row corresponds to a link, and the component of each row corresponds to the link number of the link, the connection node number, the probability that the link is normal (normal probability), and the failure frequency of the link.

  Here, the link failure frequency and failure rate are different concepts, but the relationship of “link failure frequency = link normal probability × link failure rate” is known.

  The technology of this example obtains the communication network failure frequency from the normality probability and failure rate of the link. However, in order to simplify the explanation, in this example, the input failure frequency is stored in the storage unit 1104. The link failure rate is converted into the link failure frequency by the above equation and input (implementation of the above conversion is simple and executed by the matrix processing unit).

  Further, as shown in FIG. 16, the storage unit 1104 also secures data specifying the K node. The failure frequency to be obtained is the failure frequency at which the K nodes are disconnected.

  The data input as an example in FIG. 16 corresponds to the communication network having the configuration shown in FIG. In FIG. 12, 121a to 125a are node numbers, and 121 to 125 are link numbers.

  The auxiliary storage unit 1103 stores given data in a matrix form of 2 rows and 2 columns.

  The matrix processing unit 1106 has two functions of “matrix generation” and “matrix operation”. In the matrix generation function, when an operation rate or link existence probability a and a failure rate λ are given as inputs, Data in a matrix format shown in the following Expression 19 is output. Conversely, when a matrix of the form shown in Equation 19 is input, values of existence probability a and failure rate λ are output.

  In the matrix operation function, when the following two matrices shown in Equation 20 are given, the operation shown in Equation 21 is performed.

  However, the calculation of the last line in [Expression 21] is actually calculated as shown in Expression 22 below.

  Further, in the matrix calculation function, the following calculation 23 can be performed. This can be easily realized by changing the procedure for obtaining the square root of x in the normal data x in one variable format to a matrix.

  The degeneration unit 1107 includes, as basic devices, a node counter, a device that counts the degree of each node (the number of links connected to each node), a degree 1 degeneration execution device that executes degree 1 degeneration, and a degree 2 A serial degeneration execution device that executes serial degeneration for two links connected to a node that is not a K node, a parallel degeneration execution device that executes parallel degeneration for two links in a parallel configuration, and a type 1 degree 2 degeneration Type 1 degenerate execution device, type 2 degenerate execution value for executing type 2 degeneration 2 type, type 3 degenerate execution device for executing type 3 degeneration 2 and type 4 degenerate execution for executing type 4 degeneration 2 Apparatus, type 5 reduction execution device for executing type 5 order 2 reduction, type 6 reduction execution device for executing type 6 reduction of order 2, reduction of order 2 of type 7 Having a star conversion execution device - type 7 degenerate execution device for executing, type 8 degenerate execution device for executing the order 2 degeneracy of type 8, delta - delta to perform the star transformation.

  Regarding the device that counts the node counter and the degree of each node (the number of links connected to each node), the implementation method and configuration of these devices have already been reported in Patent Document 1. In addition, although the failure frequency is not dealt with in patent document 1, the one part apparatus of this patent document 1 is utilized for a part of this example.

  As shown in FIG. 13, each degeneration execution device collects data from the storage unit 1104, uses the functions of the matrix processing unit 1106, performs each degeneration operation, and rewrites data in the storage unit 1104. 131 and a temporary storage device 132 that temporarily stores numerical values necessary for calculation. The data structure in the temporary storage device 132 is a matrix with 2 rows and 2 columns.

  The processing procedure of the degeneration control device 131 of each degeneration execution device will be described below. Note that all matrix operations used in each processing procedure are executed using the matrix processing unit 1106.

First, the processing procedure of the degeneration control device of the order 1 degeneration execution device will be described.
A node number of degree 1 is extracted from the data in the storage unit 1104 using a node counter. The following operations are performed for each of the extracted nodes (hereinafter represented by n).

“If If n is not a K node, erase all the data in the row containing the node n.
Else (if n is a K node) Erase all data in a row containing node n. However, when the link normal probability of the link i connected to n is Ai and the failure rate is λi, the matrix shown in the following Expression 24 is stored in the temporary storage device 132.

Next, the processing procedure of the serial degeneration execution device will be described.
First, the serial structure is determined by the following procedure.
Procedure 1: A node number of degree 2 is extracted from the data in the storage unit 1104 using a node counter.
Procedure 2: Two links connected to each of the extracted nodes (hereinafter referred to as n) are extracted from the data in the storage unit 1104 and are denoted as L (1) and L (2), respectively.

Procedure 3: A node that is connected to the link L (1) and is not n is extracted from the data in the storage unit 1104 and is defined as n (1).
Procedure 4. A node that is connected to the link L (2) and is not n is extracted from the data in the storage unit 1104 and is defined as n (2).
Procedure 5: If the node n is not a K node, the serial structure can be discriminated and the procedure is terminated.

  If the serial structure can be determined, the lines corresponding to the link L (1) and the link L (2) are deleted from the data in the storage unit 1104, and a new line determined as follows is added to the data in the storage unit 1104.

Link number: L (1).
Connection node number: n (1), n (2).
Link normal probability: A value obtained from the serial degeneracy equation shown in the embodiment of the present invention.
Link failure frequency: A value obtained from the serial degenerative equation shown in the embodiment of the present invention.

  Further, the matrix data represented by the following formula 25 is stored in the temporary storage device.

Next, the processing procedure of the parallel degeneration execution device will be described.
First, the parallel structure is determined by the following procedure.
Procedure 1: The pair of connection nodes of each link is checked from the data in the storage unit 1104.
Procedure 2: If the pair of connection nodes of the two links completely matched, the parallel structure could be determined.

  If the parallel structure can be determined, the row corresponding to one link is deleted, and the normal probability and failure frequency of the other link are rewritten using the parallel degeneracy formula shown in the embodiment of the present invention. Note that the matrix processing unit 1106 is used for this rewriting operation. Then, the matrix data represented by the above formula 25 is stored in the temporary storage device 132.

Next, a processing procedure of the type 1 degeneration execution device will be described.
First, the type 1 structure is determined by the following procedure.
Procedure 1: A node number of degree 2 is extracted from the data in the storage unit 1104 using a node counter.
Procedure 2: Two links connected to each of the extracted nodes (hereinafter referred to as n) are extracted from the data in the storage unit 1104 and are denoted as L (1) and L (2), respectively.

Procedure 3: A node that is connected to the link L (1) and is not n is extracted from the data in the storage unit 1104 and is defined as n (1).
Procedure 4: A node that is connected to the link L (2) and is not n is extracted from the data in the storage unit 1104 and is set as n (2).
Procedure 5: If n, n (1), and n (2) are all K nodes, the type 1 structure has been determined and the procedure is terminated.

  If the type 1 structure can be determined, the rows corresponding to the link L (1) and the link L (2) are deleted from the data in the storage unit 1104, and a new row determined as follows is added.

Link number: L (1).
Connection node number: n (1), n (2).
Link normal probability: It is obtained from the type 1 degeneration shown in the embodiment of the present invention.
Link failure frequency: obtained from the type 1 degeneration shown in the embodiment of the present invention.

  Then, the value of the matrix Ω ′ obtained from the type 1 correction coefficient equation shown in the embodiment of the present invention is stored in the temporary storage device 132.

Next, the processing procedure of the type 2 degeneration execution device will be described.
First, the type 2 structure is determined by the following procedure.
Procedure 1: A node number of degree 2 is extracted from the data in the storage unit 1104 using a node counter.
Procedure 2: Two links connected to each of the extracted nodes (hereinafter referred to as n) are extracted from the data in the storage unit 1104 and are defined as L (1) and L (2), respectively.
Procedure 3: A node that is connected to the link L (1) and is not n is extracted from the data in the storage unit 1104 and is defined as n (1).

Procedure 4: A node that is connected to the link L (2) and is not n is extracted from the data in the storage unit 1104 and is set as n (2).
Procedure 5: A link connected to n (1) and n (2) is searched from the data in the storage unit 1104. If there is a link, L (3) is set.
Procedure 6: If only the node n is a K node, the type 2 structure has been determined, and the procedure is terminated.

  If the type 2 structure can be determined, the line corresponding to the link L (3) is deleted from the data in the storage unit 1104, and the following operation is performed.

The normality probability and failure frequency of L (1) are rewritten to values obtained from the type 2 degeneracy equation shown in the embodiment of the present invention.
The normal probability and failure frequency of L (2) are rewritten to values obtained from the above type 2 degenerative equation.

  The temporary storage device 132 stores the value of Ω ′ obtained from the type 2 correction coefficient equation shown in the embodiment of the present invention.

Next, a processing procedure of the type 3 degeneration execution device will be described.
First, the type 3 structure is determined by the following procedure.
Procedure 1: A node number of degree 2 is extracted from the data in the storage unit 1104 using a node counter.
Procedure 2: Two links connected to each of the extracted nodes (hereinafter referred to as n) are extracted from the data in the storage unit 1104 and are denoted as L (1) and L (2), respectively.

Procedure 3: A node that is connected to the link L (1) and is not n is extracted from the data in the storage unit 1104 and is defined as n (1).
Procedure 4: A node that is connected to the link L (2) and is not n is extracted from the data in the storage unit 1104 and is set as n (2).

Procedure 5: A link connected to n (1) and n (2) is searched from the data in the storage unit 1104. If there is a link, L (3) is set.
Procedure 6: If the nodes n and n (1) are K nodes and n (2) is not a K node, the type 3 structure can be determined.
Procedure 7: If the nodes n and n (2) are K nodes and n (1) is not a K node, the type 3 structure can be determined, and the procedure is terminated.

  If the type 3 structure can be determined in this way, the row corresponding to the link L (3) is deleted from the data in the storage unit 1104, and the following operation is performed.

The normality probability and failure frequency of L (1) are rewritten to values obtained from the type 3 degeneracy equation shown in the embodiment of the present invention.
The normality probability and failure frequency of L (2) are rewritten to values obtained from the above type 3 degeneracy equation.

  The temporary storage device 132 stores the value of Ω ′ obtained from the type 3 correction coefficient equation shown in the embodiment of the present invention.

Next, the processing procedure of the type 4 degeneration execution device will be described.
First, the type 4 structure is determined by the following procedure.

Procedure 1: A node number of degree 2 is extracted from the data in the storage unit 1104 using a node counter.
Procedure 2: Two links connected to each of the extracted nodes (hereinafter referred to as n) are extracted from the data in the storage unit 1104 and are denoted as L (1) and L (2), respectively.

Procedure 3: A node that is connected to the link L (1) and is not n is extracted from the data in the storage unit 1104 and is defined as n (1).
Procedure 4: A node that is connected to the link L (2) and is not n is extracted from the data in the storage unit 1104 and is set as n (2).

Procedure 5: A node of degree 2 connected to n (1) and n (2) is searched from the data in the storage unit 1104 (excluding n), and if it exists, it is set as n (3).
Procedure 6: If the nodes n, n (1), and n (3) are K nodes and n (2) is not a K node, the type 4 structure can be determined.
Procedure 7: If the nodes n, n (2), and n (3) are K nodes and n (1) is not a K node, the type 4 structure can be determined, and the procedure ends.

  If the type 4 structure can be determined in this way, the row corresponding to the link connected to the node n (3) is deleted from the data in the storage unit 1104, and the following operation is performed.

The normality probability and failure frequency of L (1) are rewritten to values determined from the type 4 degenerative equation shown in the embodiment of the present invention.
The normal probability and failure frequency of L (2) are rewritten to values determined from the above type 4 degeneracy.

  The temporary storage device 132 stores the value of Ω ′ obtained from the type 4 correction coefficient equation shown in the embodiment of the present invention.

Next, the processing procedure of the type 5 degeneration execution device will be described.
First, the type 5 structure is determined by the following procedure.

Procedure 1: A node number of degree 2 is extracted from the data in the storage unit 1104 using a node counter.
Procedure 2: Two links connected to each of the extracted nodes (hereinafter referred to as n) are extracted from the data in the storage unit 1104 and are denoted as L (1) and L (2), respectively.

Procedure 3: A node that is connected to the link L (1) and is not n is extracted from the data in the storage unit 1104 and is defined as n (1).
Procedure 4: A node that is connected to the link L (2) and is not n is extracted from the data in the storage unit 1104 and is set as n (2).

Procedure 5: A node of degree 2 connected to n (1) and n (2) is searched from the data in the storage unit 1104 (excluding n), and if it exists, it is set as n (3).
Step 6: If the nodes n and n (3) are not K nodes and the n (1) and n (2) are not K nodes, the type 5 structure has been determined, and the procedure ends.

  If the type 5 structure can be determined in this way, the rows corresponding to the links connected to the links L (1), L (2), and n (3) are deleted from the data in the storage unit 1104, and newly Add three rows I-III determined as follows.

Line I:
Link number: L (1).
Connection node number: n (1), n.
Link normal probability: A value determined from the type 5 degeneracy formula shown in the embodiment of the present invention.
Link failure frequency: A value determined from the type 5 degeneracy formula.

Line II:
Link number: L (2).
Connection node number: n, n (3).
Link normal probability: A value determined from the above type 5 degeneracy formula.
Link failure frequency: A value determined from the type 5 degeneracy formula.

Line III:
Link number: L (3).
Connection node number: n (3), n (2).
Link normal probability: A value determined from the above type 5 degeneracy formula.
Link failure frequency: A value determined from the type 5 degeneracy formula.

  Here, n (1), n, n (2) are designated as K nodes.

  Then, the temporary storage device 132 stores the value of Ω ′ obtained from the type 5 correction coefficient equation shown in the embodiment of the present invention.

Next, a processing procedure in the type 6 degeneration execution device will be described.
First, the type 6 structure is determined by the following procedure.

Procedure 1: A node number of degree 2 is extracted from the data in the storage unit 1104 using a node counter.
Procedure 2: Two links connected to each of the extracted nodes (hereinafter referred to as n) are extracted from the data in the storage unit 1104 and are defined as L (1) and L (2), respectively.

Procedure 3: A node that is connected to the link L (1) and is not n is extracted from the data in the storage unit 1104 and is defined as n (1).
Procedure 4: A node that is connected to the link L (2) and is not n is extracted from the data in the storage unit 1104 and is set to n (2).

Procedure 5: If the order of n (1) is 2, there is one node (not n) connected to n (1), and that node is n (3). A link connecting n (1) and n (3) is L (3). Otherwise, go to step 7.
Procedure 6: A link L (4) connecting n (2) and n (3) exists, and n and n (1) are not K nodes, and n (2) and n (3) are not K nodes. Since the type 6 structure has been determined, the procedure is terminated.

Procedure 7: If the order of n (2) is 2, there is one node (not n) connected to n (2), and that node is n (3). Let L (3) be the link connecting n (2) and n (3).
Procedure 8: A link L (4) connecting n (1) and n (3) exists, and n and n (2) are not K nodes, and n (1) and n (3) are not K nodes. Since the type 6 structure has been determined, the procedure is terminated.

  In this way, if the type 6 structure can be determined and the total number of K nodes is 2, the row corresponding to the node of degree 2 and the link connected to them is stored in the storage unit. Delete from 1104 and perform the following operations.

  The normal probability and failure frequency of the link L (4) are rewritten to values determined from the type 6 degeneracy equation shown in the embodiment of the present invention. The temporary storage device 132 stores the value of Ω ′ obtained from the type 2 correction coefficient equation shown in the embodiment of the present invention.

  If the total number of K nodes is not 2, the row corresponding to L (3) in the determined structure is deleted from the storage unit 1104, and the following operation is performed.

  Respective normal probabilities and failure frequencies of the links L (1), L (2), and L (3) are rewritten to values determined from the type 6 degenerative equation shown in the embodiment of the present invention. The temporary storage device 132 stores the value of Ω ′ obtained from the type 6 correction coefficient equation shown in the embodiment of the present invention.

Next, a processing procedure in the type 7 degeneration execution device will be described.
First, the type 7 structure is determined by the following procedure.

Procedure 1: A node number of degree 2 is extracted from the data in the storage unit 1104 using a node counter.
Procedure 2: Two links connected to each of the extracted nodes (hereinafter referred to as “n”) are extracted from the data in the storage unit 1104 and are denoted as L (1) and L (2), respectively.

Procedure 3: A node that is connected to the link L (1) and is not n is extracted from the data in the storage unit 1104 and is defined as n (1).
Procedure 4: A node that is connected to the link L (2) and is not n is extracted from the data in the storage unit 1104 and is set as n (2).

Procedure 5: If the order of n (1) is 2, there is one node (not n) connected to n (1), and that node is n (3). Let L (3) be the link connecting n (1) and n (3). Otherwise, go to step 7.
Procedure 6: There is a node n (4) of degree 2 connected to both n (2) and n (3), n, n (1) and n (4) are K nodes, and n (2) and If n (3) is not a K node, the type 7 structure has been determined and the procedure ends.

Procedure 7: If the order of n (2) is 2, there is one node (not n) connected to n (2), and that node is n (3). Let L (3) be the link connecting n (2) and n (3).
Procedure 8: There exists a node n (4) connected to both n (1) and n (3), n, n (2) and n (4) are K nodes, and n (1) and n (3 ) Is not a K node, the type 7 structure has been determined, and the procedure ends.

  If the type 7 structure can be determined in this way, the rows corresponding to the two links connected to the node n (4) are deleted from the storage unit 1104, and the following operation is performed.

  The normal probability and failure frequency of the link L (4) are determined from the type 7 degeneracy equation shown in the embodiment of the present invention. The temporary storage device 132 stores the value of Ω ′ obtained from the type 7 correction coefficient equation shown in the embodiment of the present invention.

Next, a processing procedure in the type 8 degeneration execution device will be described.
First, the type 8 structure is determined by the following procedure. This first defines the following sub-procedures.

Sub-procedure = chain determination:
Procedure 1: A node number of degree 2 is extracted from the data in the storage unit 1104 using a node counter.
Procedure 2: Two links connected to each of the extracted nodes (hereinafter referred to as n) are extracted from the data in the storage unit 1104 and are defined as L (1) and L (2), respectively.

Procedure 3: A node that is connected to the link L (1) and is not n is extracted from the data in the storage unit 1104 and is defined as n (1).
Procedure 4: A node that is connected to the link L (2) and is not n is extracted from the data in the storage unit 1104 and is set as n (2).

Procedure 5: If the order of n (1) is 2, there is one node (not n) connected to n (1), and that node is n (3). Let L (3) be the link connecting n (1) and n (3). Otherwise, go to step 6.
Procedure 6: If the order of n (2) is 2, there are two nodes (not n) connected to n (2), and that node is n (3). Let L (3) be the link connecting n (2) and n (3).

  Procedure 7: If all the nodes confirmed to be of degree 2 in the above procedure are K nodes and the other two nodes are not K nodes, the structure called “chain” (see FIG. 27) is determined. Is done.

The type 8 structure determination using such a sub-procedure is performed according to the following procedure. Procedure 1: The chain is determined by the sub-procedure.
Procedure 2: When two chains are identified and the chains share two nodes, a type 8 structure is determined.

  If a type 8 structure is confirmed, there should be two chains. The row relating to the link constituting the one chain is deleted from the storage unit 1104, and the following operation is performed.

  The normality probability and failure frequency of the remaining link of the chain are determined from the type 8 degeneracy equation shown in the embodiment of the present invention. The temporary storage device 132 stores the value of Ω ′ obtained from the type 8 correction coefficient equation shown in the embodiment of the present invention.

  Next, a processing procedure in the delta-star conversion execution device will be described. A processing technique for determining a structure to which delta-star conversion can be applied from the storage unit 1104 is described in Patent Document 1.

  If a structure to which the delta-star conversion can be applied is determined by the technique described in Patent Document 1, the conversion is executed, and the normal probability and failure frequency of the link after execution are shown in the embodiment of the present invention. It is determined according to the details of the delta-star conversion. Then, the matrix data represented by Equation 25 is stored in the temporary storage device 132.

  The control unit 1105 in FIG. 11 calculates the failure frequency of the communication network based on the following processing procedure, and displays and outputs it on the screen of the display device via the display display unit 1108 and the display memory 1109. The arithmetic processing is executed by the matrix processing unit 1106.

Procedure 1: N ₀ = number of nodes in the communication network. Let N = 0. The auxiliary storage unit 1103 stores the matrix data expressed by Equation 25 above.
Procedure 2: If N ₀ = N, end. No further reduction is possible.
Step 3: assigns a value of N to _{N 0.}

  Procedure 4: The degree 1 reduction is executed, and the data in the auxiliary storage unit 1103 is rewritten to “already stored data” × “data stored in the temporary storage device 132”.

  Procedure 5: Serial degeneration is executed, and the data in the auxiliary storage unit 1103 is rewritten to “stored data” × “data stored in the temporary storage device 132”.

  Procedure 6: Parallel degeneration is executed, and the data in the auxiliary storage unit 1103 is rewritten to “stored data” × “data stored in the temporary storage device 132”.

  Procedure 7: Type 1 degeneration is executed, and the data in the auxiliary storage unit 1103 is rewritten to “stored data” × “data stored in the temporary storage device 132”.

  Procedure 8: Type 2 degeneration is executed, and the data in the auxiliary storage unit 1103 is rewritten to “already stored data” × “data stored in the temporary storage device 132”.

  Step 9: Type 3 degeneration is performed, and the data in the auxiliary storage unit 1103 is rewritten to “stored data” × “data j stored in the temporary storage device 132.

  Step 10: Type 4 degeneration is performed, and the data in the supplementary storage unit 1103 is rewritten to “already stored data” × “data stored in the temporary storage device 132”.

  Step 11: Type 5 degeneration is performed, and the data in the auxiliary storage unit 1103 is rewritten to “already stored data” × “data stored in the temporary storage device 132”.

  Day 12: Type 6 degeneration is executed, and the data in the auxiliary storage unit 1103 is rewritten to “stored data” × “data stored in the temporary storage device 132”.

  Step 13: Type 7 degeneration is performed, and the data in the auxiliary storage unit 1103 is rewritten to “stored data” × “data stored in the temporary storage device 132”.

  Procedure 14: Type 8 degeneration is performed, and the data in the auxiliary storage unit 1103 is rewritten to “stored data” × “data stored in the temporary storage device 132”.

  Procedure 15: Delta-star conversion is executed, and the data in the auxiliary storage unit 1103 is rewritten to “stored data” × “data stored in the temporary storage device 132”.

  Step 16: Set the number of all nodes after degeneration to N, and return to the processing of step 2.

  Hereinafter, this calculation example will be described by taking the data shown in FIG. 16 and the communication network shown in FIG. 12 as examples.

  When the communication network failure frequency calculation apparatus of this example is used, the data representing the communication network in FIG. 12 is degenerated into one link through the steps shown in FIG.

  The following describes how the data structure of the storage unit 1104 is rewritten by this degeneration process.

  The data shown in FIG. 17 is obtained by applying the degree 1 degeneration at stage 1 in FIG. 14 to the communication network shown in FIG. Here, the first line is simply deleted.

  The data in FIG. 18 is obtained by applying the serial degeneration to the data in FIG. 17, that is, by applying the serial degeneration in step 2 in FIG. 14. The normal probability and the failure frequency of the link 142 shown in FIG. 18 were obtained from the following formula 26 based on the degenerative formula related to serial degeneration.

  The (1,1) component on the right side in the equation 16 is the normal probability, and the (2,1) component is the failure frequency.

  The data in FIG. 19 is obtained by applying the parallel degeneration to the data in FIG. 18, that is, by applying the parallel degeneration in step 3 in FIG. 14. The normal probability and the link failure frequency of the link 146 shown in FIG. 19 were obtained from the following equation 27 based on the parallel degeneracy equation.

  The data in FIG. 20 is obtained by applying the type 1 degree 2 degeneration to the data in FIG. 19, that is, by applying the type 1 degree 2 degeneration in step 4 in FIG. 14. The normal probability and the link failure frequency of the link 144 shown in FIG. 20 are obtained from the following formula 28 based on the degeneracy formula for type 1.

  At this time, the temporary storage device 132 stores data represented by the following formula 29.

  By applying the parallel degeneration again to the data in FIG. 20, that is, by applying the parallel degeneration in step 5 in FIG. 14, the data in FIG. 21 is obtained. The normal probability and the failure frequency of the link 145 shown in FIG. 21 can be obtained from the parallel degeneracy equation by the following equation 30.

  The finally determined failure frequency can be obtained from the obtained data in FIG. 21 and the data stored in the temporary storage device 132 by a matrix operation represented by the following equation (31).

  The (2,1) component of the matrix on the right side in Equation 31 represents the required communication network failure frequency, and its value is “0.00083”.

  As described above with reference to FIGS. 11 to 21, in the communication network failure frequency calculation apparatus of this example, each link is used by using the normal probability and failure rate of each link constituting the communication network. Matrix data including the normal probability of each link given in advance and the product of the normal probability and the failure rate in order to calculate the failure frequency, which is the average number of times per unit time at which communication between nodes connected by Storage unit 1104 for storing, degeneration unit 1107 for performing degeneration for each link between designated nodes, and normality probability in the formula used for calculating the operating rate of the link degenerated by this degeneration unit 1107 in storage unit 1104 The matrix processing unit 1106 that calculates the product of the normal probability and the failure rate of the link that has been degenerated by the degeneration unit 1107, using the expression replaced with the stored matrix data, and the degeneration unit 1107 The product of the normal probability and the failure rate finally obtained by the repetition of the calculation of the product of the normal probability and the failure rate by the degeneration and matrix processing unit 1106 is calculated between the specified nodes before the link reduction operation. And a control unit 1105 that outputs the failure frequency. In particular, in the storage unit 1104, matrix data including the normal probability of each link given in advance and zero (0), the product of the normal probability and failure rate, and the normal probability of the link, more specifically, given in advance The normal probability of each link obtained is stored as the (1,1) component and (2,2) component in the matrix data of 2 rows and 2 columns, and 0 is stored as the (1,2) component of the matrix data. 1) The product of the normal probability and the failure rate is stored as a component. Then, the matrix processing unit 1106 stores the normal probability in the calculation formula of the link operation rate according to each degeneration operation including the parallel degeneration, the serial degeneration, the degree 1 degeneration, and the degree 2 degeneration by the degeneration unit 1107. The product of the normal probability of the link degenerated by the degeneration unit 1107 and the failure rate is calculated using the formula replaced with the matrix data stored in 1104. Further, the matrix processing unit 1106 stores, in the storage unit 1104, the normal probability in the calculation formula of the correction coefficient used for calculating the link operation rate according to the reduction operation of the degree 1 reduction and the order 2 reduction by the reduction unit 1106. The correction coefficient is calculated using the correction coefficient expression replaced with the matrix data.

  Thus, in the communication network failure frequency calculation device of this example, by converting the formula used in the degeneration method, which is a calculation method that has been used to calculate the operation rate of the conventional communication network, in a matrix format. It is used as a failure frequency calculation. Since the degeneracy method is an extremely efficient method, according to this example, the calculation of the failure frequency can be performed very quickly.

  In addition, this invention is not limited to the example demonstrated using FIGS. 11-21, A various change is possible in the range which does not deviate from the summary. For example, in this example, the row example shown in Equation 1 is defined and used, but the arrangement of the normal probability Ai and the failure rate λ is not limited to the row example shown in Equation 1.

  The computer configuration example of this example may also be a computer configuration without a keyboard or optical disk drive. In this example, an optical disk is used as a recording medium, but 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 explanatory drawing which shows the structural example of a serial-parallel communication network. It is explanatory drawing which shows the parallel degeneration operation example with respect to a communication network. It is explanatory drawing which shows the example of serial degeneration operation with respect to a communication network. It is explanatory drawing which shows the structural example of the communication network which cannot apply serial degeneration operation. It is explanatory drawing which shows the example of 2 degree reduction operation with respect to a communication network. It is explanatory drawing which shows the example which applied degree 2 degeneration to the communication network in FIG. It is explanatory drawing which shows the example of an applicable type of order 2 degeneration. It is explanatory drawing which shows the example of 1 degree reduction operation with respect to a communication network. It is explanatory drawing which shows the structural example of the communication network where degeneration is difficult. It is explanatory drawing which shows the delta-star conversion operation example with respect to a communication network. It is a block diagram which shows the structural example of the communication network failure frequency calculation apparatus concerning this invention. It is explanatory drawing which shows the structural example of the communication network used as the object of the communication network failure frequency calculation process by the communication network failure frequency calculation apparatus in FIG. It is a block diagram which shows the detailed structural example of the degeneracy part in FIG. It is explanatory drawing which shows the example of degeneracy operation of the communication network by the communication network failure frequency calculation apparatus in FIG. It is explanatory drawing which shows the example of a chain structure of the communication network of the degeneracy object by the communication network failure frequency calculation apparatus in FIG. It is explanatory drawing which shows the 1st data structure example memorize | stored in the memory | storage part in FIG. It is explanatory drawing which shows the 2nd data structure example memorize | stored in the memory | storage part in FIG. It is explanatory drawing which shows the 3rd data structure example memorize | stored in the memory | storage part in FIG. It is explanatory drawing which shows the 4th example of a data structure memorize | stored in the memory | storage part in FIG. It is explanatory drawing which shows the 5th example of a data structure memorize | stored in the memory | storage part in FIG. It is explanatory drawing which shows the 6th data structure example memorize | stored in the memory | storage part in FIG.

Explanation of symbols

  1-5, 41-43, 51, 51 ', 52, 61, 61', 62, 63, 71, 71 ', 72, 71a-71g, 71a'-71g', 72a-72g, 72a'-72g ' 73a to 73g, 73d 'to 73g', 74c to 74g, 75f to 75g, 76g, 101 to 103, 101 'to 103', 141 to 146: link, 141a to 145a: node, 131: degeneration control device, 132 : Temporary storage device 1101: Input device 1102: Display device 1103: Auxiliary storage unit 1104: Storage unit 1105: Control unit 1106: Matrix processing unit 1107: Degeneration unit 1108: Display display unit 1109: Display memory.

Claims (8)

A device that calculates the failure frequency, which is the average number of times per unit time at which communication between nodes connected by each link is disrupted, using the normal probability and failure rate of each link that constitutes the communication network. And
Storage means for storing matrix data including a normal probability of each link given in advance and a product of the normal probability and the failure rate;
Degeneration means for performing degeneration for each link between specified nodes;
The normal probability and failure rate of the link degenerated by the degeneration means are replaced with the normal probability in the expression used for calculating the operation rate of the link degenerated by the degeneration means by using the matrix data stored in the storage means. Processing means for calculating a product of
The product of the normal probability and the failure rate finally obtained by the reduction of the reduction by the reduction means and the calculation of the product of the normal probability and the failure rate by the processing means is the designation before the link reduction operation. A communication network failure frequency calculation apparatus, comprising: a control unit that outputs the failure frequency between the nodes as described above. A device that calculates the failure frequency, which is the average number of times per unit time at which communication between nodes connected by each link is disrupted, using the normal probability and failure rate of each link that constitutes the communication network. And
Storage means for storing matrix data comprising the normal probability of each link given in advance and zero (0), the product of the normal probability and failure rate, and the normal probability of the link;
Degeneration means for performing degeneration for each link between specified nodes;
The normal probability and failure rate of the link degenerated by the degeneration means are replaced with the normal probability in the expression used for calculating the operation rate of the link degenerated by the degeneration means by using the matrix data stored in the storage means. Processing means for calculating a product of
The product of the normal probability and the failure rate finally obtained by the reduction of the reduction by the reduction means and the calculation of the product of the normal probability and the failure rate by the processing means is the designation before the link reduction operation. A communication network failure frequency calculation apparatus, comprising: a control unit that outputs the failure frequency between the nodes as described above. The communication network failure frequency calculation device according to claim 1 or 2,
The storage means is
The normal probability of each link given in advance is stored as (1,1) component and (2,2) component in the matrix data of 2 rows and 2 columns, and 0 as the (1,2) component of the matrix data, A communication network failure frequency calculation apparatus that stores the product of the normal probability and the failure rate as a (2,1) component. A communication network failure frequency calculation device according to any one of claims 1 to 3,
The processing means includes
The matrix data in which the normal probability in the calculation formula for the link utilization rate corresponding to each reduction operation including parallel reduction, serial reduction, degree 1 reduction, and order 2 reduction by the reduction means is stored in the storage means A communication network failure frequency calculation apparatus that calculates a product of a normal probability and a failure rate of a link that has been degenerated by the degeneration means, using the expression replaced with: The communication network failure frequency calculation device according to any one of claims 1 to 4,
The processing means includes
The normal probability in the calculation formula of the correction coefficient used for calculating the link utilization rate corresponding to each reduction operation of degree 1 reduction and order 2 reduction by the reduction means is replaced with the matrix data stored in the storage means. A communication network failure frequency calculation apparatus comprising means for calculating a correction coefficient using a correction coefficient equation.   The program for making a computer run as each means in the communication network failure frequency calculation apparatus in any one of Claims 1-5. A computer apparatus that calculates a failure frequency that is an average number of times per unit time at which communication between nodes connected by each link is interrupted using a normal probability and a failure rate of each link that constitutes a communication network, which is given in advance. A communication network failure frequency calculation method,
A first procedure for storing in a storage device matrix data including a normal probability of each link given in advance and a product of the normal probability and the failure rate;
A second procedure for performing degeneration for each link between designated nodes;
The normality of the link degenerated in the second procedure is replaced with the normal probability in the equation used to calculate the availability of the link degenerated in the second procedure by the matrix data stored in the storage device. A third procedure for calculating the product of the probability and the failure rate;
The product of the normal probability and the failure rate finally obtained by the repetition of the degeneration in the second procedure and the calculation of the product of the normal probability and the failure rate in the third procedure is used as a link degeneration operation. A communication network failure frequency calculation method, comprising: a fourth procedure for outputting the failure frequency between the designated nodes before performing the operation. A computer apparatus that calculates a failure frequency that is an average number of times per unit time at which communication between nodes connected by each link is interrupted using a normal probability and a failure rate of each link that constitutes a communication network, which is given in advance. A communication network failure frequency calculation method,
A first procedure for storing, in a storage device, matrix data composed of the normal probability of each link given in advance and zero (0), the product of the normal probability and failure rate, and the normal probability of the link;
A second procedure for performing degeneration for each link between designated nodes;
The normality of the link degenerated in the second procedure is calculated using an equation in which the normal probability in the equation used to calculate the availability of the link degenerated in the second procedure is replaced with the matrix data stored in the storage device. A third procedure for calculating the product of the probability and the failure rate;
The product of the normal probability and the failure rate finally obtained by the repetition of the degeneration in the second procedure and the calculation of the product of the normal probability and the failure rate in the third procedure is expressed as a link degeneration operation. And a fourth procedure for outputting as a failure frequency between the designated nodes before performing the communication.

Images