CN107018011A - A kind of network reduction method of holding network performance reliability - Google Patents
A kind of network reduction method of holding network performance reliability Download PDFInfo
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Abstract
The present invention is a kind of network reduction method of holding network performance reliability, solves the problem of large scale network performance reliability assessment computation complexity is high.Specifically include following steps：Step one：The network performance model that model is rewarded based on Markov is set up, network performance index is determined；Step 2：Monte Carlo simulation method assesses network performance reliability；Step 3：The figure of connected sets is kept to change on the basis of method for simplifying, for the constant carry out network reduction of network performance reliability；Step 4：Simulating, verifying is carried out using the performance reliability assessment method of proposition.The invention provides the method simplified to large-scale communication network network and the appraisal procedure of its performance reliability, the method for simplifying maintains the performance reliability of network, and the algorithm complex and experiment cost that effectively reduction network performance reliability is assessed.
Description
Technical field
The invention belongs to network service and reliability engineering field, and in particular to a kind of holding network performance reliability
Network reduction method.
Background technology
Dependence of the society of information age to communication network is more and more stronger, normal operation of the network reliability to communication network
Play an important role.With the rapid expansion of network size, usage frequency, the quick increase of network load and single device can
The reasons such as the raising by property, the problem of network congestion and delay etc. are relevant with network performance has been increasingly becoming in network reliability must
The factor that must be considered, the research of the connected sets based on graph theory studied also by most of network reliability, steering is focused on
Network performance and service quality, cause the assessment complexity of network performance reliability to improve.On the one hand, commented using analytical Calculation
Estimate network performance reliability, for the polymorphic sex chromosome mosaicism of structure and node complicated in large scale network, capacity, flow etc. need to be considered
Factor so that the assessment difficulty of its performance reliability is greatly promoted.On the other hand, using the method for reliability test (with reference to text
Offer [1]：Chen Yang, Huang Ning, Kang Rui, wait LAN ftp business reliability tests and assessment technology [J] BJ University of Aeronautics ＆ Astronautics
Journal, 2011,37 (1):91-94.) assess network performance reliability and face that the time is oversize, expense is too high, workload is big etc. and ask
Topic.
Therefore, how research, which reduces the difficulty of network performance reliability assessment and experiment cost, has important value.Wherein,
It is applicability most wide effective way to simplify reduction of the network to realize network size.Current existing network reduction method is more
It is limited to the figure transform method for connected sets, (bibliography [2]:Shooman A M,Kershenbaum A.Exact
graph-reduction algorithms for network reliability analysis[C]//Global
Telecommunications Conference,1991.GLOBECOM'91.'Countdown to the New
Millennium.Featuring a Mini-Theme on:Personal Communications Services.IEEE,
1991:1412-1420. translate：Shooman A M, Kershenbaum A. are used for the accurate figure simplification calculation that network reliability is analyzed
Method [C], global communication meeting, 1991：1412-1420) lack to relevant factors of performance such as influence communication network congestion, delays
Consider；The existing network reduction method (bibliography [3] for considering performance:Li Haoping, Xiao Xiaoqiang, Kuang Luobei, wait to be based on opening up
Flutter simplified Self-similar Network relevant parameter analysis [J] microcomputer informations, 2008,24 (18):186-188.) assume network
In each node relevant parameter it is constant, gone here and there in the case where not influenceing the principle of network performance, parallel connection simplify, many shapes of node are not considered
State, and then performance reliability is not yet considered in this simplification, it is difficult to meet the simplification demand of network performance reliability assessment.It is based on
Problem above, is badly in need of proposing a kind of network reduction method of holding network performance reliability.
The content of the invention
The invention aims to solve the problem of large scale network performance reliability assessment complexity is high, it is proposed that one
Plant the network reduction method for keeping network performance reliability.
A kind of network reduction method for holding network performance reliability that the present invention is provided, comprises the following steps：
Step one：The network performance model that model (MRM) is rewarded based on Markov is set up, network performance index is determined.
Initially set up continuous time Markov Chain (CTMC) model of node.Node CTMC models consider the state of node
Space, each node is considered as an independent M/M/1/n queuing model.Regard packet number difference in node as node different
State, the state being likely to occur in all-network is all listed, and determine changed between each state probability (namely turn
Move probability).Then set up MRM network performance models, i.e., it is each by imparting system on the basis of CTMCs state space
The different award value of state, single node CTMC models couplings in network are got up, the performance metric of calculating network：Averagely reach number
According to bag overall delay.
Step 2：Monte Carlo simulation method assesses network performance reliability.
For the research of network performance reliability, time delay be the network user because can direct feeling to and the performance water most paid close attention to
It is flat, based on the network performance model in step one, network failure is combined with network performance model, Monte Carlo simulation method is used
Calculating network performance reliability, assumes initially that nodes finite capacity, link has certain probability of malfunction, with fault-free
Network delay is threshold value, the state progress random sampling of opposite side and node, when then total by the average arrival packet of step one
Prolong calculating network time delay, network delay and threshold value are compared and judge whether network breaks down, the statistics after Multi simulation running
As a result the network performance reliability based on time delay is obtained.
Step 3：The figure of connectivity reliability is kept to change on the basis of method for simplifying, it is constant for network performance reliability
Carry out network reduction.
Simplified basic ideas are based on scheming change reduction method, to add route matrix and joint behavior parameter, bag
The change of the parameters such as memory space and service rate is included, it is equal for constraint with the packet loss and number-of-packet of part before and after simplifying, if
Meter reduction rule.If local packet loss and number-of-packet is constant, the time delay of whole net will be maintained, thus performance reliability
Will be approximate.First according to the adjacency matrix of network, route matrix, side reliability matrix, and node capacity and node serve
Rate, judges whether network can simplify；Then sequentially find the node of degree one in network, two nodes of degree and parallel edges, based on when
Prolong the simplification of progress degree one, degree two simplifies and connection in series-parallel simplifies until network can not be streamlined any further.
Step 4：Simulating, verifying is carried out using the performance reliability assessment method of proposition.
The method for simplifying proposed using step 3 is simplified to network, then the performance reliability of calculating network；Utilize
Emulation mode is emulated to the performance reliability of network in step 2.Above-mentioned two reliability value is contrasted to verify network reduction
Method is to keeping the validity of the performance reliability of the network.
Wherein, the detailed process of described step one is：
First according to the continuous time Markov model of node, obtain node and be in state Xi(Xi=1,2 ..., n)
Probability：
In formula：ΓiRepresent node i packet arrival rate, μiNode i service rate is represented,xiRepresent node i data
Bag number, πi(xi) represent that node is in state xiWhen probability；When node is in state xniWhen, probability is πi(xni), now after
It is continuous to reach packet, it will appear from packet loss；
Then for whole network, when given external data bag arrival rate is γ, the source point S and purpose of network are determined
Node d, the route matrix of network is R={ rij }, and wherein rij represents the routing probability between node i and j；Each saved in network
The arrival rate Γ i of point：
In formula：γ represents given external data bag arrival rate, ΓiRepresent the packet arrival rate of each node, rij tables
Show the routing probability between node i and j, πj(nj) represent that node j is in xnShape probability of state；I=s represents that node i is source point；
Then, model, calculating network performance metric are rewarded with Markov, its fundamental formular is：
E (X)=∑Ωfiπi, (3)
Wherein, Ω is state space, πiFor state i probability, fiFor the corresponding award values of state i；
During calculating network packet loss loss rate, fiIt is designated as fLi, calculated by following formula：
In calculating network during number-of-packet total number of packets, fiIt is designated as, calculated by following formula：
Thus it is derived by network performance metric analytic sensitivity：
Average total packet loss (Expected total loss rate)：
Average total drop probabilities (Expected total loss probability)：
E (l)=E (L)/γ (5)
Average total number is according to bag number (Expected total number of packets)：
Averagely reach packet overall delay (Expected total delay of non-lost packets)：
E (D)=E (N)/γ (1-E (l)) (7).
Wherein, described step two detailed process is：
Step 1：According to the adjacency matrix of network, route matrix, side reliability matrix, the memory space of each node is vectorial,
The network parameters such as node serve rate vector sum external flow arrival rate；Calculate the network delay when the side in network is all normal
D threshold values are used as failure criterion；
Step 2：Set simulation sample number, initiation parameter；A random number a is produced for each edge, then compares a and every
The size of bar side reliability；If reliability is more than a, then it is assumed that the link is reliable；If reliability is less than a, the link failure；By
This, generates the new adjacency matrix of a consideration link-failure state；
Step 3：The new route matrix of generation is that the routing probability on failure side is zero, and the routing probability on other sides is constant；
Step 4：By new route matrix, calculate the flow arrival rate of each node, further according to formula (7) calculate now
The time delay E (D) of network；If D≤DThreshold value, this emulation fault-free；Continue to emulate the simulation times until completing to set；
Step 5：Calculating network performance reliability estimate R=p/K, wherein p are fault-free simulation times, and K is total emulation
Number of times.
Wherein, described step three concrete methods of realizing is：
Network is first determined whether with the presence or absence of one node of degree, two nodes of degree and parallel-connection structure, if in the presence of network can letter
Change；For spending the node for one, if not being starting point s or terminal d, it is clear that the routing probability r=of coupled ground link
0, flow arrival rate Γ=0；Now, the directly node of deletion degree one and dependence edge, do not influence on network performance, if degree one is saved
Point is starting point or terminal, and the node of node degree of can be considered two is then simplified according to the reduction of degree two principle based on time delay；
The time delay value changes that the node of deletion degree two will cause network analysis to calculate；Need to change route matrix, also need to change
The memory space n and service rate μ of respective nodes, because the complexity accurately solved uses approximate processing, therefore the storage of node is empty
Between and service rate simplify network after according to following rule：
n′3=n3+n2/(k3-k_ariv3+1) (8)
μ′3=μ3-μ2/n2-ln(k3-k_ariv3+1) (9)
Wherein k3 is spends the number of degrees of two node adjacent nodes, and k_ariv3 flows into the side of the node for flow in route matrix
Number, n2 is the memory space of two nodes of degree, and μ 2 is the service rate of two nodes of degree；Side is only deleted for parallel connection reduction, without changing
Node in dynamic network, therefore only need to relatively change between the routing probability of link, node 1 and 2 and have two sides, routing probability
Respectively r (a) and r (b), is that a routing probability is r by this structure reduction12, there is joint on=r (a)+r (b) side before and after simplifying
The flow and performance parameter of point are constant；Network reduction is carried out until degree one is not present in network according to above-mentioned rule, spends two nodes
And parallel-connection structure.
A kind of network reduction method of holding network performance reliability of the present invention, advantage is with good effect：
(1) present invention adds the network ginseng of configuration layer on the basis of the figure change method for simplifying of connected sets is kept
Count, performance modeling is carried out with Markov reward model, method for simplifying design is carried out by constraint of retention property reliability and real
It is existing, it is proposed that for the network reduction method that network performance reliability is constant, the algorithm complex that reduction Reliability of Network is assessed,
Reduce network size in order to which reliability test is implemented.
(2) present invention proposes a kind of method for simplifying of retention property reliability, compensate in theory for considering performance
Network reduction method deficiency, compared to the actual conditions that existing method is closer to large-scale communication network network, disclosure satisfy that
The simplification demand of network performance Reliability assessment.
Brief description of the drawings
The CTMC models of Fig. 1 nodes.
Network before Fig. 2 simplifies.
Fig. 3 performance reliabilities cover Caro simulation contact surface.
Performance reliability simulation result before Fig. 4 network reductions.
The whole net method for simplifying flow chart of Fig. 5 retention property reliabilitys.
Fig. 6 degree one simplifies.
Fig. 7 degree two simplifies.
Fig. 8 connection in series-parallel simplifies.
Network after Fig. 9 simplification.
Performance reliability simulation result after Figure 10 network reductions.
Embodiment
Below in conjunction with drawings and examples, the present invention is described in further detail.
The present invention proposes a kind of network reduction method for keeping network performance reliability constant, comprises the following steps：
Step one：Set up according to the network performance model that model (MRM) is rewarded based on Markov, determine that network performance refers to
Mark
Step 1.1：Such as the CTMC models that accompanying drawing 1 is node, obtain node and be in state Xi(Xi=1,2 ..., ni) it is general
Rate.
Node CTMC models consider the state space of node, and each node is considered as an independent M/M/1/niQueuing mould
Type, the packet of node reaches obedience Poisson distribution, and service time obeys exponential distribution, has n memory space.(with reference to text
Offer [4] K.Trivedi, Probability and Statistics with Reliability, Queuing, and
Computer Science Applications[M],second ed.,John Wiley and Sons,2001.ISBN
Number0-471-33341-7. translate：K.Trivedi. the probability statistics second edition in computer application and Reliability Engineering, about
Han Weili Publishers International Press, New York, 2001.ISBN numberings：0-471-33341-7) regard packet number difference in node as node not
Same state, each node i will have ni+ 1 state, each packet takes a memory space, state xiRepresent have in node
I packet, it is assumed that node arrival rate Γ and node serve rate μ is independent with node state, then node is in state xi(xi=1,
2,…,ni) probability calculated by equation below：
In formula：ΓiRepresent node i packet arrival rate, μiNode i service rate is represented,xiRepresent number in node i
According to bag number, πi(xi) represent that node is in state xiWhen probability.When node is in state xniWhen, probability is πi(xni), now
Packet is continued to, packet loss is will appear from.
Step 1.2：On the basis of step 1.1, obtain evaluating network performance index：Averagely reach packet overall delay.
It is first in order to evaluate the performance reliability of network in given external data bag arrival rate γ for whole network
The packet that first calculate network individual node reaches rate.(bibliography [5] Jackson J R.Networks of
waiting lines[J].Operations research,1957,5(4):518-521. translate：J.R.Jackson. network
Queuing [J] operational research 1957,5 (4):The source point s and destination node d of network 518-521.) are determined, the route matrix of network is R
={ rij }, wherein rij represent the routing probability between node i and j.The arrival rate Γ of each node in networki：
In formula：γ represents given external data bag arrival rate, ΓiRepresent the packet arrival rate of each node, rijTable
Show the routing probability between node i and j, πj(nj) represent that node j is in xniShape probability of state, i=s represents that node i is source point.
Then, MRM models, calculating network performance metric are used, MRM fundamental formulars are：
E (X)=∑Ωfiπi, (3)
Wherein, Ω is state space, πiFor state i probability, fiFor the corresponding award values of state i.
During calculating network packet loss loss rate, fiIt is designated as fLi, calculated by following formula：
In calculating network during number-of-packet total number of packets, fiIt is designated asCalculated by following formula：
Thus it is derived by network performance metric analytic sensitivity：
Average total packet loss (Expected total loss rate)：
Average total drop probabilities (Expected total loss probability)：
E (l)=E (L)/γ (5)
Average total number is according to bag number (Expected total number of packets)：
Averagely reach packet overall delay (Expected total delay of non-lost packets)：
E (D)=E (N)/γ (1-E (l)) (7)
Case such as accompanying drawing, figure is the typical network topology structure of 17 nodes, and it is node v (1) to select source point s, eventually
Point d is node v (17).The routing probability summation that need to only ensure to pass in and out each node during design route is respectively 1, each edge subscript
The numeral of note is routing probability rij, it is assumed that all node serve rate μ=100, all nodal cache space size n=50, initially
Arrival rate γ=80.
It is as shown in table 1 below according to the arithmetic analysis calculating network performance metric values in step one.
Table 1
Step 2：Based on Monte Carlo simulation method, network performance reliability is assessed.Method flow diagram is as shown in Figure 3.
Step 2.1：According to the adjacency matrix of network, route matrix, side reliability matrix, the memory space of each node to
Measure, the network parameter such as node serve rate vector sum external flow arrival rate.Calculate the network when the side in network is all normal
Time delay DThreshold valueIt is used as failure criterion.
Step 2.2：Set simulation sample number, initiation parameter.For each edge produce a random number a, then compare a with
The size of each edge reliability.If reliability is more than a, then it is assumed that the link is reliable；Reliability is less than a, then the link failure.By
This, generates the new adjacency matrix of a consideration link-failure state.
Step 2.3：The new route matrix of generation is that the routing probability on failure side is zero, and the routing probability on other sides is constant.
Step 2.4：By new route matrix, the flow arrival rate of each node is calculated, is calculated now further according to formula (7)
The time delay E (D) of network.If D≤DThreshold value, this emulation fault-free.Continue to emulate until the simulation times of setting.
Step 2.5：Calculating network performance reliability estimate R=p/K, wherein p are fault-free simulation times, and K is total imitative
True number of times.
With the performance reliability that E (D)=0.149 is network case in threshold calculations accompanying drawing 2, it is assumed that each edge in network
Reliability is p (e)=0.99, takes sample size K=10^5, carries out 50 emulation, according to the flow of above-mentioned appraisal procedure, to figure
Network carries out the emulation acquired results of performance reliability as shown in Figure 4 in 2.
Step 3：The figure of connected sets is kept to change on the basis of method for simplifying, it is constant for network performance reliability
Network reduction is carried out, method flow diagram is as shown in Figure 5.
Step 3.1：According to the adjacency matrix of network, the capacity and node of route matrix, side reliability matrix, and node
Service rate.Network is judged with the presence or absence of one node of degree, two nodes of degree and parallel-connection structure, if in the presence of network can simplify.
Step 3.2：The node of degree of determining whether one, the simplification of progress degree one successively if having, until no longer existing in network
Spend a node；If no, skipping this step.Degree one simplifies as shown in Figure 6：
For spending the node for one, if not being source point s or terminal d, it is clear that the routing probability r of coupled ground link
=0, flow arrival rate Γ=0.Now, the directly node of deletion degree one and dependence edge, do not influence on network performance, if degree one
Node is starting point or terminal, and the node of node degree of can be considered two then carries out letter according to the reduction principle of degree two based on time delay
Change.
Step 3.3：The node of degree of determining whether two, the simplification of progress degree two if having, the node of deletion degree two connects two
End points；If no, skipping this step.Degree two simplifies such as accompanying drawing 7：
Node 2 is that the routing probability between two nodes of degree, node 1 and 2 is r (b), between node 2 and next node 3
Routing probability one is set to r23Behind=1, therefore deletion of node 2, the routing probability on the side between increase connecting node 1 and node 3 is r
(b).However, the node of degree two deleted has flow arrival, according to analytical performance model, there is certain packet loss, delete in the node
Except the flow arrival rate of posterior nodal point 3 will increase, whole net packet loss and packet sum will decline, therefore delete the node and will cause
The time delay value changes that network analysis is calculated.In order to keep the network delay before and after simplifying constant, do not need singly to change route matrix,
Also need the performance parameter of change respective nodes, including capacity n and service rate μ.Because the complexity accurately solved is using approximate place
Reason, thus the memory space of node and service rate after network is simplified according to following rule：
n′3=n3+n2/(k3-k_ariv3+1) (8)
μ′3=μ3-μ2/n2-ln(k3-k_ariv3+1) (9)
In formula：niRepresent the capacity of node, μiThe service rate of node is represented, r (i) represents routing probability, k3For node 3
The number of degrees, k_ariv3The side number of the node is flowed into for flow in route matrix.
Step 3.4：Judge whether parallel edges occur, in parallel simplified, return to step 3.1 is carried out if having.Parallel connection simplifies such as
Accompanying drawing 8.
Side is only deleted in parallel connection reduction, without changing the node in network, therefore only need to relatively change the route of link
Probability, the most simply, as shown in Figure 8.There are two sides between node 1 and 2, routing probability is respectively r (a) and r (b), and this is tied
Structure is reduced to a routing probability for r12=r (a)+r (b) side, has the flow of artis and performance parameter constant before and after simplifying,
The performance metric of final analytical Calculation will equally keep constant.
According to method for simplifying set forth above, the simplification of whole net retention property reliability is set up, the case to Fig. 2 carries out letter
Change, the figure after simplifying is as shown in Figure 9.And before and after network reduction, nodal community contrast such as table 2 below：
Table 2
Step 4：Simplified for case, simulating, verifying is carried out using the performance reliability assessment method of proposition.
From accompanying drawing 4, accompanying drawing 10, Multi simulation running result takes the performance reliability R_P ≈ before average, network reduction
0.96, the performance reliability R_P ≈ 0.91 after network reduction, smaller, the relative error 5% compared with before reduction.Because degree
Two reductions belong to approximate simplification, have a certain degree of influence to the performance reliability of network.
Claims (4)
1. a kind of network reduction method of holding network performance reliability, it is characterised in that：Comprise the following steps：
Step one：The network performance model that model is rewarded based on Markov is set up, network performance index is determined；
Initially set up the continuous time Markov chain model of node；Consider the state space of node, each node is considered as one
Independent M/M/1/n queuing models；Regard packet number difference in node as node different state, can in all-network
The state that can occur all is listed, and the probability changed between each state is determined；Then set up and reward mould based on Markov
The network performance model of type, i.e., on the basis of continuous time markovian state space, pass through each shape of imparting system
The different award value of state, single node continuous time Markov chain model in network is combined, the performance degree of calculating network
Amount：Averagely reach packet overall delay；
Step 2：Monte Carlo simulation method assesses network performance reliability；
Nodes finite capacity is assumed initially that, link has certain probability of malfunction, using fault-free network time delay as threshold value,
The state of opposite side and node carries out random sampling, then by the average arrival packet total delay calculation network delay of step one,
Network delay and threshold value are compared and judge whether to break down, the statistical result after Multi simulation running obtains the net based on time delay
Network performance reliability；
Step 3：Keep on the basis of the figure change method for simplifying of connected sets, carried out for network performance reliability is constant
Network reduction；
First according to the adjacency matrix of network, route matrix, side reliability matrix, and node capacity and node serve rate,
Judge whether network can simplify；Then the node of degree one in network, two nodes of degree and parallel edges are sequentially found, is entered based on time delay
Row degree one simplifies, and degree two simplifies and in parallel simplified until network can not be streamlined any further；
Step 4：Simulating, verifying is carried out using the performance reliability assessment method of proposition；
The method for simplifying proposed using step 3 is simplified to network, then the performance reliability of calculating network；Utilize step
Emulation mode is emulated to the performance reliability of network in two；Above-mentioned two reliability value is contrasted to verify network reduction method
To the validity for the performance reliability for keeping the network.
2. the network reduction method of a kind of holding network performance reliability according to claim 1, it is characterised in that described
The step of one detailed process be：
First according to the continuous time Markov model of node, obtain node and be in state Xi(Xi=1,2 ..., n) general
Rate：
In formula：ΓiRepresent node i packet arrival rate, μiNode i service rate is represented,xiRepresent node i packet
Number, πi(xi) represent that node is in state xiWhen probability；When node is in state xniWhen, probability is πi(xni), now proceed to
Up to packet, packet loss will appear from；
Then for whole network, when given external data bag arrival rate is γ, the source point S and destination node of network are determined
D, the route matrix of network is R={ rij, wherein rijRepresent the routing probability between node i and j；Each node in network
Arrival rate Γi：
In formula：γ represents given external data bag arrival rate, ΓiRepresent the packet arrival rate of each node, rijRepresent section
Routing probability between point i and j, πj(nj) represent that node j is in xnShape probability of state；I=s represents that node i is source point；Then,
Model, calculating network performance metric are rewarded with Markov, its fundamental formular is：
E (X)=∑Ωfiπi, (3)
Wherein, Ω is state space, πiFor state i probability, fiFor the corresponding award values of state i；
During calculating network packet loss loss rate, fiIt is designated as fLi, calculated by following formula：
In calculating network during number-of-packet total number of packets, fiIt is designated asCalculated by following formula：
Thus it is derived by network performance metric analytic sensitivity：
Average total packet loss (Expected total loss rate)：
Average total drop probabilities (Expected total loss probability)：
E (l)=E (L)/γ (5)
Average total number is according to bag number (Expected total number of packets)：
Averagely reach packet overall delay (Expected total delay of non-lost packets)：
E (D)=E (N)/γ (1-E (l)). (7)
3. the network reduction method of a kind of holding network performance reliability according to claim 1, it is characterised in that described
The step of two detailed processes be：
Step 1：According to the adjacency matrix of network, route matrix, side reliability matrix, the memory space vector of each node, node
The network parameters such as service rate vector sum external flow arrival rate；Calculate the network delay D thresholds when the side in network is all normal
Value is used as failure criterion；
Step 2：Set simulation sample number, initiation parameter；A random number a is produced for each edge, then compares a and each edge
The size of reliability；If reliability is more than a, then it is assumed that the link is reliable；If reliability is less than a, the link failure；Thus,
The new adjacency matrix of one consideration link-failure state of generation；
Step 3：The new route matrix of generation is that the routing probability on failure side is zero, and the routing probability on other sides is constant；
Step 4：By new route matrix, the flow arrival rate of each node is calculated, then now net is calculated in the formula (7) of basis
The time delay E (D) of network；If D≤D threshold values, this emulation fault-free；Continue to emulate the simulation times until completing to set；
Step 5：Calculating network performance reliability estimate R=p/K, wherein p are fault-free simulation times, and K is total simulation times.
4. the network reduction method of a kind of holding network performance reliability according to claim 1, it is characterised in that described
The step of three concrete methods of realizing be：
Network is first determined whether with the presence or absence of one node of degree, two nodes of degree and parallel-connection structure, if in the presence of network can simplify；It is right
In the node that degree is one, if not being starting point s or terminal d, it is clear that the routing probability r=0 of coupled ground link, flow
Arrival rate Γ=0；Now, the directly node of deletion degree one and dependence edge, do not influence on network performance, if one node of degree is
Initial point or terminal, the node of node degree of can be considered two are then simplified according to the reduction of degree two principle based on time delay；
The time delay value changes that the node of deletion degree two will cause network analysis to calculate；Need to change route matrix, also need to change corresponding
The memory space n and service rate μ of node, because the complexity accurately solved uses approximate processing, therefore the memory space of node and
Service rate is after network is simplified according to following rule：
n′3=n3+n2/(k3-k_ariv3+1) (8)
μ′3=μ3-μ2/N2-ln(K3-k_ariv3+1) (9)
Wherein k3To spend the number of degrees of two node adjacent nodes, k_ariv3The side number of the node, n are flowed into for flow in route matrix2
To spend the memory space of two nodes, μ2To spend the service rate of two nodes；
Side is only deleted for parallel connection reduction, without changing the node in network, therefore only need to relatively change the route of link
There are two sides between probability, node 1 and 2, routing probability is respectively r (a) and r (b), is a routing probability by this structure reduction
For r12=r (a)+r (b) side, has the flow of artis and performance parameter constant before and after simplifying；Network is carried out according to above-mentioned rule
Simplify until being not present in network and spend one, spend two nodes and parallel-connection structure.
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