Research Article Longest Path Reroute to Optimize the Optical Multicast Routing in Sparse Splitting WDM Networks

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1 International Optic Volume 0, Article ID 9, page Reearch Article Longet Path Reroute to Optimize the Optical Multicat Routing in Spare Splitting WDM Network Huanlin Liu, Hongyue Dai, Fei Zhai, Yong Chen, and Chengying Wei School of Communication and Information Engineering, Chongqing Univerity of Pot and Telecommunication, Chongqing 000, China Correpondence hould be addreed to Huanlin Liu; Received 9 September 0; Accepted 9 November 0 Academic Editor: Vaily Spirin Copyright 0 Huanlin Liu et al Thi i an open acce article ditributed under the Creative Common Attribution Licene, which permit unretricted ue, ditribution, and reproduction in any medium, provided the original work i properly cited Limited by the pare light-plitting capability in WDM network, ome node need to reroute the optical packet to different detination node with the high cot of routing for reducing packet lo poibility In the paper, the longet path reroute optimization algorithm i put forward to jointly optimize the multicat routing cot and wavelength channel aignment cot for pare plitting WDM network Baed on heuritic algorithm, the longet path reroute routing algorithm call multiple longet path in exiting multicat tree to reroute the path paing from the node which are violating the light-plitting contraint to the node which are not violating light-plitting contraint with few wavelength channel and low rerouting cot And a wavelength cot control factor i deigned to elect the reroute path with the lowet cot by comparing the multicat rerouting path cot increment with the equivalent wavelength channel required cot increment By adjuting wavelength cot control factor, we can uually get the optimized multicat routing according to the actual network available wavelength converion cot Simulation reult how that the propoed algorithm can get the low-cot multicat tree and reduce the required number of wavelength channel Introduction Optical multicat ha attracted much coniderable interet due to upporting efficiently the tranport for multicat application and providing flexible acce to the immene bandwidth of the optical fiber and WDM network [ ] The claical multicat requet are realized by the way of repeating unicat in optical layer becaue of the contraint by network node light-plitting and leading to the problem of low wavelength reource utilization Therefore, how to upport multicat application in optical WDM network i becoming a reearch topic in recent year Several reearcher tudied the multicat problem in optical network with all or pare multicat capable (MC) node But the problem analyzed in [7] i that the MC node i complicated and expenive So, Ali and Deogun propoed a low-cot novel architecture called Tap-and-Continue (TaC) to contruct optical multicat node architecture without MC node [7] ThepropoedTaCnodecanreducetheroutingcotforthe route from ource to detination which i contructed a a trial intead of fiber link in MC node In optical WDM network, an efficient olution of the multicat routing problem i to contruct a multicat tree which cover the network ource and all the detination node [, 9] Unlike the multicat routing problem in IP layer, the etablihment of the optical multicat routing not only need to determine a route for the ource to each detination node, but alo need to aign an idle wavelength channel for thi route under certain contraint, uch a node light-plitting and wavelength number limit The problem of optical multicat routing belong to the claical NPcomplete problem The approximate optimal olution baed on heuritic algorithm i an available method [0 ] After propoing a low-cot novel architecture called Tap-and- Continue (TaC) for realizing multicat, Ali and Deogun defined and formulated the problem of routing a multicat eion in a network equipped only with TaC cro-connect, and a heuritic algorithm multiple-detination trail (MDT) i propoed to find the low-cot multicat routing for the multicat requet [7] For olving the routing problem of multiple-detination minimum-cot trail in WDM network equipped only with TaC cro-connect, the author in [7]

2 International Optic analyzed the routing optimization by finding an optimal trail that tart from a ource node and viit all detination To decreae the optimization method complexity, Ali and Deogun developed a heuritic MDT algorithm which find a feaibletrailinpolynomialtime[7]mdtalgorithmincluded two tep [7] In Step, a Steiner tree for the multicat eion wa found by uing the MPH (minimum path heuritic) In Step, rerouting around thi tree wa performed Rerouting allow internal node that have two or more branche to accommodate the multicat connection But for the ame multicat requet, the cot of etablihing a trail i higher than that of etablihing a route with optical tree tructure In [0,, ], four centralized algorithm are put forward to contruct light-foret with pare MC node to atify the optical multicat requet But thee algorithm do not conider the optimization of the routing cot A ditributed optical multicat routing algorithm wa propoed in [] Although the algorithm can olve the routing and wavelength aignment problem imultaneouly, it alo only optimize the multicat routing cot without conidering the number of wavelength cot Therefore, the exiting optical multicat routing optimize the multicat routing cot or optimize number of wavelength required independently, which lead to the problem of high wavelength reource conumption or high multicat routing cot potentially In thi paper, we conider the reduction of multicat routing cot and number of wavelength a an integrated optimization goal for WDM network with TaC node The longet path reroute joint optimization of wavelength and cot (LPR-JOWC) baed on heuritic algorithm i propoed to jointly optimize multicat routing and wavelength aignment cot LPR-JOWC algorithm reroute the node on multicat route tree which violate the light-plitting contraint through longet path reroute trategy to get low number of wavelength for keeping more detination hare the wavelengthchannelwithlowroutingcotandlowwavelength channel conumption The ret of the paper i organized a follow In Section, we dicu the optical multicat routing problem And we put forward a longet path reroute to jointly optimize the rerouting cot and required wavelength aignment cot in Section In Section, the longet path reroute rerouting performance i imulated and analyzed in Section Optical Multicat Routing Problem Decription The wavelength-routed optical witching node architecture with TaC equipment, configured withn input/output fiber, W wavelength channel per fiber, i hown in Figure The ource node can replicate an optical packet to multiple packet,whiletherelaynodewithtachouldatifythe light-plitting contraint The multicat routing need to atify the following contraint () Wavelength Continuity Contraint Alight-pathmut ue the ame wavelength on all the link from ource λ λ w λ λ w N λ λ w Demux Demux Demux WRS λ WRS λ WRS λ w TCM λ λ λ w λ λ λ w Tx Rx Local tation λ λ w : wavelength WRS: wavelength routed witch Tx: tranmitter Mux: multiplexer TCM TCM Mux Mux Mux : witch TCM: TaC module Rx: receiver Demux: demultiplexer Figure : Optical witching node architecture with TaC 7 Source node Detination node Cot link λ λ w λ λ w N λ λ w Figure : An example of a weighted undirected graph for multicat routing to detination node if the node in optical network do not have wavelength converter () Wavelength Ditinct Contraint All light-path haring the ame link mut ue ditinct wavelength () Light-Splitting Contraint Becaue TaC node in optical network cannot erve a a branching node of the multicat tree, o the degree of all the routing tree node except the ource hould be le than Figure how a weighted, undirected graph and a multicat requet r(, D) = r(, (,, 7)) The hortet path

3 International Optic heuritic algorithm i ued to find the lower cot tree from to D, andthereultinglowercottreeimarkedwithbold line Obviouly, the lower cot tree violate the light-plitting contraint, o the path P(, ) or P(, ) hould be aigned to another wavelength An optical network can be modeled a a weighted, undirected graph G(V, E, w, c), wherev i the et of node, E i the et of link, and w i the number of wavelength per fiber link Each edge e = (u, V) E i weighted by a real value named link cot c(e) Aume that R(, D) repreent the multicat requet, the ource node i, and D (d,d,,d m ) {V {}} repreent the detination node The node et Di named the multicat group An optical multicat tree T(V T,E T ) i a ubgraph of G panning the ource node and the et of detination node D {V {}}, V T V, E T E According to the above definition, let T k (, D k ) be the multicat tree for the requet R(, D) on the kth wavelength optical network: here D k DThecotofopticaltreeT k i defined a the um of the cot of all fiber link edge on tree T k,whichihownin c(t k (, D k )) = c (e) e T k (,D k ) Similarly, the total cot of multicat tree T k with ame ource node on different wavelength network i defined in c (T) = w k= () c(t k (, D k )) () The number of wavelength required i defined a () If the wavelength k i ued by the multicat tree T,theny k =; otherwie, y k =0: W (T) = w k= y k () The optical multicat routing algorithm with joint optimization of wavelength and route cot need to find an optical multicat tree with low route cot between a ource and the detination while aigning fewer wavelength for the route tree while nonviolating light-plitting contraint So, the optimization objective function of the problem i defined a follow: () optimization objective function: min [ w k= () retricted by c(t k (, D k )) + δ W (T)], () P λ (,d i ), d i D, () λ w P λ (,d i ) (u, V), λ w () d i D Equation () and () repreent the wavelength independence contraint and the wavelength continuity contraint, repectively If light-path ue wavelength λ on the route tree when packet travere from ource to all detination node, P λ (,d i ) =;otherwie,pλ (,d i ) =0 If light-path ue wavelength λ between the intermediate node u and V,here(u, V) Eand u, V V,thenP λ (,d i ) (u, V) =;otherwie,pλ (,d i )(u, V) =0 () Wavelength aignment cot control factor δ: δ i defined a the ratio of the wavelength aignment cot to the reroute path tree cot increment According to the control factor, we can flexibly implement the minimized cot to reolve the light-plitting contraint by rerouting the tree or increae wavelength aignment To reduce the routing cot, rerouting the path to detination with a new wavelength may increae the number of wavelength Thu, there i a tradeoff between the choice of a routing path on ued or not new wavelength If the δ i large which indicate that the wavelength channel i expenive and care ource, it mayprefertofindalongerreroutingpathontheame wavelength network rather than a horter routing path on a new wavelength network to get total low cot Otherwie, it may prefer to find the horter rerouting path on a new wavelength network Longet Path Rerouting Algorithm According to the definition of optical multicat routing problem, the optimization goal of the problem i to reduce the multicat routing cot which i related to the route path and number of wavelength Since the problem belong to NP-complete problem, o in thi paper, we propoe an optimized olution baed on heuritic algorithm to olve the optical multicat routing problem with joint optimization of wavelength and cot which i called longet path reroute joint optimization of wavelength and cot (LPR-JOWC) algorithm LPR-JOWC algorithm include two procee Firt we contruct the lower cot multicat tree by uing hortet path algorithm Second, we reroute the node on the tree which violate the light-plitting contraint by LPR-JOWC algorithm In the LPR-JOWC algorithm, the longer path ha the priority to reroute the tree with low tree route cot by reducing the number of wavelength The proce of LPR- JOWC algorithm i a follow: firtly, the hortet path algorithm i ued to find the lower cot multicat route tree T from ource to all detination Secondly, ome tree path are modified and rerouted to keep away from the node on the tree which violate the light-plitting contraint, where we firt check the farthet path from ource node to one detination with maximal route cot to reroute the violation node Latly, the available wavelength are aigned to the modified multicat tree Therefore, the LPR-JOWC algorithm guarantee that the multicat tree require fewer wavelength and lower route cot alo In order to decribe the LPR-JOWC algorithm, ome definition are introduced in advance a follow () T(V i ) i the ubtree whoe root i node et V i,wherev i ithenodeetwhichidirectlyadjacenttotheource node with i node degree

4 International Optic () Edge(P(, d)) i the et of all edge on the path P(, d) () Far(V i ) i the farthet detination node with the maximal route cot in ubtree T(V i ) () Live(Far(V i )) i the edge et whoe one endpoint belonged to Far(V i ) () UNREACH i the et of multicat detination node which have not been routed by multicat route tree () G i the graph of G that remained by removing edge and node included in et of Edge(P(, d)) (7) P j (, d) i the fewer cot path from ource node to detination node d in the jth wavelength layered graph G j () c(p j (, d)) i the cot of path P j (, d) So, the tep of LPR-JOWC algorithm are hown a follow Step Input network topology graph G(V, E, w, c)initialize the wavelength cot control factor δ value which repreent the ratio of wavelength cot and reroute path length cot increment k i the wavelength index, etting k = G k repreent kth layered wavelength network in w wavelength network G Step Let G k =G Call the hortet path algorithm to find the lower cot multicat tree T for multicat requet If there are node on the tree T violating the light-plitting contraint, then go to Step Otherwie, output the lower cot multicat treeandgototheend Step Divide the tree T into ubtree according to degree of ource node, and tore the ubtree rooted by V i a T(V i ) For each ubtree, find the farthet (maximal cot) detination Far(V i ),thepathp k (, Far(V i )), theedge(p k (, Far(V i ))), and the lower cot path of each Far(V i ) in ubtree T(V i )Remove the Edge(P k (, Far(V i ))) from graph G k and obtain ubgraph G k Then, contruct node et UNREACH and edge et Live(Far(V i )) in graph G k If UNREACH i not empty and k w, go to Step ; ele, output the cot optimized multicat tree T Step Chooe the farthet detination node in et of UNREACHandtoreitinvariableV Contructaubgraph SG for each Far(V i ) in ubtree T(V i ),andletsg = {G j,g j Live(Far(V i )), j=,,,k+} Step Find the lower reroute cot path for node V in SG et If the path P(, V) i found, then we aign path P(, V) to the correponding wavelength j and remove the detination V and other detination paed by path (P(, V)) from et UNREACH; Edge(P(, V)) i excluded from graph G j,and renew Live(Far(V i ))Ele,letk = k+ifk>w,thealgorithm top and return FALSE If k w,gotostep Furthermore, ome notation in the algorithm need to be introduced and tated here () If P j (, V) pae detination {V, V,,V k } in UNREACH on G j, then cot c(p(, V)) = c(p(, V)) c(p(, V )) c(p(, V k )) () If P j (, V) ue the (k + )th wavelength graph, where j i equal to k+,thecotofpathp j (, V) hould be increaed by δ An example of LPR-JOWC algorithm execution i hown in Figure A multicat requet i r(, {,,,,, }), and value of parameter δ i et to Firt, a hown in Figure (a), we get the lower cot tree T by performing Step Then, we find G =G Edge(, ) Edge(, ) Edge(, ) and UNREACH = {, } in Figure (b) Becaue detination i thefarthetnodeinunreach,bystepand,wetry to find the lower cot path from to We find the path P (,)= 9 in G,andc(P (, )) = ;the extended path P (, ) = in G Live(Far(7)), c(p (, )) = 9; pathp (, ) = 7, c(p (, )) = 7 + δ = in G The extended path P (, ) ha lower cot, o detination i routed by the extended path of detination Similarly, we find the path P (, ) =, c(p (, )) = Thenumberofwavelengthuedi ThefinalreultihowninFigure(d)markedinblackline with one number of wavelength Simulation and Analyi Performance of the propoed LPR-JOWC algorithm i imulated and analyzed in thi ection The multiple-detination trial (MDT) heuritic algorithm propoed in [7] wa ued for comparion with our propoed LPR-JOWC algorithm To generate random network, we ue a random graph generator developedbysalamaetal[]inthimodel,edgeareplaced connecting the pair of node u, V with probability: P e (u, V) =βexp d (u, V), (7) Lα where d(u, V) i the link ditance from node u to V and L i the maximum ditance between two node We et α = 0, β = The link cot function c(e) i defined a the current total bandwidth reerved on the link e Sourcenodeand detination node (multicat requet) are randomly elected in the graph Simulation i being run for 00 time with different topologie The average tree cot of LPR-JOWC and MDT algorithm under different number of detination are hown in Figure In Figure, we can ee that, a the detination node number increae,theaveragetreecotaloriewiththeincreae of detination node, more and more node on hortet tree violate the light-plitting Thi lead to more path needing to reroute with the longer path or aign new wavelength channel and therefore to more multicat tree route cot or wavelength cot Thu, the average tree cot increae a the number of detination node increae But, the average tree cot generated by the LPR-JOWC algorithm i lower than the

5 International Optic (a) The lower cot tree T (b) G (c) G Live(Far(7)) 0 9 (d) LPR-JOWC optimized cot tree T Figure : An example of LPR-JOWC algorithm execution The average tree cot MDT LPR, δ=0 Number of detination LPR, δ = 00 LPR, δ = 0 Figure : Average tree cot veru number of detination MDT algorithm The reaon i that the cot of etablihing a trail i higher than that of etablihing an optimized reroute tree for the ame multicat requet Furthermore, a the wavelength control factor δ increae, the multicat tree cot increae alo But the multicat tree cot increaing peed i low when the wavelength cot control factor δ i low The reaon i that the proportion of new aignment wavelength cot i little in the total re-route multicat tree cot Figurehowthenumberofrequiredwavelengthchannel veru the number of detination node for the propoed LPR-JOWC algorithm when the number of network node i0infigure,wecanobervethattheconumption wavelength number increae a the multicat requirement detination node increae The reaon i that the more multicat detination node need more wavelength channel conumptiontoavoidthenodelight-plittingthu,themulticat tree total cot increae Moreover, a the wavelength control factor δ increae, the conumption wavelength number decreae The reaon i that more multicat tree node chooe the longet path reroute to avoid the light-plitting and to decreae the increment of number of wavelength So,

6 International Optic Number of wavelength LPR-JOWC, δ=0 LPR-JOWC, δ = 00 Number of detination LPR-JOWC, δ = 0 Figure : Required number of wavelength channel veru number of detination the wavelength cot control factor δ balance the number of wavelength Concluion In thi paper, we propoe an optimized LPR-JOWC to olve the optical multicat routing problem with joint optimization of wavelength and cot baed on heuritic algorithm In the LPR-JOWC algorithm, the longet path ha the priority to reroute node violating the light-plitting to reduce the rerouting total cot by decreaing the number of wavelength The imulation and analyi indicate that the propoed LPR- JOWC algorithm can get the low-cot multicat tree and alo can reduce the number of wavelength The LPR-JOWC algorithm perform better in term of average tree cot in comparion with the exiting MDT algorithm Conflict of Interet The author declare that there i no conflict of interet regarding the publication of thi paper Acknowledgment Thi reearch wa funded by the National Nature Science Foundation of China (NSFC 7077), by the Scientific Reearch Fund of Chongqing Municipal Commiion (KJ00), and by the Baic and Frontier Reearch Program of Chongqing (CSTC 0jcyjA00) Reference problem in WDM network: exact olution and heuritic algorithm, Optical Communication and Networking, vol 7, no, pp, 0 [] H-L Liu, X Xue, Y Chen, Q Fang, and S Huang, An efficient dynamic multicat traffic-grooming algorithm for WDM network, Photonic Network Communication, vol, no, pp 9 0, 0 [] JLee,BCYeo,J-SKim,MSJang,andJKChoi, Energy efficient calable video coding baed cooperative multicat cheme with elective layer forwarding, IEEE Communication Letter, vol 7, no, pp 9, 0 []HLiu,XHu,YChen,THu,andSHuang, Scheduling baed on minimal converion degree with repect to wavelength converion and coding in optical multicat node, IEEE Communication Letter,vol,no,pp9 9,0 [] S Huang, Y Wang, and H Liu, Multi-ource multi-core routing algorithm baed on network coding in optical multicat network, Chongqing Univerity of Pot and Telecommunication,vol,no,pp 9,0 [] X Wang, M Hou, X Yi, and M Huang, A QoS multicat routing algorithm baed on tabu-hierarchy genetic algorithm in IP/DWDM optical Internet, in Network Architecture, Management, and Application III,vol0ofProceeding of SPIE,pp 0 0, Shanghai, China, December 00 [7] MAliandJSDeogun, Cot-effectiveimplementationofmulticating in wavelength-routed network, Lightwave Technology,vol,no,pp,000 []LHSaharabuddheandBMukherjee, Light-tree:optical multicating for improved performance in wavelength-routed network, IEEE Communication Magazine, vol 7, no, pp 7 7, 999 [9] X Zhang, J Y Wei, and C Qiao, Contrained multicat routing in WDM network with pare light plitting, Journal of Lightwave Technology,vol,no,pp97 97,000 [0] F Zhou, M Molnár, and B Couin, Ditance priority baed multicat routing in WDM network conidering pare light plitting, in Proceeding of the th IEEE Singapore International Conference on Communication Sytem (ICCS 0), pp 709 7, IEEE, Guangzhou, China, November 00 [] H Liu, Y Xie, Li Zhen, and B Zhang, Study on minimizing network coding link baed on immune algorithm for optical multicat network, Chongqing Univerity of Pot and Telecommunication, vol, no, pp, 0 [] W-Y Teng and S-Y Kuo, All-optical multicating on wavelength-routed WDM network with partial replication, in Proceeding of the IEEE International Conference on Information Networking (ICOIN 0), pp, Beppu City, Japan, 00 [] C-Y Hieh and W Liao, All-optical multicat routing in pare plitting WDM network, IEEE Journal on Selected Area in Communication,vol,no,pp,007 [] T Rahman, G Ellina, and M Ali, Lightpath- and lighttree-baed groupcat routing and wavelength aignment in meh optical network, Optical Communication and Networking,vol,no,ArticleID7,ppA A,009 [] H F Salama, D S Reeve, and Y Vinioti, Evaluation of multicat routing algorithm for real-time communication on high-peed network, IEEEJournalonSelectedAreain Communication,vol,no,pp,997 [] D D Le, F Zhou, and M Molnar, Minimizing blocking probability for the multicat routing and wavelength aignment

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