CN105956357A - Method for evaluating anti-interference capability of network system - Google Patents
Method for evaluating anti-interference capability of network system Download PDFInfo
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Abstract
The invention discloses a method for evaluating the anti-interference capability of a network system. The invention aims at evaluating whether the network system still can guarantee that the capability of connecting Original and Destination pairs (OD pairs) according to a path length meeting a preset value condition under the action of various types of factors. The method comprises the steps: firstly enabling the anti-interference capability of the network system to be converted into path length preset value ranges corresponding to all OD pairs; secondly simulating a natural ripple spread phenomenon, and carrying out one-off ripple spread relay race in the network, so as to solve all paths, meeting the corresponding preset value condition, among all OD pairs in the network (not just solving the shortest path among the OD pairs and not all paths among the OD pairs); and finally carrying out the statistic analysis of the sharing condition of nodes and links in the paths with the lengths meeting the preset value range condition. The method can be used for solving a problem of anti-interference capability evaluation of a physical network and an extract virtual network.
Description
Technical field:
The invention provides a kind of method assessing network system capacity of resisting disturbance, belong to complication system engineering, safe and scientific and work
Journey, computerized algorithm and management optimization field.
Background technology:
Network system relates to the every aspect of actual life, has the most both included real physical network, such as network of highways, includes again taking out
The virtual network of elephant, such as decision tree.One of all-network system what is common is that at all: will be originally by network topology structure
Isolated Node connectedness gets up, thus sets up various contacts or relation between node, in order to make all nodes as an entirety
Change system and jointly realize specific systemic-function.Such as, a systemic-function of network of highways seeks to realize any two city
Between town can be access；One systemic-function of decision tree seeks to realize completing certain task under certain given precondition
Conceptual design.Due to various interference factors (such as: random natural disaster, artificial calculated attack, system components functional fault,
Etc.) existence, in network system link and node have the probability being disconnected at any time.When in network system some link and
When node disconnects due to interference factor, whether network system also ensures that given system function based on remaining link and node
Achieve？Answer this problem, it is necessary to the capacity of resisting disturbance of network system is estimated.
The common thinking being estimated the capacity of resisting disturbance of network system at present has two big classes.The concern of first kind Evaluation example is burnt
Point is: under interference factor effect, network system is disintegrated and become two or more the most disjunct, independent sub-network system
Probability is (such as, based on the road network after earthquake, if having at least two cities and towns, the most no longer there is any route can
With connection each other；And for example, in production schedule decision tree, after some production unit fault, if can cause the system cannot be again
Produce any product, i.e. Product Status cannot be arrived from feed states).The focus of Equations of The Second Kind Evaluation example is: dry
Disturbing under factor effect, in network, the probability that optimum contacts or iptimum relationship is destroyed between node is (after such as, based on earthquake
Road network, whether the shortest path between certain two cities and towns is destroyed；And for example, in production schedule decision tree, when some production unit
After fault, whether the production decision that can bring maximum profit can be the most feasible).
It is true that above-mentioned two big class network system capacity of resisting disturbance appraisal procedures only only account for two kinds of extreme cases: or network
System break-down becomes multiple sub-network system independent of each other, or the optimal route in network system is affected.But,
In actual life, network user or policymaker institute most concerned be not often both extreme cases, but following one is more
Pervasive situation: under interference factor effect, whether network system also ensures that the system merit realizing certain minimum level specified
Energy？Such as, based on the road network after earthquake, if also ensure that and have at least one length to be not more than certain between any two cities and towns
The route of individual given threshold value connect each other (length can not realize sending in time of disaster relief material more than the route of given threshold value, thus
There is no essential meaning)；And for example, in production schedule decision tree, when after some production unit fault, if yet suffering from one can
The production decision of row can guarantee that and realizes certain predetermined profit level (investor of production line can't doggedly have to maximum profit
Can not, as long as but can ensure that and realize certain rate of return on investment).
It is clear that " whether network system also ensures that the systemic-function realizing certain minimum level specified " covers " network
Whether system can be disintegrated becomes multiple sub-network system independent of each other " and " whether the optimal route in network system can be by shadow
Ring " both extreme cases.Thus: " whether network system also ensures that the systemic-function realizing certain minimum level specified "
It it is a kind of generalization thinking that the capacity of resisting disturbance of network system is estimated.By this generalization thinking, network system is resisted
Interference performance is estimated meeting very much current demand, and (result being estimated by two kinds of extreme thinkings is usually unable to meet very well
Current demand: because network system disintegrates usually small probability event, can't often occur in daily life, ordinary people examines
Consider this problem to entertain imaginary or groundless fears a little；And optimal route is affected usually Great possibility, ordinary people can accept " gold nothing
Pure gold " this reason, unless there are compulsive perfectionist).
But, the existing method being estimated the capacity of resisting disturbance of network system is the most all to come by one of two kinds of extreme thinkings
Design.By " whether network system also ensures that the systemic-function realizing certain minimum level specified " this generalization thinking
The method being estimated the capacity of resisting disturbance of network system also rarely has report.
From the point of view of quantitative calculation and analysis, by " network system whether also ensure that realize certain minimum level specified be
System function " this generalization thinking assesses the capacity of resisting disturbance of network system, first has to must be able to calculating electrical path length of finding a way out full
All (rather than wherein one or part) paths of foot specified criteria, such as, length owning less than given threshold value in road network
Route, is capable of all production decisions no less than given threshold value profit in production schedule decision tree.But, path length of finding a way out
It is not a nothing the matter for existing method that degree meets all paths of specified criteria, can describe on mathematical model
Become the front k bar optimum path problems of (that is: multiple starting point, multiple terminals) the most.Most method for optimizing route
Only consider one to one (that is: one starting point, a terminal) optimum path problems.Existing solve front k bar optimal path and ask
The method of topic is typically iterative a series of (quantity is the hugest) to one first optimum path problems, solution procedure
The most loaded down with trivial details and poor efficiency, such as, for a starting and terminal point to (be commonly referred to as an OD to) later, needs based on front (k-1)
Bar optimal path reconstructs the new network of a series of substantial amounts, then to each new Solution To The Network the first optimal path, just can look for
Go out the kth optimal path in former network.For the most problems, in addition it is also necessary to each OD to repeating above-mentioned loaded down with trivial details ask
Solution preocess.When network system is the hugest (that is: have OD much more very to), want fast and effeciently to solve more to many before
K bar optimum path problems, existing method is the most helpless.This is also that the most existing method seldom can be by " net
Whether network system also ensures that the systemic-function realizing certain minimum level specified " this generalization thinking to be to assess network system
Capacity of resisting disturbance, it may be assumed that because existing method cannot effectively solve all routes less than given threshold value of length in network.
Document [1] and document [2] report a kind of ripples broadcast algorithm recently, it is not necessary to the iteration in other existing method
Repetitive operation, just can solve the front k bar optimal path for one to one problem in disposable computing.The method of the present invention
In will improve this ripples broadcast algorithm, in order to realize in disposable computing, solving all front k bar of the most problems
Shortest path.Then, the method for the present invention will be found out path in network system by these all front k bar optimal paths and meet
All paths of specified criteria, then analyze node and the shared situation of link in these paths meeting specified criteria, it is possible to by " net
Whether network system also ensures that the systemic-function realizing certain minimum level specified " this generalization thinking the most quantitatively comments
Estimate the capacity of resisting disturbance of network system.
[1] Hu, X.B., M.Wang, D.Hu, M.S.Leeson, E.L.Hines, and E.Di Paolo, " A Ripple-Spreading Algorithm
For the k Shortest Paths Problem, " 2012 the 3rd Global Congress on Intelligent Systems (GCIS 2012), PP:
202-208,6-8 Nov 2012, Wuhan, China.
[2] Hu, X.B., M.Wang, M.S.Leeson, E.L.Hines, and E.Di Paolo, " A Deterministic Agent-Based Path
Optimization Method by Mimicking the Spreading of Ripples ", Evolutionary Computation, in press, 20l6
(Open Access available online, doi:10.1162/EVCO_a_00156).
Summary of the invention:
The invention aims to provide a kind of method assessing network system capacity of resisting disturbance.With assessment network system various dry
Disturb and under factor effect, whether also ensure that the path realized by meeting corresponding default codomain condition connects each starting and terminal point pair
The ability of (that is, OD to).The present invention solves the problems referred to above, in brief, first network system is resisted by the method for the present invention
Interference performance requires that changing into each path of OD pair corresponding presets codomain, and the ripples diffusing phenomenon then simulating nature exist
Network is carried out the diffusion relay race of disposable ripples, with obtain in network each OD between length meet and corresponding preset codomain bar
All paths of part (are not to only demand OD to it by " whether the optimal route in network system can be affected " this extreme thinking
Between shortest path, be not that this is extreme by " whether network system can be disintegrated becomes multiple sub-network system independent of each other "
Thinking ask OD between all paths), all these length of last statistical analysis meets in the corresponding path presetting codomain condition
Node and the shared situation of link, thus by " whether network system also ensures that the system realizing certain minimum level specified
Function " this generalization thinking carrys out the capacity of resisting disturbance of qualitative assessment network system.
Determine by " whether network system also ensures that the systemic-function realizing certain minimum level specified " this generalization thinking
The capacity of resisting disturbance of amount assessment network system, can be described as following mathematical problem.
Assume that having a network system (can be reality physical network system, such as: network of highways, it is also possible to be abstract virtual network
System, such as: decision tree), comprise NNIndividual node and NEBar links.Link between node can be represented by an adjacency matrix A,
(i, j)=1 represents one link of existence between node i to node j to elements A therein；(i, j)=0 represents that node i is to knot to A
Not link between some j.Assume to exist between node i to node j a link, then the weighted value of this link can be designated as CE(i, j).
The weighted value C of linkE(i j) will be used for calculating the length in path.Vacation lets p represent a paths, and path P comprises NL>=2 knots
Point, P (i) represents the i-th node of path P, 1≤i≤NL, 1≤P (i)≤NN.Use CP(P) length of path P is represented, its
It is calculated as follows:
Assume that again network system has NODIndividual starting and terminal point is to (that is, OD to).OD to indicate which node between connection
Situation is only interested to capacity of resisting disturbance assessment；In other words, OD to node in addition between connection will not be
The research contents of capacity of resisting disturbance assessment.For a directed networks (that is, the link between node i to node j and node j
Link between node i is not the same thing, such as, A (i, j)=1 do not represent A (j, i)=1；It is clear that indirected net
Network is a kind of special case of directed networks；So the method for directed networks is completely suitable for Undirected networks), always have: 1≤NOD
≤NN×(NN-1).The starting point remembering the s OD centering is Os, terminal is Ds, 1≤s≤NOD。
The method of the assessment network system capacity of resisting disturbance of the present invention includes following key step:
(step 1) determines to be studied in network system all OD pair.That is, according to the requirement of particular problem, all OD are determined
To number NOD, and starting point O of the s OD centeringsWith terminal Ds, 1≤s≤NOD。
Network system capacity of resisting disturbance is required that changing into each path of OD pair corresponding presets codomain by (step 2).That is,
Capacity of resisting disturbance requirement according to particular problem, to each OD pair, respectively specifies that a corresponding path presets codomain.
Remember that the path of the s OD pair presets codomain for [LPT(s, 1), LPT(s, 2)], 1≤s≤NOD, wherein LPT(s, 1) is s
The path lower limit of the individual OD satisfied requirement to defining, LPT(s, 2) then defines the path upper limit meeting requirement.One
For as, different OD presets codomain to can there be different paths, it is possibility to have identical path presets codomain,
This depends entirely on the requirement of particular problem.
(step 3), to each OD pair, is found out and is met path and preset all roads warp of codomain condition.That is, for s
Individual OD pair, 1≤s≤NOD, find out all path P meeting following condition in network:
P (1)=Os, P (NL)=Ds； (2)
LPT(s, 1) ＜ CP(P) ＜ LPT(s, 2), or LPT(s, 1)≤CP(P) ＜ LPT(s, 2),
Or LPT(s, 1) ＜ CP(P)≤LPT(s, 2), or LPT(s, 1)≤CP(P)≤LPT(s, 2). (3)
Its conditional (2) requires that the starting point of path P is Os, terminal is Ds；Condition (3) is to path preset value territory condition
Generalization defines, it is desirable to the length of path P is preset in codomain interval the path of the s OD pair；Given for one
OD to for, the default codomain interval of condition (3) is open interval on earth, right open interval is closed on a left side, interval closed at the right is opened on a left side or
Closed interval, depends on the requirement of particular problem；In same network system, for different OD pair, condition (3) pre-
If the opening and closing in codomain interval is it may is that different, this also depends on the requirement of particular problem；The preset value of condition (3)
Interval, territory can not have lower limit, i.e. is equivalent to LPT(s, 1)=-∞, this is similarly dependent on the requirement of particular problem.Apparent:
If for any OD pair, having LPT(s, 1)=-∞ and LPT(s, 2)=∞, then exactly by " whether network system can be disintegrated becomes
Multiple sub-network systems independent of each other " this extreme thinking assessment network system capacity of resisting disturbance；And if for arbitrarily
OD pair, there is LPT(s, 1)=LPT(s, 2)=CP(Ps *), Ps *The s OD between shortest path, then be exactly by " network
Whether the optimal route in system can be affected " this extreme thinking assessment network system capacity of resisting disturbance.
(step 4) add up all OD between meet respective paths length and preset the node of all Lu Jingzhong and the chain of codomain condition
The shared situation connect.I.e., it is assumed that ΩPIt is the set meeting all roads warp that path presets codomain condition, statistics network system
In each node occur in Ω with intermediate point (rather than beginning or end)PNumber of times in contained path, note node n is at ΩPContained
Path occurs in that B altogether with intermediate pointNN () is secondary, 1≤n≤NN；Meanwhile, in statistics network system, the link of each bar occurs in ΩP
Number of times in contained path, note link m is at ΩPContained path occurs in that B altogetherEM () is secondary, 1≤m≤NE；Further, it is also possible to
In statistics network system, each node occurs in Ω with intermediate pointPIn number of times in all paths of the s OD pair, remember node n
At ΩPIn all paths of the s OD pair occur in that B altogether with intermediate pointN-OD(s, n) secondary, 1≤s≤NOD, 1≤n≤NN；
In statistics network system, the link of each bar occurs in Ω againPIn number of times in all paths of the s OD pair, note link m is at ΩPIn
All paths of the s OD pair occur in that B altogetherE-OD(s, m) secondary, 1≤s≤NOD, 1≤m≤NE。
(step 5) is based on ΩP, BN(n), BN-OD(s, n), BE(m), and BE-OD(s, m), analyze each OD between meet corresponding
Path presets all roads of codomain condition through probability all off under various interference factor effects, wherein,
S=1 ..., NOD, n=1 ..., NN, m=1 ..., NE.Analysis method and process depend primarily on type and the feature of particular problem.Example
As, following analysis can be done: assume ΩPIn altogether contain NPPaths, then the most always have 0≤BN(n)/NP≤ 1 (premise
Condition is: can not comprise the point of repetition in a paths)；If BN(n)/NP≈ 1, then illustrate, the overwhelming majority meets corresponding road
Electrical path length presets the road of codomain condition through all passing through node n, therefore, if the disturbed probability of node n is very big, then
The ability of the systemic-function that network system realizes certain minimum level specified is the lowest；In like manner, if BE(m)/NP≈ 1, and
If the link disturbed probability of m is the biggest, then network system realizes the ability of systemic-function of certain minimum level specified
The lowest.
Path in above-mentioned (step 3) presets codomain condition (3) can be to use the form in multi-domain interval.Such as,
For the s OD pair, 1≤s≤NOD, the path P meeting network system capacity of resisting disturbance requirement must is fulfilled for following path
Default codomain condition:
LPT(s, 1)≤CP(P)≤LPT(s, 2), and LPT(s, 3)≤CP(P)≤LPT(s, 4), (4)
Wherein, LPT(s, 2) ＜ LPT(s, 3), then [LPT(s, 1), LPT(s, 2)] be the s OD to defining first codomain interval,
[LPT(s, 3), LPT(s, 4)] it is that the s OD is to defining second codomain interval.The s OD is to needing several codomain on earth
Interval, and the opening and closing what state that each codomain is interval, both depend on the requirement of particular problem.
Above-mentioned (step 3) is the committed step of the method for the present invention, is also the difficult point place of the method realizing the present invention.Realize
(step 3) solves all OD between meet respective paths length and preset all roads of codomain condition through (being equivalent to more to
K bar shortest route problems before many), in theory, can be by constantly iteration with rerun and existing solve an OD to it
Between shortest path first (that is, solving the algorithm of one to one the 1st shortest route problem) and achieve the goal, it may be assumed that choose one
OD pair, based on primitive network solve this OD between shortest path, for this OD between the 1st shortest path；Based on
1 shortest path, (each new network is by primitive network deletion the 1st shortest path the one of contained link to reconstruct a series of new network
Kind may combination and obtain), to this OD of each new Solution To The Network between shortest path, in the most all new networks
The shortest person in short path, it is simply that in primitive network this OD between the 2nd shortest path；The most constantly iteration, so that it may according to
This OD between before (k-1) bar shortest path, and solve this OD between kth shortest path, k ＞ 1 (generally along with
K increases and needs the quantity of new network of reconstruct can be the biggest)；If the length first of kth shortest path in an iterative process
Secondary more than corresponding path is preset the upper limit of codomain with this OD, then iterative process stops, and causes before this is solved
K bar shortest path meets this path of OD pair preset all paths of codomain condition be exactly this OD between meet anti-dry
Disturb the path of Capability Requirement；Then to each OD to repeating above-mentioned iterative process, with obtain each OD between meet
Respective paths length presets the path of codomain condition, thus finds out all paths meeting capacity of resisting disturbance requirement in network system.
But, realize (step 3) of the method for the present invention by the method for above-mentioned this continuous iteration and repetition, be unusual poor efficiency,
Especially when network system be on a grand scale, the number of OD pair is a lot of again simultaneously when, by above-mentioned continuous iteration and the method for repetition
Solve that to meet all paths of capacity of resisting disturbance requirement in network system the most unpractical.
In order to complete (step 3) quickly and efficiently, the method for the present invention have developed a kind of ripples broadcast algorithm specially, by simulation
The ripples diffusing phenomenon of nature are carried out the diffusion relay race of disposable ripples in primitive network and (be need not iterative reconstruction any newly
Network, it is not required that repeat to carry out ripples diffusion relay race), it is possible to solve all OD between meet respective paths length
Preset all paths of codomain condition.
Traditional ripples broadcast algorithm solve an OD between the basic thought of shortest path be: initial ripples are with OD pair
In starting point to be wave source link to external diffusion along each bar of starting point；When ripples arrive a node, can excite at this node
Go out new ripples, new ripples with this node as wave source and along this node each bar link continue to external diffusion；All ripples have
Identical diffusion velocity；When the terminal of OD centering has ripples to arrive for the first time, the path that arrival ripples are passed by is exactly OD pair
Between the 1st shortest path, and when the terminal kth of OD centering time has ripples to arrive, the path that arrival ripples are passed by is exactly
OD between kth shortest path.Whole process is as ripples diffusion relay race in network: initial ripples from point out
Sending out the most each node and gradually excite the ripples that make new advances, all ripples competitively spread to terminal, see that who reaches home at first.
Wanting to be completed (step 3) by the diffusion relay race of disposable ripples, traditional ripples diffusion is calculated by the method for the present invention
Method has carried out following 2 main improvement: first because (step 3) to be solved be one more to many before k bar shortest path
Problem, so the starting point of each OD pair can respectively produce initial ripples, i.e. ripples diffusion relay race is not initial from one
Ripples start, but from the beginning of multiple initial ripples；Second, if certain the new ripples gradually inspired from initial ripples
All OD that corresponding current path length has been above this initial ripples wave source node place are pre-to corresponding path
If codomain upper limit maximum, then these new ripples will be withered away, i.e. these new ripples are the most considered by stopping diffusion.
Specifically, the ripples broadcast algorithm that (step 3) of the method for the present invention is improved includes following key step:
(step 1) specifies a ripples diffusion velocity constant v, and for ensureing the optimality of algorithm, v need to meet following condition:
0 ＜ v≤min (CE(i, j)), (5)
That is, v must be not more than link length the shortest in network system；General recommendation takes v=min (CE(i, j)).
(step 2) sets the current emulation moment as t=0；Initializing current ripples number is NR=0；To each as starting point arbitrarily
There is the node n of (no matter how many times occur, as long as occurring) in OD centering, produced initial ripples at this node,
NR=NR+ 1, the starting point of these initial ripples is set to RO(NR)=n, wave source node is set to RE(NR)=n, radius is set to RR(NR)=0, currently
Path is set to RCPL(NR)=0, ripples state is set to RS(NR)=1 (1 represents active, and 0 represents inactive), ripples path length
The degree upper limit is set to all OD that starting point is node n and corresponding path is preset codomain upper limit maximum, is denoted as RMaxR(NR)。
(step 3) if NRIn individual ripples, at least the state of ripples is 1 (that is, active), then circulation carries out following son
Step:
(step 3.1) makes t=t+1；
(step 3.2) is to arbitrarily enlivening ripples r, i.e. if RSR ()=1, then its ripples radius increases to RR(r)=RR(r)+v,
That is, ripples radius increases length by the diffusion length of a unit of time；
(step 3.3) is to all of node and enlivens ripples and performs following conditional operation: if enliven the wave source node of ripples r with
Link is had, i.e. A (R between node nE(r), n)=1, and if RR(r)≥CE(RE(r), n), i.e. ripples r arrives and finishes
Point n, then, produce new ripples in node n, make NR=NR+ 1, new ripples starting point is RO(NR)=ROR (), wave source node is
RE(NR)=n, radius is RR(NR)=RR(r)-CE(RE(r), n), a length of R of current pathCPL(NR)=RCPL(r)+CE(RE(r), n), ripples
Ripples state is set to RS(NR)=1, the ripples path upper limit is RMaxR(NR)=RMaxR(r)；
Any one is enlivened ripples r by (step 3.4), if its radius is not less than from the all-links of node RE (r)
The maximum of length, then these ripples become inactive, i.e. RS(r)=0；
Any one is enlivened ripples r by (step 3.5), if its current path length is more than its ripples path upper limit, i.e.
If RCPL(r) ＞ RMaxRR (), then these ripples become inactive, i.e. RS(r)=0.
The node n that each was occurred in any OD centering by (step 4) as terminal, checks the institute that this node was produced
There are ripples: assume that ripples r is the ripples that node n produced, i.e. assume RE(r)=n, then, compare working as of ripples r
Front path RCPL(r) with ROR () be starting point, the path of with n as terminal OD pair presets codomain, i.e. judges ripples
Whether the current path length of ripples r meets corresponding path is preset codomain condition, if it is satisfied, then backtracking ripples r is walked
The path crossed a, it is simply that path meeting system rejection to disturbance Capability Requirement；By institute produced by the terminal of all OD pair of backtracking
There is the path that the ripples meeting condition are passed by, it is possible to obtain network system meets all paths of capacity of resisting disturbance requirement.
The method of the assessment network system capacity of resisting disturbance of the present invention can be to use various appropriate formulation form (such as, nets
Link in network can represent without adjacency matrix A, but uses the data structure of link vector table；Each variable used
Not necessarily, core is the meaning of variable and the operation of variable is calculated process, such as, the method for the present invention symbol itself
(step 3.2) of the ripples broadcast algorithm proposed updates ripples radius, i.e. RR(r)=RRR ()+v, can be with arbitrarily becoming
Quantity symbol is rewritten, and e.g., W (m)=W (m)+z, even without " ripples " and " radius " these vocabulary wordings, but abstractively
Say into: vector RRThe r element RRR () increases v, its effect is the same；The constant value used not necessarily, example
As, in algorithm when representing the state of ripples r, use RSR ()=1 represents enlivens and RSR ()=0 represents inactive, in fact 1 and 0
The two constant value the most not necessarily, as long as active state and disabled state can be distinguished, can give RS(r) compose any often
Numerical value).
The step of the method for the present invention divides and can also suitably adjust, such as: the ripples broadcast algorithm that the method for the present invention is proposed
(step 3.1) and (step 3.2) sub-steps can be merged into；If need not clearly point out or use simulation time
Variable t, can initialize simulation time variable t=0 in (step 2), (step 3.1) can delete completely.
The method of the assessment network system capacity of resisting disturbance of the present invention has the advantages that and present method avoids " net
Whether network system can be disintegrated becomes multiple sub-network system independent of each other " and " whether the optimal route in network system can be subject to
Impact " the extreme thinking of both limitation (i.e., or the small probability event being confined in this daily life of periods of network disruption is examined
Consider, or be confined to the insignificant problem of perfectionism), it is achieved that by " whether network system also ensures that realize that certain specifies minimum
The systemic-function of degree " this generalization thinking assesses the capacity of resisting disturbance of network system, thus meets very much current demand,
The decision support with practical value to typical scenario in daily life can be provided for the designer of network system and user；The present invention
Method by simulation nature ripples diffusing phenomenon carry out in a network disposable ripples diffusion relay race, thus realize exist
Disposable computing fast and effeciently solves in network each OD between length meet corresponding codomain condition of presetting and own
Path；The method of the present invention both may be used for reality physical network capacity of resisting disturbance evaluation problem (such as: the network of communication lines, electrical network,
Communication network, etc.), may be used for again abstract virtual network capacity of resisting disturbance evaluation problem (such as: decision tree, ecological net,
Food chain, etc.).
Accompanying drawing illustrates:
Accompanying drawing provides the schematic diagram of the method for the assessment network system capacity of resisting disturbance of the present invention:
The key step schematic diagram of the method for the assessment network system capacity of resisting disturbance of Fig. 1: the present invention.
In the method for the assessment network system capacity of resisting disturbance of Fig. 2: the present invention in order to solve all OD between to meet system anti-dry
Disturb the key step schematic diagram of the ripples broadcast algorithm in all paths of Capability Requirement.
The exemplary plot of the difference between method and traditional appraisal procedure of the assessment network system capacity of resisting disturbance of Fig. 3: the present invention.
Detailed description of the invention:
Below in conjunction with the accompanying drawings, a kind of method assessing network system capacity of resisting disturbance of the present invention is existed for solving assessment network system
Whether also ensure that under various interference factor effects that the path realized by meeting corresponding default codomain condition connects each starting point eventually
The optimal way that the problem of the ability of (that is, OD to) is used by point is described further.
Fig. 1 gives the key step included by method of the assessment network system capacity of resisting disturbance of the present invention:
(step 1), according to the requirement of particular problem, determines all starting and terminal points pair to be studied in network system.
Network system capacity of resisting disturbance is required that changing into each path of OD pair corresponding presets codomain by (step 2), i.e.
Capacity of resisting disturbance requirement according to particular problem, to each OD pair, respectively specifies that a corresponding path presets codomain.
(step 3), to each OD pair, is found out and is met respective paths length and preset all roads warp of codomain condition, i.e. to often
One OD pair, electrical path length of finding a way out presets codomain lower limit more than or not less than respective paths length, and is less than or is not more than corresponding
Path presets all paths of the codomain upper limit.
(step 4) add up all OD between meet respective paths length and preset the node of all Lu Jingzhong and the chain of codomain condition
The shared situation connect, including: statistics meets the sum that respective paths length presets the road warp of codomain condition；In statistics network system
Each node occur in intermediate point (rather than beginning or end) meet respective paths length preset codomain condition Lu Jingzhong time
Number；In statistics network system, the link of each bar occurs in the number of times meeting the Lu Jingzhong that respective paths length presets codomain condition；Statistics
In network system, each node occurs in each OD road warp to meeting respective paths length and preset codomain condition with intermediate point
In number of times；In statistics network system, the link of each bar occurs in each OD and presets codomain condition to meeting respective paths length
The number of times of Lu Jingzhong.
(step 5), based on the statistical data obtained by (step 4), according to type and the feature of particular problem, analyzes each OD
Meet respective paths length between to and preset all roads of codomain condition through possibility all off under various interference factor effects
Property.
(step 3) in the method for the present invention is crucial and difficult point place, need fast and effeciently to solve all OD between
Meet all paths of system rejection to disturbance Capability Requirement.To this end, the method for the present invention further provides one for (step 3)
Just can be found the ripples broadcast algorithm in all paths meeting system rejection to disturbance Capability Requirement by disposable operation, Fig. 2 gives
This key step included by ripples broadcast algorithm:
(step 1) selectes a suitable ripples diffusion velocity constant v.All ripples in ripples broadcast algorithm all will be by this
Identical speed v is diffused.It is emphasized that: in some concrete network problem, the speed that different linking is allowed can
Can be different, but this has no effect on the use of diffusion velocity constant v, because allow the net of friction speed for different linking
Network problem, first finds out the maximal rate that all-links is allowed, then carrys out phase by maximal rate with each ratio linking institute's permissible velocity
Link weight should be increased, for example, it is assumed that maximal rate is link A (i, 3 times of permissible velocity j), the then weighted value of this link
Need to be adjusted to CE(i, j)=3 × CE(i, j), after being then based on adjusting, the weighted value of all-links is selected further according to condition (5)
Diffusion velocity constant v.
(step 2) sets the current emulation moment as t=0；Initializing current ripples number is NR=0；To each as starting point arbitrarily
There is the node n of (no matter how many times occur, as long as occurring) in OD centering, produced initial ripples at this node,
NR=NR+ 1, the starting point of these initial ripples is set to RO(NR)=n, wave source node is set to RE(NR)=n, radius is set to RR(NR)=0, currently
Path is set to RCPL(NR)=0, ripples state is set to RS(NR)=1 (1 represents active, and 0 represents inactive), ripples path length
The degree upper limit is set to all OD that starting point is node n and corresponding path is preset codomain upper limit maximum, is denoted as RMaxR(NR)。
It is emphasized that: although selecting numerical value " 1 " to represent that ripples state is active in this specification, numerical value " 0 " represents ripples shape
State is inactive, but when the method for the concrete application present invention, can select whether any numerical value indicates differentiation ripples flexibly
Active.
(step 3) checks all NRIndividual ripples the most also enliven ripples？If NRAt least ripples in individual ripples
State is active, then circulate and carry out following sub-step:
(step 3.1) simulation time t increases a simulation time unit, i.e. t=t+1 (it is noted that used here as imitative
Between true time, t is to be a dynamic process changed with simulation time to clearly show ripples diffusion relay race, thus has
Help understanding method and debugging routine；If need not clearly point out the change of simulation time, then can save without simulation time t
Go this sub-step)；
(step 3.2) is to arbitrarily enlivening ripples r, i.e. if RSR ()=1, then its ripples radius increases to RR(r)=RR(r)+v,
That is, ripples radius increases length by the diffusion length of a simulation time unit；
(step 3.3) is to all of node and enlivens ripples and performs following conditional operation: if enliven the wave source node of ripples r with
Link is had, i.e. A (R between node nE(r), n)=1, and if RR(r)≥CE(RE(r), n), i.e. ripples r arrives and finishes
Point n, then, produce new ripples in node n, make NR=NR+ 1, new ripples starting point is RO(NR)=ROR (), wave source node is
RE(NR)=n, radius is RR(NR)=RR(r)-CE(RE(r), n), a length of R of current pathCPL(NR)=RCPL(r)+CE(RE(r), n), ripples
Ripples state is set to RS(NR)=1, the ripples path upper limit is RMaxR(NR)=RMaxR(r)；
Any one is enlivened ripples r by (step 3.4), if its radius is not less than from node RER all-links that () is set out
The maximum of length, then these ripples become inactive, i.e. RS(r)=0 (the state change of these type of ripples is set to inactive,
The arithmetic speed of algorithm can be greatly improved, even if because these type of ripples continue diffusion, any new ripples can not be inspired, so
If continuing the calculating resource these type of ripples being diffused computing by simply wasting computing hardware)；
Any one is enlivened ripples r by (step 3.5), if its current path length is more than its ripples path upper limit, i.e.
If RCPL(r) ＞ RMaxRR (), then these ripples become inactive, i.e. RSR the state of these type of ripples (is changed and is set to not by ()=0
Active, it is also possible to be greatly improved the arithmetic speed of algorithm, because if these type of ripples continue diffusion, the new route found is also only
Can be the path being unsatisfactory for system rejection to disturbance Capability Requirement, assessment system rejection to disturbance ability is not had extra value, if so continued
Continue the calculating resource these type of ripples being diffused computing computing hardware will be also simply wasted).
The node n that each was occurred in any OD centering by (step 4) as terminal, checks the institute that this node was produced
There are ripples: assume that ripples r is the ripples that node n produced, i.e. assume RE(r)=n, then, compare working as of ripples r
Front path RCPL(r) with ROR () be starting point, the path of with n as terminal OD pair presets codomain, i.e. judges ripples
Whether the current path length of ripples r meets corresponding path is preset codomain condition, if it is satisfied, then backtracking ripples r is walked
The path crossed a, it is simply that path meeting system rejection to disturbance Capability Requirement；By institute produced by the terminal of all OD pair of backtracking
Have and meet respective paths length and preset the path that the ripples of codomain condition are passed by, it is possible to obtain network system meets anti-interference
All paths of Capability Requirement.
One of difference between method and traditional appraisal procedure of the assessment network system capacity of resisting disturbance that Fig. 3 gives the present invention
Individual simple examples.In the example of fig. 3, network system only one of which OD pair, this OD between a total of 5 paths.?
Assessment interference factor network system is connected this OD on when affecting of ability, traditional appraisal procedure or by " network system is
No meeting is disintegrated and is become multiple sub-network system independent of each other " this extreme thinking carries out, i.e. exemplified by Fig. 3 left-hand component
Extreme case 1；Carry out by " whether the optimal route in network system can be affected " this extreme thinking, i.e. Fig. 3
Extreme case 2 exemplified by right-hand component.Assess by extreme case in Fig. 31, need Analysis interference factor make this OD between
The probability that all 5 paths all simultaneously switch off.Assess by extreme case in Fig. 32, need Analysis interference factor to make this OD
The probability that shortest path between to disconnects.The method of the present invention is then to be estimated the anti-interference of network system by pervasive situation
Ability, need Analysis interference factor make this OD between the possibility that all simultaneously switches off less than the path of certain predetermined threshold value of all length
Property, i.e. the pervasive situation exemplified by Fig. 3 mid portion, need Analysis interference factor make this OD between front 3 shortest paths
The probability that footpath all simultaneously switches off.Further the example of Fig. 3 is placed on one and rushes for the actual scene that terminal goes to have a meeting from starting point
Middle understanding, extreme case 1 consideration is that: road network disconnects the probability causing at all to reach home from starting point；Extremely
Situation 2 consideration is that: road network fault causes walking shortest path and arrives in the probability of terminal from starting point；Pervasive situation is examined
The problem considered is: road network fault causes (such as: before 10 o'clock of the morning) to arrive in the probability of terminal from starting point on time.
Which problem is real-life participant's real concern be？Obviously, it is " meeting-place can be arrived in attend a meeting " on time
Problem.Fig. 3 illustrates, and the method for the present invention can efficiently solve in actual life network system capacity of resisting disturbance
Problem the most deeply concerned.
Claims (10)
1. whether the method assessing network system capacity of resisting disturbance, in order to assess network system under various interference factor effects
Also ensure that and realize connecting each starting and terminal point ability to (that is, OD to) by meeting the corresponding path presetting codomain condition,
It is characterized in that: it is pre-that first network system capacity of resisting disturbance is required to change into each path of OD pair corresponding by the method for the present invention
If codomain, then find out each OD in network between length to meet the corresponding all paths presetting codomain condition (be not by " net
Whether the optimal route in network system can be affected " this extreme thinking only find out OD between shortest path, be not by
" whether network system can be disintegrated becomes multiple sub-network system independent of each other " this extreme thinking find out OD between all
Path), all these length of last statistical analysis meets the node in the corresponding path presetting codomain condition and the shared feelings of link
Condition, thus by " whether network system also ensures that the systemic-function realizing certain minimum level specified " this generalization thinking
Carry out the capacity of resisting disturbance of qualitative assessment network system.
In the method for the present invention, by " whether network system also ensures that the systemic-function realizing certain minimum level specified " this
One generalization thinking carrys out the capacity of resisting disturbance of qualitative assessment network system, can be described as following mathematical problem.
Assume there is a network system, comprise NNIndividual node and NEBar links.Link between node can be by an adjacency matrix A table
Showing, (i, j)=1 represents one link of existence between node i to node j to elements A therein；(i, j)=0 represents node i to A
Not link between node j.Assume to exist between node i to node j a link, then the weighted value of this link can be designated as
CE(i, j).The weighted value C of linkE(i j) will be used for calculating the length in path.Vacation lets p represent a paths, and path P comprises
NL>=2 nodes, P (i) represents the i-th node of path P, 1≤i≤NL, 1≤P (i)≤NN.Use CP(P) path P is represented
Length, it is calculated as follows:
Assume that again network system has NODIndividual starting and terminal point is to (that is, OD to).OD to indicate which node between connection
Situation is only interested to capacity of resisting disturbance assessment；In other words, OD to node in addition between connection will not be
The research contents of capacity of resisting disturbance assessment.The starting point remembering the s OD centering is Os, terminal is Ds, 1≤s≤NOD。
The method of the assessment network system capacity of resisting disturbance of the present invention includes following key step:
(step 1) determines to be studied in network system all OD pair.That is, according to the requirement of particular problem, all OD are determined
To number NOD, and starting point O of the s OD centeringsWith terminal Ds, 1≤s≤NOD。
Network system capacity of resisting disturbance is required that changing into each path of OD pair corresponding presets codomain by (step 2).That is,
Capacity of resisting disturbance requirement according to particular problem, to each OD pair, respectively specifies that a corresponding path presets codomain.
Remember that the path of the s OD pair presets codomain for [LPT(s, 1), LPT(s, 2)], 1≤s≤NOD, wherein LPT(s, 1) is s
Individual OD meets the path lower limit that capacity of resisting disturbance requires, L to definePT(s, 2) then define meet capacity of resisting disturbance want
The path upper limit asked.It is said that in general, different OD is to different paths can be had to preset codomain, it is possibility to have identical
Path preset codomain, this depends entirely on the requirement of particular problem.
(step 3), to each OD pair, is found out and is met path and preset all roads warp of codomain condition.That is, for s
Individual OD pair, 1≤s≤NOD, find out all path P meeting following two condition in network, its conditional 1 is:
P (1)=Os, P (NL)=Ds；
Its conditional 2 (that is, the path meeting system rejection to disturbance Capability Requirement presets codomain condition) is:
LPT(s, 1) ＜ CP(P) ＜ LPT(s, 2), or LPT(s, 1)≤CP(P) ＜ LPT(s, 2),
Or LPT(s, 1) ＜ CP(P)≤LPT(s, 2), or LPT(s, 1)≤CP(P)≤LPT(s, 2).
The starting point that its conditional 1 requires path P is Os, terminal is Ds；Condition 2 is the generalization to path preset value territory condition
Definition, it is desirable to the length of path P is preset in codomain interval the path of the s OD pair；For one given OD pair
For, the default codomain interval of condition 2 is open interval on earth, right open interval is closed on a left side, interval closed at the right is opened on a left side or closed interval,
Depend on the requirement of particular problem；In same network system, for different OD pair, the default codomain interval of condition 2
Opening and closing is it may is that different, and this also depends on the requirement of particular problem；The default codomain interval of condition 2 can not have
Lower limit, i.e. be equivalent to LPT(s, 1)=-∞, this is similarly dependent on the requirement of particular problem.Apparent: if for arbitrarily
OD pair, there is LPT(s, 1)=-∞ and LPT(s, 2)=∞, then exactly by " network system whether can disintegrate become multiple independently of one another
Sub-network system " this extreme thinking assessment network system capacity of resisting disturbance；And if for any OD pair, had
LPT(s, 1)=LPT(s, 2)=CP(PS *), PS *The s OD between shortest path, then be exactly by " the optimum in network system
Whether route can be affected " this extreme thinking assessment network system capacity of resisting disturbance.
(step 4) add up all OD between meet respective paths length and preset the node of all Lu Jingzhong and the chain of codomain condition
The shared situation connect.I.e., it is assumed that ΩPIt is the set meeting all roads warp that path presets codomain condition, statistics network system
In each node occur in Ω with intermediate point (rather than beginning or end)PNumber of times in contained path, note node n is at ΩPContained
Path occurs in that B altogether with intermediate pointNN () is secondary, 1≤n≤NN；Meanwhile, in statistics network system, the link of each bar occurs in ΩP
Number of times in contained path, note link m is at ΩPContained path occurs in that B altogetherEM () is secondary, 1≤m≤NE；Further, it is also possible to
In statistics network system, each node occurs in Ω with intermediate pointPIn number of times in all paths of the s OD pair, remember node n
At ΩPIn all paths of the s OD pair occur in that B altogether with intermediate pointN-OD(s, n) secondary, 1≤s≤NOD, 1≤n≤NN；
In statistics network system, the link of each bar occurs in Ω againPIn number of times in all paths of the s OD pair, note link m is at ΩPIn
All paths of the s OD pair occur in that B altogetherE-OD(s, m) secondary, 1≤s≤NOD, 1≤m≤NE。
(step 5) is based on ΩP, BN(n), BN-OD(s, n), BE(m), and BE-OD(s, m), analyze each OD between meet corresponding
Path presets all roads of codomain condition through probability all off under various interference factor effects, wherein,
S=1 ..., NOD, n=1 ..., NN, m=1 ..., NE.Analysis method and process depend primarily on type and the feature of particular problem.Example
As, following analysis can be done: assume ΩPIn altogether contain NPPaths, then the most always have 0≤BN(n)/NP≤ 1 (premise
Condition is: can not comprise the point of repetition in a paths)；If BN(n)/NP≈ 1, then illustrate, the overwhelming majority meets corresponding road
Electrical path length presets the road of codomain condition through all passing through node n, therefore, if the disturbed probability of node n is very big, then
The ability of the systemic-function that network system realizes certain minimum level specified is the lowest；In like manner, if BE(m)/NP≈ 1, and
If the link disturbed probability of m is the biggest, then network system realizes the ability of systemic-function of certain minimum level specified
The lowest.
A kind of method assessing network system capacity of resisting disturbance the most according to claim 1, is characterized in that: all solving
OD between meet respective paths length preset all roads of codomain condition through time, can be existing by the ripples diffusion of simulation nature
Purpose is realized as carrying out disposable ripples diffusion relay race (that is, ripples broadcast algorithm) in primitive network.
Ripples broadcast algorithm solve an OD between the basic thought of shortest path be: initial ripples rising with OD centering
Point links to external diffusion along each bar of starting point for wave source；When ripples arrive a node, one can be inspired at this node
New ripples, new ripples link with this node as wave source and along each bar of this node and continue to external diffusion；All ripples have identical
Diffusion velocity；When the terminal of OD centering for the first time has ripples to arrive, the path that arrival ripples are passed by be exactly OD between
1st shortest path, and when the terminal kth time of OD centering has ripples to arrive, the path that arrival ripples are passed by is exactly OD pair
Between kth shortest path.Whole process is as a ripples diffusion relay race in network: initial ripples exist from starting point
In network, each node gradually excites the ripples that make new advances, and all ripples competitively spread to terminal, see that who reaches home at first.OD between
Front k bar shortest path in meet respective paths length preset those paths of codomain condition be exactly this OD between meet system and resist
All paths that interference performance requires.When multiple OD pair, then need to produce initial in each starting point of OD pair simultaneously
Ripples, in order to carry out the diffusion relay race of disposable ripples.
Specifically, the ripples broadcast algorithm that the method for the present invention is proposed includes following key step:
(step 1) specifies a ripples diffusion velocity constant v, and for ensureing the optimality of algorithm, v need to meet following condition:
0 ＜ v≤min (CE(i, j)),
That is, v must be not more than link length the shortest in network system；General recommendation takes v=min (CE(i, j)).It is emphasized that:
In some concrete network problem, the speed that different linking is allowed is probably different, but this to have no effect on diffusion velocity normal
The use of amount v, because allow the network problem of friction speed for different linking, first finds out the maximum speed that all-links is allowed
Degree, then come to each ratio linking institute's permissible velocity corresponding to increase link weight, for example, it is assumed that maximal rate is by maximal rate
(i, 3 times of permissible velocity j), then the weighted value of this link needs to be adjusted to C link AE(i, j)=3 × CE(i, j), then base
After adjusting, the weighted value of all-links selectes diffusion velocity constant v further according to above-mentioned scattered velocity constant inequality condition.
(step 2) sets the current emulation moment as t=0；Initializing current ripples number is NR=0；To each as starting point arbitrarily
There is the node n of (no matter how many times occur, as long as occurring) in OD centering, produced initial ripples at this node,
Make NR=NR+ 1, the starting point of these initial ripples is set to R0(NR)=n, wave source node is set to RE(NR)=n, radius is set to RR(NR)=0, when
Front path is set to RCPL(NR)=0, ripples state is set to RS(NR)=1 (1 represents active, and 0 represents inactive), ripples path
Length limit is set to all OD that starting point is node n and corresponding path is preset codomain upper limit maximum, is denoted as
RMaxR(NR)。
(step 3) if NRIn individual ripples, at least the state of ripples is 1 (that is, active), then circulation carries out following son
Step:
(step 3.1) makes t=t+1；
(step 3.2) is to arbitrarily enlivening ripples r, i.e. if RSR ()=1, then its ripples radius increases to RR(r)=RR(r)+v,
That is, ripples radius increases length by the diffusion length of a unit of time；
(step 3.3) is to all of node and enlivens ripples and performs following conditional operation: if enliven the wave source node of ripples r with
Link is had, i.e. A (R between node nE(r), n)=1, and if RR(r)≥CE(RE(r), n), i.e. ripples r arrives and finishes
Point n, then, produce new ripples in node n, make NR=NR+ 1, new ripples starting point is R0(NR)=R0(r), wave source node
For RE(NR)=n, radius is RR(NR)=RR(r)-CE(RE(r), n), a length of R of current pathCPL(NR)=RCPL(r)+CE(RE(r), n),
Ripples state is set to RS(NR)=1, the ripples path upper limit is RMaxR(NR)=RMaxR(r)；
Any one is enlivened ripples r by (step 3.4), if its radius is not less than from node RER all-links that () is set out
The maximum of length, then these ripples become inactive, i.e. RS(r)=0；
Any one is enlivened ripples r by (step 3.5), if its current path length is more than its ripples path upper limit, i.e.
If RCPL(r) ＞ RMaxRR (), then these ripples become inactive, i.e. RS(r)=0.
The node n that each was occurred in any OD centering by (step 4) as terminal, checks the institute that this node was produced
There are ripples: assume that ripples r is the ripples that node n produced, i.e. assume RE(r)=n, then, compare working as of ripples r
Front path RCPL(r) with R0R () be starting point, the path of with n as terminal OD pair presets codomain, i.e. judges ripples
Whether the current path length of ripples r meets corresponding path is preset codomain condition, if it is satisfied, then backtracking ripples r is walked
The path crossed a, it is simply that path meeting system rejection to disturbance Capability Requirement；By institute produced by the terminal of all OD pair of backtracking
There is the path that the ripples meeting condition are passed by, it is possible to obtain network system meets all paths of capacity of resisting disturbance requirement.
3., according to a kind of method assessing network system capacity of resisting disturbance described in claim 1 and claim 2, it is characterized in that:
The path meeting system rejection to disturbance Capability Requirement in described method presets codomain condition can use the shape in multi-domain interval
Formula.Such as, for the s OD pair, 1≤s≤NOD, meet the path P of network system capacity of resisting disturbance requirement must be fulfilled for as
Lower path presets codomain condition:
LPT(s, 1)≤CP(P)≤LPT(s, 2), and LPT(s, 3)≤CP(P)≤LPT(s, 4),
Wherein, LPT(s, 2) ＜ LPT(s, 3), then [LPT(s, 1), LPT(s, 2)] be the s OD to defining first codomain interval,
[LPT(s, 3), LPT(s, 4)] it is that the s OD is to defining second codomain interval.The s OD is to needing several codomain on earth
Interval, and the opening and closing what state that each codomain is interval, both depend on the requirement of particular problem.
4., according to a kind of method assessing network system capacity of resisting disturbance described in claim 1 and claim 2, it is characterized in that:
Described method can (such as, the link in network can be without adjacency matrix A table to use various appropriate formulation forms
Show, but use the data structure of link vector table；Not necessarily, core is variable to each variable symbol used itself
Meaning and the operation of variable is calculated process, such as, (step 3.2) of the ripples broadcast algorithm that the method for the present invention is proposed
Middle renewal ripples radius, i.e. RR(r)=RRR ()+v, can rewrite with aleatory variable symbol, e.g., and W (m)=W (m)+z, even
Need not " ripples " and " radius " these vocabulary wordings, but say into abstractively: vector RRThe r element RRR () increases v,
Its effect is the same；The constant value used not necessarily, such as, in algorithm when representing the state of ripples r, uses RS(r)=1
Represent and enliven and RSR ()=0 represents inactive, 1 and 0 the two constant value is the most in fact, as long as can distinguish
Active state and disabled state, can give RSR () composes any constant value).
5., according to a kind of method assessing network system capacity of resisting disturbance described in claim 1 and claim 3, it is characterized in that:
The step of described method divides and can suitably adjust, such as: (the step of the ripples broadcast algorithm that the method for the present invention is proposed
3.1) and (step 3.2) can be merged into a sub-steps；If need not clearly point out or use simulation time variable t,
Can initialize simulation time variable t=0 in (step 2), (step 3.1) can delete completely.
6., according to a kind of method assessing network system capacity of resisting disturbance described in claim 1 and claim 2, it is characterized in that:
Described method can be according to the type of particular problem and feature, and a statistical analysis all length meets corresponding default codomain condition
The shared situation of the node in path.
7., according to a kind of method assessing network system capacity of resisting disturbance described in claim 1 and claim 2, it is characterized in that:
Described method can be according to the type of particular problem and feature, and a statistical analysis all length meets corresponding default codomain condition
The shared situation of the link in path.
8., according to a kind of method assessing network system capacity of resisting disturbance described in claim 1 and claim 2, it is characterized in that:
Described method can apply to the capacity of resisting disturbance evaluation problem of reality physical network.
9., according to a kind of method assessing network system capacity of resisting disturbance described in claim 1 and claim 2, it is characterized in that:
Described method can apply to the capacity of resisting disturbance evaluation problem of abstract virtual network.
10. according to a kind of method assessing network system capacity of resisting disturbance described in claim 1 and claim 2, its feature
It is: described method can use various appropriate hardware computing device and software programming technique to realize.
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