CN102769554A - Link packet loss rate measuring method based on expanding Gilbert model - Google Patents

Abstract

A link packet loss rate measuring method based on an expanding Gilbert model belongs to the field of network measurement and aims at resolving the problem of large measurement error of the existing message loss rate measurement technology. The method includes the following steps: step1 initializing internal nodes according to measurement result sequence observed by leaf nodes and receiving detection packet sequence; step2 conducting sampling on detection packet sequence received by the internal nodes from top to bottom; step3 calculating parameter of each link packet loss model and calculating link loss rate according to the detection packet receiving condition of each node; step4 judging whether Markov link obtained by sampling is stable or not according to packet loss, executing step2 on no judgment and executing step5 on yes judgment; and step5 continuously conducting sampling for N times and calculating estimation value of the link loss rate according to sampling results.

Description

Link packet drop rate method of measurement based on the expansion Gilbert model

Technical field

The present invention relates to link packet drop rate method of measurement, belong to the network measure field based on the expansion Gilbert model.

Background technology

Fig. 1 is the cellular logic topological structure.(V L) describes the logical topology of network, and wherein V is a node set, and L is the link set of connected node with T=.Node o is the root node of T, and all probe messages are multicast to the whole network from o.

Node set

is represented all leaf nodes, the i.e. recipient node of probe messages.Each nonleaf node has a node at least, and child node is gathered with d (k)={ d _i(k) | 1≤i≤n _kExpression, n _kIt is node k child node number.Each non-root node k has a father node, representes with f (k).Link (k, f (k)) ∈ L is designated as link k, definition f ¹=f and f ⁿ(k)=f (f ^N-1(k)), n is a positive integer.If k=f ⁿ(j) set up, claim that then node j is descendants's node of k, the relation between the two is designated as j＜k.Be designated as a (U) to the nearest common ancestor of all nodes in the set ; If the father node of all nodes is identical among the set U, the node among the U is exactly the brotgher of node so.(V (k), L (k)) expression is the subtree of root with node k, and the leaf node set of this subtree is R (k)=R ∩ V (k).

Along with network size enlarges and the raising of network security demand, utilize the intermediate node cooperation to the network link parameter (packet loss and delay etc.) measure the more and more difficult that becomes.Network layer scanning technology (Network Tomography) can be realized the measurement of network link parameter under the condition that need not the intermediate node cooperation, be one of new technology that enjoys at present the concern of domestic and international academia.

Link packet Loss Rate (abbreviation packet loss) is one of important indicator of reflection network performance situation, also is that the performance that the network layer scanning technology needs emphasis to solve is inferred problem.In present network layer scanning technology research, link packet Loss Rate supposition technology is mainly carried out the packet loss of link process prescription based on Bernoulli Jacob (Bernoulli) model, supposes that promptly the process of losing of each message is separate on the link.There is document to propose to use the Gilbert model to carry out the description of packet loss of link process, as shown in Figure 2, p ₁₀After the expression current message is lost, next message transmissions probability of successful; p ₀₁Expression current message transmission success, the probability of next message dropping.In real network, when previous message dropping, the very big (p of the probability of a back message dropping ₁₀＜＜1); When previous message transmissions is successful, the also very big (p of a back message transmissions probability of successful ₀₁＜＜1), so can know p ₀₁+ p ₁₀＜1.Link packet drop rate under the Gilbert model can pass through formula θ=p ₁₀/ (p ₀₁+ p ₁₀) calculate.And then use maximal possibility estimation (MLE) or expectation maximization (EM) algorithm to carry out the calculating of model parameter.

Packet loss underestimation problem to MLE algorithm and the existence of EM algorithm; There is document to propose a kind ofly (to be abbreviated as MCMC based on Markov Chain Monte Carlo; Markov chain Meng Tekaer theory) link packet drop rate method of measurement; Obtain stable Markov chain through the Gibbs sampling and carry out the calculating of link packet drop rate, but the limitation of Bernoulli model on description packet loss of link process influenced the accuracy of this method.

Because the main cause of message dropping is that the congested buffering area that causes overflows in the network, so message dropping has tense dependence (Temporal Dependency) on time-domain.If a message dropping is on certain node, and the probability that message is following closely lost on this node should be very big.Tense dependence to message dropping; There is document to propose a kind of link packet drop rate estimation method based on gilbert (Gilbert) model; Use the MLE algorithm to carry out calculation of parameter, and compare based on the method for measurement of Bernoulli model, this method has better accuracy.But because the Gilbert model can only be described the relation between adjacent two messages, therefore along with the rising of link packet drop rate, its measure error also obviously increases.

Summary of the invention

The present invention seeks to provides a kind of link packet drop rate method of measurement based on the expansion Gilbert model in order to solve the big problem of measure error of existing message dropping rate measuring technique.

Link packet drop rate method of measurement based on the expansion Gilbert model according to the invention is sent n detection packet, measurement result sequence X that leaf node observe with the multicast mode to leaf node from source node o _k=(x _{K, 1}, x _{K, 2}..., x _{K, n}), if leaf node k receives detection packet i, then x _{K, i}=1; Otherwise x _{K, i}=0, i=1,2 ..., n;

Internal node receives detection packet sequence Y _c=(y _{C, 1}, y _{C, 2}..., y _{C, n}), if internal node c receives detection packet i, then y _{C, i}=1; Otherwise y _{C, i}=0, c=1,2 ..., r, r are the quantity of internal node;

(f (k), the packet loss on k) is θ to link _k=p _Ab(a, b=0,1,2,3), whole Network Packet Loss model parameter is Θ=(θ ₁, θ ₂, θ ₃... θ _r),

This method may further comprise the steps:

Step 1, initialization: the measurement result sequence X that observes according to leaf node _kThe initialization internal node receives detection packet sequence Y ⁽⁰⁾, internal node receives detection packet sequence Y ⁽⁰⁾The inner factor by formula

Carry out initialization;

By formula

$p_{\mathrm{ab}}=\left\{\begin{array}{cc}\underset{l=1}{\overset{M}{\mathrm{\Σ}}}{m}_l/m_0& a=0;b=1\\ \underset{l=4}{\overset{M}{\mathrm{\Σ}}}{m}_l/\underset{l=3}{\overset{M}{\mathrm{\Σ}}}{m}_l& a=3;b=3\\ \underset{l=b}{\overset{M}{\mathrm{\Σ}}}{m}_l/\underset{l=a}{\overset{M}{\mathrm{\Σ}}}{m}_l& a=\mathrm{1,2};b=a+1\\ 1-p_{\left(a\right)(b+1)}& a=\mathrm{0,1,2};b=0\\ 1-p_{\left(a\right)\left(a\right)}& a=3;b=0\end{array}\right.$

Each packet loss of link model parameter Θ of initialization ⁽⁰⁾, l is for lose the length of message, l ∈ [0, M], m continuously in the formula _lThe expression message is lost the number that length is l continuously, and M representes that message loses the maximum of length continuously;

Step 2, from top to bottom inner each node is received detection packet sequence and sample, the Q time sampled result is Y ^(Q), preceding Q sampled result Y=(Y ⁽¹⁾, Y ⁽²⁾..., Y ^(Q)), obtain r bar Markov chain,

The sampling of each internal node, judge that by following formula the condition posterior probability of this internal node distributes:

$p(y_{c,j}=0|X,Y_{c,-j},\mathrm{\Θ})$

$\∝\underset{k\∈R\left(c\right)}{\mathrm{\Π}}p\left(x_{k,j}\right|y_{c,j}=0)\·\underset{m=1}{\overset{3}{\mathrm{\Π}}}p(y_{c,m}=0|y_{c,j-m},{\mathrm{\θ}}_1)$

$=\underset{k\∈R\left(c\right)}{\mathrm{\Π}}(1-x_{k,j})[p_{01}{y}_{c,j-1}+p_{12}(1-y_{c,j-1})y_{c,j-2}$

$+p_{23}(1-y_{c,j-1})(1-y_{c,j-2})y_{c,j-3}$

$+p_{33}(1-y_{c,j-1})(1-y_{c,j-2})(1-y_{c,j-3})]$

$p(y_{c,j}=1|X,Y_{c,-j},\mathrm{\Θ})$

$\∝\underset{k\∈R\left(c\right)}{\mathrm{\Π}}p\left(x_{k,j}\right|y_{c,j}=1)\·\underset{m=1}{\overset{3}{\mathrm{\Π}}}p(y_{c,j}=1|y_{c,j-m},{\mathrm{\θ}}_1)$

$=\underset{k\∈R\left(c\right)}{\mathrm{\Π}}[(1-x_{k,j}){\mathrm{\α}}_k+x_{k,j}(1-{\mathrm{\α}}_k)][\left(p_{00}{y}_{c,j-1}\right)$

$+p_{10}(1-y_{c,j-1})y_{c,j-2}+p_{20}(1-y_{c,j-1})(1-y_{c,j-2})y_{c,j-3}$

$+p_{30}(1-y_{c,j-1})(1-y_{c,j-2})(1-y_{c,j-3})]$

R in the formula (s) is the corresponding leaf node set of internal node c;

Step 3, according to formula

$p_{\mathrm{ab}}=\left\{\begin{array}{cc}\underset{l=1}{\overset{M}{\mathrm{\Σ}}}{m}_l/m_0& a=0;b=1\\ \underset{l=4}{\overset{M}{\mathrm{\Σ}}}{m}_l/\underset{l=3}{\overset{M}{\mathrm{\Σ}}}{m}_l& a=3;b=3\\ \underset{l=b}{\overset{M}{\mathrm{\Σ}}}{m}_l/\underset{l=a}{\overset{M}{\mathrm{\Σ}}}{m}_l& a=\mathrm{1,2};b=a+1\\ 1-p_{\left(a\right)(b+1)}& a=\mathrm{0,1,2};b=0\\ 1-p_{\left(a\right)\left(a\right)}& a=3;b=0\end{array}\right.$

Calculate each packet loss of link model parameter Θ, and receive the situation calculating link packet drop rate A=(α of detection packet according to each node ₁, α ₂, α ₃..., α _Q), Q is the quantity of link,

The Q time result of calculation is Θ ^(Q)With A ^(Q), preceding Q packet loss model parameter and packet loss are Θ=(Θ ⁽¹⁾, Θ ⁽²⁾..., Θ ^(Q)) and A=(A ⁽¹⁾, A ⁽²⁾..., A ^(Q));

Step 4, judge according to packet loss A whether the r bar Markov chain that sampling obtains is stable,

If stable, execution in step five; If unstable, execution in step two;

Step 5, continuation sampling N time obtain N link packet drop rate A '=(A ^(Q+1), A ^(Q+2)..., A ^(Q+N)), and according to formula $\hat{A}=\frac{A^{(Q+1)}+A^{(Q+2)}+...+A^{(Q+N)}}{N}$

Obtain the estimated value

of each link packet drop rate and accomplish the link packet drop rate measurement

Wherein, N=40～80.

Advantage of the present invention: the defective that is directed against the link packet Loss Rate method of measurement existence of present layer scanning technology Network Based; This paper proposes a kind of link packet drop rate method of measurement based on expansion Gilbert model, uses expansion Gilbert model to carry out the description of packet loss of link process.Because the advantage of expansion Gilbert model in describing the packet loss of link process, this method is being improved aspect the accuracy with comparing based on the method for measurement of Bernoulli model and Gilbert model measuring.Along with the rising of link packet drop rate, this advantage is more obvious, reaches at 50% o'clock at link packet drop rate, and accuracy rate of measuring has improved about 50%.

Description of drawings

Fig. 1 is an existing network logical topology structure chart;

Fig. 2 is existing Gilbert packet loss model sketch map;

Fig. 3 is a four condition expansion Gilbert packet loss model sketch map;

Fig. 4 is simple and easy network topology structure figure;

Fig. 5 is the flow chart based on the link packet drop rate method of measurement of expanding Gilbert model according to the invention.

Embodiment

Embodiment one: this execution mode is described below in conjunction with Fig. 1 to Fig. 5; The said link packet drop rate method of measurement of this execution mode based on the expansion Gilbert model; Send n detection packet, measurement result sequence X that leaf node observe with the multicast mode to leaf node from source node o _k=(x _{K, 1}, x _{K, 2}..., x _{K, n}), if leaf node k receives detection packet i, then x _{K, i}=1; Otherwise x _{K, i}=0, i=1,2 ..., n;

Internal node receives detection packet sequence Y _c=(y _{C, 1}, y _{C, 2}..., y _{C, n}), if internal node c receives detection packet i, then y _{C, i}=1; Otherwise y _{C, i}=0, c=1,2 ..., r, r are the quantity of internal node, also equal the number of links in the network simultaneously;

(f (k), the packet loss on k) is θ to link _k=p _Ab(a, b=0,1,2,3), whole Network Packet Loss model parameter is Θ=(θ ₁, θ ₂, θ ₃... θ _r),

This method may further comprise the steps:

Step 1, initialization: the measurement result sequence X that observes according to leaf node _kThe initialization internal node receives detection packet sequence Y ⁽⁰⁾, internal node receives detection packet sequence Y ⁽⁰⁾The inner factor by formula

Carry out initialization;

By formula

$p_{\mathrm{ab}}=\left\{\begin{array}{cc}\underset{l=1}{\overset{M}{\mathrm{\Σ}}}{m}_l/m_0& a=0;b=1\\ \underset{l=4}{\overset{M}{\mathrm{\Σ}}}{m}_l/\underset{l=3}{\overset{M}{\mathrm{\Σ}}}{m}_l& a=3;b=3\\ \underset{l=b}{\overset{M}{\mathrm{\Σ}}}{m}_l/\underset{l=a}{\overset{M}{\mathrm{\Σ}}}{m}_l& a=\mathrm{1,2};b=a+1\\ 1-p_{\left(a\right)(b+1)}& a=\mathrm{0,1,2};b=0\\ 1-p_{\left(a\right)\left(a\right)}& a=3;b=0\end{array}\right.$

Each packet loss of link model parameter Θ of initialization ⁽⁰⁾, l is for lose the length of message, l ∈ [0, M], m continuously in the formula _lThe expression message is lost the number that length is l continuously, and M representes that message loses the maximum of length continuously;

Step 2, from top to bottom inner each node is received detection packet sequence and sample, the Q time sampled result is Y ^(Q), preceding Q sampled result Y=(Y ⁽¹⁾, Y ⁽²⁾..., Y ^(Q)), obtain r bar Markov chain,

The sampling of each internal node, judge that by following formula the condition posterior probability of this internal node distributes:

$p(y_{c,j}=0|X,Y_{c,-j},\mathrm{\Θ})$

$\∝\underset{k\∈R\left(c\right)}{\mathrm{\Π}}p\left(x_{k,j}\right|y_{c,j}=0)\·\underset{m=1}{\overset{3}{\mathrm{\Π}}}p(y_{c,m}=0|y_{c,j-m},{\mathrm{\θ}}_1)$

$=\underset{k\∈R\left(c\right)}{\mathrm{\Π}}(1-x_{k,j})[p_{01}{y}_{c,j-1}+p_{12}(1-y_{c,j-1})y_{c,j-2}$

$+p_{23}(1-y_{c,j-1})(1-y_{c,j-2})y_{c,j-3}$

$+p_{33}(1-y_{c,j-1})(1-y_{c,j-2})(1-y_{c,j-3})]$

$p(y_{c,j}=1|X,Y_{c,-j},\mathrm{\Θ})$

$\∝\underset{k\∈R\left(c\right)}{\mathrm{\Π}}p\left(x_{k,j}\right|y_{c,j}=1)\·\underset{m=1}{\overset{3}{\mathrm{\Π}}}p(y_{c,j}=1|y_{c,j-m},{\mathrm{\θ}}_1)$

$=\underset{k\∈R\left(c\right)}{\mathrm{\Π}}[(1-x_{k,j}){\mathrm{\α}}_k+x_{k,j}(1-{\mathrm{\α}}_k)][\left(p_{00}{y}_{c,j-1}\right)$

$+p_{10}(1-y_{c,j-1})y_{c,j-2}+p_{20}(1-y_{c,j-1})(1-y_{c,j-2})y_{c,j-3}$

$+p_{30}(1-y_{c,j-1})(1-y_{c,j-2})(1-y_{c,j-3})]$

R in the formula (s) is the corresponding leaf node set of internal node c;

P in the above-mentioned formula ₀₁, p ₁₂, p ₂₃By formula

$p_{\mathrm{Ab}}=\left\{\begin{array}{cc}\underset{l=1}{\overset{M}{\mathrm{\Σ}}}{m}_l/m_0& a=0;b=1\\ \underset{l=4}{\overset{M}{\mathrm{\Σ}}}{m}_l/\underset{l=3}{\overset{M}{\mathrm{\Σ}}}{m}_l& a=3;b=3\\ \underset{l=b}{\overset{M}{\mathrm{\Σ}}}{m}_l/\underset{l=a}{\overset{M}{\mathrm{\Σ}}}{m}_l& a=\mathrm{1,2};b=a+1\\ 1-p_{\left(a\right)(b+1)}& a=\mathrm{0,1,2};b=0\\ 1-p_{\left(a\right)\left(a\right)}& a=3;b=0\end{array}\right.$ Obtain.

Step 3, according to formula

$p_{\mathrm{ab}}=\left\{\begin{array}{cc}\underset{l=1}{\overset{M}{\mathrm{\Σ}}}{m}_l/m_0& a=0;b=1\\ \underset{l=4}{\overset{M}{\mathrm{\Σ}}}{m}_l/\underset{l=3}{\overset{M}{\mathrm{\Σ}}}{m}_l& a=3;b=3\\ \underset{l=b}{\overset{M}{\mathrm{\Σ}}}{m}_l/\underset{l=a}{\overset{M}{\mathrm{\Σ}}}{m}_l& a=\mathrm{1,2};b=a+1\\ 1-p_{\left(a\right)(b+1)}& a=\mathrm{0,1,2};b=0\\ 1-p_{\left(a\right)\left(a\right)}& a=3;b=0\end{array}\right.$

Calculate each packet loss of link model parameter Θ, and receive the situation calculating link packet drop rate A=(α of detection packet according to each node ₁, α ₂, α ₃..., α _Q), Q is the quantity of link,

The Q time result of calculation is Θ ^(Q)With A ^(Q), preceding Q packet loss model parameter and packet loss are Θ=(Θ ⁽¹⁾, Θ ⁽²⁾..., Θ ^(Q)) and A=(A ⁽¹⁾, A ⁽²⁾..., A ^(Q));

Step 4, judge according to packet loss A whether the r bar Markov chain that sampling obtains is stable,

If stable, execution in step five; If unstable, execution in step two;

Step 5, continuation sampling N time obtain N link packet drop rate A '=(A ^(Q+1), A ^(Q+2)..., A ^(Q+N)), and according to formula $\hat{A}=\frac{A^{(Q+1)}+A^{(Q+2)}+...+A^{(Q+N)}}{N}$

Obtain the estimated value

of each link packet drop rate and accomplish the link packet drop rate measurement

Wherein, N=40～80.

Provide a concrete embodiment below in conjunction with Fig. 3 and Fig. 4:

Fig. 3 is four condition expansion Gilbert model (LRL model) structure, and its relevant parameter defines as follows:

(1) S _l(l=0,1,2,3): link recurs the state of l message dropping, is the successful state of message transmissions during l=0;

(2) p _Ab(a, b=0,1,2,3): packet loss of link is transformed into the probability of state b by state a.

Under the situation of given link packet drop rate prior probability distribution,, after the Markov chain is stable, continue the estimated value that the some rounds of sampling obtain the packet loss of link model parameter through the Markov chain of Gibbs sampling sequential sampling each parameter of acquisition and hidden variable.Fig. 4 provides the network topology of one four node, sends n detection packet, measurement result sequence X that leaf node observe with the multicast mode to leaf node (node 2 and node 3) from source node o _k=(x _{K, 1}, x _{K, 2}..., x _{K, n}), k=2,3, if leaf node k receive j (j=1,2 ... n) individual detection packet, then x _{K, j}=1; Otherwise x _{K, j}=0.Internal node (node 1) receives detection packet sequence Y _i=(y _{I, 1}, y _{I, 2}..., y _{I, n}), i=1, if internal node i receive j (j=1,2 ... n) individual detection packet, then y _{I, j}=1; Otherwise y _{I, j}=0.(f (r), the packet loss on r) is θ to link _r, whole Network Packet Loss model parameter is Θ=(θ ₁, θ ₂, θ ₃).

Suppose that the prior probability that each link packet is lost meets the Beta distribution:

θ _r～Beta(a _r，b _r)，r＝1，2，3

Associating posterior probability distribution density function is:

$p(\mathrm{\Θ},X,Y)\∝\underset{j=1}{\overset{n}{\mathrm{\Π}}}\underset{k=2}{\overset{3}{\mathrm{\Π}}}p\left(y_{i,j}\right|\mathrm{\Θ},X)\·p(\mathrm{\Θ},X)$

$\&Proportional;\left[{{\mathrm{\&theta;}}_1}^{a_1-1+\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}(1-{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002015718600011.png"\; state="\{\{state\}\}">y</figure-callout>}}_{1,j})}{(1-{\mathrm{\&theta;}}_1)}^{b_1-1+\underset{j=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; y"\; filenames="HDA00002015718600011.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{y}_{}{}_{1,j}}\right]$

$\&CenterDot;\left[{{\mathrm{\&theta;}}_2}^{a_2-1+\underset{j=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; y"\; filenames="HDA00002015718600011.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{y}_{}{}_{1,j}(1-{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="HDA00002015718600011.png,HDA00002015718600022.png"\; state="\{\{state\}\}">x</figure-callout>}}_{2,j})}{(1-{\mathrm{\&theta;}}_2)}^{b_2-1+\underset{j=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; y"\; filenames="HDA00002015718600011.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{y}_{}{}_{1,j}{x}_{2,j}}\right]$

$\&CenterDot;\left[{{\mathrm{\&theta;}}_3}^{a_3-1+\underset{j=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; y"\; filenames="HDA00002015718600011.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{y}_{}{}_{1,j}(1-{\mathrm{<figure-callout\; id="3"\; label="x"\; filenames="HDA00002015718600011.png,HDA00002015718600022.png"\; state="\{\{state\}\}">x</figure-callout>}}_{3,j})}{(1-{\mathrm{\&theta;}}_3)}^{b_3-1+\underset{j=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; y"\; filenames="HDA00002015718600011.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{y}_{}{}_{1,j}{x}_{3,j}}\right]$

The condition posterior probability that can be obtained packet loss of link model parameter Θ and hidden variable Y by associating posterior probability distribution density function distributes; Extract Θ and Y through condition posterior probability distribution sampling; Obtain stable Markov chain, thereby calculate the estimated value of each packet loss of link model parameter.

Embodiment two: this execution mode is described further execution mode one, N=50.

Embodiment three: this execution mode is described further execution mode one, and whether stable process is the Markov chain that obtains according to packet loss A judgement sampling in the step 4:

Whether preceding 10% sampled value in preceding Q the sampling surpasses threshold value with the absolute error of back 20% sample value mathematic expectaion, and as if surpassing, expression is stable; If be no more than, expression is unstable;

The threshold value span is 1 * 10 ^-3～2 * 10 ^-3

Claims (3)

1. the link based on the expansion Gilbert model goes bag rate method of measurement, sends n detection packet, measurement result sequence X that leaf node observe with the multicast mode with leaf node from source node o _k=(x _{K, 1}, x _{K, 2}..., x _{K, n}), if leaf node k receives detection packet i, then x _{K, i}=1; Otherwise x _{K, i}=0, i=1,2 ..., n;

Internal node receives detection packet sequence Y _c=(y _{C, 1}, y _{C, 2}..., y _{C, n}), if internal node c receives detection packet i, then y _{C, i}=1; Otherwise y _{C, i}=0, c=1,2 ..., r, r are the quantity of internal node;

(f (k), the packet loss on k) is θ to link _k=p _Ab(a, b=0,1,2,3), whole Network Packet Loss model parameter is Θ=(θ ₁, θ ₂, θ ₃... θ _r),

It is characterized in that this method may further comprise the steps:

Step 1, initialization: the measurement result sequence X that observes according to leaf node _kThe initialization internal node receives detection packet sequence Y ⁽⁰⁾, internal node receives detection packet sequence Y ⁽⁰⁾The inner factor by formula

Carry out initialization;

By formula

$p_{\mathrm{ab}}=\left\{\begin{array}{cc}\underset{l=1}{\overset{M}{\mathrm{\&Sigma;}}}{m}_l/m_0& a=0;b=1\\ \underset{l=4}{\overset{M}{\mathrm{\&Sigma;}}}{m}_l/\underset{l=3}{\overset{M}{\mathrm{\&Sigma;}}}{m}_l& a=3;b=3\\ \underset{l=b}{\overset{M}{\mathrm{\&Sigma;}}}{m}_l/\underset{l=a}{\overset{M}{\mathrm{\&Sigma;}}}{m}_l& a=\mathrm{1,2};b=a+1\\ 1-p_{\left(a\right)(b+1)}& a=\mathrm{0,1,2};b=0\\ 1-p_{\left(a\right)\left(a\right)}& a=3;b=0\end{array}\right.$

Each packet loss of link model parameter Θ of initialization ⁽⁰⁾, l is for lose the length of message, l ∈ [0, M], m continuously in the formula _lThe expression message is lost the number that length is l continuously, and M representes that message loses the maximum of length continuously;

Step 2, from top to bottom inner each node is received detection packet sequence and sample, the Q time sampled result is Y ^(Q), preceding Q sampled result Y=(Y ⁽¹⁾, Y ⁽²⁾..., Y ^(Q)), obtain r bar Markov chain,

The sampling of each internal node, judge that by following formula the condition posterior probability of this internal node distributes:

$p(y_{c,j}=0|X,Y_{c,-j},\mathrm{\&Theta;})$

$\&Proportional;\underset{k\&Element;R\left(c\right)}{\mathrm{\&Pi;}}p\left(x_{k,j}\right|y_{c,j}=0)\&CenterDot;\underset{m=1}{\overset{3}{\mathrm{\&Pi;}}}p(y_{c,m}=0|y_{c,j-m},{\mathrm{\&theta;}}_1)$

$=\underset{k\&Element;R\left(c\right)}{\mathrm{\&Pi;}}(1-x_{k,j})[p_{01}{y}_{c,j-1}+p_{12}(1-y_{c,j-1})y_{c,j-2}$

$+p_{23}(1-y_{c,j-1})(1-y_{c,j-2})y_{c,j-3}$

$+p_{33}(1-y_{c,j-1})(1-y_{c,j-2})(1-y_{c,j-3})]$

$p(y_{c,j}=1|X,Y_{c,-j},\mathrm{\&Theta;})$

$\&Proportional;\underset{k\&Element;R\left(c\right)}{\mathrm{\&Pi;}}p\left(x_{k,j}\right|y_{c,j}=1)\&CenterDot;\underset{m=1}{\overset{3}{\mathrm{\&Pi;}}}p(y_{c,j}=1|y_{c,j-m},{\mathrm{\&theta;}}_1)$

$=\underset{k\&Element;R\left(c\right)}{\mathrm{\&Pi;}}[(1-x_{k,j}){\mathrm{\&alpha;}}_k+x_{k,j}(1-{\mathrm{\&alpha;}}_k)][\left(p_{00}{y}_{c,j-1}\right)$

$+p_{10}(1-y_{c,j-1})y_{c,j-2}+p_{20}(1-y_{c,j-1})(1-y_{c,j-2})y_{c,j-3}$

$+p_{30}(1-y_{c,j-1})(1-y_{c,j-2})(1-y_{c,j-3})]$

In the formula: R (s) is the corresponding leaf node set of internal node c;

Step 3, according to formula

$p_{\mathrm{ab}}=\left\{\begin{array}{cc}\underset{l=1}{\overset{M}{\mathrm{\&Sigma;}}}{m}_l/m_0& a=0;b=1\\ \underset{l=4}{\overset{M}{\mathrm{\&Sigma;}}}{m}_l/\underset{l=3}{\overset{M}{\mathrm{\&Sigma;}}}{m}_l& a=3;b=3\\ \underset{l=b}{\overset{M}{\mathrm{\&Sigma;}}}{m}_l/\underset{l=a}{\overset{M}{\mathrm{\&Sigma;}}}{m}_l& a=\mathrm{1,2};b=a+1\\ 1-p_{\left(a\right)(b+1)}& a=\mathrm{0,1,2};b=0\\ 1-p_{\left(a\right)\left(a\right)}& a=3;b=0\end{array}\right.$

Calculate each packet loss of link model parameter Θ, and receive the situation calculating link packet drop rate A=(α of detection packet according to each node ₁, α ₂, α ₃..., α _Q), Q is the quantity of link,

The Q time result of calculation is Θ ^(Q)With A ^(Q), preceding Q packet loss model parameter and packet loss are Θ=(Θ ⁽¹⁾, Θ ⁽²⁾..., Θ ^(Q)) and A=(A ⁽¹⁾, A ⁽²⁾..., A ^(Q));

Step 4, judge according to packet loss A whether the r bar Markov chain that sampling obtains is stable,

If stable, execution in step five; If unstable, execution in step two;

Step 5, continuation sampling N time obtain N link packet drop rate A '=(A ^(Q+1), A ^(Q+2)..., A ^(Q+N)), and according to formula $\hat{A}=\frac{A^{(Q+1)}+A^{(Q+2)}+...+A^{(Q+N)}}{N}$

Obtain the estimated value

of each link packet drop rate and accomplish the link packet drop rate measurement

Wherein, N=40～80.

2. according to the said link packet drop rate method of measurement of claim 1, it is characterized in that N=50 based on the expansion Gilbert model.

3. according to the said link packet drop rate method of measurement of claim 1, it is characterized in that whether stable process is the Markov chain that obtains according to packet loss A judgement sampling in the step 4 based on the expansion Gilbert model:

Whether preceding 10% sampled value in preceding Q the sampling surpasses threshold value with the absolute error of back 20% sample value mathematic expectaion, and as if surpassing, expression is stable; If be no more than, expression is unstable;

The threshold value span is 1 * 10 ^-3～2 * 10 ^-3

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