An Optimization Algorithm of Spare Capacity Allocation by Dynamic Survivable Routing

Transcription

1 An Optimization Algoithm of Spae Capacity Allocation by Dynamic Suvivable Routing Zuxi Wang, Li Li *, Gang Sun, and Hanping Hu Institute fo Patten Recognition and Atificial Intelligence, Huazhong Univesity of Science and Technology; National Key Laboatoy of Science &Technology on multi-spectal infomation pocessing Wuhan, China Abstact. The suvivability of MPLS netwoks has eceived consideable attention in ecent yeas. One of the key tasks is to oute backup paths and allocate spae capacity in the netwok to povide the QoS guaanteed communication sevices to a set of failue scenaios. This is a complex multi-constaint optimization poblem, called the spae capacity allocation (SCA). In this pape, a dynamic suvivable outing (DSR) algoithm using the chaotic optimization theoy is poposed to solve it. Compaing taditional SCA algoithm, numeical esults show that DSR has the satisfying QoS pefomances. Keywods: Netwok Suvivability, Spae Capacity Allocation, Suvivable Routing, Chaos Optimization, MPLS. 1 Intoduction With the apid development of the Intenet, netwok is used to tansmit all kinds of eal-time sevices. To espond quickly to netwok faults and avoid the oute cache left lage amounts of data, esulting in deceased netwok pefomance and QoS, netwok suvivability have become an impotant eseach issue. MPLS (Multi Potocol Label Switching) poposed by IETF has gadually become one of the coe technology of IP backbone netwok, and its netwok suvivability have attached boad attentions. Netwok suvivability of MPLS include two components, suvivable netwok design and estoation schemes [11]. Duing design stage, suvivable stategy is integated into the netwok design. Then in Failue ecovey stage, e-outing scheme and ecovey path switching scheme ae mostly adopted. The eouting ecovey scheme without ecovey path can establish a backup path on-command to estoe taffic tansmission afte the detection of a failue. Since the calculation of new outes and esouce esevation of new path ae time-consuming, it is consideably slowe than ecovey path switching mechanisms. In the case of ecovey path switching, taffic is switched to the pe-established ecovey path when the failue occus. So the ecovey is vey fast. But the pe-established ecovey path eseve a pat of netwok esouces. * Coesponding autho. Y. Tan, Y. Shi, and K.C. Tan (Eds.): ICSI 2010, Pat II, LNCS 6146, pp , Spinge-Velag Belin Heidelbeg 2010

2 440 Z. Wang et al. On a given two-connected mesh netwok, deciding how much spae capacity allocation should to eseved on links and how to oute backup paths to potect given woking path fom a set of failue scenaios is usually teated as a key issue. It is called spae capacity allocation poblem. Thee ae some existing schemes [1, 2, 4, 5, 6, 7, 9, 10] to solve this poblem. Pevious eseach on spae capacity allocation of mesh-type netwoks uses eithe mathematical pogamming techniques o heuistics to detemine the spae capacity allocation as well as backup paths fo all taffic demands. Related methods like Banch and Bound (BB) [6], Genetic Algoithm (GA) [10], Simulated Annealing (SA) [2] and Spae Link Placement Algoithm (SLPA) [5] adopt the way of poblem solving. All of above methods ae still in the pe-planning phase which can only be implemented centally. So a distibuted scheme called Resouce Aggegation fo Fault Toleance (RAFT) is poposed by Dovolos [4] fo IntSev sevices using the esouce Resevation Potocol (RSVP) [1]. Since the RAFT scheme has not consideed the chance of spae capacity shaing, two dynamic outing schemes, called Shaing with Patial outing Infomation (SPI) and Shaing with Complete outing Infomation (SCI) wee pesented in pape [7]. But the edundancy of SPI is not vey close to the optimal solutions and the pe-flow-based infomation is necessay fo SCI. Then Yu Liu and David Tippe [9] poposed a Successive Suvivable Routing (SSR) algoithm which unaveled the SCA poblem stuctue using a matix-based model. Howeve, Yu Liu and David Tippe did not give an effective seach stategy in the state space of SCA poblem. So the convegence time of algoithm is unstable and the algoithm is not optimal. To solve this poblem, combining the matix-based model fom SSR and chaos optimization method, we popose a dynamic suvivable outing algoithm that can dynamically estoe the failue, based on the given woking path and bandwidth and delay constaints. So we can maximize the estoation speed and povide the QoS guaanteed communication sevices. 2 Poposed Dynamic Suvivable Routing Scheme In this section, we descibe the dynamic suvivable outing scheme, which use a matix-based model fom SSR and chaos optimization method. As the matix-based model descibes the SCA poblem stuctue, chaos optimization method is applied to the optimized computation fo backup paths and spae capacity allocation. They coopeate to achieve seamless sevices upon failues. Since the algoithm not only povides the suvivable sevices, but also minimize the total cost of spae capacity in the backup path selection pocess dynamically, we call it dynamic suvivable outing (DSR). 2.1 Notations and Definitions To descibe the SCA poblem, a netwok is epesented by an undiected gaph with N nodes, L links and R flows. Then a set of matix-based definitions and optimization model ae given as follows. N,L,R,K, numbes of nodes, links, flows and failue scenaios; A N*L =[a nl ], node link incidence matix;

3 An Optimization Algoithm of Spae Capacity Allocation 441 B R*N =[b n ], flow node incidence matix; T K*L =[t kl ], failue link incidence matix, t kl =1 if link l fails in failue k; U R*K =[u k ], failue flow incidence matix, u k =1 if failue k will affect flow s woking path; C R*L =[c l ], woking path link incidence matix, c l =1 if link l is used on flow s woking path; D R*L =[d l ], backup path link incidence matix, d l =1 if link l is used on flow s backup path; S L*K =[s lk ], spae povision matix, s lk is spae capacity on link l fo failue k; W=Diag({w }), diagonal matix of demand bandwidth w of flow ; M R*L =[m l ], flow tabu-link matix, m l =1 if link l should not be used on flow s backup path; h L*1, vecto of link spae capacity; v ={v l }, vecto of cost on additional link spae capacity fo flow. Given above notation and definitions, based on the matix-based model of SSR, the spae capacity allocation poblem can be fomulated as follows. Objective function: min e T h (1) Constaints: D,h h S (2) M + D 1 (3) DA T = B(mod 2) (4) S = w T d u ) (5) S ( = R S = 1 The objective function (1) is to minimize the total spae capacity by the backup paths selection and spae capacity allocation. Constaints (2), (5) and (6) calculate h and S. Constaint (3) guaantees that each backup path is link-disjoint fom its woking path. Constaint (4) guaantees that the given backup paths ae feasible. 2.2 Poposed Algoithm As a univesal phenomenon in nonlinea system, chaos has stochastic popety, egodic popety and egula popety, whose egodicity can be used as a kind of optimization mechanism to effectively avoid the seach being tapped into local optimum [3]. In the poposed algoithm, chaos optimization method is applied to the optimized computation fo backup paths and spae capacity allocation. The adopted Logistic map [8] can be fomulated as equation (7), whee u is a contol paamete. When u=4, 0 x 0 1, the logistic map become chaotic behavio. xn+ 1 = uxn (1 xn ) (7) Unde the above definition, DSR solves the oiginal multi-commodity flow poblem by patitioning it into a sequence of single flow poblems. Using the logistic map, DSR algoithm tavesals the state space fomed by flows of netwok. Because of the stochastic popety, egodic popety and egula popety, each flow s backup path (6)

4 442 Z. Wang et al. can be optimized dynamically. The implementation flow of DSR algoithm is given as follows. Fist of all, based on the netwok topology and QoS equiements, we calculate the woking paths and backup paths fo each pai of nodes to povide the heuistic infomation. Step 1: the flows of netwok ae numbeed 1~R; Step 2: initialize the logistic map with m diffeent values, and then obtain m esult values by n iteations; Step 3: quantify the inteval (0, 1) unifomly with R level and map to each flow, e.g. the value afte iteation in the inteval (0, 1/R) is mapped to the flow with numbe 1, othes map to the flow accoding to thei iteation value; Step 4: accoding to the step 3 s ule, map m iteation value geneated by the m logistic map with one iteative opeation to m flows, and then push the numbe of m flows into the stack ST; Step 5: pop ST, if ST is null, tun to step 4, othewise get the numbe of flow : (1) Accoding to the numbe, get the woking path c, then calculate the u and m (2) Collect the cuent netwok state infomation, and update the spae povision matix S (3) Calculate S by fomula S = S S and constaint (5), then get h - =max S - (4) Let d * = e m denote the altenative backup path fo flow, and * ) ( * T S = w d u, then calculate * h = max( S + S * ) * (5) Calculate v by fomula v = { vl} = φ( h ( e m )) φ( h ) w-hee φ is a function fomulated bandwidth cost of each link Step 6: fist exclude all the tabu links maked in the binay flow tabu-link vecto m of flow, then use the shotest path algoithm with link weight v to find the updated backup path d new Step 7: eplace the oiginal backup path d when it has a highe path cost than updated backup path d, then the spae povision matix S and link spae capacity vecto h new ae updated accodingly. If satisfy the optimization solution, expot it and exit, else tun to step 6. 3 Pefomance Discussion In this pape, the objective is not only to oute an eligible backup path, but also minimize the total cost of esouce esevation and povide suvivable sevices. To evaluate them, we do expeiment with medium sized netwok topology moe times. In the liteatue [9], compaed with othe classic algoithms, SSR pesent bette pefomance. So we just compae poposed algoithm with SSR in expeiments. In the figues of optimization pocedue, sampling point epesents the spae capacity cost of all the backup paths which is sampled at an inteval of 5 iteations. All the flows have one unit bandwidth demand. The temination condition of algoithm was set that the eseved capacity did not change afte 300 iteations.

5 An Optimization Algoithm of Spae Capacity Allocation 443 Shown in figue 1, thee ae 17 nodes and 31 links in the topology of expeiment netwok. Assume that the taffic exist between any two nodes, R=136 can be calculated Fig. 1. Topology of expeiment netwok Fo the expeiment netwok, we did 10 goup expeiments. Each goup algoithms ae epeated fo 10 times, and the iteation times, convegence time and eseved capacity ae used to epesent the algoithm pefomance. One of optimization pocedue of SSR and DSR ae shown in Fig. 2, 3 espectively. Fig. 2. Optimization pocedue of SSR Fig. 3. Optimization pocedue of DSR Fo lack of space, the iteation times and convegence value of eseved capacity of fist fou optimization pocedue of two algoithms ae shown in Table 1. The statistics of all the 10 goup expeiments ae shown in Table 2. (Note: IT = iteation times, CVRC = convegence value of eseved capacity, CT = convegence time) Table 1. IT and CVRC of two algoithms fo fist fou optimization pocedue Optimization SSR based on DSR based on pocedue andom seach chaos optimization IT CVRC IT CVRC

6 444 Z. Wang et al. Table 2. Statistics fo SSR and DSR SSR based on andom seach DSR based on chaos optimization IT CVRC CT IT CVRC CT Maximum Minimum Aveage Accoding to the expeimental data, compaed with SSR, the aveage iteation times of DSR is educed by pecent, the aveage convegence time of DSR is educed to pecent. The eseved capacity of two algoithms is vey close. So DSR has bette pefomance than SSR. Since the minimum always appea in the fist five optimization pocess of 10 optimization pocesses, we can balance the eseved capacity and convegence time and choose the best in them. 4 Conclusion In this pape, we do Reseach on the backup path choice, which is the key poblem of Failue ecovey. Analyzing the SCA poblem, a backup paths calculation method called DSR algoithm based on chaos optimization is poposed. The poposed algoithm povides backup paths to guaantee the netwok suvivability, and minimizes the netwok bandwidth cost fo esouce esevation to impove the utilization ate of netwok esouce simultaneously. The expeiment esults indicate that DSR algoithm has good pefomance on esouce esevation and convegence time, and convege to an optimal value fast on stable netwok conditions. Compaed with taditional SCA algoithms, the poposed DSR algoithm can maximize the estoation speed and povide the QoS guaanteed communication sevices. Acknowledgments. This wok was suppoted by the gants fom the National Natual Science Foundation of China (No ), and Natual Science Foundation of Hubei povince (2007ABA015), and by the gant fom Ph.D. Pogams Foundation of Ministy of Education of China (No ), and by Beijing Key Laboatoy of Advanced Infomation Science & Netwok Technology and Railway Key Laboatoy of Infomation Science & Engineeing (No. XDXX1008). Refeences 1. Baden, R., Zhang, L., Beson, S., Hezog, S., Jamin, S.: Resouce ReSeVation Potocol (RSVP) Vesion 1 Functional Specification, IETF. RFC 2205 (1997) 2. Van Caenegem, B., Van Pays, W., De Tuck, F., Demeeste, P.M.: Dimensioning of suvivable WDM netwoks. IEEE J. Select. Aeas Commum. 16(7), (1998) 3. Cui, C., Zhao, Q.: Resech on impoved chaos optimization algoithm. Science Technology and Engineeing 3 (2007) 4. Dovolis, C., Ramanathan, P.: Resouce aggegation fo fault toleance in integated sevice netwoks. ACM Comput. Commun. Rev. 28(2), (1998)

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