CN107018011B - Network simplifying method for keeping network performance reliability - Google Patents
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Abstract
The invention discloses a network simplifying method for keeping network performance reliability, which solves the problem of high computation complexity of large-scale network performance reliability evaluation. The method specifically comprises the following steps: the method comprises the following steps: establishing a network performance model based on a Markov reward model, and determining a network performance index; step two: evaluating the reliability of the network performance by a Monte Carlo simulation method; step three: on the basis of a graph change simplification method for maintaining the communication reliability, network simplification is carried out aiming at the unchanged reliability of network performance; step four: and carrying out simulation verification by using the proposed performance reliability evaluation method. The invention provides a method for simplifying a large-scale communication network and an evaluation method of performance reliability of the large-scale communication network.
Description
Technical Field
The invention belongs to the technical field of network communication and reliability, and particularly relates to a network simplifying method for keeping network performance reliability.
Background
The society of the information age has stronger dependence on the communication network, and the network reliability plays an important role in the normal operation of the communication network. With the rapid expansion of network scale, the reasons of the use frequency, the rapid increase of network load, the improvement of the reliability of a single device, and the like, the problems related to network performance, such as network congestion and delay, become factors which must be considered in the network reliability, and the research on the network reliability turns to the research on the network performance and the service quality from the initial research on the connection reliability based on graph theory, so that the evaluation complexity of the network performance reliability is improved. On one hand, the network performance reliability is evaluated by analytical calculation, and for the complex structure and node polymorphism problems in a large-scale network, factors such as capacity and flow need to be considered, so that the evaluation difficulty of the performance reliability is greatly improved. On the other hand, the evaluation of network performance reliability by using a reliability test method (reference [1 ]: chenyang, huangning, kangjie, etc.. local area network FTP service reliability test and evaluation technology [ J ]. the university of aerospace, 2011,37(1):91-94.) faces the problems of too long time, too high cost, large workload, etc.
Therefore, it is of great value to research how to reduce the difficulty of network performance reliability evaluation and the test cost. Among them, simplifying the network to achieve the reduction of the network size is an effective approach with the widest applicability. The existing network simplification methods are mostly limited to graph transformation methods for connectivity reliability, (reference [2]: Shooman A M, Kershenbaum A. exact graph-reduction algorithm for network reliability analysis [ C ]// Global Communications Conference,1991.GLOBECOM '91.' Countdown to the New millennium. watering a Mini-communication: Personal Communications services. IEEE,1991: 1412-; the existing network simplifying method considering performance (reference [3] Lihao Ping, Xiaoxiao Qiang, Kunlibei, etc. self-similar network related parameter analysis [ J ] based on topology simplification microcomputer information 2008,24(18):186 and 188.) assumes that the related parameters of each node in the network are unchanged, and serial connection and parallel connection simplification are carried out under the principle of not influencing network performance, and the multi-state of the node is not considered, so that the simplification does not consider performance reliability, and the simplification requirement of network performance reliability evaluation is difficult to meet. Based on the above problems, it is urgently needed to provide a network simplification method for maintaining the reliability of network performance.
Disclosure of Invention
The invention aims to solve the problem of high complexity of large-scale network performance reliability evaluation, and provides a network simplification method for maintaining network performance reliability.
The invention provides a network simplifying method for keeping network performance reliability, which comprises the following steps:
the method comprises the following steps: and establishing a network performance model based on a Markov Reward Model (MRM) and determining a network performance index.
A continuous-time markov chain (CTMC) model of the nodes is first built. The node CTMC model considers the state space of nodes, and each node is regarded as an independent M/M/1/niA queuing model. The different numbers of data packets in the nodes are regarded as different states of the nodes, all the states possibly occurring in the network are listed, and the probability of transition (namely the transition probability) among the states is determined. Then establishing an MRM network performance model, namely combining single-node CTMC models in the network by endowing different reward values to each state of the system on the basis of the state space of the CTMCs to calculate the performance metric of the network: average total time delay of arriving data packet.
Step two: the Monte Carlo simulation method evaluates the reliability of the network performance.
For the research of the reliability of the network performance, the time delay is the most concerned performance level because a network user can directly feel, the network fault is combined with the network performance model based on the network performance model in the step one, the reliability of the network performance is calculated by a Monte Carlo simulation method, firstly, the node capacity in the network is assumed to be limited, a certain fault probability exists in a link, the fault-free network time delay is taken as a threshold value, the states of edges and nodes are randomly sampled, then, the network time delay is calculated by the total time delay of the average arrival data packet in the step one, the network time delay is compared with the threshold value to judge whether the network has faults, and the reliability of the network performance based on the time delay is obtained by the statistical result after multiple times of simulation.
Step three: on the basis of the graph change simplification method for maintaining the communication reliability, network simplification is carried out aiming at the unchanged reliability of network performance.
The basic simplified thought is based on a graph change reduction method, a routing matrix and node performance parameters are added, including the change of parameters such as storage space and service rate, and a reduction rule is designed by taking the local packet loss rate and the data packet number before and after simplification as constraints. If the local packet loss rate and the data packet number are not changed, the time delay of the whole network is maintained, and therefore the performance reliability is approximate. Firstly, judging whether the network can be simplified or not according to an adjacency matrix, a routing matrix, an edge reliability matrix, the capacity of a node and the service rate of the node of the network; and then sequentially finding a degree-one node, a degree-two node and a parallel edge in the network, and carrying out degree-one simplification, degree-two simplification and series-parallel simplification based on time delay until the network can not be simplified any more.
Step four: and carrying out simulation verification by using the proposed performance reliability evaluation method.
Simplifying the network by using the simplification method provided by the step three, and then calculating the performance reliability of the network; and simulating the performance reliability of the network by using the simulation method in the second step. And comparing the two reliability values to verify the effectiveness of the network simplification method on maintaining the performance reliability of the network.
The specific process of the first step is as follows:
firstly, according to a continuous time Markov model of a node, obtaining that the node is in a state Xi( X i1,2, n):
in the formula:iindicating the packet arrival rate, mu, of node iiWhich represents the service rate of the node i,
xiindicates the number of data packets of node i, pii(xi) Indicating that the node is in state xiProbability of time; when the node is in state xniWhen the probability is pii(xni) When the data packet continues to arrive, the packet loss will occur;
then, for the whole network, when the given external data packet arrival rate is gamma, determining a source point S and a destination node d of the network, wherein a routing matrix of the network is R ═ rij }, wherein rij represents the routing probability between nodes i and j; arrival rate i of each node in the network:
in the formula: gamma denotes a given external packet arrival rate,iindicating the packet arrival rate, r, of each nodeijRepresenting the routing probability, π, between nodes i and jj(nj) Indicating that node j is at xniProbability of a state; i-s denotes that node i is the source point; then, using a Markov reward model to calculate the network performance metric, the basic formula is as follows:
E(X)＝∑Ωfiπi， (3)
wherein, omega is a state space, piiProbability of being state i, fiThe reward value corresponding to the state i;
when calculating the network packet loss rate, fiIs denoted by fLiCalculated from the following equation:
f, when calculating the total number of packets in the networkiIs marked as
Calculated from the following formula:
the analytic calculation formula of the network performance measurement is derived as follows:
average total loss rate (Expected total loss rate):
average total loss probability (Expected total loss probability):
E(l)＝E(L)/γ (5)
average total number of packets (Expected total number of packets):
average total delay of packets arriving (Expected total delay of non-lost packets):
E(D)＝E(N)/γ(1-E(l)) (7)。
wherein, the second step comprises the following specific processes:
step 1: according to network parameters such as an adjacency matrix, a routing matrix, an edge reliability matrix, a storage space vector of each node, a node service rate vector, an external traffic arrival rate and the like of a network; calculating a network delay D threshold value when all sides in the network are normal as a fault criterion;
step 2: setting the number of simulation samples and initializing parameters; generating a random number a for each edge, and comparing a with the reliability of each edge; if the reliability is greater than a, the link is considered to be reliable; if the reliability is less than a, the link fails; thereby, a new adjacency matrix considering the link failure state is generated;
and step 3: generating a new routing matrix, namely, the routing probability of the fault edge is zero, and the routing probabilities of other edges are unchanged;
and 4, step 4: calculating the flow arrival rate of each node by the new routing matrix, and calculating the time delay E (D) of the network at the moment according to a formula (7); if E (D) is less than or equal to DThreshold valueThe simulation has no fault; continuing simulation until the set simulation times are finished;
and 5: and calculating the estimated value R of the network performance reliability, which is p/K, wherein p is the number of times of fault-free simulation, and K is the total number of times of simulation.
The third specific implementation method comprises the following steps:
firstly, judging whether a first-degree node, a second-degree node and a parallel structure exist in the network, if so, simplifying the network; for a node with the degree of one, if the node is not the starting point s or the end point d, obviously, the routing probability r of a link connected with the node is 0, and the traffic arrival rate is 0; at the moment, the degree one node and the related edges are directly deleted, the network performance is not influenced, and if the degree one node is a starting point or an end point, the node can be regarded as a degree two node, and simplification is carried out according to a degree two reduction principle based on time delay;
the deletion degree two nodes cause the delay value of the network analysis calculation to change; the routing matrix needs to be changed, and the storage space n and the service rate mu of the corresponding node need to be changed, and the storage space and the service rate of the node are simplified according to the following rules after the network is simplified because the complexity of the precise solution adopts approximate processing:
n′3＝n3+n2/(k3-k_ariv3+1) (8)
μ′3＝μ3-μ2/n2-ln(k3-k_ariv3+1) (9)
wherein k3 is the degree of the adjacent node of the degree two node, k _ ariv3 is the number of edges flowing into the node in the routing matrix, n2 is the storage space of the degree two node, and μ 2 is the service rate of the degree two node; for parallel reduction, only edges are deleted without changing nodes in the network, so that only the routing probability of a link is relatively changed, two edges exist between the nodes 1 and 2, the routing probabilities are r (a) and r (b), and the structure is reduced into a routing probability r12The edge of r (a) + r (b), the flow and performance parameters of the relevant nodes before and after simplification are unchanged; and simplifying the network according to the rule until the first degree, the second degree and the parallel connection structure do not exist in the network.
The invention relates to a network simplifying method for keeping network performance reliability, which has the advantages and positive effects that:
(1) on the basis of a graph change simplification method for maintaining the communication reliability, the network parameters of a configuration layer are added, a Markov reward model is used for performance modeling, the simplification method is designed and realized by taking the performance reliability as the constraint, the network simplification method for the unchanged network performance reliability is provided, the algorithm complexity of network reliability evaluation is reduced, and the network scale is reduced so as to facilitate the implementation of a reliability test.
(2) The invention provides a simplification method for maintaining performance reliability, theoretically makes up the defects of a network simplification method considering performance, is closer to the actual situation of a large-scale communication network compared with the existing method, and can meet the simplification requirement of network performance reliability evaluation.
Drawings
The CTMC model of the nodes of fig. 1.
Fig. 2 simplifies the front network.
FIG. 3 is a Monte Carlo simulation flow chart for performance reliability.
Figure 4 shows the results of performance reliability simulation before network simplification.
FIG. 5 is a simplified method flow diagram of the entire network that maintains performance reliability.
Fig. 6 is a degree one simplification.
Fig. 7 is a degree two simplification.
Fig. 8 is a simplified series-parallel connection.
Fig. 9 is a simplified network.
Figure 10 shows the results of performance reliability simulations after network simplification.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The invention provides a network simplifying method for keeping the reliability of network performance unchanged, which comprises the following steps:
the method comprises the following steps: establishing a network performance model based on a Markov Reward Model (MRM), and determining network performance indexes, wherein the step 1.1 is as follows: FIG. 1 shows a CTMC model of a node, which obtains the node in the state Xi(Xi＝1,2,...,ni) The probability of (c).
The node CTMC model considers the state space of nodes, and each node is regarded as an independent M/M/1/niThe queuing model, the data packets of the nodes are subject to Poisson distribution, the service time is subject to exponential distribution, and n is totaliA storage space. (reference [4 ]]K.Trivedi,Probability and Statistics with Reliability,Queuing,andComputer Science Applications[M]Second ed., John Wiley and Sons,2001.ISBNNumber 0-471-: trivedi, second edition of probability statistics in computer applications and reliability engineering, john william international press, 2001.ISBN number: 0-471-i+1 states, each packet occupying a memory space, state xiIndicating that i data packets exist in the node, and assuming that the node arrival rate and the node service rate mu are independent of the node state, the node is in the state xi(xi＝1,2,…,ni) The probability of (c) is calculated by the following formula:
in the formula:iindicating the packet arrival rate, mu, of node iiWhich represents the service rate of the node i,
xiindicates the number of data packets in node i, pii(xi) Indicating that the node is in state xiProbability of time. When the node is in state xniWhen the probability is pii(xni) When the data packet continues to arrive, packet loss will occur.
Step 1.2: on the basis of the step 1.1, obtaining an evaluation network performance index: average total time delay of arriving data packet.
For the whole network, at the time of giving the external data packet arrival rate gamma, in order to evaluate the performance reliability of the network, the data packet arrival rate of a single node of the network is firstly calculated. (reference [5 ]]Jackson J R.Networks ofwaiting lines[J]Operations research,1957,5(4): 518-: queuing for j.r.jackson.network [ J]Operational research 1957,5(4): 518-. Arrival rate of each node in the networki：
In the formula: gamma denotes a given external packet arrival rate,iindicating the packet arrival rate, r, of each nodeijRepresenting the routing probability, π, between nodes i and jj(nj) Indicating that node j is at xniThe probability of a state, i ═ s, indicates that node i is the source.
Then, using MRM model to calculate the network performance measurement, the MRM basic formula is:
E(X)＝∑Ωfiπi， (3)
wherein, omega is a state space, piiProbability of being state i, fiThe prize value corresponding to state i.
When calculating the network packet loss rate, fiIs denoted by fLiCalculated from the following equation:
f, when calculating the total number of packets in the networkiIs marked as
Calculated from the following formula:
the analytic calculation formula of the network performance measurement is derived as follows:
average total loss rate (Expected total loss rate):
average total loss probability (Expected total loss probability):
E(l)＝E(L)/γ (5)
average total number of packets (Expected total number of packets):
average total delay of packets arriving (Expected total delay of non-lost packets):
E(D)＝E(N)/γ(1-E(l)) (7)
for example, as shown in the figure, a typical network topology with 17 nodes is shown, where the source point s is selected as the node v (1) and the destination point d is selected as the node v (17). When designing the route, only the total probability of the route entering and exiting each node is ensured to be 1, and the number marked on each edge is the route probability rijAssume that the all-node service rate μ is 100, the all-node cache space size n is 50, and the initial arrival rate γ is 80.
The network performance metric values are analytically calculated according to the algorithm in the first step as shown in the following table 1.
TABLE 1
Step two: and evaluating the reliability of the network performance based on a Monte Carlo simulation method. A method flow diagram is shown in fig. 3.
Step 2.1: according to network parameters such as an adjacency matrix, a routing matrix, an edge reliability matrix, a storage space vector of each node, a node service rate vector, an external traffic arrival rate and the like of the network. Calculating the network time delay D when the edges in the network are all normalThreshold valueAs a fault criterion.
Step 2.2: setting the number of simulation samples and initializing parameters. A random number a is generated for each edge, and the reliability of a and each edge is compared. If the reliability is greater than a, the link is considered to be reliable; and if the reliability is less than a, the link fails. Thus, a new adjacency matrix is generated that takes into account the link failure state.
Step 2.3: the routing probability of the fault edge which generates the new routing matrix is zero, and the routing probabilities of other edges are unchanged.
Step 2.4: routing of new routesAnd (3) a matrix is used for calculating the flow arrival rate of each node, and then the time delay E (D) of the network at the moment is calculated according to a formula (7). If E (D) is less than or equal to DThreshold valueAnd the simulation has no fault. And continuing the simulation until the set simulation times.
Step 2.5: and calculating the estimated value R of the network performance reliability, which is p/K, wherein p is the number of times of fault-free simulation, and K is the total number of times of simulation.
The reliability of the network case in fig. 2 is calculated by using e (d) ═ 0.149 as a threshold, assuming that the reliability of each edge in the network is p (e) ═ 0.99, taking the sample size K ^ 10^5, performing 50 simulations, and performing the reliability of the network in fig. 2 according to the above flow of the evaluation method, and the result of performing the reliability simulation is shown in fig. 4.
Step three: on the basis of the graph change simplification method for maintaining the communication reliability, the network is simplified aiming at the unchanged reliability of the network performance, and a flow chart of the method is shown in fig. 5.
Step 3.1: according to the adjacency matrix, the routing matrix, the edge reliability matrix of the network, the capacity of the node and the service rate of the node. And judging whether the network has a first node, a second node and a parallel structure, if so, simplifying the network.
Step 3.2: judging whether a degree-one node exists or not, and if so, sequentially simplifying the degree-one node until the degree-one node does not exist in the network; if not, the step is skipped. The first simplification is shown in figure 6:
for a node with a degree of one, if the node is not the source point s or the destination point d, it is obvious that the routing probability r of the link connected with the node is 0, and the traffic arrival rate is 0. At this time, the degree one node and the related edge are directly deleted, so that the network performance is not influenced, and if the degree one node is a starting point or an end point, the node can be regarded as a degree two node, and simplification is performed according to a degree two reduction principle based on time delay.
Step 3.3: judging whether a degree two node exists, if so, simplifying the degree two, deleting the degree two node, and connecting two end points of the degree two node; if not, the step is skipped. Degree two is simplified as the attached figure 7:
n′3＝n3+n2/(k3-k_ariv3+1) (8)
μ′3＝μ3-μ2/n2-ln(k3-k_ariv3+1) (9)
in the formula: n isiIndicating the capacity of the node, muiRepresenting service rate of the node, r (i) representing routing probability, k3Degree of node 3, k _ ariv3The number of edges flowing into the node for traffic in the routing matrix.
Step 3.4: and (4) judging whether parallel edges appear or not, if so, carrying out parallel simplification, and returning to the step 3.1. The parallel connection is simplified as shown in figure 8.
Parallel reduction only deletes edges without changing nodes in the network, and therefore only the routing probability of links needs to be changed relatively, which is simplest, as shown in fig. 8. Two edges are arranged between the nodes 1 and 2, the routing probabilities are r (a) and r (b), and the structure is reduced into a routing probability r12The traffic and performance parameters of the relevant nodes before and after simplification are unchanged, and the finally analyzed and calculated performance metric is also unchanged.
According to the simplification method proposed above, simplification of the reliability of the performance of the whole network is established, and the case of fig. 2 is simplified, and the simplified graph is shown in fig. 9. And before and after the network is simplified, the node attribute pairs are as follows 2:
TABLE 2
Step four: and simplifying the case, and performing simulation verification by using the proposed performance reliability evaluation method.
As can be seen from fig. 4 and 10, the multiple simulation results are averaged, the performance reliability R _ P before the network simplification is approximately equal to 0.96, and the performance reliability R _ P after the network simplification is approximately equal to 0.91, which is slightly smaller than that before the reduction, with a relative error of 5%. This is because the degree two reduction is an approximate simplification, and has a certain influence on the performance reliability of the network.
Claims (3)
1. A network simplifying method for maintaining network performance reliability is characterized in that: the method comprises the following steps:
the method comprises the following steps: establishing a network performance model based on a Markov reward model, and determining a network performance index;
firstly, establishing a continuous time Markov chain model of a node; the node CTMC model considers the state space of nodes, and each node is regarded as an independent M/M/1/niThe queuing model, the data packets of the nodes are subject to Poisson distribution, the service time is subject to exponential distribution, and n is totaliA storage space; the different numbers of data packets in the nodes are regarded as different states of the nodes, all the states possibly occurring in the network are listed, and the probability of conversion among the states is determined; then, a network performance model based on a Markov reward model is established, namely, on the basis of the state space of a continuous time Markov chain, the network performance measurement is calculated by combining the continuous time Markov chain models of single nodes in the network by endowing different reward values to each state of the system: average total time delay of arriving data packet;
step two: evaluating the reliability of the network performance by a Monte Carlo simulation method;
firstly, supposing that the capacity of nodes in a network is limited and a link has a certain fault probability, randomly sampling the states of edges and nodes by taking the fault-free network delay as a threshold, then calculating the network delay by the average total delay of the arriving data packets in the step one, comparing the network delay with the threshold to judge whether a fault occurs or not, and obtaining the reliability of the network performance based on the delay by the statistical result after multiple times of simulation;
step three: on the basis of a graph change simplification method for maintaining the communication reliability, network simplification is carried out aiming at the unchanged reliability of network performance;
firstly, judging whether the network can be simplified or not according to an adjacency matrix, a routing matrix, an edge reliability matrix, the capacity of a node and the service rate of the node of the network; sequentially finding a degree-one node, a degree-two node and parallel edges in the network, and carrying out degree-one simplification, degree-two simplification and parallel simplification based on time delay until the network can not be simplified any more;
step four: carrying out simulation verification by using the proposed performance reliability evaluation method;
simplifying the network by using the simplification method provided by the step three, and then calculating the performance reliability of the network; simulating the performance reliability of the network by using the simulation method in the second step; comparing the two reliability values to verify the effectiveness of the network simplification method on maintaining the performance reliability of the network;
the third specific implementation method comprises the following steps:
firstly, judging whether a first-degree node, a second-degree node and a parallel structure exist in the network, if so, simplifying the network; for a node with the degree of one, if the node is not the starting point s or the end point d, obviously, the routing probability r of a link connected with the node is 0, and the traffic arrival rate is 0; at the moment, the degree one node and the related edges are directly deleted, the network performance is not influenced, and if the degree one node is a starting point or an end point, the node can be regarded as a degree two node, and simplification is carried out according to a degree two reduction principle based on time delay;
the deletion degree two nodes cause the delay value of the network analysis calculation to change; the routing matrix needs to be changed, and the storage space n and the service rate mu of the corresponding node need to be changed, and the storage space and the service rate of the node are simplified according to the following rules after the network is simplified because the complexity of the precise solution adopts approximate processing:
n′3＝n3+n2/(k3-k_ariv3+1) (8)
μ′3＝μ3-μ2/n2-ln(k3-k_ariv3+1) (9)
wherein k is3Degree of two-node neighbor node, k _ ariv3Number of edges, n, for the traffic in the routing matrix to flow into the node2To measure the storage space of two nodes, mu2Service rate of a degree two node;
for parallel reduction, only edges are deleted without changing nodes in the network, so that only the routing probability of a link is relatively changed, two edges exist between the nodes 1 and 2, the routing probabilities are r (a) and r (b), and the structure is reduced into a routing probability r12The edge of r (a) + r (b), the flow and performance parameters of the relevant nodes before and after simplification are unchanged; and simplifying the network according to the rule until the first degree, the second degree and the parallel connection structure do not exist in the network.
2. The method according to claim 1, wherein the specific process of the step one is as follows:
each packet occupies a memory space, state xiIndicating that i data packets exist in the node, and assuming that the node arrival rate and the node service rate mu are independent of the node state, the node is in the state xiThe probability of (c) is calculated by the following formula: wherein x isi＝1,2,…,ni；
In the formula:iindicating the packet arrival rate, mu, of node iiWhich represents the service rate of the node i,
wiindicates the number of data packets in node i, pii(xi) Indicating that the node is in state xiProbability of time; when the node is in state xniWhen the probability is pii(xni) When the data packet continues to arrive, the packet loss will occur;
then, for the whole network, when the given external data packet arrival rate is gamma, determining a source point S and a destination node d of the network, wherein the routing matrix of the network is R ═ RijIn which r isijRepresenting the routing probability between nodes i and j; arrival rate of each node in the networki：
In the formula: gamma denotes a given external packet arrival rate,iindicating the packet arrival rate, r, of each nodeijRepresenting the routing probability, π, between nodes i and jj(nj) Indicating that node j is at xniProbability of a state, i ═ s, denotes that node i is the source; then, using a Markov reward model to calculate the network performance metric, the basic formula is as follows:
E(X)＝∑Ωfiπi， (3)
wherein, omega is a state space, piiProbability of being state i, fiThe reward value corresponding to the state i;
when calculating the network packet loss rate, fiIs denoted by fLiCalculated from the following equation:
f, when calculating the total number of packets in the networkiIs marked as
Calculated from the following formula:
the analytic calculation formula of the network performance measurement is derived as follows:
average total loss rate (Expected total loss rate):
average total loss probability (Expected total loss probability):
E(l)＝E(L)/γ (5)
average total number of packets (Expected total number of packets):
average total delay of packets arriving (Expected total delay of non-lost packets):
E(D)＝E(Ｎ)/γ(1-E(l))。 (7)
3. the method according to claim 1, wherein the step two includes the following specific steps:
step 1: according to the network parameters of the adjacency matrix, the routing matrix, the edge reliability matrix, the storage space vector of each node, the node service rate vector and the external traffic arrival rate of the network; calculating the network time delay D when the edges in the network are all normalThreshold valueAs a fault criterion;
step 2: setting the number of simulation samples and initializing parameters; generating a random number a for each edge, and comparing a with the reliability of each edge; if the reliability is greater than a, the link is considered to be reliable; if the reliability is less than a, the link fails; thereby, a new adjacency matrix considering the link failure state is generated;
and step 3: generating a new routing matrix, namely, the routing probability of the fault edge is zero, and the routing probabilities of other edges are unchanged;
and 4, step 4: calculating the flow arrival rate of each node by the new routing matrix, and calculating the time delay E (D) of the network at the moment according to a formula (7); if E (D) is less than or equal to DThreshold valueThe simulation has no fault; continuing simulation until the set simulation times;
and 5: and calculating the estimated value R of the network performance reliability, which is p/K, wherein p is the number of times of fault-free simulation, and K is the total number of times of simulation.
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