A reliability evaluation method, device and equipment of a binary node multi-state network

Abstract

The application relates to a reliability evaluation method, device and equipment of a binary node multi-state network. The method comprises the following steps: acquiring a network topology, node probability, link capacity distribution and traffic demand; constructing a constraint model of node state to link effective capacity, and forcibly setting the capacity of adjacent links of a failed node to zero; enumerating node state combinations and performing two-stage pruning, first, eliminating combinations in which source or sink nodes fail, then, constructing an induced subgraph for the remaining combinations, and eliminating combinations that are not connected or in which the maximum flow under the maximum capacity is not greater than the demand; performing multi-state minimum cut set search on the remaining induced subgraph, and calculating conditional reliability by using a recursive disjoint sum algorithm; and finally, obtaining global reliability by weighting and accumulating the prior probability and conditional reliability of each combination through a total probability formula. The method can greatly reduce the calculation complexity while keeping the accuracy of full state enumeration, and is suitable for reliability evaluation of large-scale critical infrastructures such as communication networks and power systems.

Description

Technical Field

[0001] This application relates to the technical field, and in particular to a reliability assessment method, apparatus, and device for a binary node multi-state network. Background Technology

[0002] With the continuous expansion of critical infrastructure such as communication networks, power systems, transportation networks, supply chain networks, and computing networks, reliability assessment of complex network systems has become a crucial foundation for system design, operation monitoring, maintenance optimization, and risk decision-making. Unlike traditional two-state networks, multi-state networks (MSNs) can describe the operational capabilities of components under different degradation levels or capacity grades, making them more suitable for characterizing real-world engineering systems.

[0003] In reliability assessment of two-terminal multi-state networks, reliability is typically defined as the probability that a flow of at least the preset required traffic can be successfully transmitted from the source node to the sink node. Existing research primarily employs indirect and direct methods. Direct methods calculate reliability by enumerating the network state vectors and calculating the maximum flow in each state; indirect methods typically first search for the minimum path set vector of the multi-state network (…). d -MP) or multi-state minimum cut set vector ( d -MC), and then obtain reliability through probability union or state space decomposition.

[0004] In classic MSN studies, nodes and components are typically assumed to have similar multi-state properties, and the failure behaviors of each component are independent of each other. Based on this independence, existing methods can use the "node-component equivalence transformation" technique to transfer node reliability to the virtual components connected to them, thereby transforming the hybrid model containing node failures into a pure component failure model.

[0005] However, in scenarios such as large-scale integrated circuits, heterogeneous communication base stations, and distributed computing clusters, nodes often strictly exhibit only two states: normal or failed, and the node's state has a "veto" effect on adjacent components. Once a node fails, the capacity of all components adjacent to that node immediately drops to 0, resulting in a complete blockage of the local transmission channel. This type of network combines the characteristics of binary nodes and multi-state components, and this paper refers to it as a binary node multi-state network (BN-MSN).

[0006] The existing implementations closest to this invention include the following categories: The first type is the probabilistic flow method based on full-state enumeration. This method enumerates all possible component state vectors and calculates the maximum flow for each one, then accumulates the state probabilities that meet the flow requirements, which can obtain accurate results. However, it encounters a severe combinatorial explosion problem when the network scales up.

[0007] The second category is indirect reliability assessment methods based on multi-state minimum path set vectors or multi-state minimum cut set vectors. These methods first search for multi-state minimum path sets or multi-state minimum cut sets, and then calculate the probability union of the corresponding events. While these methods are computationally efficient in traditional multi-state networks, they typically rely on the independence of component states or the equivalence of node-component relationships, making it difficult to handle scenarios where node failure triggers the failure of adjacent components.

[0008] The third category is reliability methods for two-state networks with node failures. These methods address component failure driven by node failures through recursive combination of subnetworks or conceptual mapping. However, their models and solution logic are mainly applicable to binary-state systems and are difficult to directly handle binary-node multi-state networks with multi-state component capacities.

[0009] The existing technology has at least the following shortcomings: First, traditional multi-state network reliability assessment methods generally assume that the states of components are independent of each other. When a node failure causes the capacity of adjacent components to be forced to zero, the states of components become correlated through common endpoint nodes, and the independence assumption no longer holds, leading to a deviation between the assessment results and the actual system behavior.

[0010] Secondly, existing node-component equivalent transformation methods are mostly applicable to two-state networks or situations where node and component failures can be handled independently. For networks with both binary nodes and multi-state components, node failures not only change topological connectivity but also alter the effective capacity of adjacent components, making it difficult for traditional equivalent transformations to maintain model realism.

[0011] Third, the full-state enumeration method requires enumerating combinations of node states and combinations of component states. If the number of nodes is m and the number of components is n, and nodes have two states and components have multiple capacity states, then the total state space grows exponentially with m and n, leading to the "curse of dimensionality" and making it impossible to complete the reliability assessment of large-scale networks within an effective time.

[0012] Fourth, without node state pruning, many node state combinations correspond to subgraphs that do not have source-sink connectivity, or cannot meet flow requirements even at maximum capacity. Continuing to perform multi-state minimum cut set search on these combinations will cause unnecessary computational overhead and severely restrict evaluation efficiency.

[0013] Therefore, how to establish a reliability model that can accurately characterize the mechanism of "node failure leading to adjacent component failure", and effectively reduce the state space enumeration scale and the number of multi-state minimum cut set searches while ensuring the accuracy of reliability calculation, and improve the efficiency of two-end reliability assessment of binary node multi-state networks, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0014] Therefore, it is necessary to provide a reliability assessment method, apparatus, and equipment for binary node multi-state networks that can effectively support quantitative reliability assessment of large-scale complex systems such as communication networks, addressing the aforementioned technical problems.

[0015] A reliability assessment method for a binary node multi-state network, the method comprising: Obtain target data for the binary node multi-state network to be evaluated. The target data includes the communication network topology, the state probability data of each node, the capacity state distribution data of each link, and the traffic transmission demand threshold from the source node to the sink node.

[0016] Based on the target data and the binary state probability data of each node, a constraint model of node state on the effective capacity of the link is constructed. The constraint model is used to set the effective capacity of all links associated with the current node to zero when any node fails, and to maintain the original capacity state of the link when the current node is normal.

[0017] Enumerate the state combinations of each node in the binary node multistate network, and perform first-level pruning on the state combinations based on the state of the source node and the sink node, removing state combinations in which the source node or sink node is in an ineffective state.

[0018] For each state combination that has passed the first-level pruning, construct an inducer subgraph consisting of all current normal nodes and the links between normal nodes. Perform connectivity detection and second-level pruning on the inducer subgraph. After removing the state combinations corresponding to inducer subgraphs where the source node and sink node are not connected, calculate the maximum transmittable flow when all links in each inducer subgraph are at maximum capacity. Remove the state combinations corresponding to inducer subgraphs where the maximum transmittable flow is not greater than the flow transmission demand threshold.

[0019] By using the induced subgraph corresponding to each state combination retained after pruning, the effective capacity state of each link in the induced subgraph is determined based on the capacity state distribution of the links and the constraint results of the node states. A multi-state minimum cut set search is performed on the induced subgraph to obtain the critical link state vectors that satisfy the requirement to cut the traffic transmission capacity between the source node and the sink node. The conditional reliability of the induced subgraph under the traffic transmission demand threshold is calculated using a recursive disjoint sum algorithm.

[0020] The probability of occurrence of each retained state combination is multiplied by the corresponding induced subgraph conditional reliability and then summed to obtain the global reliability evaluation result of the binary node multi-state network under the traffic transmission demand threshold.

[0021] A reliability assessment device for a binary node multi-state network, the device comprising: The data acquisition module is used to acquire target data of the binary node multi-state network to be evaluated. The target data includes the communication network topology, the state probability data of each node, the capacity state distribution data of each link, and the traffic transmission demand threshold from the source node to the sink node.

[0022] The constraint model construction module is used to construct a constraint model of node state on the effective capacity of the link based on the target data and the binary state probability data of each node. The constraint model is used to set the effective capacity of all links associated with the current node to zero when any node fails, and to maintain the original capacity state of the link when the current node is normal.

[0023] The first-level pruning module is used to enumerate the state combinations of each node in the binary node multi-state network, and perform first-level pruning on the state combinations based on the state of the source node and the sink node, eliminating state combinations in which the source node or sink node is in an ineffective state.

[0024] The second-level pruning module is used to construct a induced subgraph consisting of all current normal nodes and the links between normal nodes for each state combination that has passed the first-level pruning. It performs connectivity detection and second-level pruning on the induced subgraph, removes the state combinations corresponding to the induced subgraphs where the source node and sink node are not connected, calculates the maximum transmittable traffic when all links in each induced subgraph are at maximum capacity, and removes the state combinations corresponding to the induced subgraphs where the maximum transmittable traffic is not greater than the traffic transmission demand threshold.

[0025] The reliability calculation module is used to determine the effective capacity state of each link in the induced subgraph corresponding to each state combination retained after pruning, based on the capacity state distribution of the links and the constraint results of the node states. It performs a multi-state minimum cut set search on the induced subgraph to obtain the critical link state vectors that satisfy the requirement to cut the traffic transmission capacity between the source node and the sink node. It then uses a recursive disjoint sum algorithm to calculate the conditional reliability of the induced subgraph under the traffic transmission demand threshold.

[0026] The global reliability aggregation module is used to multiply the occurrence probability of each retained state combination with the corresponding induced subgraph conditional reliability and then sum them up to obtain the global reliability evaluation result of the binary node multi-state network under the traffic transmission demand threshold.

[0027] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps: Obtain target data for the binary node multi-state network to be evaluated. The target data includes the communication network topology, the state probability data of each node, the capacity state distribution data of each link, and the traffic transmission demand threshold from the source node to the sink node.

[0028] Based on the target data and the binary state probability data of each node, a constraint model of node state on the effective capacity of the link is constructed. The constraint model is used to set the effective capacity of all links associated with the current node to zero when any node fails, and to maintain the original capacity state of the link when the current node is normal.

[0029] Enumerate the state combinations of each node in the binary node multistate network, and perform first-level pruning on the state combinations based on the state of the source node and the sink node, removing state combinations in which the source node or sink node is in an ineffective state.

[0030] For each state combination that has passed the first-level pruning, construct an inducer subgraph consisting of all current normal nodes and the links between normal nodes. Perform connectivity detection and second-level pruning on the inducer subgraph. After removing the state combinations corresponding to inducer subgraphs where the source node and sink node are not connected, calculate the maximum transmittable flow when all links in each inducer subgraph are at maximum capacity. Remove the state combinations corresponding to inducer subgraphs where the maximum transmittable flow is not greater than the flow transmission demand threshold.

[0031] By using the induced subgraph corresponding to each state combination retained after pruning, the effective capacity state of each link in the induced subgraph is determined based on the capacity state distribution of the links and the constraint results of the node states. A multi-state minimum cut set search is performed on the induced subgraph to obtain the critical link state vectors that satisfy the requirement to cut the traffic transmission capacity between the source node and the sink node. The conditional reliability of the induced subgraph under the traffic transmission demand threshold is calculated using a recursive disjoint sum algorithm.

[0032] The probability of occurrence of each retained state combination is multiplied by the corresponding induced subgraph conditional reliability and then summed to obtain the global reliability evaluation result of the binary node multi-state network under the traffic transmission demand threshold.

[0033] The aforementioned reliability assessment method, apparatus, and device for binary node multi-state networks firstly constructs a constraint model of node states on the effective capacity of links. This explicitly embeds the actual physical constraint that node failure causes the capacity of adjacent links to be reduced to zero into the reliability assessment process, overcoming the model distortion problem caused by the assumption of independent node and component states in traditional methods. This constraint model ensures that the assessment results can truly reflect the blocking effect of node failures on local transmission channels in binary node multi-state networks, guaranteeing the accuracy of reliability assessment from a mechanistic perspective. Secondly, a two-level progressive pruning strategy is adopted. After enumerating node state combinations, the first-level pruning is performed based on the source and sink node states. Then, for combinations that pass the initial screening, an induced subgraph is constructed and connectivity detection and second-level pruning are performed. This effectively eliminates a large number of node state combinations that do not contribute to reliability, significantly compressing the problem scale of subsequent multi-state minimum cut set search, recursive disjointness, and probability calculations, and significantly reducing the overall computational complexity. Furthermore, the global reliability is obtained by weighting and accumulating the occurrence probability of each retained state combination with the corresponding conditional reliability of the induced subgraph using the full probability formula. This process does not rely on random sampling or approximate estimation, and can maintain accurate evaluation results completely consistent with the traditional state enumeration method while significantly improving computational efficiency. Finally, it has good engineering practicality and scalability, and can effectively support the quantitative reliability assessment and operation and maintenance decisions of large-scale complex network systems such as communication networks and distributed computing clusters. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating a reliability assessment method for a binary node multi-state network in one embodiment. Figure 2 This is a schematic diagram of a binary node multi-state network (BN-MSN) in one embodiment; Figure 3 This is a flowchart of a full probability decomposition reliability solution based on node state combinations in one embodiment; Figure 4 Here is a flowchart of the BN-MSN reliability accuracy assessment algorithm in one embodiment; Figure 5 Here is a schematic diagram of a baseline network in one embodiment, wherein, Figure 5 (1) is the first type of Net network diagram. Figure 5 (2) is the second type of Net network diagram. Figure 5 (3) is the third type of Net network diagram. Figure 5 (4) is the fourth type of Net network diagram; Figure 6 This is a structural block diagram of a reliability evaluation device for a binary node multi-state network in one embodiment; Figure 7 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0036] In one embodiment, such as Figure 1 As shown, a reliability evaluation method for a binary node multi-state network is provided, including the following steps: Step 102: Obtain the target data of the binary node multi-state network to be evaluated. The target data includes the communication network topology, the state probability data of each node, the capacity state distribution data of each link, and the traffic transmission demand threshold from the source node to the sink node.

[0037] Specifically, consider a directed network G=(V,E,W), where V is a set of nodes with n=|V| nodes, the source node is denoted as s, and the sink node is denoted as t∈V; E is a set of links with m=|E| links, and each link is represented as... , ; It is a maximum state vector composed of the maximum capacity of each link; each link The basic state space vector is This indicates the multiple capacity levels that the link may be in; the state probability data for each node is... (v∈V) represents the probability that node v is in a normal state; the traffic transmission demand threshold is denoted as d, which represents the minimum number of traffic units that need to be successfully transmitted from the source node to the sink node.

[0038] Step 104: Based on the target data and the binary state probability data of each node, construct a constraint model of the node state on the effective capacity of the link. The constraint model is used to set the effective capacity of all links associated with the current node to zero when any node fails, and to maintain the original capacity state of the link when the current node is normal.

[0039] Specifically, since each node in BN-MSN has a binary state of normal or failed, let ;when At that time, node The probability of being in a normal state is ;when At that time, node If a link fails, the capacity state of all its adjacent links is forcibly reduced to 0. For each link... Its effective capacity status depends on the link's own state. The effective capacity state is determined by the states of its endpoint nodes u and v, as follows:

[0040] When the effective capacity of a link is 0, it indicates that the link is in a completely interrupted state. Equation (1) explicitly embeds the dependency relationship of "node failure causing adjacent link failure" into the link capacity state. Therefore, even if the capacity states of multiple links are independent of each other, as long as they share the same failed node, their effective capacity will be set to zero simultaneously, thus forming a node-link state dependency relationship. Figure 2 As shown, the mechanism of this constraint model is as follows: the binary state variable of the node is used as the constraint condition, and the capacity state variable of the link is used as the constrained object. The binary state variable of the node acts on the capacity state variable of the link to determine the effective capacity state of the link: when any endpoint node of the link fails, the effective capacity of the link is forced to be zero; when both endpoint nodes of the link are normal, the effective capacity of the link is equal to its own capacity state.

[0041] Step 106: Enumerate the state combinations of each node in the binary node multi-state network, and perform first-level pruning on the state combinations based on the state of the source node and the sink node, removing state combinations in which the source node or sink node is in a failed state.

[0042] Specifically, define all possible combinations of node states. As a combination of candidate node states, ρ= This represents the total number of original node state combinations. Each node state combination represents a working / failed state configuration for each node in the network. For each enumerated node state combination, a first-level pruning is performed based on the states of the source and sink nodes—if the state variable of the source node s or the sink node t is 0, i.e. or If the state combination of a node does not have a valid source or sink node in the induced subgraph, it is impossible to satisfy the transmission requirement from s to t, and the state combination can be directly eliminated. For example, state combination The node was removed due to source node failure. This pruning criterion is based on the fact that if a source or sink node fails, there is no valid transmission start or end point in the network, and the combination of node states does not contribute to the reliability assessment results.

[0043] Step 108: For each state combination that has passed the first-level pruning, construct an inducer subgraph consisting of all current normal nodes and the links between normal nodes. Perform connectivity detection and second-level pruning on the inducer subgraph. After removing the state combinations corresponding to inducer subgraphs where the source node and sink node are not connected, calculate the maximum transmittable traffic when all links in each inducer subgraph are at maximum capacity. Remove the state combinations corresponding to inducer subgraphs where the maximum transmittable traffic is not greater than the traffic transmission demand threshold.

[0044] Specifically, let Represents the combination of node states The induced subgraph below, where This is the current set of surviving nodes. This is the set of links induced by the set of surviving nodes. Connectivity is checked on the constructed induced subgraph: a depth-first search (DFS) or breadth-first search (BFS) algorithm is used to determine if a connected path exists between the source node s and the sink node t in the induced subgraph. If no connected path exists, the induced subgraph corresponding to this state combination cannot form an effective transmission channel from the source to the sink, contributing nothing to reliability, and the state combination is removed in the second-level pruning. For example, when nodes v2 and v3 fail simultaneously, there is no connected path between the source node and the sink node in the induced subgraph, and this combination is removed.

[0045] Furthermore, the induced subgraph The capacity of each link is taken as its maximum capacity value. Under the maximum capacity configuration, the maximum flow value from source node s to sink node t is calculated using a maximum flow algorithm (such as the Ford-Fulkerson algorithm or the Dinic algorithm). ,in Induced subgraph The maximum state vector is formed by the maximum capacity of each link in the process. Determine the relationship between this maximum flow value and the traffic transmission demand threshold d: If... If a node's state combination is not found, then that node is removed. This pruning criterion is based on the following: Representative node state combination The physical upper limit of the lower network capacity, which is satisfied by any actual link state x. ,therefore ;like Then it is inevitable Under this node state combination, the network cannot meet the reliability requirements. The above pruning criterion does not delete any state combinations that may meet the reliability requirements, thus effectively compressing the search space while ensuring the accuracy of the evaluation results.

[0046] Step 110: Using the induced subgraph corresponding to each state combination retained after pruning, determine the effective capacity state of each link in the induced subgraph based on the capacity state distribution of the link and the constraint results of the node state. Perform a multi-state minimum cut set search on the induced subgraph to obtain the critical link state vectors that satisfy the cut-off traffic transmission capacity between the source node and the sink node. Calculate the conditional reliability of the induced subgraph under the traffic transmission demand threshold using a recursive disjoint sum algorithm.

[0047] Specifically, after the first and second levels of pruning, the set of node state combinations retained is denoted as . ,and Much smaller than the original number of node state combinations 2 n For each state combination retained after pruning The corresponding inducible graph The effective capacity state of each link in the induced subgraph is determined based on the capacity state distribution of the links and the constraint results of the node states. Specifically, the effective capacity vector of each link in the induced subgraph is calculated based on equation (1). Due to the combination of node states It has been confirmed that the state of all nodes in the induced subgraph is normal. Therefore, the effective capacity of each link in the induced subgraph is equal to its own capacity state. After determining the effective capacity state of each link, a multi-state minimum cut set search is performed on the induced subgraph. Multi-state minimum cut set (d-MC) refers to the critical state vector where, given a flow demand d, the maximum flow between the source and sink is less than d+1 when the link state vector does not exceed the cut set vector. The goal of the search is to obtain all critical link state vectors that satisfy the requirement to cut the flow transmission capacity between the source and sink, i.e., all d-MC vectors. Let the set of d-MC vectors obtained from the search be {z_i,1, z_i,2, …, z_i,σ_i}, where σ_i is the total number of d-MC vectors in the induced subgraph. The d-MC search can be implemented using existing multi-state network minimum cut set search algorithms, such as the enumeration method based on the maximum flow minimum cut theorem, which traverses the link capacity state combinations and uses the maximum flow algorithm to determine whether they are cut set vectors.

[0048] Specifically, based on the obtained set of multi-state minimum cut set vectors, the conditional reliability of the induced subgraph under the traffic transmission demand threshold is calculated using the Recursive Sumof Disjoint Products (RSDP) algorithm. The calculation method is as follows: First, initialize the cumulative union probability value to zero, and set up a queue of multi-state minimum cut set vectors to be processed, initially containing all the searched d-MC vectors; then, take a d-MC vector from the queue. Calculate the event corresponding to the d-MC vector. probability of occurrence This probability is that the link state vector x in the induced subgraph does not exceed The joint probability of each component value is calculated by multiplying the probabilities of each link state, since the link capacity states are independent under a given combination of node states. The calculated event probability is then recursively deintersected and merged with the cumulative union probability value to obtain an updated cumulative union probability value. A deintersecting constraint is generated between the current event and the processed events, and this constraint is applied to the probability calculation of events corresponding to unprocessed d-MC vectors in the queue. The steps of extraction, calculation, and merging are repeated until the queue is empty. The final cumulative union probability value is then used as the union probability of all events corresponding to d-MC vectors. The conditional reliability of the induced subgraph is equal to the unit probability minus the union probability, i.e.:

[0049] Step 112: Multiply the occurrence probability of each retained state combination by the corresponding induced subgraph conditional reliability and sum them up to obtain the global reliability evaluation result of the binary node multi-state network under the traffic transmission demand threshold.

[0050] Specifically, for each retained node state combination The probability (prior probability) of this combination is calculated using the following formula:

[0051] in, The total number of network nodes. Let v be the probability that node v is in a normal state. For node j in the combination The state values ​​are set (1 for normal, 0 for failure). Then, according to the law of total probability, the prior probability of each retained node state combination is multiplied by the corresponding conditional reliability of the induced subgraph and summed to obtain the global reliability of the BN-MSN network under the traffic demand d. :

[0052] Global reliability This is the probability that at least d+1 units of traffic can be successfully transmitted from the source node to the sink node.

[0053] The aforementioned reliability assessment method for binary node multi-state networks firstly constructs a constraint model of node states on the effective capacity of links. This explicitly embeds the actual physical constraint that node failure causes the capacity of adjacent links to be reduced to zero into the reliability assessment process, overcoming the model distortion problem caused by the assumption of independent node and component states in traditional methods. This constraint model ensures that the assessment results can truly reflect the blocking effect of node failures on local transmission channels in binary node multi-state networks, guaranteeing the accuracy of reliability assessment from a mechanistic perspective. Secondly, a two-level progressive pruning strategy is adopted. After enumerating node state combinations, the first-level pruning is performed based on the source and sink node states. Then, for the combinations that pass the initial screening, an induced subgraph is constructed and connectivity detection and second-level pruning are performed. This effectively eliminates a large number of node state combinations that do not contribute to reliability, significantly compressing the problem scale of subsequent multi-state minimum cut set search, recursive disjointness, and probability calculations, and significantly reducing the overall computational complexity. Furthermore, the global reliability is obtained by weighting and accumulating the occurrence probability of each retained state combination with the corresponding conditional reliability of the induced subgraph using the full probability formula. This process does not rely on random sampling or approximate estimation, and can maintain accurate evaluation results completely consistent with the traditional state enumeration method while significantly improving computational efficiency. Finally, it has good engineering practicality and scalability, and can effectively support the quantitative reliability assessment and operation and maintenance decisions of large-scale complex network systems such as communication networks and distributed computing clusters.

[0054] In one embodiment, each node v in the binary node multi-state network is defined as a binary state variable, where a value of 1 indicates the node is normal, and a value of 0 indicates the node is failed. Each link is defined as its own capacity state vector, which describes the state of the link at different capacity levels. The enhanced capacity model is established based on the binary state variables and the capacity state vectors, wherein the effective capacity state of each link is:

[0055] in, This represents the valid state of the component. For nodes binary state variables, For nodes binary state variables, The state of a component is its own state; when the effective capacity of the link is 0, it indicates that the link is in a completely failed state; wherein, the binary state variable of the node is used as a constraint condition, the capacity state variable of the component is used as the constrained object, and the binary state variable of the node acts on the capacity state variable of the link to determine the effective capacity state of the link.

[0056] In one embodiment, the currently enumerated node state combinations are read, and the state variable values ​​of the source node and the sink node are determined. If the state variable values ​​of the source node and the sink node are 0, the state combination is removed. For each state combination that passes the first-level pruning, a induced subgraph is constructed, consisting of all nodes with a value of 1 and links with both ends having a value of 1. A depth-first search or breadth-first search is performed on the induced subgraph to determine whether there is a connected path between the source node and the sink node. If there is no connected path, the state combination is removed. For state combinations that pass the connectivity test, the capacity of each link in the induced subgraph is set to its maximum capacity value. Under the maximum capacity configuration, the maximum flow value from the source node to the sink node is calculated. If the maximum flow value is not greater than the traffic transmission demand threshold, the state combination is removed. After the first-level pruning removes the state combinations where the source node or the sink node is invalid, the second-level pruning sequentially performs connectivity determination and maximum transmission capacity determination on the combinations that pass the first-level pruning.

[0057] It is worth noting that for any combination of node states The induced subgraph generated by this combination is determined if any of the following conditions are met. It can be pruned without performing subsequent d-MC search and recursive disjoint sum probability calculation: (1) Boundary failure criterion: if the source point s or sink point t fails, i.e. or (2) Connectivity and flow criteria: If the induced subgraph The source point s and the sink point t are not connected, or they are in the maximum state vector. Maximum flow under Then the combination is a pair No contribution. Criterion 1 is based on the fact that if the source or sink fails, there is no valid source or sink in the induced subgraph, making it impossible to satisfy the transmission requirement from s to t. Criterion 2 is based on... Representative node state combination The physical upper limit of the lower network capacity, which is satisfied by any actual link state x. From the monotonicity of the maximum stream function, we know that ;like Then it is inevitable Under this node state combination, the network cannot meet the reliability requirements. The above pruning criterion does not delete any state combinations that might meet the reliability requirements, thus ensuring the accuracy of the evaluation results.

[0058] In one embodiment, each node in the binary node multi-state network has only two states: normal and failed, and each link has multiple capacity level states.

[0059] In one embodiment, the effective capacity state vector of each link in the induced subgraph corresponding to the node state combination retained after pruning is obtained, wherein the value range of each element in the effective capacity state vector is an integer range from zero to the maximum capacity of the link; a multi-state minimum cut set search is performed on the induced subgraph to search for all critical state vectors that satisfy the requirement of cutting off traffic transmission between the source and sink, wherein the critical state vector is a multi-state minimum cut set vector, and all multi-state minimum cut set vectors constitute a multi-state minimum cut set vector set; based on the multi-state minimum cut set vector set, the union probability of all link state vectors in the induced subgraph not being less than any multi-state minimum cut set vector is calculated using a recursive disjoint sum algorithm, and the unit probability is subtracted from the union probability to obtain the conditional reliability of the induced subgraph under the traffic transmission requirement threshold.

[0060] In one embodiment, the cumulative union probability is initialized to zero, and a queue of multi-state minimum cut set vectors to be processed is set up. The queue initially contains all the multi-state minimum cut set vectors obtained through searching. A multi-state minimum cut set vector is taken from the queue, and the probability of occurrence of the event corresponding to the current multi-state minimum cut set vector is calculated. The probability of occurrence of the event is the joint probability that the state vectors of each link in the induced subgraph do not exceed the values ​​of each component in the current multi-state minimum cut set vector. The capacity states of each link are independent of each other under a given combination of node states. The occurrence probability and the cumulative union probability value are recursively merged into a non-intersecting state to obtain an updated cumulative union probability value. A non-intersecting constraint condition between the current event and the processed events is generated, and the non-intersecting constraint condition is applied to the probability calculation of the event corresponding to the unprocessed multi-state minimum cut set vector in the queue. The steps of taking out, calculating, and merging are repeated until the queue is empty. The final cumulative union probability value is used as the union probability, and the conditional reliability of the induced subgraph is obtained by subtracting the union probability from the unit probability.

[0061] In one embodiment, the probability of occurrence is calculated for each retained combination of node states:

[0062] in, Let be the probability of a combination of node states occurring. Let be the probability that node j is in a normal state. The total number of network nodes. For each combination of node states, obtain the conditional reliability of the induced subgraph corresponding to each retained combination of node states:

[0063] in, For a binary node multi-state network, the maximum transmittable traffic from the source node to the sink node is determined under the link state vector x. For traffic transmission demand threshold, The total number of multi-state minimum cut set vectors. The first induced subgraph corresponding to the node state combination A multi-state minimum cut set vector is generated; the occurrence probability of each retained state combination is multiplied by the corresponding induced subgraph conditional reliability and then summed to obtain the global reliability evaluation result of the binary node multi-state network under the traffic transmission demand threshold:

[0064] in, For global reliability, This represents the number of candidate node state combinations.

[0065] One embodiment provides a reliability assessment method for binary-node multi-state networks. This method addresses network scenarios prevalent in critical infrastructures such as communication networks, power systems, transportation networks, and distributed computing clusters, where nodes strictly exhibit only two states: normal or failed, and node failure directly leads to the zeroing of capacity in adjacent components. It proposes a reliability assessment scheme that significantly reduces the state space enumeration scale and the number of multi-state minimum cut set searches while ensuring the accuracy of reliability calculations. This network type is called a binary-node multi-state network (BN-MSN). This embodiment uses communication networks as a typical application scenario for illustration; however, those skilled in the art should understand that this method is also applicable to complex network systems with similar node-component dependency characteristics, such as power transmission networks, transportation networks, and distributed computing clusters.

[0066] In one embodiment, with Figure 2 The 5-node, 7-link BN-MSN example illustrates the execution process of the method of this invention. The network contains 5 nodes and 7 links. The normal operation probability of all nodes is p_v=0.9, and the capacity state vector of all links is consistent as b_i=(0,1,2,3), i.e., the maximum capacity W_i=3. Their state distribution probability vectors are all p_i=(0.25,0.25,0.25,0.25), and the network transmission requirement is d=4. During the node state enumeration process, there are a total of 2 original node state combinations. 5=32 possibilities. After the first level of pruning, combinations where either source node v1 or sink node v5 is failed are removed. For example, S=(0,1,1,1,1) is removed due to source node failure. After the second level of pruning, connectivity checks remove combinations where the source and sink are not connected in the induced subgraph. For example, when nodes v2 and v3 fail simultaneously, there is no connected path between the source and sink. After the second level of pruning, maximum flow determination removes combinations where the maximum flow is ≤4 under maximum capacity. For example, when nodes v2 and v3 fail simultaneously, the induced subgraph has only two links, and the maximum flow is 3≤4; this combination is removed. Taking the typical unpruned state S0=(1,1,1,1,1) where all nodes are normal as an example, the probability of this combination occurring is Pr(S0)=0.9. 5 =0.59049, its induced subgraph is similar to the original Figure 1 Therefore, the effective capacity of all links remains in its original state. A d-MC search is performed on this induced subgraph to obtain a set of 4-MC vectors. Then, the RSDP algorithm is applied to process the 4-MC set, and the conditional reliability Pr(φ(x)≥5|S0)=0.143799 for the induced subgraph satisfying d+1=5 is calculated. Finally, all unpruned node state combinations are weighted and accumulated according to equation (4) to obtain the global reliability R5=0.090486 of the BN-MSN network at d=4. This example shows that the pruning criterion can directly eliminate a large number of non-contributing state combinations during the node state enumeration stage, thereby reducing the number of subsequent d-MC searches and improving computational efficiency.

[0067] In one embodiment, such as Figure 3 As shown, the original BN-MSN reliability problem is first decomposed into the reliability problem of the induced subgraph G^{S_i} under each node state combination S_i. Then, d-MC search and RSDP probability union calculation are performed on each induced subgraph to obtain the conditional reliability of each subgraph. Finally, the overall network reliability is obtained by aggregation using the full probability formula. In the specific implementation process, for Figure 2 The 5-node, 7-link BN-MSN shown has a total of 32 possible node state combinations. For each node state combination S_i (e.g., S0=(1,1,1,1,1)), its prior probability Pr(S0)=0.9 is calculated according to equation (3). 5 =0.59049; For the induced subgraph corresponding to this combination, after performing d-MC search, σ_i d-MC vectors are obtained, and the conditional reliability is calculated according to equation (2) using the RSDP algorithm; finally, full probability aggregation is performed according to equation (4). Figure 2The decomposition process shows that this invention transforms the global BN-MSN reliability problem into a series of smaller-scale induced subgraph reliability assessment problems through a "layered decoupling" solution logic, significantly reducing the complexity of full-state enumeration. In particular, after pruning, the actual number of node state combinations |Ω_valid| participating in subsequent calculations is much smaller than the original total number of node state combinations. n This further improves computational efficiency.

[0068] In one embodiment, such as Figure 4 The algorithm flow shown includes the following main steps: Step 1, obtain the BN-MSN input data G=(V,E,W), the state probability set P_v of each node, the state vector b_j of each link, and the traffic demand d; Step 2, enumerate the node state combination S_i and simultaneously perform pruning judgment, including boundary failure criterion judgment and connectivity and traffic criterion judgment, eliminate combinations that do not meet the pruning conditions and calculate the prior probability Pr(S_i) of the retained combination; Step 3, construct the induced subgraph G^{S_i} for the retained node state combinations, and determine the effective capacity state of each link based on equation (1); Step 4, perform d-MC search on the induced subgraph to obtain all d-MC vectors; Step 5, calculate the conditional reliability of the induced subgraph based on the RSDP algorithm according to equation (2); Step 6, accumulate the total reliability according to equation (4) and output the network reliability R_{d+1}. Figure 2 Taking the 5-node, 7-link network shown as an example, in Figure 4 Under the algorithm flow shown, approximately 12 effective combinations remain after pruning of the original 32 node state combinations. For the induced subgraph corresponding to the all-normal state S0, the conditional reliability calculated by RSDP is 0.143799. Other effective node state combinations undergo the same process sequentially. Finally, the global reliability R5 = 0.090486 is obtained by summing the results. The core of this algorithm flow is "decomposition-pruning-integration": first, the node state combinations are decomposed; then, the search space is compressed using pruning criteria; finally, the d-MC search and RSDP probability calculation are integrated into each effective induced subgraph.

[0069] In one embodiment, such as Figure 5 These are schematic diagrams of four typical baseline network topologies provided in embodiments of the present invention, wherein... Figure 5 (1) is the first type of Net network diagram. Figure 5 (2) is the second type of Net network diagram. Figure 5 (3) is the third type of Net network diagram. Figure 5 (4) This is the fourth type of Net network diagram. Four benchmark networks are used to verify the accuracy and efficiency of the method of this invention. The capacity status distribution of each network node and link is shown in Table 3. In the specific experimental implementation, Figure 5(1) The first type of Net network is a relatively simple small-scale network, used to initially verify the effectiveness of the pruning strategy; Figure 5 (2) The second type of Net network and Figure 5 (3) The third type of Net network is a medium-scale network, in which Figure 5 (3) The structure of the third type of Net network is relatively simple. Figure 5 (2) The second type of Net network is more complex and is used to test the adaptability of the method of the present invention under different network topologies; Figure 5 (4) The fourth type of Net network is a large-scale benchmark network with a more complex structure, used to test the performance of the method of this invention when the full-state enumeration method cannot complete the computation in an effective time. Five comparison algorithms were designed for the experiment: SE (full-state enumeration method), PM-NP (the method of this invention without pruning strategy), PM-R1 (only boundary failure criterion enabled), PM-R2 (only connectivity and flow criteria enabled), and PM-Full (the complete method of this invention). All experiments were implemented on a personal computer with an AMD Ryzen 7 5800H @ 3.20 GHz CPU and 32GB RAM using Python 3.9. Experimental results show that, Figure 5 On the four benchmark networks shown, the PM-Full method achieves the same reliability results as SE at all demand levels, proving the accuracy of the method of the present invention. At the same time, the computation time of PM-Full is significantly lower than that of SE. For example, in Net(1), the computation time of PM-Full is only about 0.4% of that of SE. In Net(2), when d=1, SE takes 1425 seconds while PM-Full only takes 3.01 seconds. In Net(3), SE takes more than 80,000 seconds while PM-Full completes within 109 seconds. In Net(4), SE takes more than 200,000 seconds while PM-Full completes within the range of 82.64 to 10896.64 seconds.

[0070] In one embodiment, such as Figure 6 As shown, a reliability assessment device for a binary node multi-state network is provided, comprising: a data acquisition module 602, a constraint model construction module 604, a first-level pruning module 606, a second-level pruning module 608, and a reliability calculation module 610, wherein: The data acquisition module 602 is used to acquire target data of the binary node multi-state network to be evaluated. The target data includes the communication network topology, the state probability data of each node, the capacity state distribution data of each link, and the traffic transmission demand threshold from the source node to the sink node.

[0071] The constraint model construction module 604 is used to construct a constraint model of node state on the effective capacity of the link based on the target data and the binary state probability data of each node. The constraint model is used to set the effective capacity of all links associated with the current node to zero when any node fails, and to maintain the original capacity state of the link when the current node is normal.

[0072] The first-level pruning module 606 is used to enumerate the state combinations of each node in the binary node multi-state network, and perform first-level pruning on the state combinations according to the state of the source node and the sink node, eliminating state combinations in which the source node or sink node is in an ineffective state.

[0073] The second-level pruning module 608 is used to construct an induced subgraph consisting of all current normal nodes and the links between normal nodes for each state combination that has passed the first-level pruning. The induced subgraph is then subjected to connectivity detection and second-level pruning. After removing the state combinations corresponding to the induced subgraphs where the source node and sink node are not connected, the maximum transmittable flow in each induced subgraph is calculated when all links are at maximum capacity. The state combinations corresponding to the induced subgraphs where the maximum transmittable flow is not greater than the flow transmission demand threshold are then removed.

[0074] The reliability calculation module 610 is used to determine the effective capacity state of each link in the induced subgraph corresponding to each state combination retained after pruning, based on the capacity state distribution of the links and the constraint results of the node states. It performs a multi-state minimum cut set search on the induced subgraph to obtain the critical link state vectors that satisfy the cut-off traffic transmission capacity between the source node and the sink node. It uses a recursive disjoint sum algorithm to calculate the conditional reliability of the induced subgraph under the traffic transmission demand threshold.

[0075] The global reliability aggregation module 612 is used to multiply the occurrence probability of each retained state combination with the corresponding induced subgraph conditional reliability and then sum them up to obtain the global reliability evaluation result of the binary node multi-state network under the traffic transmission demand threshold.

[0076] Specific limitations regarding the reliability assessment device for a binary node multi-state network can be found in the limitations of the reliability assessment method for a binary node multi-state network described above, and will not be repeated here. Each module in the aforementioned reliability assessment device for a binary node multi-state network can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0077] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 7As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements a reliability assessment method for a binary node multi-state network. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0078] Those skilled in the art will understand that Figures 6-7 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0079] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to perform the following steps: Obtain target data for the binary node multi-state network to be evaluated. The target data includes the communication network topology, the state probability data of each node, the capacity state distribution data of each link, and the traffic transmission demand threshold from the source node to the sink node.

[0080] Based on the target data and the binary state probability data of each node, a constraint model of node state on the effective capacity of the link is constructed. The constraint model is used to set the effective capacity of all links associated with the current node to zero when any node fails, and to maintain the original capacity state of the link when the current node is normal.

[0081] Enumerate the state combinations of each node in the binary node multistate network, and perform first-level pruning on the state combinations based on the state of the source node and the sink node, removing state combinations in which the source node or sink node is in an ineffective state.

[0082] For each state combination that has passed the first-level pruning, construct an inducer subgraph consisting of all current normal nodes and the links between normal nodes. Perform connectivity detection and second-level pruning on the inducer subgraph. After removing the state combinations corresponding to inducer subgraphs where the source node and sink node are not connected, calculate the maximum transmittable flow when all links in each inducer subgraph are at maximum capacity. Remove the state combinations corresponding to inducer subgraphs where the maximum transmittable flow is not greater than the flow transmission demand threshold.

[0083] By using the induced subgraph corresponding to each state combination retained after pruning, the effective capacity state of each link in the induced subgraph is determined based on the capacity state distribution of the links and the constraint results of the node states. A multi-state minimum cut set search is performed on the induced subgraph to obtain the critical link state vectors that satisfy the requirement to cut the traffic transmission capacity between the source node and the sink node. The conditional reliability of the induced subgraph under the traffic transmission demand threshold is calculated using a recursive disjoint sum algorithm.

[0084] The probability of occurrence of each retained state combination is multiplied by the corresponding induced subgraph conditional reliability and then summed to obtain the global reliability evaluation result of the binary node multi-state network under the traffic transmission demand threshold.

[0085] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0086] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0087] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A reliability assessment method for a binary node multi-state network, characterized in that, The method includes: Obtain target data for the binary node multi-state network to be evaluated. The target data includes the communication network topology, state probability data of each node, capacity state distribution data of each link, and traffic transmission demand threshold from the source node to the sink node. Based on the target data and the binary state probability data of each node, a constraint model of node state on the effective capacity of the link is constructed. The constraint model is used to set the effective capacity of all links associated with the current node to zero when any node fails, and to maintain the original capacity state of the link when the current node is normal. Enumerate the state combinations of each node in the binary node multi-state network, and perform first-level pruning on the state combinations according to the state of the source node and the sink node, eliminating state combinations in which the source node or the sink node is in a failed state. For each state combination that has passed the first-level pruning, a induced subgraph is constructed, consisting of all current normal nodes and the links between the normal nodes. The induced subgraph is then subjected to connectivity detection and second-level pruning. After removing the state combinations corresponding to the induced subgraphs where the source node and the sink node are not connected, the maximum transmittable flow in each induced subgraph is calculated when all links are at maximum capacity. The state combinations corresponding to the induced subgraphs where the maximum transmittable flow is not greater than the flow transmission demand threshold are then removed. By using the induced subgraph corresponding to each state combination retained after pruning, the effective capacity state of each link in the induced subgraph is determined according to the capacity state distribution of the link and the constraint results of the node state. A multi-state minimum cut set search is performed on the induced subgraph to obtain all critical link state vectors that satisfy the requirement to cut off the traffic transmission capacity between the source node and the sink node. The conditional reliability of the induced subgraph under the traffic transmission demand threshold is calculated using a recursive disjoint sum algorithm. The probability of occurrence of each retained state combination is multiplied by the corresponding induced subgraph conditional reliability and then summed to obtain the global reliability evaluation result of the binary node multi-state network under the traffic transmission demand threshold.

2. The method according to claim 1, characterized in that, Based on the target data and the binary state probability data of each node, a constraint model of node state on the effective capacity of the link is constructed, including: Each node v in the binary node multi-state network is defined as a binary state variable. A value of 1 indicates that the node is normal, and a value of 0 indicates that the node is failed. Each link is defined as its own capacity state vector, which is used to describe the state of the link under different capacity levels. The enhanced capacity model is established based on the binary state variables and the capacity state vector, wherein the effective capacity state of each link is: in, This represents the valid state of the component. For nodes binary state variables, For nodes binary state variables, For the component's own state; When the effective capacity of the link is 0, it indicates that the link is in a completely failed state. In this system, the binary state variables of nodes serve as constraints, and the capacity state variables of components serve as the constrained objects. The binary state variables of nodes act on the capacity state variables of the chain to determine the effective capacity state of the chain.

3. The method according to claim 1, characterized in that, Enumerate the state combinations of each node in the binary node multi-state network, and perform first-level pruning on the state combinations based on the states of the source node and the sink node, removing state combinations in which the source node or sink node is in a failed state, including: Read the currently enumerated node state combinations, determine the state variable values ​​of the source node and the sink node, and if the state variable values ​​of the source node and the sink node are 0, then remove the state combination. For each state combination that has passed the first-level pruning, a induced subgraph is constructed consisting of all nodes with a value of 1 and links with both ends nodes having a value of 1. A depth-first search or breadth-first search is performed on the induced subgraph to determine whether there is a connected path between the source node and the sink node. If there is no connected path, the state combination is removed. For state combinations that pass connectivity detection, the capacity of each link in the inducer subgraph is set to its maximum capacity value. Under the maximum capacity configuration, the maximum flow value from the source node to the sink node is calculated. If the maximum flow value is not greater than the traffic transmission demand threshold, the state combination is removed. After the first-level pruning removes the state combinations where the source node or the sink node is ineffective, the second-level pruning performs connectivity determination and maximum transmission capacity determination on the combinations that pass the first-level pruning.

4. The method according to any one of claims 1 to 3, characterized in that, In the binary node multi-state network, each node has only two states: normal and failed, and each link has multiple capacity level states.

5. The method according to claim 4, characterized in that, Calculating the conditional reliability of the induced subgraph under the traffic transmission demand threshold includes: Obtain the effective capacity state vector of each link in the induced subgraph corresponding to the node state combination retained after pruning, wherein the value range of each element in the effective capacity state vector is an integer range from zero to the maximum capacity of the link; Perform a multi-state minimum cut set search on the induced subgraph to find all critical state vectors that satisfy the requirement to cut off the flow transmission between the source and sink. The critical state vectors are multi-state minimum cut set vectors, and all multi-state minimum cut set vectors constitute a multi-state minimum cut set vector set. Based on the set of multi-state minimum cut set vectors, the union probability of all link state vectors in the induced subgraph being no less than any multi-state minimum cut set vector is calculated using a recursive disjoint sum algorithm. The unit probability is then subtracted from the union probability to obtain the conditional reliability of the induced subgraph under the traffic transmission demand threshold.

6. The method according to claim 5, characterized in that, Based on the set of multi-state minimum cut set vectors, the probability of the union of all link state vectors in the induced subgraph being no less than any multi-state minimum cut set vector is calculated using a recursive disjoint sum algorithm, including: Initialize the cumulative union probability value to zero, and set up a queue of multi-state minimum cut set vectors to be processed. The queue initially contains all the multi-state minimum cut set vectors obtained by the search. Take a multi-state minimum cut set vector from the queue, calculate the probability of occurrence of the event corresponding to the current multi-state minimum cut set vector, the probability of occurrence of the event is the joint probability that the state vectors of each link in the inducer graph do not exceed the values ​​of each component in the current multi-state minimum cut set vector, and the capacity states of each link are independent of each other under a given combination of node states. The occurrence probability and the cumulative union probability value are recursively merged into a non-intersecting form to obtain an updated cumulative union probability value. Non-intersecting constraints are generated between the current event and the processed events. The non-intersecting constraints are then applied to the probability calculation of events corresponding to unprocessed multi-state minimum cut set vectors in the queue. Repeat the steps of extracting, calculating, and merging until the queue is empty. Use the final cumulative union probability value as the union probability, and subtract the union probability from the unit probability to obtain the conditional reliability of the induced subgraph.

7. The method according to claim 6, characterized in that, The occurrence probability of each retained state combination is multiplied by the corresponding induced subgraph conditional reliability and then summed to obtain the global reliability evaluation result of the binary node multi-state network under the traffic transmission demand threshold, including: Calculate the probability of occurrence for each retained combination of node states: in, Let be the probability of a combination of node states occurring. Let be the probability that node j is in a normal state. The total number of network nodes. For node state combinations; Obtain the conditional reliability of the induced subgraph corresponding to each retained node state combination: in, For a binary node multi-state network, the maximum transmittable traffic from the source node to the sink node is determined under the link state vector x. For traffic transmission demand threshold, The total number of multi-state minimum cut set vectors. The first induced subgraph corresponding to the node state combination A multi-state minimum cut set vector; The probability of occurrence of each retained state combination is multiplied by the corresponding conditional reliability of the induced subgraph, and then summed to obtain the global reliability evaluation result of the binary node multi-state network under the traffic transmission demand threshold: in, For global reliability, This represents the number of candidate node state combinations.

8. A reliability evaluation device for a binary node multi-state network, characterized in that, The device includes: The data acquisition module is used to acquire target data of the binary node multi-state network to be evaluated. The target data includes the communication network topology, the state probability data of each node, the capacity state distribution data of each link, and the traffic transmission demand threshold from the source node to the sink node. The constraint model construction module is used to construct a constraint model of node state on the effective capacity of the link based on the target data and the binary state probability data of each node. The constraint model is used to set the effective capacity of all links associated with the current node to zero when any node fails, and to maintain the original capacity state of the link when the current node is normal. The first-level pruning module is used to enumerate the state combinations of each node in the binary node multi-state network, and perform first-level pruning on the state combinations according to the state of the source node and the sink node, eliminating state combinations in which the source node or the sink node is in a failed state. The second-level pruning module is used to construct an induced subgraph consisting of all current normal nodes and the links between the normal nodes for each state combination that has passed the first-level pruning. The module performs connectivity detection and second-level pruning on the induced subgraph, removes the state combinations corresponding to the induced subgraphs where the source node and the sink node are not connected, calculates the maximum transmittable traffic when all links in each induced subgraph are at maximum capacity, and removes the state combinations corresponding to the induced subgraphs where the maximum transmittable traffic is not greater than the traffic transmission demand threshold. The reliability calculation module is used to determine the effective capacity state of each link in the induced subgraph corresponding to each state combination retained after pruning, based on the capacity state distribution of the link and the constraint results of the node state. It performs a multi-state minimum cut set search on the induced subgraph to obtain all critical link state vectors that satisfy the requirement to cut off the traffic transmission capacity between the source node and the sink node. It then uses a recursive disjoint sum algorithm to calculate the conditional reliability of the induced subgraph under the traffic transmission demand threshold. The global reliability aggregation module is used to multiply the occurrence probability of each reserved state combination with the corresponding induced subgraph conditional reliability and then sum them to obtain the global reliability evaluation result of the binary node multi-state network under the traffic transmission demand threshold.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

Images