CN101296133B - Speculation method for link packet loss rate - Google Patents
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Abstract
The invention relates to a method for speculating link packet loss ratio on the basis of an internal monitor. The method puts the monitor in an initial logical topology tree, collects all observation data of the initial logical topology tree and then establishes the packet loss sequence of leaf nodes corresponding to each sub-tree so as to speculate the packet loss ratio of each inside link. The method of the invention has the advantages of low complexity and the packet loss ratio speculated being closer to actual packet loss ratio.
Description
Technical field
The present invention relates to a kind of network guessing method, especially a kind of estimation method of the link packet drop rate based on the internal monitoring device.
Background technology
Network measure is the necessary condition that realizes the monitoring and the management of network.But along with the continuous growth of the scale and the complexity of present the Internet and communication network, they are evolved into a kind of distributed system of loose control gradually.This distributed network makes the collection of performance information of network internal link become very difficult, and traditional queuing model based on the route layer goes the method for phase-split network performance more and more not fit into this large scale network.Propose a kind of new measuring technique in recent years in the world, be called network tomography.It is mainly by measuring the performance parameter of inferring network internal end to end, as link packet drop rate, delay.
Link packet drop rate is one of most important parameter of reflection network internal performance.The method of inferring at present link packet drop rate in the network chromatographic technique mainly be maximum Likelihood, EM (Expectation Maximiation, expectation maximization, down with) and pseudo-likelihood method of estimation or the like.But the likelihood method of estimation need be found the solution the root of one group of equation of higher order, and the EM method need go to approach a limiting value by continuous iteration.Along with increasing of number of network node, the increase that the complexity of these methods and computing time can be rapid, thus limited the use in practice of these methods.
The method of present existing supposition loss of link rate all is based on the observed result of leaf node, known to having no for the packet loss situation of internal node.If disposed a monitor at certain internal node, the packet loss sequence of this node correspondence just can be observed so.
Summary of the invention
The estimation method that the purpose of this invention is to provide a kind of low complex degree based on the link packet drop rate of internal monitoring device.
Technical scheme of the present invention is:
S1: in the initial logic topological tree of appointment, the initial logic topological tree is divided into some stalk trees, and places monitor at above-mentioned division node place based on the limited division methods of the subtree degree of depth, the limited division methods of monitor number;
S2: the observation data of all leaf nodes of collection initial logic topological tree and the observation data at all internal monitoring device places, set up the packet loss sequence that every stalk is set corresponding leaf node according to these two parts data;
S3:, infer the packet loss that its inner every link according to the packet loss sequence that step S2 obtains for every stalk tree;
S4: the inner link packet loss of all subtrees is gathered together, obtain the packet loss of the inner link of initial logic topological tree.
Divide the initial logic topological tree based on the limited division methods of the limited division methods of the subtree degree of depth, monitor number described in the step S1, the method of placing monitor is: if the maximum of the degree of depth of all subtrees is certain, then adopt the limited division methods of the subtree degree of depth, make the number of monitor minimize; If the number of monitor is certain, then adopt based on the limited division methods of monitor number, make the maximum of the degree of depth of all subtrees minimize.
The limited division methods of the described subtree degree of depth may further comprise the steps:
S11: LST is carried out initialization assignment LST=T, that stalk tree of degree of depth maximum in the subtree that obtains for all divisions of LST here, T is the initial logic topological tree;
S12: satisfying
Condition under, obtain leaf node k, a R here
LSTRefer to the set of the leaf node of LST, H (j) is meant the distance of node j to the root node of LST;
S13: according to f
n(k)=f (f
(n-1)(k)) recursively obtain the ancestor node of above-mentioned node k
Node k with
Between h is arranged
MaxThe bar link;
S14: at internal node
Dispose a monitor, so just can obtain one with
Be the subtree of root node, its degree of depth is h
Max
S15: the monitor that tree T is originally disposed has been divided into some stalk trees, finds out LST in these subtrees, if the degree of depth of LST is greater than h
Max, forward the S12 step to, otherwise, withdraw from.
The limited division methods of described monitor number may further comprise the steps:
S21:, for binary tree, obtain the maximum h of the subtree degree of depth if the number of monitor is no more than M
MaxThe upper bound be H
Upper=max{[log
2M]+1, H-1-[log
2M] }, wherein H is the degree of depth of initial logic topological tree T;
S22: utilize the limited division methods of the subtree degree of depth of step S11-S15 to obtain the number F (H of monitor
Upper), and satisfy M 〉=F (H
Upper);
S23: make h=H
UpperIf, M 〉=F (h), then the h value subtracts 1, and circulation judges whether M 〉=F (h) once more, up to when satisfy M＜F (h), withdrawing from, the h value tax that obtains at last to H
End, and satisfy F (H
End)＞M 〉=F (H
End+ 1) condition.
S24: make S=H
End+ 1, the depth capacity that obtains subtree is S, disposes F (H according to the limited division methods of the subtree degree of depth then
End+ 1)≤a M monitor.
Be to adopt demonstration formula method or maximal possibility estimation MLE method or expectation maximization EM method to infer the packet loss of inner every the link of every stalk tree among the step S3, scale according to subtree is decided, when the scale of subtree is smaller, can directly utilize the MLE algorithm to ask; When the scale of subtree is bigger, can directly obtain according to explicit formula.
Show according to simulation result, in initial logic tree, put into the more approaching real packet loss of link packet drop rate that link packet drop rate that the method for monitor obtains is under equal conditions obtained than the method for not putting monitor, and the packet loss of each the stalk tree that is divided into is independently of one another, the deduction process can walk abreast and carry out, thereby has reduced the complexity of calculating.
Description of drawings
Fig. 1 is the flow chart of the estimation method of the link packet drop rate based on the internal monitoring device of the present invention;
Fig. 2 is of the present invention based on the limited partitioning algorithm flow chart of the subtree degree of depth;
Fig. 3 is of the present invention based on the limited partitioning algorithm flow chart of monitor number.
Embodiment
Following examples are used to illustrate the present invention, but are not used for limiting the scope of the invention.
With reference to figure 1, on network interface, successively realize successively according to the following steps based on the estimation method of the link packet drop rate of internal monitoring device:
Step (1): for the logical topology tree of given network, place some monitors, it is divided into some stalk trees in the inside of logic tree.Concrete partitioning algorithm has two kinds: 1) maximum of the degree of depth of all subtrees is given, how to dispose monitor and makes the number of monitor minimize, and we have provided algorithm TDA-DL, the flow chart of its algorithm as shown in Figure 1, and it is optimum; 2) number of monitor is given, how to dispose monitor and makes the maximum of the degree of depth of all subtrees minimize.We have provided algorithm TDA-ML, and the flow chart of its algorithm as shown in Figure 2.After monitor that initial logic tree is disposed was divided into some stalks trees, each monitor played a part the sender of bag both as the root node of certain stalk tree.As the leaf node of another stalk tree, play a part the recipient of bag again.
Step (2): collect the observation data of all leaf nodes of initial logic tree and the observation data at all internal monitoring device places, just can obtain the packet loss sequence of leaf node of the correspondence of every stalk tree by these two parts data.
Step (3):, can infer the packet loss of its inner every link according to the packet loss sequence of its leaf node to every stalk tree.Concrete estimation method can adopt maximal possibility estimation, EM (expectation maximiation) or directly obtain according to explicit formula, and it is fixed to adopt which kind of method to come according to the scale of subtree on earth.When the scale of subtree is smaller, can directly utilize the maximal possibility estimation algorithm to ask, because the precision of maximal possibility estimation algorithm is a global optimum, and the computation complexity of this moment is also smaller.When the scale of subtree is bigger, can directly obtain according to explicit formula, because it only needs direct numerical computations, do not need to solve an equation or iteration, reduced the complexity of calculating greatly.
Step (4): because the inevitable link as certain subtree of every link of initial logic tree exists, the packet loss of the inner link of all subtrees is gathered together, just obtained the packet loss of every the link in inside of initial logic tree.
Referring to figs. 2 and 3, provide the detailed description of above-mentioned steps below.
At first set up the packet loss model of network to be measured.Here at network to be measured be tree topology, and the logical topology structure of its correspondence (logic tree in fact) is known, and remains unchanged in the process of measuring.With symbol with this logic tree brief note be T=(V, L), wherein V is all node set, L is all link set.The root node 0 of tree is the sender of detection packet, and all leaf nodes are recipients of detection packet, and the set that all leaf nodes constitute represents obviously have with R
Each node k ∈ V/{0} for except root node has unique father's node f (k).Further, recursively define the ancestor node j=f of k
n(k)=f (f
(n-1)(k)), also can be write as k＜j or j＞k.For the sake of simplicity, we are with (f (k), k) ∈ L represents link k.For each the node k beyond the leaf node, the number of its child nodes is d (k), and the set of child nodes is
The same in the image pattern opinion, we are designated as T (k)=(V (k), L (k)) to the subtree that with node k is root node, and the set of the leaf node that comprises among the T (k) is R (k)=R ∩ V (k).
We suppose that the packet loss of every link obeys Bernoulli Bernoulli Jacob and distribute, and the packet loss on the packet loss on the different link and same the link is independently of one another.The probability that detection packet is lost on link k ∈ L is θ
kWith random process X=(X
k)
K ∈ VRepresent the loss situation of detection packet in network, wherein X
kValue be 0 or 1.When detection packet arrives node k, X
kValue is 1, otherwise value is 0.Thereby for node k and its child nodes j ∈ D (k), their packet loss satisfies following relation: 1) if X
k=0, X is arranged so
j=0; 2) P[X
j=0|X
k=1]=θ
jAnd P[X
j=1|X
k=1]=1-θ
jIf sent N detection packet from root node, so
Be illustrated in the corresponding 0-1 sequence in node k place.If
Expression node k has received i detection packet, otherwise expression is not received.
Internal node at some networks to be measured is placed monitor, and whole original logic tree T is divided into some stalk trees.The method of present existing supposition loss of link rate all is based on the observed result of leaf node, known to having no for the packet loss situation of internal node.If disposed a monitor at certain internal node, the packet loss sequence of this node correspondence just can be observed so.What discuss below is exactly how to dispose monitor in original logic tree, and we are converted into two subproblems to this problem:
1., so how to dispose monitor and make the number of monitor minimize if the maximum of the degree of depth of all subtrees is given.
2., so how to dispose monitor and make the maximum of the degree of depth of all subtrees minimize if the number of monitor is given.
We use h with the number that M represents monitor
MaxThe depth capacity of representing all subtrees.If make that the number of monitor is as far as possible few, so the degree of depth that we will every as much as possible stalk tree near or equal h
MaxFor each leaf node k, definition H (k) is its distance to the root node of tree, Shu the degree of depth so
That stalk tree (if there are many, selecting wherein one arbitrarily) of degree of depth maximum is represented with LST in the subtree that all divisions are obtained.For first subproblem, we have proposed the partitioning algorithm of the tree of the limited TDA-DL of a kind of subtree degree of depth by name.As shown in Figure 2.
Algorithm 1:TDA-DL
Initialization LST=T, T are the initial the darkest subtrees of the degree of depth.
For the LST that finds, select a leaf node k, it satisfies
Here R
LSTRefer to the set of the leaf node of LST.
According to f
n(k)=f (f
(n-1)(k)) recursively find the ancestor node of the node k that selects above
Because the degree of depth of LST is greater than h
MaxThereby,
Certainly exist.
Node k with
Between h is arranged
MaxThe bar link, we are at internal node
Dispose a monitor, so just can obtain one with
Be the subtree of root node, its degree of depth is h
Max
The monitor that tree T is originally disposed has been divided into some stalk trees, finds out LST in these subtrees, if the degree of depth of LST is greater than h
Max, forwarded for the 2nd step to, otherwise, withdraw from.
Prove that below this algorithm is optimum.
If h
MaxBe given, M
AlgThe number of the needed monitor of expression TDA-DL algorithm, M
MinThe number of needed minimum monitor on the representation theory.M is arranged so
Alg=M
Min
Below we provide the proof of top conclusion.If node j and k satisfy k=f
n(j) or j=f
n(k), wherein n is a positive integer, use so d (j, k)=n represents the distance of node j and k.If do not satisfy, we represent node j and the nearest common ancestor's node of k with j ∨ k, this time, the distance definition of node j and k be d (j, k)=max{d (j, j ∨ k), d (k, j ∨ k) }.In the 2nd step of TDA-DL algorithm, select a LST middle distance root node middle distance leaf node farthest, use v
iRepresent the node selected for the i time.Because the TDA-DL algorithm has been disposed M altogether
AlgIndividual monitor, the set of all nodes of electing is so
According to the method for monitor deployment in the TDA-DL algorithm, except last stalk tree, the preceding M that marks off
AlgThe degree of depth of stalk tree all equals h
MaxSo for two node v arbitrarily
iAnd v
j(i ≠ j), all satisfy d (v
i, v
j) 〉=h
Max, and if only if v
i＜v
jOr v
j＜v
iThe time, d (v
i, v
j)=h
MaxSet up.Below we the proof take which type of deployment strategy all to need M
AlgIndividual monitor covers the M that elects
AlgIndividual node
The scope that monitor covers is to be not more than h to its distance
MaxAll nodes.If d is (v
i, v
j)＞h
Max, need two monitors could cover v so
iAnd v
jIf d is (v
i, v
j)=h
Max, v is arranged so
i＜v
jOr v
j＜v
iBe without loss of generality, be assumed to v
i＜v
jThe surface looks only need be at v
jThe place disposes a monitor just can be v
iAnd v
jCan both cover, but in fact, this moment v
jCan be as the leaf node of other stalk tree, we need the another one monitor to go to cover it.So at d (v
i, v
j)=h
MaxSituation under still need to dispose two monitors and remove to cover v
iAnd v
jThis explanation is for the M that selects
AlgIndividual node, a monitor can only cover one of them no matter be deployed in everywhere.So we need M at least
AlgIndividual monitor could cover this M
AlgIndividual node this means M
Alg≤ M
MinBecause M
MinThe number of needed minimum monitor on the representation theory, thus M is arranged
Alg〉=M
MinThereby can release M
Alg=M
Min
Because TDA-DL is optimum, thereby for a given network and h
Max, just can obtain M with the TDA-DL algorithm
Min, we use M
Min=F (h
Max) expression.
Second subproblem is how to dispose the feasible maximum of dividing the degree of depth of subtree of a given M monitor to minimize.Here our algorithm that proposed a kind of TDL-ML by name based on TDL-DL solves this problem, as shown in Figure 3.
Algorithm 2:TDA-ML
1. if our number of the monitor disposed is no more than M, so the maximum h of the subtree degree of depth
MaxHave a upper bound, at first we find out this upper bound.For binary tree, we are at [the log of original subtree
2M]+all nodes of 1 layer all dispose monitor, and this needs at the most
Individual monitor.The maximum that is divided into the degree of depth of subtree according to this method is max{[log
2M]+1, H-1-[log
2M] }, be designated as H
Upper, H so
UpperBe h
MaxA upper bound.
2. can obtain the number F (H of monitor with TDL-DL
Upper), and satisfy M 〉=F (H
Upper).Make h=H
UpperIf, M 〉=F (h), then the h value subtracts 1, and circulation judgement once more, up to withdrawing from when satisfying M＜F (h), the h value that obtains is at last composed to H
End, it satisfies F (H
End)＞M 〉=F (D
End+ 1).
3. make S=H
End+ 1, dispose F (H according to our needs of TDL-DL algorithm
End+ 1)≤a M monitor.If under the situation of placing the no more than M of monitor number, because the TDL-DL algorithm is optimum, H so
End+ 1 is exactly the minimum value of S.This TDL-DL algorithm is at S=H
EndJust we are needed for+1 o'clock deployment strategy.
For one tree, the observed result of given all leaf nodes provides an explicit estimation of obtaining the loss of link rate with observed result below.
According to the packet loss model of logic tree in the step 1, for any one internal node k, can set up is the two-layer tree of node of divergence one by one with it.This two-layer tree is made up of an input virtual link and some output virtual links.Input virtual link representative be path from root node 0 to node k, the representative of every output virtual link be a subtree that child nodes is a root node with k.The detection packet from the root node transmission that the packet loss pk of input virtual link represents does not reach the probability of node k, can represent with the packet loss on the link
Thereby the packet loss of link k can be used the packet loss p of input virtual link
kExpression
θ
k＝1-(1-p
k)/(1-p
f(k)) (2)
Every output virtual link representative be a subtree that child nodes is a root node with k, the set of these subtrees can be expressed as
Wherein d (k) is the number of the child nodes of node k.Subtree
In the set of leaf node be
It is the subclass of R (k).For subtree T (k), define a new stochastic variable T
k
X wherein
iWhether be illustrated in leaf node k place detection packet loses.If the transmission number of detection packet is N, so the 0-1 sequence
What represent is the corresponding packet drop of subtree T (k).The packet loss of subtree T (k) is defined as for certain detection packet, and the probability that its each leaf node is not all received can be expressed as l
k=P[T
k=0].
If internal node k has the individual child nodes of d (k), its output virtual link is so
We do as giving a definition:
And
B wherein
i∈ 0, and 1} (1≤i≤m).
Their estimated value can be come out with the observed result direct representation of leaf node:
And
Wherein
Be to satisfy in the observation sample
Number,
Be to satisfy in the observation sample
Number.Below we provide the input virtual link packet loss p
kWith
And
Relational expression.
For any internal node k ∈ V/R ∪ 0},
R wherein
11 ... 1(k) expression probability
According to formula (2), the packet loss θ on the link k
kEstimated value can be expressed as
Can obtain by formula (3)
Wherein
And
According to law of great number, when N → ∞,
Converge on actual value r
11 ... 1(k) and
Converge on actual value r
1 (i)(k), thus have
And
Estimator in this explanation formula (4)
Be θ
kConsistent Estimation, this estimator be with the observed result of leaf node explicit obtain packet loss on the link.Thereby we can utilize demonstration formula (3) and (4) to obtain the packet loss of inner every the link of each subtree.
Claims (8)
1. the estimation method of a link packet drop rate may further comprise the steps:
S1: in the initial logic topological tree of appointment, the initial logic topological tree is divided into some stalk trees, and places monitor at above-mentioned division node place based on the limited division methods of the subtree degree of depth, the limited division methods of monitor number;
S2: the observation data of all leaf nodes of collection initial logic topological tree and the observation data at all internal monitoring device places, set up the packet loss sequence that every stalk is set corresponding leaf node according to these two parts data;
S3:, infer the packet loss that its inner every link according to the packet loss sequence that step S2 obtains for every stalk tree;
S4: the inner link packet loss of all subtrees is gathered together, obtain the packet loss of the inner link of initial logic topological tree.
2. the estimation method of link packet drop rate as claimed in claim 1, it is characterized in that, divide the initial logic topological tree based on the limited division methods of the limited division methods of the subtree degree of depth, monitor number described in the step S1, the method of placing monitor is: if the maximum of the degree of depth of all subtrees is certain, then adopt the limited division methods of the subtree degree of depth, make the number of monitor minimize; If the number of monitor is certain, then adopt based on the limited division methods of monitor number, make the maximum of the degree of depth of all subtrees minimize.
3. the estimation method of link packet drop rate as claimed in claim 2 is characterized in that, the limited division methods of the described subtree degree of depth may further comprise the steps:
S11: LST is carried out initialization assignment LST=T, that stalk tree of degree of depth maximum in the subtree that obtains for all divisions of LST here, T is the initial logic topological tree;
S12: satisfying
Condition under, obtain leaf node k, a R here
LSTRefer to the set of the leaf node of LST, H (j) is the distance of node j to the root node of LST;
S13: according to f
n(k)=f (f
(n-1)(k)) recursively obtain the ancestor node of above-mentioned node k
Node k with
Between h is arranged
MaxThe bar link;
S14: at internal node
Dispose a monitor, so just can obtain one with
Be the subtree of root node, its degree of depth is h
Max
S15: the monitor that tree T is originally disposed has been divided into some stalk trees, finds out LST in these subtrees, if the degree of depth of LST is greater than h
Max, forward the S12 step to, otherwise, withdraw from.
4. the estimation method of link packet drop rate as claimed in claim 3 is characterized in that, the limited division methods of described monitor number may further comprise the steps:
S21:,, obtain the maximum h of the subtree degree of depth for binary tree if the number of monitor is no more than M
MaxThe upper bound be H
Upper=max{[log
2M]+1, H-1-[log
2M] }, wherein H is the degree of depth of initial logic topological tree T;
S22: utilize the limited division methods of the subtree degree of depth of step S11-S15 to obtain the number F (H of monitor
Upper), and satisfy M 〉=F (H
Upper);
S23: make h=H
UpperIf, M 〉=F (h), then the h value subtracts 1, and circulation judges whether M 〉=F (h) once more, up to when satisfy M＜F (h), withdrawing from, the h value tax that obtains at last to H
End, and satisfy F (H
End)＞M 〉=F (H
End+ 1) condition;
S24: make S=H
End+ 1, the depth capacity that obtains subtree is S, disposes F (H according to the limited division methods of the subtree degree of depth then
End+ 1)≤a M monitor.
5. the estimation method of link packet drop rate as claimed in claim 1 is characterized in that, among the step S3 is to adopt demonstration formula method to infer the packet loss of inner every the link of every stalk tree.
6. the estimation method of link packet drop rate as claimed in claim 1 is characterized in that, among the step S3 is to adopt maximum Likelihood to infer the packet loss of inner every the link of every stalk tree.
7. the estimation method of link packet drop rate as claimed in claim 1 is characterized in that, among the step S3 is to adopt expectation maximization EM method to infer the packet loss of inner every the link of every stalk tree.
8. the estimation method of link packet drop rate as claimed in claim 1, it is characterized in that, scale according to subtree among the step S3 is determined, adopts demonstration formula method or maximum Likelihood or expectation maximization EM method to infer the packet loss of inner every the link of every stalk tree.
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| CN1921422A (en) * | 2006-09-07 | 2007-02-28 | 华为技术有限公司 | Method for estimating bag-losing ratio |
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