CN101854693A - Method for calculating route stability applied to mobile ah hoc network - Google Patents

Abstract

The invention discloses a method for calculating route stability which is applied to a mobile ah hoc network. The method comprises the following steps of: firstly, describing degree of correlation between adjacent links by introducing a related factor, exporting five basic properties which shall be met by the related factor by analyzing correlationship between stable events of the two adjacent links to define intension of the related factor correctly; secondly, decomposing the probability of combined stability of the two adjacent links, namely subpath stability, into the stable marginal probability of each link, namely a correlation structure between the stability of each link and the stable events of the two adjacent links similar to Copula function; thirdly, approximately estimating the related factor through improved Kendall related coefficient, so that occurrence of the related factor is obtained in a physical network by a method for counting a sample sequence; and finally, obtaining a calculation formula of the stability of a whole path. The method can calculate the route stability by combining the method for calculating the stability of any single link, so that the method has great universality.

Description

Be applied to the route stability computational methods of mobile ad-hoc network

Technical field

The invention belongs to the cordless communication network technical field, particularly the route stability computational methods of mobile ad-hoc network.

Background technology

Mobile Ad Hoc network (being mobile ad-hoc network) is a kind of special mobile radio networks, no center control nodes, communication between the node often needs the forwarding of intermediate node could realize (multi-hop route), and the mobile meeting of the quick random of node causes the frequent variations of network topology structure, thereby causes regular heavy-route operation.In Ad hoc network, select the route of stability high (longevity) to ensure it is crucial, can reduce various unnecessary cost (as time-delay, bandwidth, power etc.) that heavy-route number of times and heavy-route cause and the life period that increases route so effectively for the QoS that end-to-end communication is provided.In recent years, continue to bring out, become the focus of current research based on the QoS routing algorithm (stablizing routing algorithm) of stability.In various stable routing algorithm, it is the most basic foundation of Route Selection that the stability in path is estimated, and its accuracy depends on the stable validity of estimating of single link and the accuracy of path stability computational methods.The stability of single link can be estimated to draw from various existing mobility models.And path stability computational methods accurately whether, determined whether the stability of entire path accurate, will greatly influence the performance of routing algorithm.

Great majority all adopt the path stability computational methods of following two quasi-traditions based on the QoS routing algorithm of stability at present:

(1) based on the method for link independence assumption: promptly suppose in the path separately between each link, the form of taking advantage of by each link stability connection is calculated the stability of entire path.

(2) the most weak link criterion method: with the stability of the most weak in the path (stability minimum) link stability as this path.

Yet above two class computational methods are not all considered the correlation between the link, and differ far away with the network condition of reality, can not accurately reflect actual path stable case.In fact, whether the existence of each Radio Link has certain correlation in mobile Ad hoc network.For example, as node n _a, n _bBetween have under the situation of link node n _a, n _cBetween the existence of link make node n _b, n _cBetween exist link more likely.This is because node n _b, n _cAll at n _aOne jump the scope that has limited two node random distribution in the neighborhood.Therefore, the computational methods of considering the link correlation have caused some concerns: if any method utilize the correlation between the link to draw the enclosed type expression formula of calculating the route availability; The method that has takes advantage of form to be similar to the real path of replacement stability with a connection that is similar to independence assumption, wherein joins the factor of taking advantage of and is converted to by iterative algorithm by each link stability.Yet above method is too complicated again and impracticable.

For this reason, the present invention proposes a kind of new path stability computational methods that are applied to mobile ad-hoc network.

Summary of the invention

Technical problem: the path stability computational methods that the objective of the invention is to propose a kind of new mobile ad-hoc network.This method had both been considered the correlation between the link, calculating path stability exactly, fairly simple and be suitable for application on mathematics again, solved the computational methods of current this respect or too simple and be not inconsistent preferably with the real network situation, otherwise too complicated and be difficult to practical difficult situation.And the present invention's calculating path stability that both can combine with any single link stability computational methods has very big versatility; Can easily be applied to arbitrary distance vector routing protocol again and select to stablize route, have good application prospects.

Technical scheme: as shown in Figure 1, (loop-free) path R in the mobile Ad hoc network is by m+1 node (n _i, i=0,1 ..., m) (in order) m bar adjacent link (l of being linked to be in succession _i, i=1,2 ..., m) form.And formed m-1 single sub path (r in succession with uplink _i, i=1,2 ..., m-1).L wherein _iCorresponding to node to (n _I-1, n _i), r _iCorresponding to adjacent link (l _i, l _I+1).

If probability space (Ω, F, P), A _i∈ F, i=1,2..., m.Wherein Ω is a sample space, and F is a field of events, and P is the probability measure on the F, A _iExpression link l _iStable incident, and its probability P _i=P (A _i) supposition known (can obtain by any link stability computational methods).Have only when all links of forming path R and stablize, path R could stablize.Therefore the stable representations of events of path R is

Then its probability of stability can be expressed as:

$P_R=P\left(\underset{i=1}{\overset{m}{\mathrm{\Π}}}{A}_i\right)=P\left(A_1\right)\×P(A_2/A_1)\×P(A_3/A_1{A}_2)...P(A_m/A_1...A_{m-1})---\left(1\right)$

In mobile Ad hoc network, that each node can be considered to independently is individual (speed, the direction of motion, position etc. that show as each node are separate).Therefore, two do not have the link of common points separate.It is relevant that two links of (common points is arranged) that the stable incident of arbitrary link only is adjacent in the R of path are stablized incident, has nothing to do and stablize incident with other link.Like this,

$P_R=P\left(A_1\right)\×P(A_2/A_1)\×P(A_3/A_2)...P(A_m/A_{m-1})$

$=P_1\×\frac{P\left(A_2{A}_1\right)}{P_1}\×\frac{P\left(A_3{A}_2\right)}{P_2}...\frac{P\left(A_m{A}_{m-1}\right)}{P_{m-1}}---\left(2\right)$

If under the separate assumed condition of link, the probability of stability of path R can be expressed as:

$P_R^{\mathrm{LIAM}}=P_1\×P_2\×...P_m---\left(3\right)$

If adopt the most weak link criterion, the probability of stability of path R can be expressed as:

$P_R^{\mathrm{WLR}}=\min \{P_i,i=\mathrm{1,2}...m\}---\left(4\right)$

By preceding definition as can be known, subpath r _iStable incident is A _iA _I+1, its probability of stability is P (A _iA _I+1), and 0≤P (A _iA _I+1)≤min{P _i, P _I+1.For trying to achieve the probability of stability of subpath ri, first analysis incident A _iAnd A _I+1Correlation.Definition correlation factor ρ _iRepresent the complementary degree of two incidents.By analyzing ρ as can be known _iMust satisfy following fundamental property: 1) as P (A _iA _I+1)=min{P _i, P _I+1, i.e. the appearance of small probability event, then ρ are depended in the appearance of big probability event fully _i=1.2) as P (A _iA _I+1)=P _iP _I+1, promptly two incidents are separate, then ρ _i=0.3) as P (A _iA _I+1)=0, i.e. two incident objectionable intermingling, then ρ _i=-1.4) as P (A _iA _I+1)＞P _iP _I+1, ρ then _i＞0 i.e. appearance of the two incidents characteristic that is proportionate.5) as P (A _iA _I+1)＜P _iP _I+1, ρ then _i＜0 i.e. appearance of two incidents is the negative correlation characteristic.Can get thus-1≤ρ _i≤ 1.

For trying to achieve A _iWith A _I+1Joint probability, at first introducing Sklar theorem: H is a l dimension joint distribution function, F ₁..., F _lBe its marginal distribution function, must have a Copula function so, make:

H(z ₁，…，z _l)＝C(F ₁(z ₁)，…，F _l(z _l)) (5)

Wherein C () represents the Copula function.If marginal distribution function F ₁..., F _lBe continuous, C () is exactly unique so; If F ₁..., F _lBe not continuous entirely, C () is unique no longer just so.By the Sklar theorem as can be seen, continuous multivariate joint probability distribution function can be divided into one dimension marginal distribution function and multidimensional correlation structure two parts, and wherein correlation structure is represented by the Copula function.

Inspired by the Sklar theorem, with A _iWith A _I+1The probability of product event (subpath r _iThe probability of stability) be divided into their marginal probability (probability of each incident) and the correlation structure (being similar to the Copula function) of two incidents.

$P_{r_i}=P\left(A_i{A}_{i+1}\right)=f_i\left({\mathrm{\ρ}}_i\right)\×\min \{P\left(A_i\right),P\left(A_{i+1}\right)\}=f_i\left({\mathrm{\ρ}}_i\right)\×\min \{P_i,P_{i+1}\},-1\≤{\mathrm{\ρ}}_i\≤1---\left(6\right)$

Wherein, 0≤f _i(ρ _i)≤1 presentation of events A _iAnd A _I+1Correlation structure.By ρ _iFundamental property as can be known, f _i(ρ _i) (1,1) excessively, (0, max (P _i, P _I+1)) and (1,0) 3 points, and be ρ _iMonotonically increasing function.Now provide f _i(ρ _i) be ρ _iThe proof of monotonically increasing function as follows:

Be without loss of generality, establish P _i≤ P _I+1Therefore, min{P _i, P _I+1}=P _iGet f by formula (6) _i(ρ _i)=P (A _I+1/ A _i).According to ρ _iDefinition and fundamental property as can be known: as 0≤ρ _i≤ 1 o'clock, ρ _iIncrease and mean incident A _iGeneration to incident A _I+1The positive influences (positive correlation) that take place increase, then f _i(ρ _i)=P (A _I+1/ A _i) increase.As-1≤ρ _i≤ 0 o'clock, ρ _iIncrease and mean incident A _iGeneration to incident A _I+1The negative effect (negative correlation) that takes place reduces, then f _i(ρ _i)=P (A _I+1/ A _i) increase.And work as ρ _i=0, f _i(ρ _i)=P _I+1Getting unique value (is f _i(ρ _i) point (0, P _I+1) continuously).Problem must be demonstrate,proved thus.

f _i(ρ _i) can obtain by interpolation method: according to existing condition and with various interpolation methods commonly used (as Lagrange, Newton, Hermits and cubic spline interpolation etc.) relatively, select simple hyperbolic function as interpolating function below:

f _i(ρ _i)＝(a ₁ρ _i+a ₂)/(a ₃ρ _i+1)，-1≤ρ _i≤1 (7)

With f _i(ρ _i) the each point substitution formula (7) of crossing, alignment equation group and finding the solution obtains: a ₁=a ₂=max{P _i, P _I+1, a ₃=2 * max{P _i, P _I+1}-1.Can get thus,

f _i(ρ _i)＝(max{P _i，P _i+1}×ρ _i+max{P _i，P _i+1})/((2×max{P _i，P _i+1}-1)ρ _i+1) (8)

This hyperbolic function has monotonically increasing character, and simple and unified form has satisfied f with one for it _i(ρ _i) every requirement.Providing its monotonically increasing below proves:

If-1≤ρ ' _i＜ρ " _i≤ 1, and 0≤max{P _i, P _I+1}≤1 item

$f_i\left({\mathrm{\ρ}}_i^{\′}\right)-f_i\left({\mathrm{\ρ}}_i^{\′\′}\right)=\frac{2\×\max \{P_i,P_{i+1}\}(1-\max \{P_i,P_{u+1}\left\}\right)({\mathrm{\ρ}}_i^{\′}-{\mathrm{\ρ}}_i^{\′\′})}{((2\×\max \{P_i,P_{i+1}\}-1){\mathrm{\ρ}}_i^{\′}+1)((2\×\max \{P_i,P_{i+1}\}-1){\mathrm{\ρ}}_i^{\′\′}+1)}\≤0.$

Problem must be demonstrate,proved thus.

Yet for trying to achieve subpath r _iThe probability of stability, also need obtain ρ _iOccurrence.In fact, ρ _iOccurrence and non-availability, now adopt a kind of coefficient correlation τ _i(improved Kendall coefficient correlation) is similar to ρ _iIf the stability on the F indicates stochastic variable X _i, X _I+1,

Obviously, X _i, X _I+1Correlation and incident A _iAnd A _I+1Correlation (ρ _i) essential connection arranged.And the Kendall coefficient correlation can be described X well _i, X _I+1Between correlation.If (X _i, X _I+1) measured value (sample) sequence be (X _i(k), X _I+1(k)), 1≤k≤N, k represent different sampling times, and N is a total sample number.Make sign=(X _i(k1)-X _i(k2)) * (X _I+1(k1)-X _I+1(k2)), 1≤k1＜k2≤N.If sign＞0, then (X _i(k1), X _I+1(k1)), (X _i(k2), X _I+1(k2)) be positive correlation (harmony); If sign＜0, then (X _i(k1), X _I+1(k1)), (X _i(k2), X _I+1(k2)) be negative correlation (discordant).Order

$I_{k1,k2}=\left\{\begin{array}{cc}1& \mathrm{if\; sign}>0\\ 0& \mathrm{if\; sign}\&le;0\end{array}\right.,$ $I_{k1,k2}^{\&prime;}=\left\{\begin{array}{cc}1& \mathrm{if\; sign}<0\\ 0& \mathrm{if\; sign}\&GreaterEqual;0\end{array}\right.,$ $c=\underset{1\&le;k1<k2\&le;N}{\mathrm{\&Sigma;}}{I}_{k1,k2},$ $d=\underset{1\&le;k1<k2\&le;N}{\mathrm{\&Sigma;}}{I}_{k1,k2}^{\&prime;}.$

Therefore, c represents harmonious with number, and d represents to be discord to number.Then define τ _iFor:

${\mathrm{\&tau;}}_i=\frac{c-d}{c+d}---\left(9\right)$

In fact, τ _iBe more or less the same with the definition of Kendall coefficient correlation, can regard improved Kendall coefficient correlation as.So τ _iEqually X can be described well _i, X _I+1Between correlation, and then reflect incident A preferably _iAnd A _I+1Correlation (ρ _i).Through proof as can be known, when total sample number N is tending towards infinite, τ _iSatisfy correlation factor ρ fully _iFundamental property.Therefore, τ in this case _iWith ρ _iBe of equal value.Its proof is as follows:

X _i(k1), X _i(k2) be X _iSample value, so they can be considered to separate and and X _iWith the stochastic variable that distributes.In like manner, X _I+1(k1), X _I+1(k2) can be considered to separate and and X _I+1With the stochastic variable that distributes.Obviously, X _i(k1) and X _I+1(k2) be independently; X _i(k2) and X _I+1(k1) also be independently.By the front definition as can be known, if sign＞0 then must be one of following situation: (i) X _i(k1)=1, X _i(k2)=0, X _I+1(k1)=1, X _I+1(k2)=0; (ii) X _i(k1)=0, X _i(k2)=1, X _I+1(k1)=0, X _I+1(k2)=1.If sign＜0, then must be one of following situation: (iii) X _i(k1)=1, X _i(k2)=0, X _I+1(k1)=0, X _I+1(k2)=1; (iv) X _i(k1)=0, X _i(k2)=1, X _I+1(k1)=1, X _I+1(k2)=0.Therefore,

$P(\mathrm{sign}>0)=P\left(X_i\left(k1\right)\right)=1,X_i\left(k2\right)=0,X_{i+1}\left(k1\right)=1,X_{i+1}\left(k2\right)=0)+$

$P\left(X_i\left(k1\right)\right)=0,X_i\left(k2\right)=1,X_{i+1}\left(k1\right)=0,X_{i+1}\left(k2\right)=1).$

$=2\&times;P\left({\stackrel{\&OverBar;}{A}}_i{\stackrel{\&OverBar;}{A}}_{i+1}\right)P\left(A_i{A}_{i+1}\right)$

In like manner,

In addition, when certain incident total sample number is tending towards infinite,

The frequency that this incident occurs converges on its probability.Therefore can get:

N (N-1)/2 gets the sum (number that comprises sign=0) of various values for sign.Below according to ρ _iFundamental property proved one by one.

Character 1) be without loss of generality, establish P _i≤ P _I+1As P (A _iA _I+1)=min{P _i, P _I+1The time, P (sign＞0)=2 * P _i* (1-P _I+1)＞0 (P _i≠ 0, P _I+1≠ 1), P (sign＜0)=0.When total sample number N → ∞, c＞＞d, therefore

Character 2) as P (A _iA _I+1)=P _iP _I+1The time, P (sign＞0)=2 * P _iP _I+1(1-P _i) (1-P _I+1), in like manner, P (sign＜0)=2 * P _iP _I+1(1-P _i) (1-P _I+1), so P (sign＞0)=P (sign＜0).When total sample number N → ∞, c=d, therefore

Character 3) demonstration congeniality 1), can get $\underset{N\&RightArrow;\&infin;}{\lim }\frac{c-d}{c+d}=-1.$

Character 4) with character 5) as P (A _iA _I+1) when increasing,

Increase,

With

Reduce.Therefore, P (sign＞0) increases, and P (sign＜0) reduces.When total sample number N → ∞, c increases, and d reduces, therefore

Increase promptly

Be P (A _iA _I+1) monotonically increasing function.Demonstrate,proving in conjunction with the front can proper P (A _iA _I+1)＞P (A _i) P (A _I+1),

As P (A _iA _I+1)＜P (A _i) P (A _I+1),

Problem must be demonstrate,proved thus.

Yet actual central N can only get finite value.Therefore, ρ _iCan only use τ _iApproximate representation is promptly:

${\mathrm{\&rho;}}_i\&cong;{\mathrm{\&tau;}}_i---\left(10\right)$

In conjunction with formula (2), formula (6), formula (8), formula (9) and formula (10), can try to achieve the probability of stability of entire path R.

$P_R=P_1\&times;\frac{f_1\left({\mathrm{\&rho;}}_1\right)\&times;\min \{P_1,P_2\}}{P_1}...\frac{f_{m-1}\left({\mathrm{\&rho;}}_{m-1}\right)\&times;\min \{P_{m-1},P_m\}}{P_{m-1}}---\left(11\right)$

Innovative point of the present invention is as follows:

1) the present invention promptly is applied to the route stability computational methods of mobile ad-hoc network, its feature at first is to introduce correlation factor and describes degree of correlation between the adjacent link, and then the correlation structure between the structure link, obtain adjacent link and unite stable probability (subpath stability), thereby draw the stability of entire path.

2) according to any two link correlations in the mobile Ad hoc network, the entire path stability is decomposed into the stability of respectively forming subpath and the relational expression between the stability of respectively forming link, thereby has rationally simplified the complexity of path stability computing formula.

3), derive five fundamental propertys that correlation factor should satisfy, thereby accurately defined the intension of correlation factor by the dependency relation between the stable incident of analyzing adjacent two links.

4) according to the Sklar theorem, two links that the associating probability of stability of adjacent two links (subpath stability) is broken down into the stable marginal probability of each link (stability of each link) and is similar to the Copula function are stablized the correlation structure between the incident.According to the fundamental property of correlation factor, this correlation structure can obtain according to simple hyperbola interpolating function.

5) come the approximate evaluation correlation factor by improving the Kendall coefficient correlation, thereby can utilize the method for statistical sample sequence in real network, to obtain the occurrence of correlation factor.Improved Kendall coefficient correlation can reflect preferably that adjacent two links stablize the correlation between the incident; When total sample number was tending towards infinite, improved Kendall coefficient correlation satisfied the fundamental property of correlation factor fully.

Beneficial effect:

1) the present invention had both considered the correlation between the link, calculating path stability exactly, fairly simple and be suitable for application on mathematics again, solved the computational methods of current this respect or too simple and be not inconsistent preferably with the real network situation, otherwise too complicated and be difficult to practical difficult situation.

2) the present invention's calculating path stability that can combine with any single link stability computational methods has very big versatility.

3) the present invention can easily be applied to arbitrary distance vector routing protocol and selects to stablize route, has good application prospects.

Description of drawings

Fig. 1 is a path R schematic diagram.

Fig. 2 arrives destination node D route requests process schematic diagram for source node S.

Fig. 3 is the path stability computational methods flow chart that is applied to mobile ad-hoc network.

Embodiment

The first step: set up network topology, the initialization network environment.

Second step: select a certain link stability computational methods, utilize selected method, each node of network calculates the stability of forming link with neighbor node.For example, utilize histogram method, each network node can be jumped broadcast packet (as the hello message in the AODV agreement) statistics becomes link with other each groups of nodes life time and corresponding number of times by one.And calculate the link stability according to following formula:

H wherein _dFor its life time of a certain link is the d number of times of second, g is the current age of this link, and T=2s is set.

Need to prove that the embodiment of the invention just illustrates calculating the link stability with histogram method, but is not limited to this, also can adopt other link stability computational methods.

The 3rd step: each mobile node periodically sends one and jumps broadcast packet and receive the jumping broadcast packet that neighbor node sends.One jumps broadcast packet makes each node can add up the information that other node entered or left one jumping communication range in time, and then the stability of acquisition and respective nodes composition link indicates stochastic variable (X _i) sample sequence.

The 4th step: as shown in Figure 2, if when source node S need calculate the stability of route of destination node D, S is just to all neighbor nodes broadcasting routing request packet (wrapping as the RREQ in the AODV agreement).Make routing request packet comprise following territory: sample sequence Samseq, current path stability Cpath, upstream link stability Clink.

The 5th step: when the first hop node A when source node S is received this routing request packet, the stability that at first Samseq is initialized as link S → A indicates the stochastic variable sample sequence, and, transmit this bag then with the stability that Cpath and Clink are initialized as link S → A.

The 6th step: when the second hop node B in downstream when node A receives routing request packet, at first utilize the stability sign stochastic variable sample sequence of node A and B and the Samseq in the routing request packet, and according to the improved Kendall coefficient correlation (τ of formula (9) calculating corresponding to subpath S → B _i), calculate the stability of current path S → B and Cpath is updated to this stability according to formula (8), (10) and (11) then, the stability that then Samseq is updated to link A → B indicates the stochastic variable sample sequence, at last Clink is updated to the stability of link A → B and transmits this routing request packet.

The 7th step: after each hop node of downstream is received this routing request packet, six operations set by step.Finally, when destination node D receives routing request packet, just can calculate the stability of entire path S → D.

More than a kind of path stability computational methods that the embodiment of the invention provided are described in detail, for one of ordinary skill in the art, thought according to the embodiment of the invention, part in specific embodiments and applications all can change, in sum, this description should not be construed as limitation of the present invention.

The path stability computational methods flow chart that the present invention promptly is applied to mobile ad-hoc network as shown in Figure 3.

Claims (4)

1. path stability computational methods that are applied to mobile ad-hoc network, it is characterized in that: at first, introduce correlation factor and describe degree of correlation between the adjacent link, by the dependency relation between the stable incident of analyzing adjacent two links, derive five fundamental propertys that correlation factor should satisfy, thereby accurately defined the intension of correlation factor, secondly, according to the Sklar theorem, be that to be decomposed into the stable marginal probability of each link be that the stability of each link and two links that are similar to the Copula function are stablized the correlation structure between the incident to the subpath stability with the associating probability of stability of adjacent two links; Once more, come the approximate evaluation correlation factor, thereby can utilize the method for statistical sample sequence in real network, to obtain the occurrence of correlation factor by improved Kendall coefficient correlation; Finally, draw the stability computing formula of entire path R:

Be specially:

According to any two link correlations in the mobile Ad hoc network, the entire path stability is decomposed into the stability of respectively forming subpath and the relational expression between the stability of respectively forming link, thereby rationally simplifies the complexity of path stability computing formula; In mobile Ad hoc network, it is individual that each node can be considered to independently, and the speed, the direction of motion, position etc. that promptly show as each node are separate, and therefore, two do not have the link of common points separate; It is relevant that two links with common points that the stable incident of arbitrary link only is adjacent in the R of path are stablized incident, has nothing to do and stablize incident with other link; Therefore, the stability with entire path can be expressed as:

Wherein R represents a loop-free path, by m+1 node n _i, the m bar adjacent link l that is linked to be in succession _iForm l _iCorresponding to node to (n _I-1, n _i), A _iExpression link l _iStable incident, A _i∈ F, i=1,2..., m, F are field of events, P is the probability measure on the F, and P _i=P (A _i), i=1,2 ... m.

2. the path stability computational methods of mobile ad-hoc network according to claim 1, it is characterized in that described introducing correlation factor describes degree of correlation between the adjacent link, by the dependency relation between the stable incident of analyzing adjacent two links, derive five fundamental propertys that correlation factor should satisfy, thereby accurately defined the intension of correlation factor; If adjacent link (l _i, l _I+1) formed subpath r _i, subpath r _iStable incident is A _iA _I+1, its probability of stability is P (A _iA _I+1), and 0≤P (A _iA _I+1)≤min{P _i, P _I+1; For trying to achieve subpath r _iThe probability of stability, first analysis incident A _iAnd A _I+1Correlation; Definition correlation factor ρ _iRepresent the complementary degree of two incidents; ρ _iMust satisfy following five fundamental propertys:

1) as P (A _iA _I+1)=min{P _i, P _I+1, i.e. the appearance of small probability event, then ρ are depended in the appearance of big probability event fully _i=1;

2) as P (A _iA _I+1)=P _iP _I+1, promptly two incidents are separate, then ρ _i=0;

3) as P (A _iA _I+1)=0, i.e. two incident objectionable intermingling, then ρ _i=-1;

4) as P (A _iA _I+1)＞P _iP _I+1, ρ then _i＞0 i.e. appearance of the two incidents characteristic that is proportionate;

5) as P (A _iA _I+1)＜P _iP _I+1, ρ then _i＜0 i.e. appearance of two incidents is the negative correlation characteristic;

Can get thus-1≤ρ _i≤ 1.

3. the path stability computational methods of mobile ad-hoc network according to claim 1, it is characterized in that the theorem according to Sklar, is that to be decomposed into the stable marginal probability of each link be that the stability of each link and two links that are similar to the Copula function are stablized the correlation structure between the incident to the subpath stability with the associating probability of stability of adjacent two links; According to the fundamental property of correlation factor, this correlation structure can obtain according to simple hyperbola interpolating function; Inspired by the Sklar theorem, with A _iWith A _I+1The probability of product event is subpath r _iThe probability of stability marginal probability that is divided into them be the probability of each incident and the correlation structure that is similar to two incidents of Copula function;

,-1≤ρ _i≤ 1, wherein, 0≤f _i(ρ _i)≤1 presentation of events A _iAnd A _I+1Correlation structure; By ρ _iFundamental property as can be known, f _i(ρ _i) (1,1) excessively, (0, max (P _i, P _I+1)) and (1,0) 3 points, and be ρ _iMonotonically increasing function; Therefore, f _i(ρ _i) can obtain by interpolation method, select simple hyperbolic function as interpolating function: f _i(ρ _i)=(a ₁ρ _i+ a ₂)/(a ₃ρ _i+ 1) ,-1≤ρ _i≤ 1.With f _i(ρ _i) the each point substitution following formula of crossing, the alignment equation group is also found the solution and can be got f _i(ρ _i)=(max{P _i, P _I+1} * ρ _i+ max{P _i, P _I+1)/((2 * max{P _i, P _I+1}-1) ρ _i+ 1); This hyperbolic function has monotonically increasing character, and simple and unified form has satisfied f with one for it _i(ρ _i) every requirement.

4. the path stability computational methods of mobile ad-hoc network according to claim 1, it is characterized in that coming the approximate evaluation correlation factor, thereby can utilize the method for statistical sample sequence in real network, to obtain the occurrence of correlation factor by improved Kendall coefficient correlation; For trying to achieve subpath r _iThe probability of stability, also need obtain ρ _iOccurrence, in fact, ρ _iOccurrence and non-availability, adopt a kind of improved Kendall coefficient correlation coefficient τ _iApproximate ρ _i, the stability of establishing on the F indicates stochastic variable

Obviously, X _i, X _I+1Correlation and incident A _iAnd A _I+1Correlation ρ _iEssential connection is arranged, and X can be described well the Kendall coefficient correlation _i, X _I+1Between correlation; If (X _i, X _I+1) sample sequence be (X _i(k), X _I+1(k)), 1≤k≤N, k represent different sampling times, and N is a total sample number, make sign=(X _i(k1)-X _i(k2)) * (X _I+1(k1)-X _I+1(k2)), 1≤k1＜k2≤N; If sign＞0, then (X _i(k1), X _I+1(k1)), (X _i(k2), X _I+1(k2)) be harmonious; If sign＜0, then (X _i(k1), X _I+1(k1)), (X _i(k2), X _I+1(k2)) be discordant, order

$I_{k1,k2}=\left\{\begin{array}{cc}1& \mathrm{if\; sign}>0\\ 0& \mathrm{if\; sign}\&le;0\end{array}\right.,$ $I_{k1,k2}^{\&prime;}=\left\{\begin{array}{cc}1& \mathrm{if\; sign}<0\\ 0& \mathrm{if\; sign}\&GreaterEqual;0\end{array}\right.,$ $c=\underset{1\&le;k1<k2\&le;N}{\mathrm{\&Sigma;}}{I}_{k1,k2},$ $d=\underset{1\&le;k1<k2\&le;N}{\mathrm{\&Sigma;}}{I}_{k1,k2}^{\&prime;};$

Therefore, c represents harmonious with number, and d represents to be discord to number.Then define τ _iFor: In fact, τ _iBe more or less the same with the definition of Kendall coefficient correlation, can regard improved Kendall coefficient correlation as, so τ _iEqually X can be described well _i, X _I+1Between correlation, and then reflect incident A preferably _iAnd A _I+1Correlation ρ _i, through proof as can be known, when total sample number N is tending towards infinite, τ _iSatisfy correlation factor ρ fully _iFundamental property, therefore, τ in this case _iWith ρ _iBe of equal value, yet actual central N can only get finite value, therefore, ρ _iCan only use τ _iApproximate representation is promptly:

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