CN109194524A - A kind of distributed traffic allocation algorithm end to end - Google Patents

A kind of distributed traffic allocation algorithm end to end Download PDF

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CN109194524A
CN109194524A CN201811182207.XA CN201811182207A CN109194524A CN 109194524 A CN109194524 A CN 109194524A CN 201811182207 A CN201811182207 A CN 201811182207A CN 109194524 A CN109194524 A CN 109194524A
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link
flow
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terminal
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CN109194524B (en
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王靖瑶
郑华青
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Xiamen University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/50—Network service management, e.g. ensuring proper service fulfilment according to agreements
    • H04L41/5061—Network service management, e.g. ensuring proper service fulfilment according to agreements characterised by the interaction between service providers and their network customers, e.g. customer relationship management
    • H04L41/5067—Customer-centric QoS measurements
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/142—Network analysis or design using statistical or mathematical methods
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/145—Network analysis or design involving simulating, designing, planning or modelling of a network
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L45/00—Routing or path finding of packets in data switching networks
    • H04L45/302—Route determination based on requested QoS
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/08—Configuration management of networks or network elements
    • H04L41/0803—Configuration setting
    • H04L41/0823—Configuration setting characterised by the purposes of a change of settings, e.g. optimising configuration for enhancing reliability

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Abstract

A kind of distributed traffic allocation algorithm end to end is related to network flow distribution field, and the present invention is the following steps are included: step 1: establishing non-convex optimization problem；Step 2: by selecting suitable variable, converting non-convex optimization problem to the convex optimization problem of family's equivalence；Step 3: proposing fully distributed optimal assignment of traffic algorithm.The present invention is the non-recessed utility function of optimization, fully distributed, based on optimal control method, has the advantages that improve internet security, reduces communication price, and can save very big calculation amount.

Description

A kind of distributed traffic allocation algorithm end to end
Technical field
The present invention relates to network flows to distribute field, more particularly to a kind of distributed traffic allocation algorithm end to end.
Background technique
In recent years, as IP Video service occupies leading position in Internet application, meet user for Video Applications The growing demands of Internet applications such as service become the developing direction of Future Internet.The welcome journey of IP Video Applications Spend higher and higher, this brings immense pressure to the configuration of network bandwidth resources.For example, according to publication on June 1st, 2016 " Cisco's future network development service trend white paper ", the year two thousand twenty IP video flowing will occupy entire consumer network's flow 82%, 70% compared to 2015 has a distinct increment；Moreover, white paper prediction IP video flowing will be 2015 to 2020 Between increase by three times.Therefore, the development trend of future network is exactly that should handle growing Video Applications demand well, also The service of high-quality is provided to other Internet applications user such as Video Applications.However, existing data transfer rate end to end point With scheme (such as transmission control protocol and congestion control mechanisms based on window, i.e. Transmission Control Protocol) and network traffic engineering scheme (such as equal cost multiple paths load-balancing mechanism, i.e. ECMP agreement based on stream) can not provide such service.
Existing Transmission Control Protocol and ECMP agreement have following defects that
1, video content may be by with different solution code frequency decodings or with the decoding layer decoder of different numbers, and solution The frequency of code is higher or the decoding number of plies is more, and user is higher to the satisfaction of service quality.Therefore, for describing user to clothes The utility function of business quality satisfaction is the step-shaped function about decoding rate.Because such utility function be it is non-recessed, So optimizing such utility function has difficulty substantially.However, being currently available that transmission mechanism such as Transmission Control Protocol end to end It is only capable of optimizing recessed utility function, thus non-recessed utility function can not be optimized, the higher service of user cannot be also provided Quality.
2, usually occurs " elephant stream " phenomenon in current network, " elephant stream " phenomenon refers to: few bandwidth is held in network The flow transformation task of larger proportion is carried, and remaining bandwidth is in idle state.Traditional ECMP agreement is not because be base In the method for optimization, so being likely to result in " elephant stream " phenomenon.
3, existing how to influence user couple with network traffic engineering mechanism end to end in default of theory support In the satisfaction of Video Applications service and other application service, the stability of whole network even how is influenced, is all not Know.
Therefore, it is very that exploitation, which can optimize non-recessed utility function, fully distributed, based on optimal control method, It is necessary.
Summary of the invention
It is an object of the invention to solve the above problem in the prior art, a kind of distributed traffic end to end point is provided With algorithm, which is the non-recessed utility function of optimization, fully distributed, based on optimal control method, there is raising net Network safety reduces the advantages that communication price, and can save very big calculation amount.
In order to achieve the above objectives, the present invention adopts the following technical scheme:
A kind of distributed traffic allocation algorithm end to end, comprising the following steps:
Step 1: establishing the non-convex optimization problem based on users satisfaction degree；
Step 2: by selecting suitable variable, converting non-convex optimization problem to the optimization problem of family's equivalence；
Step 3: proposing fully distributed optimal assignment of traffic algorithm.
In step 1, the method for the non-convex optimization problem based on users satisfaction degree is established are as follows:
subject to
1s,lxs,l≤cl,l∈Ls,s∈S (26)
Fx=0 (27)
(xs,rs)∈Xs,s∈S (29)
The utility function of the optimization problem are as follows:
Wherein, α and ι is respectively given positive integer, and j ∈ { 0,1,2 ..., α }, s are the node of transmitted traffic, rsFor section The sum for all flows that point s is issued；Given node s, fractional order functionWith rsAs independent variable, with set {ps,0,...,ps,j-1,ps,j,ps,j+1,...,ps,αIn element as the corresponding parameter of corresponding order,Order be j/ ι, Its relevant parameter is ps,j, the relevant users satisfaction degree of characterization transmitted traffic node s；It is the mark of summation operation, table Show and variable j is enabled to rise to α from 0, corresponding functional value is added；Equally, ∑s∈SIt is also the mark of summation operation, expression enables variable S not repeatedly traverses the value in set S, and corresponding functional value is added；B is the node for transmitting flow；D is the terminal of flow；l For the link for transmitting flow；elIt (b) is the node being connected with node b through link l；It is issued by node s, is with node d Terminal, the flow transmitted through link l；It is transmitted by node b, using node d as terminal, the flow that is transmitted through link l；For by node el(b) transmission, using node d as terminal, the flow that is transmitted through link l；S is by all transmitted traffic sections The set that point s is constituted；For the set being made of the node b of all transmission flows；LbIt is the collection for the link l being connected with node b It closes；LsIt is the set for the link l being connected with node s；clBy link l energy bearer traffic bandwidth；xs,lTo be issued by node s , the total flow transmitted through link l；xb,lThe total flow transmitted for node b through link l；xsFor the stream issued by all node s The vector constituted is measured, i.e.,xbIt is by the column vector of the constitution of all node b transmission, i.e.,VectorThe T in the upper right corner is indicated to vector xb,lDo transposition operation；X be from the column of all constitutions to Amount, i.e.,Independent variable r is by all variable rsThe column vector of composition, i.e.,1s,l、 WithBe the transversal vector with positive integer 1 for element, their element number respectively with column vector xs,l、xb,lAnd xel(b), l Element number is identical；F is class adjacency matrix；It is that node b is used to transmit to be constituted by all link l of the flow of terminal of d Set；DbThe set that the terminal d of all flows to be transmitted by node b is constituted；Ds,lIt is that node s owns through what link l was transmitted The set that the terminal d of flow is constituted；ξsAnd ζsIt is r respectively for constantsLower bound and the upper bound；And R+Respectively indicate dimension Number isWith 1 positive integer space, | Ds,l| it is vector Ds,lDimension；
Condition (1) and (2) indicate the limitation of link bearing capacity, carrying energy of the flow that link l is transmitted no more than it Power；Condition (3) expression cannot lose the limitation of flow in transmission process interior joint, and the flow for flowing into each node should be equal to stream The flow of the node out；Condition (4) indicates that the flow of transmission node b transmission is non-negative；Condition (5) indicates what node s was issued Flow is non-negative, and the total flow issued has bound；Condition (6) provides set XsDefinition.
The method of step 2 is as follows:
Choose variableBy ysIt is assumed to be stochastic variable and enables ysFor estimating μsJ-th of moment of momentum be denoted as ms,j, I.e.Wherein j ∈ { 0,1,2 ..., α } is converted non-convex optimization problem to as follows using functional analysis theory Family's optimization problem:
subject to
ms,0=1, s ∈ S (32)
Ms(0,α,ms)≥0,s∈S (33)
βsMs(0,α-2,ms)-Ms(0,α,ms)≥0 (34)
1s,lxs,l≤cl,l∈Ls,s∈S (37)
Fx=0 (38)
(xs,rs)∈Xs,s∈S (40)
The utility function of the optimization problem are as follows:
Wherein, node s, function are givenIt is with transversal vectorFor parameter and with column vectorFor the linear function of variable；Independent variable m is by all torque variable msThe column vector of composition, i.e.,Constant betasIt is the known upper bound of the sum of node s transmitted traffic；MsIt is the Hankel matrix such as following formula: It is a given sequence, k, h are elements in sequence Mark；Other marks occurred in step 2 mark corresponding with step 1 defines identical；Condition (8), (9) and (10) guarantees Estimate μsExistence；Condition (11) guarantees equationIt sets up；This family's optimization problem is equivalent to former non-convex optimization problem, And work as parameter alpha≤ι, which is convex optimization problem.
In step 3, following complete distributed traffic distribution method can be obtained using ADMM algorithm:
Algorithm 1:
Initial value: { τs}s∈S,γ
1) start
2) initializing variable value
3)x0,m0,r0,λ0
4) mark is introduced
5) mark is introduced
6) as the number of iterations k+1, variate-value relevant to transmitted traffic node s is updated as follows
7) variate-value relevant to transmission flow node b is updated as follows simultaneously
8) each transmitted traffic node s ∈ S passes through link LsTransmit flow
9) each transmission flow nodePass through link l ∈ LbTransmit flow
10) it updates and link l ∈ L as followsb,Relevant punishment parameter
11) mark is updated
12) mark is updated
13) each node s ∈ S passes through link LsTransmit information
14) each nodePass through link l ∈ LbTransmit information
x0,m0,r0,λ0For variable x, m, r, the selected iteration initial value of λ；WithIt is vector x0In element；Become AmountThe mark k in the upper right corner represents kth time repeatedly The variate-value that generation obtains；Equally, variable The mark k+1 in the upper right corner represents the variate-value that+1 iteration of kth obtains；Oeprator ← expression is by the value assignment of arrow right end Give arrow left end variable；AsIt is the set that each node s ∈ S local limit condition is constituted, i.e.,
VariableIt is defined as follows:
Wherein,WithThe mark that is for avoiding causing obscuring and introduce, they and mark l are to represent For transmitting the link of flow；Refer to the link passed through using node d by the traffic flow ingress b of terminalThe collection of composition It closes；Refer to that node b is used to transmit all links using d as the flow of terminalThe set of composition；Refer to node d For the traffic flow ingress e of terminall(b) link passed throughThe set of composition；Refer to node el(b) it is used to transmit Using d as all links of the flow of terminalThe set of composition；It is to store variable respectivelyValue and the mark that introduces；Refer to that node b passes through the link l all flows transmitted The set that terminal is constituted；
Be withFor the column vector of element, wherein
VariableIt is defined as follows:
Wherein,Refer to node el(s) it is used to transmit all links using d as the flow of terminalThe set of composition, elIt (s) is the node being connected with node s by link l；It is to store variable respectivelyValue and draw The mark entered；Ds,lRefer to the set that node s is made up of the terminal of the link l all flows sent；
MarkIt respectively represents variable to space As、R+Do project； Step parameter sequence { τ to be determineds}s∈S,It is true by such as under type with step parameter γ It is fixed:
When given communication network and convex optimization problem, wherein the decision variable of the convex optimization problem is (x, m, r), it is assumed that is calculated 1 iterative initial value of method is (x0,m0,r0), the sequence that iteration generates is { xk,mk,rk}k∈N, wherein xk,mk,rkIndicate kth time iteration The variate-value of generation, N represent the set being made of all natural numbers.If enabling iteration step length parameter { τs}s∈S,Meet such as lower inequality with γ:
Wherein, mlIt is by link l ∈ LbThe terminal number of all flows of transmission；{υsAndMeet respectively following Inequality:
Wherein,Refer to and be connected with node s, is constituted as all link l of the flow of terminal for transmitting using node d Set；Refer to the traffic flow ingress e using node d as terminall(s) set that the link l passed through is constituted, el(s) it is The node being connected with node s by link l；Refer to node el(s) it is used to transmit all chains using d as the flow of terminal The set that road l is constituted；Refer to the traffic flow ingress using node d as terminalThe collection that the link l passed through is constituted It closes；Refer to nodeFor transmitting the set constituted using d as all link l of the flow of terminal；Oeprator | | it represents and takes element number in corresponding set；
So sequence of iterations { xk,mk,rk}k∈NA solution of maximum utility function in problem, the receipts of algorithm 1 will be converged to Holding back rate is O (1/k), and wherein k is the number of iterations.
In algorithm 1, to any given step parameter γ > 0, the node s ∈ S oneself of each transmitted traffic determines its Local step parameter τs>0.Meanwhile the node s ∈ S of each transmitted traffic is also by parametric variable ms,rsWith ps as its part Privacy information does not need and other nodes sharings in network.In addition, the node s ∈ S of each transmitted traffic will also introduce auxiliary Variable zs, for storing variable xsValue so that design assignment of traffic algorithm be fully distributed.Assuming that each hair Send the known all link L being connected to it of the node s ∈ S of flows, and the traffic carrying capacity information of these known links. In addition, the node s ∈ S of each transmitted traffic also wants the set A provided in known formula (18) for more new flowsStructure.
Similarly, the node of each transmission flowIts step parameter is determined also with local messageAssuming that the node of each transmission flowThe known link L being connected with itb, And the traffic carrying capacity of known portions link is only needed, i.e., for each d ∈ Db, it only needs to know setMiddle chain The traffic carrying capacity on road.In addition, given nodeTo each of the links l ∈ Lb, variable λb,lIt is non-negative numerical variable, Represent the cost parameter of link l.
Similar to the node of transmitted traffic, the node of each transmission flowIt is also required to introduce auxiliary variable zb,l,l∈ Lb, for storing variable xb,lValue so that design assignment of traffic algorithm be fully distributed.
In algorithm 1, the upper right footmark of all variables represents the number of iterations.Specifically, at the kth iteration, in algorithm 1 Including operating as follows: in step 6, all transmitted traffic nodes update their ideal transmission data transfer rates simultaneously, which is Each transmitted traffic node solves what a simple semi definite programming problem was completed by the local message using it；The 7th In step, the node of all transmission flows updates their ideal transmission data transfer rates simultaneously, and equally, which is also each transmission The node of flow is completed using its local message；In step 10, to the node of each transmission flowEvery chain Road l ∈ LbUpdate its corresponding cost variable λb,l, this single stepping can be on one or two nodes of the link connection It calculates.Specifically, in the case where considering traffic, then the cost variable can calculate simultaneously on two nodes, otherwise It only needs to be transferred to another node after calculating on one node.
In conclusion algorithm 1 is a fully distributed assignment of traffic algorithm.This is embodied in all operations all and is The information used when locally carrying out, and calculating on each node is also all the local message that it can be used, without using Any global information.
In algorithm 1, each router only needs to make Decision of Allocation using the endpoint information stored in each data cell, If different types of flow (refer to flow have different sending node/terminals to) reaches the same transmission flow node, The node of this transmission flow makes a policy according only to the endpoint information stored in flow packet, without the transmission according to storage Node/terminal carries out decision to information.When the node and M terminal for having N number of transmitted traffic in a communication network, if each hair Data transfer rate can be sent to all terminals by sending the node of flow, then will have the flow of N × M seed type in network, with When algorithm 1 carries out assignment of traffic, the node of each transmission flow only at most needs to update M data transfer rate variable, compared to by stream The algorithm that amount type updates data transfer rate is compared, it is clear that can reduce calculating cost.
Compared with the existing technology, the beneficial effect that technical solution of the present invention obtains is:
1, satisfaction of the user to Internet applications such as Video services is modeled as about the non-recessed of data transfer rate by the present invention The Optimizing Allocation of bandwidth resources in internet is modeled as non-convex optimization problem by function, and proposes a kind of distribution Resource allocation algorithm.The algorithm can be used for the packet switching network under non-interconnected communication mode, can solve multiple terminals it Between grouping transmission problem, and the algorithm can make each router merely with local message Independent Decisiveness data cell Number, without utilizing any global information, thus, which is fully distributed.
2, compared to center type algorithm, complete distributed algorithm of the invention, which has, to be improved internet security, reduces communication The advantages that cost.
3, each router determines transmission strategy merely with the destination node information in each data cell, compared to other Algorithm can save very big calculation amount.
4, present invention can ensure that the satisfaction of user is with the speed convergence of O (1/k) to optimal value.
Detailed description of the invention
Fig. 1 is the logical of connection relationship between 8 groups of different transmitted traffic node/terminal nodes and 8 transmission flow nodes Interrogate topological diagram；
Fig. 2 is ideally that the utility function value obtained using algorithm 1 and genetic algorithm compares figure；
Fig. 3 is ideally that the transmitted traffic node/terminal obtained using algorithm 1 is to s1/d3,s4/d2,s8/d3Between The variation track figure of flow；
Fig. 4 is to occur under link disconnection, the target function value obtained using algorithm 1 and genetic algorithm；
Fig. 5 is to occur under link disconnection, and the transmitted traffic node/terminal obtained using algorithm 1 is to s1/d3,s4/d2, s8/d3Between flow variation track figure.
Specific embodiment
In order to keep technical problems, technical solutions and advantages to be solved clearer, below in conjunction with attached Figure and embodiment, are described in further details the present invention.
Fig. 1 is network model, which allows the node of each transmitted traffic to transmit flow using mulitpath.In Fig. 1 In show node-classification and each of the links bandwidth.The present embodiment is equipped with 8 groups of different transmitted traffic node/terminal nodes pair, That is s1/d3,s2/d2,s3/d3,s4/d2,s5/d5,s6/d5,s7/d7,s8/d3, the transmission path of these flows is as shown in table 1.Example Such as, according to the first row b in table 11With first row d2Corresponding is b2,b7, indicate node b1It will be with node d2For the flow of terminal It is transferred to node b2And b7。
Table 1
b1 b2 b3 b4 b5 b6 b7 b8
d2 b2,b7 b7,b8 - - d2 - b5 b5,b7
d3 b2,b7 b7,b8 b4 d3 - - b8 b3,b4
d5 b7 b1,b7,b8 b4,b8 b8 b7 d5 b6 b5,b7
d7 b2,b7 d7 - - - - b2,b8 b2
The objective utility function of the present embodiment isUsi(rsi) be similar to Stair-stepping non-recessed utility function, this function can properly describe user and be satisfied with journey in video streaming services application Degree, therefore the utility function is considered as in the present embodiment, and the bound of every kind of node transmitted traffic is ξ respectivelysi= 0.1,ζsi=3, i=1 ..., 8.
Above-mentioned objective utility function is not the polynomial type function as shown in formula (7), therefore is needed with polynomial type function Above-mentioned objective utility function is approached, to obtain parameter vector Psi, i=1 ..., 8.The method approached using quadratic sum, below Simulation result be to be directed to parameter alpha=ι=6 situation.
In simulations, consider to solve using above-mentioned polynomial function as objective utility function, be limitation item with formula (1)~(6) The Global Optimal Problem of part.In order to compare the simulated effect of algorithm 1, above-mentioned optimization problem is solved using genetic algorithm, and by base The utility function optimal value obtained by algorithm is as standard results.
The selection of iteration step length meets inequality (21) and (22) in algorithm 1.Fig. 2 is ideally (disconnected without link In the case of opening), the utility function value obtained using algorithm 1 and genetic algorithm compares figure, the result that algorithm 1 obtains point broken line table Show, corresponding mark is DFRDA Algorithm；The result that genetic algorithm obtains is indicated by the solid line, corresponding mark Genetic Algorithm；It can be seen that the utility function value that algorithm 1 obtains gradually converges to standard value (obtaining by genetic algorithm). Although this illustrates that algorithm 1 is a kind of distributed calculation method, it, which is only capable of obtaining local message, is calculated, algorithm 1 Still the optimal value of available center type algorithm (genetic algorithm) equally.
Fig. 3 is the transmitted traffic node/terminal obtained using algorithm 1 ideally (without under link disconnection) To s1/d3,s4/d2,s8/d3Between flow variation track figure, it can be seen that these data transfer rates meet the limit of bound bounded Condition processed.
Due to usually having the phenomenon that certain links disconnect suddenly or establish connection suddenly generation in network, this needs flow Allocation algorithm rapidly redistributes flow and utility function value is optimized to new optimal value, therefore assignment of traffic algorithm is necessary Robustness with higher.
In order to investigate the robustness of algorithm 1, the present invention is in 130 iteration, by node b7And b8Between link disconnect, because The transmission that flow is completed with the link is required for all transmitted traffic nodes, so by b7And b8Between link disconnect experiment. At this point, the iteration step length parameter of algorithm 1 still meets above-mentioned inequality by checking that inequality (21) and (22) are available, Therefore these parameters can be still selected to be emulated.
Fig. 4 is to occur under link disconnection, and the utility function value obtained using algorithm 1 and genetic algorithm, algorithm 1 is obtained Result with point a broken line indicate, corresponding mark be DFRDA Algorithm；The result that genetic algorithm obtains is indicated by the solid line, right Answering mark is Genetic Algorithm；Show that algorithm 1 can be divided again after there is link disconnection with quick response in Fig. 4 With flow, so that utility function value be made to converge to new optimal value, which is obtained by genetic algorithm.
Fig. 5 shows transmitted traffic node/terminal to s1/d3,s4/d2,s8/d3Between flow variation track.Equally may be used To see that algorithm 1 can be redistributed flow with quick response after link disconnection.

Claims (4)

1. a kind of distributed traffic allocation algorithm end to end, it is characterised in that: the following steps are included:
Step 1: establishing non-convex optimization problem；
Step 2: by selecting suitable variable, converting non-convex optimization problem to the convex optimization problem of family's equivalence；
Step 3: proposing fully distributed optimal assignment of traffic algorithm.
2. a kind of distributed traffic allocation algorithm end to end as described in claim 1, it is characterised in that: established in step 1 The method of non-convex optimization problem are as follows:
subject to
1s,lxs,l≤cl,l∈Ls,s∈S (2)
Fx=0 (3)
(xs,rs)∈Xs,s∈S (5)
The utility function of the optimization problem are as follows:
Wherein, α and ι is respectively given positive integer, and j ∈ { 0,1,2 ..., α }, s are the node of transmitted traffic, rsFor node s hair The sum of all flows out；Given node s, fractional order functionWith rsAs independent variable, with set {ps,0,...,ps,j-1,ps,j,ps,j+1,...,ps,αIn element as the corresponding parameter of corresponding order,Order be j/ ι, Its relevant parameter is ps,j, the relevant users satisfaction degree of characterization transmitted traffic node s；It is the mark of summation operation, table Show and variable j is enabled to rise to α from 0, corresponding functional value is added；Equally, ∑s∈SIt is also the mark of summation operation, expression enables variable S not repeatedly traverses the value in set S, and corresponding functional value is added；B is the node for transmitting flow；D is the terminal of flow；l For the link for transmitting flow；elIt (b) is the node being connected with node b through link l；It is issued by node s, is with node d Terminal, the flow transmitted through link l；It is transmitted by node b, using node d as terminal, the flow that is transmitted through link l；For by node el(b) transmission, using node d as terminal, the flow that is transmitted through link l；S is by all transmitted traffic sections The set that point s is constituted；For the set being made of the node b of all transmission flows；LbIt is the collection for the link l being connected with node b It closes；LsIt is the set for the link l being connected with node s；clBy link l energy bearer traffic bandwidth；xs,lTo be issued by node s , the total flow transmitted through link l；xb,lThe total flow transmitted for node b through link l；xsFor the flow issued by all node s The vector of composition, i.e.,xbIt is by the column vector of the constitution of all node b transmission, i.e., VectorThe T in the upper right corner is indicated to vector xb,lDo transposition operation；By the column vector of all constitutions, i.e., x isIndependent variable r is by all variable rsThe column vector of composition, i.e.,1s,l、With Be the transversal vector with positive integer 1 for element, their element number respectively with column vector xs,l、xb,lAnd xel(b),lElement Number is identical；F is class adjacency matrix；It is that node b is used to transmit the collection constituted using d as all link l of the flow of terminal It closes；DbThe set that the terminal d of all flows to be transmitted by node b is constituted；Ds,lIt is all flows that node s is transmitted through link l Terminal d constitute set；ξsAnd ζsIt is r respectively for constantsLower bound and the upper bound；And R+Respectively indicate dimension ForWith 1 positive integer space, | Ds,l| it is vector Ds,lDimension；
Condition (1) and (2) indicate the limitation of link bearing capacity, bearing capacity of the flow that link l is transmitted no more than it；Item Part (3) expression cannot lose the limitation of flow in transmission process interior joint, and the flow for flowing into each node should be equal to outflow and be somebody's turn to do The flow of node；Condition (4) indicates that the flow of transmission node b transmission is non-negative；Condition (5) indicates the flow that node s is issued It is non-negative, and the total flow issued has bound；Condition (6) provides set XsDefinition.
3. a kind of distributed traffic allocation algorithm end to end as claimed in claim 2, it is characterised in that: the method for step 2 It is as follows:
Choose variableBy ysIt is assumed to be stochastic variable and enables ysFor estimating μsJ-th of moment of momentum be denoted as ms,j, i.e.,Wherein j ∈ { 0,1,2 ..., α } is converted non-convex optimization problem to as next using functional analysis theory Race's optimization problem:
subject to
ms,0=1, s ∈ S (8)
Ms(0,α,ms)≥0,s∈S (9)
βsMs(0,α-2,ms)-Ms(0,α,ms)≥0 (10)
ms,j≤(rs)j/ι,j∈{1,...,α},s∈S (11)
1s,lxs,l≤cl,l∈Ls,s∈S (13)
Fx=0 (14)
(xs,rs)∈Xs,s∈S (16)
The utility function of the optimization problem are as follows:
Wherein, node s, function are givenIt is with transversal vectorFor parameter and with column vectorFor the linear function of variable；Independent variable m is by all torque variable msThe column vector of composition, i.e.,Constant betasIt is the known upper bound of the sum of node s transmitted traffic；MsIt is the Hankel matrix such as following formula: It is a given sequence, k, h are elements in sequence Mark；Other marks occurred in step 2 mark corresponding with step 1 defines identical；Condition (8), (9) and (10) guarantees Estimate μsExistence；Condition (11) guarantees equationIt sets up；This family's optimization problem is equivalent to former non-convex optimization problem, And work as parameter alpha≤ι, which is convex optimization problem.
4. a kind of distributed traffic allocation algorithm end to end as claimed in claim 3, it is characterised in that: in step 3, benefit Following complete distributed traffic distribution method can be obtained with ADMM algorithm:
Algorithm 1:
Initial value:
1) start
2) initializing variable value
3)x0,m0,r0,λ0
4) mark is introduced
5) mark is introduced
6) as the number of iterations k+1, variate-value relevant to transmitted traffic node s is updated as follows
7) variate-value relevant to transmission flow node b is updated as follows simultaneously
8) each transmitted traffic node s ∈ S passes through link LsTransmit flow
9) each transmission flow nodePass through link l ∈ LbTransmit flow
10) it updates and link l ∈ L as followsb,Relevant punishment parameter
11) mark is updated
12) mark is updated
13) each node s ∈ S passes through link LsTransmit information
14) each nodePass through link l ∈ LbTransmit information
x0,m0,r0,λ0For variable x, m, r, the selected iteration initial value of λ；WithIt is vector x0In element；VariableThe mark k in the upper right corner represents kth time iteration Obtained variate-value；Equally, variable The mark k+1 in the upper right corner represents the variate-value that+1 iteration of kth obtains；Oeprator ← expression is by the value assignment of arrow right end Give arrow left end variable；AsIt is the set that each node s ∈ S local limit condition is constituted, i.e.,
VariableIt is defined as follows:
Wherein,WithThe mark that is for avoiding causing obscuring and introduce, they are to represent to be used to mark l Transmit the link of flow；Refer to the link passed through using node d by the traffic flow ingress b of terminalThe set of composition；Refer to that node b is used to transmit all links using d as the flow of terminalThe set of composition；Refer to and is with node d The traffic flow ingress e of terminall(b) link passed throughThe set of composition；Refer to node el(b) it is used to transmit with d For all links of the flow of terminalThe set of composition；It is to store variable respectivelyValue and the mark that introduces；Refer to that node b passes through the link l all flows transmitted The set that terminal is constituted；
Be withFor the column vector of element, wherein
VariableIt is defined as follows:
Wherein,Refer to node el(s) it is used to transmit all links using d as the flow of terminalThe set of composition, el It (s) is the node being connected with node s by link l；It is to store variable respectivelyValue and introduce Mark；Ds,lRefer to the set that node s is made up of the terminal of the link l all flows sent；
MarkIt respectively represents variable to space As、R+Do project；It is to be determined Step parameter sequenceIt is determined with step parameter γ by such as under type:
When given communication network and convex optimization problem, wherein the decision variable of the convex optimization problem is (x, m, r), it is assumed that 1 iteration of algorithm Initial value is (x0,m0,r0), the sequence that iteration generates is { xk,mk,rk}k∈N, wherein xk,mk, the variable of rk expression kth time iteration generation Value, N represents the set being made of all natural numbers, if enabling iteration step length parameter Meet such as lower inequality with γ:
Wherein, mlIt is by link l ∈ LbThe terminal number of all flows of transmission；{υsAndMeet following differ respectively Formula:
Wherein,Refer to and be connected with node s, for transmitting the collection constituted using node d as all link l of the flow of terminal It closes；Refer to the traffic flow ingress e using node d as terminall(s) set that the link l passed through is constituted, el(s) be with The node that node s is connected by link l；Refer to node el(s) it is used to transmit all link l using d as the flow of terminal The set of composition；Refer to the traffic flow ingress using node d as terminalThe set that the link l passed through is constituted；Refer to nodeFor transmitting the set constituted using d as all link l of the flow of terminal；Oeprator | | Representative takes element number in corresponding set；So sequence of iterations { xk,mk,rk}k∈NMaximum utility function in problem will be converged to A solution, the rate of convergence of algorithm 1 is O (1/k), and wherein k is the number of iterations.
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