Split Restoration with Wavelength Conversion in WDM Networks*

Transcription

1 Spit Reoration with aveength Conversion in DM Networks* Yuanqiu Luo and Nirwan Ansari Advanced Networking Laborator Department of Eectrica and Computer Engineering New Jerse Initute of Technoog Universit Heights Newark NJ 070 Abract- In this paper we propose a path reoration agorithm for a singe fiber faut in the DM network equipped with waveength conversion. The Integer Linear rogramming (IL) formuas for minimizing the path recover co can ied the optimum soution but it is N-compete. Our heuriic agorithm reaxes the compexit b two eps. In the off-ine ep the node-ink topoog is repaced b the node-waveength topoog the aternate paths for source-deination node pairs are ied and the waveengths in each ink are assigned b maximum matching. In the on-ine ep traffics going through the faied ink are spit into subtraffics and are reored according to their priorities. The performance anasis and the simuation resuts indicate that our heuriic agorithm is practica for DM networks reoration. I. INTRODUCTION The exposive growth of data traffic imposes important emerging bandwidth requirements on toda's networks. ith the potentia of tens of terabits per second aveength Division Mutipexing (DM) is paing a major roe in the expansion of our networks. However more bandwidth in each optica channe of DM means more serious oss each time a faut occurs. A singe fiber cut coud significant downgrade the services to the wor extent. This is the reason wh the survivabiit of optica DM networks is a critica research issue. Two main approaches ensure network survivabiit: protection and reoration. rotection is pre-reserving spare resources (e.g. bandwidth) for a connection. Reoration is using the spare resources after the faut occurs to recover the disrupted traffic. In this paper we propose a spit reoration agorithm to maximize the traffic recover of a singe fiber faut in DM networks. Reoration tpica means that connections affected b a faiure are routed aong aternate paths that are determined and set up at the time of the faut detection. A number of research resuts on reoration have been reported in the iterature. Gere and Ramaswami [] reviewed the survivabiit issues of the optica aer from the point of services perspective. The frameworks of off-ine protection and on-ine reoration were proposed in []. The faut management issue in I-over-DM networks was udied in reference [3]. It recovers the singe ink faiure b ink-based or path-based reoration. Research resuts reported in the iterature thus far have addressed man important issues and difficut probems of reoration in DM networks. However none of them consider the issue of waveength conversion in the recover scheme. The reason is that waveength conversion and the * This work has been supported in part b the New Jerse Commission on Higher Education via the NJI-TOER project. reevant technoog has not been mature and has been quite expensive. ith the deveopment of waveength converters especia the ate deveopment on a-optica waveength converters [4] waveength conversion is being conceived as a necessar function for a-optica networks. ithout waveength conversion a connection can be bocked even if a intermediate inks have free waveengths. ith waveength conversion a connection can be set up as ong as a waveength is free on each intermediate ink [5]. Therefore waveength conversion reaxes the requirements on the waveength management throughout the network b aowing waveengths to be assigned on a ink-to-ink basis [6]. In this paper we formuate the reoration probem with waveength conversion in DM networks. e focus on the singe fiber fauts which are the predominant fauts in DM networks. This reoration probem is formuated as an IL optimization probem and a heuriic agorithm is proposed for fa recover. In Section II we derive the IL formuation to minimize the reoration co. Section III describes the heuriic agorithm for computing the reoration paths. Section IV anazes our simuation resuts. Concusions are given in Section V. II. ROBLEM DESCRITION Consider a DM network with n nodes. The fiber ink between each pair of nodes can support up to waveengths. Each node supports two functions: aveength Add-Drop Mutipexing (ADM) and aveength Conversion (C). ith ADM the node adds oca traffic into the outgoing inks and drops traffic from the incoming inks. ith C the node optica converts one waveength from the incoming inks into another avaiabe waveength to its outgoing inks. Reoration focuses on rerouting the disrupted traffic caused b a singe ink faiure whie minimizing the network co used for recover. Two factors contribute to the recover co: the transmission co which incudes the co to propagate the signa aong the fiber and the co for the signa regeneration; the conversion co which incudes the co to overcome the insertion osses b waveength converters and the co of optica power insertion to achieve good waveength conversion. Here we assume that the nodes in the DM network are far enough to approximate path ength with path hops and thus the transmission co is proportiona to the number of hops of the reoration path. The conversion co is proportiona to the number of waveength conversions aong the reoration path. A. Notations Given a directed graph G(NE) where N is the set of network nodes and E is the set of directed inks of a DM network G define: /03/$ IEEE 43

2 N: the node set in the DM network numbered from to n e : the directed optica ink from node i to node j : the number of waveengths in ink e : the maximum number of waveengths per ink among a inks i.e. max{ } a inks { λ λ }: waveengths supported in the network C T ( ): the transmission co for the reoration path C C ( ): the waveength conversion co for the reoration path C( ): the co for the reoration path { m }: the working paths in the network before ink T fais k : the traffic in the working path k { x }: the working paths which go through ink T; when ink T fais these paths need to be recovered x m C ( n C i ) C T ( e ) : the waveength conversion co in node i from waveength s to t : the transmission co for using ink e Furthermore we introduce the foowing indicators: sk Q e s Z e I n i ink e uses waveength s for working path k ink e uses waveength s for reoration path reoration path converts waveength s to t at node ni Given the above we need to sove for the reoration paths {... } for the faut at ink T. B. IL Formuation Using IL the above probem can be formuated as to find the reoration paths which minimize the reoration co: min C( ) () where the path reoration co: C( ) CC ( ) + CT ( ) {... } () the waveength conversion co: C ( ) C n CC ( ni ) In i t s i (3) the transmission co: C ( ) T { {... } i... n n s CT ( e ) Ze s j i (4) } subject to the foowing conraints: the waveength conversion conraint in a node: n s In Z i e s t s j (5) s I {... { n i... } i {... i (6) t I { n i... } i {... t {... } (7) the waveength conraint in a ink: i {... } i {... s {... } x sk s ( Qe + Z ) e pk s (8) j {... i and the traffic reoration conraint: x k. (9) k As indicated in () minimizing the sum of the recover co C( ) to recover a singe faiure in the DM network is the objective of the IL. The co has two factors: the waveength conversion co C C ( ) and the transmission co C T ( ). The conversion co for a specific path equas the sum of the conversion co in each node of this path (3). The transmission co for a specific path equas the sum of the transmission co in each ink of this path (4). The minimization is subject to severa conraints: fir the waveength conversion conraint in a node (5); second in a node n i a specific waveength s on appears at mo once in the incoming inks for reoration path (6) and at mo once in the outgoing inks for reoration path (7); third the waveengths in a ink are no more than the maximum number of waveengths in the whoe DM network (8). If the reoration scheme meets equation (9) it is a compete reoration a traffics in the faut ink are recovered; otherwise it is a maximum reoration which on reores as much traffics as possibe. The above IL formuation has O ( n + n ) variabes where n is the tota number of nodes in the network and is the maximum number of waveengths in the network. The conraint is in the order of O ( n + n ) where is the number of recover paths when a singe component fais. For a network with n4 and 6 the variabes to be soved are more than 44

3 s 336 Z e and more than 3584 I n v and the number of equations are more than 670. III. HEURISTIC ALGORITHM The probem formuated in Section II is a routing and waveength assignment (RA) probem. The RA probem has been shown to be N-compete and the number of variabes and equations increase rapid with the size of the DM network. So the IL formuation is not practica for on-ine arge network reoration. e empo the foowing heuriic agorithm for rapid rea-time soutions. The heuriic spit reoration (HSR) agorithm assumes that we are given: the network topoog; the traffic matrix of working paths in the DM network; the set of aternate paths between an pair of nodes; the transmission co of a inks and the conversion co of a nodes; the faied ink. The purpose of the HSR is to find the reoration paths for a singe ink faut T whie minimizing the recover co. The HSR agorithm addresses this probem in two eps. In the off-ine ep the node-ink topoog is converted into the node-waveength topoog; the aternate paths of a node pairs are ied in the order of increasing co. In the on-ine ep the traffics going through the faied ink are spit into severa subtraffics and are reored one b one according to their priorities. A. Off-Line Step λ λ λ λ λ λ λ (a) λ (b) Fig.. (a) Node-ink topoog (b) Node-waveength topoog The off-ine preprocessing contains severa subeps. Fir the node-ink topoog is converted into node-waveength topoog. Fig.. iurates an exampe: Fig. (a) is the nodeink topoog the connection between a node pair represents the actua fiber that connects the nodes and in Fig. (b) the connections are the waveengths supported b the corresponding fiber. e route the reoration paths in the node-waveength topoog because each fiber in the DM network can support the tota number of traffics that equa to λ λ : fiber : waveengths the number of waveengths. Here we assume that individua traffic demands are comparabe to the waveength bandwidth. Second the aternate paths for each node pair are rericted b the hop imit and path number imit to reduce the compexit. The waveength assignment in each node is done b maximum matching to reduce the waveength conversion co. Assume an aternate path of working path x goes through node n with incoming waveength λ a if the same waveength λ a is avaiabe in the outgoing port assign it to this path and no waveength conversion co is incurred in node n for this path; if λ a is unavaiabe in the outgoing port assign the fir avaiabe outgoing waveengths and then the waveength conversion co is added. Third cacuate the path co b summing the conversion co and transmission co of each path. The aternate paths for each node pair are sorted in the order of increasing co. The pseudo-code of the off-ine ep is given in Tabe I. In this ep the aternate paths of node pair (n i n j ) are sorted in terms of the path co. Aternate path hop imit h and aternate path number imit k shoud be set based on the atiics of reoration paths. Appropriate vaues of h and k can decrease the computationa and spatia compexit whie ensures that the reasonabe and co-effective reoration paths can be obtained. B. On-Line Step TABLE I: SEUDO-CODE OF OFF-LINE STE Input: G(NE) { m} Cc( n i ) CT( e ) aternate paths of node pair (n in j) athset aternate path hop imit h aternate path number imit k Output: i of aternate path set athset Begin G w(n we w)net_topo_conversion(g(ne)); // topoog conversion for a node pair(n in j) athset imit_path_hops(athset hk); if(athset is not empt) maximun_matching(athset ); waveength_assign(athset E wn w); avecowc_co(athset CC( n i ) ); //waveength conversion co TranCotr_co(athSet CT( e ) ); // transmission co TotaCoaveCo+TranCo; // tota co athseti(athset athset TotaCo); // i paths according to their tota co end if end for End The on-ine ep can be simp described as: hen a singe ink faut is detected spit the tota traffics going through the faied ink into severa subtraffics based on their priorities; reease the network resource aong the subtraffic paths; from the aternate path i of the off-ine cacuation seect the fir faut-ink-disjoint path as the reoration one. This ep consis of the foowing major phases and the pseudocode is ied in Tabe II. Spitting traffics: after detecting the faut in ink e spit the traffics into sub ones; sort subtraffics according to their priorities; if mutipe subtraffics have the same priorit the tie is arbitrari broken. 45

4 Notifing ink faut: forward and backward the faut notification message from the faied ink and reease the corresponding waveengths. Seecting reoration paths: for the highe priorit subtraffic seect from athset the fir aternate path with no ink on e as the reoration path and reserve the intermediate waveengths. Iteration: iterate through a other subtraffics seect the fir aternate path with disjoint waveengths from athset and reserve the intermediate waveengths. TABLE II: SEUDO-CODE OF ON-LINE STE Input: athset faied ink T { m} G w(n we w) Output: reoration path set Resath Begin Trafget_traffics(G w(n we w)t); // get traffics going through ink T TrafLispit_traffics(Traf G w(n we w)t); // spit traffics SpiLii_traffics(TrafLi); // i traffics according to their priorities if SpiLiis not empt for a subtraffics SubTraf in SpiLi Ateathget_aternate_path(athSetSubTrafT); // get the aternate path for a subtraffic Resathadd_to_set(Ateath Resath); // add the path to the Resath athsetmark_path(ateath athset); // deete the path from the athset end for end if switch_traffic(resath); // switch traffics to the recover paths End Our HSR agorithm is a reaxed inear programming [7]. The L reaxation technique reduces the computation compexit b reaxing some conrains in the IL formuation. e reax the minimum transmission co conraint (4) b bounding the hops in the reoration paths and reax the minimum conversion co conraint (3) b maximum matching. The traffic conraint in (9) is reaxed b maximum recover and some ower priorit traffics coud be bocked if necessar. IV. SIMULATIONS AND ERFORMANCE ANALYSIS The simuation runs on the NSFNET topoog with 4 nodes and inks (Fig. ). Each ink is treated as a fiber in the DM network. There are 8 waveengths in a fiber and a nodes are configured with a-optica converters. Initia 5 working paths are setup using the ea co path scheme. The traffic in each working path is one waveength bandwidth. The average number of hops of the working paths is.3 and we imit the hops of the recover paths to 5. Our HSR agorithm is compared with the dedicated path protection (D) and the shared path protection (S) in terms of the survivabiit performance. The D is aso caed + protection; it precomputes an a-ink-disjoint protection path for each working path and the protection path is reserved on for a specific working path not shared with others. The S is simiar to the D except that severa working paths ma share one protection path if possibe. In the foowing the protection path in the D or the S and the reoration path in our HSR are both caed recover path in the sense that the are both recover aternate paths in each scheme after the occurrence of a ink faut. Severa performance criteria are the indicators of the DM network survivabiit: recover co additive atenc and recover coverage. Our simuations are designed to compare these criteria Fig.. NSFNET topoog Recover co is the sum of the transmission co and conversion co of a reoration paths for a ink faut. e assume that the transmission co through a ink and the conversion co in a node are both equa to unit co in the simuation. Tabe III is severa scenarios in the simuation. Six working paths go through ink 6 and the tota co of these paths is units; five working paths go through ink 7 with the tota co of 5 units; etc. e aso incude the D scheme without waveength conversion (ND) and the S scheme without waveength conversion (NS) to compare the recover co. As showed in Tabe IV the recover co of ink 6 faut is units for the NS; 37 units for the D scheme; 34 units for the S scheme; 3 units for the HSR scheme; the ND cannot find the recover path because the same waveength is unavaiabe in an of its candidate recover paths and thus the corresponding recover co is infinite. hen ink 9 and ink 0 fai even the D scheme cannot find the recover paths within the imited hops the recover co is infinite. The HSR seects the faied-inkdisjoint reoration paths whie the D and the S seect the a-ink-disjoint paths so the HS cos ess in terms of the recover co. TABLE III: SCENARIOS scenario ink id Number of working paths tota co in the ink (unit) scenario 6 6 scenario scenario scenario scenario 5 4 scenario TABLE IV: RECOVERY COST (unit) scenario ink faut ND NS D S HSR scenario ink scenario ink scenario 3 ink scenario 4 ink scenario 5 ink scenario 6 ink average

5 Because of additiona hops and waveength conversions the recover paths ma incur additive atenc. The additive transmission atenc is due to more hops in the recover paths compared with the origina working paths. The additive conversion atenc is generated b more waveength conversions in the recover paths. Tabe V shows the additive transmission hops in these three methods. The HSR adds the ea hops to the recover paths the D adds the mo and the S is the midde one. Tabe VI iurates the additive conversions of each method. The HS has the be performance whie the D causes the mo additive waveength conversions. Due to the imit of hops and ow network degree there ma not exi recover paths for each ink faut. Tabe VII shows that the HSR and the S have 00% coverage i.e. the compete recover the traffics disconnected b the teed ink fauts whie the D on recovers 67% of the ink fauts. TABLE V: ADDITIVE TRANSMISSION HOS scenario ink faut D S HSR scenario ink scenario ink scenario 3 ink scenario 4 ink 0 -- scenario 5 ink scenario 6 ink average TABLE VI: ADDITIVE AVELENGTH CONVERSIONS scenario ink faut D S HSR scenario ink scenario ink scenario 3 ink scenario 4 ink scenario 5 ink scenario 6 ink average TABLE VII: RECOVERY COVERAGE D S HSR 67% 00% 00% V. CONCLUSIONS e have inveigated the survivabiit issue of DM networks. Our mathematica formuation and performance anasis revea severa new insights in DM networks reoration: aveength conversion: ith the impementation of waveength converters the IL formuation for the reoration issue is different from an other formuations. The waveength conversion co is one main factor of the tota recover co and waveength conversion conraints in each node add more equations and variabes. Our simuations revea that the waveength conversion functionait reaxes the waveength management in the DM networks and the waveength can be assigned on a ink-to-ink basis inead of the end-to-end basis. DM networks with waveength conversion have higher recover coverage and ess recover co. Traffic spit reoration: Disconnected traffics in the faied ink are divided into subtraffics and sorted according to their priorit. This idea is based on the observation that not a traffics in a ink have the same parameters. Even the have the same source and deination different appications ma generate different traffic parameters. Athough expicit priorit criteria are not anazed our HSR agorithm provides a framework for traffic spit reoration schemes. Heuriic reoration agorithm: Due to the arge number of equations and variabes our heuriic reoration agorithm is a practica soution for ink faut recover. aveength assignment and aternate path seection are two ke issues for effective recover. The maximum matching simpifies the N-compete probem. The imit on aternate path number and hops decreases the compexit of reoration. Mo important of a separating the computation into off-ine initiaization significant reduces the on-ine reoration time. ith this simpified on-ine processing and higher resource utiization the reoration scheme is more attractive than atic ones such as the D and the S. These points represent an important underanding in the survivabe issue of DM networks with waveength converters. The heuriic reoration agorithm can be adapted to other variations such as bi-directiona inks mutipe ink fauts and mutipe inks between one node pair. Our research in this area has expoited the impact of waveength conversion and priorit-based traffic spit reoration in the survivabe DM network operation. REFERENCES [] O. Gere and R. Ramaswami Optica aer survivabiit: a services perspective IEEE Communications Magazine vo. 38 no. 3 pp March 000. [] S. Sengupta and R. Ramamurth From network design to dnamic provisioning and reoration in optica crossconnect mesh networks: an architectura and agorithmic overview IEEE Network vo. 5 no. 4 pp Ju-Aug. 00. [3] L. Sahasrabuddhe S. Ramamurth and B. Mukherjee Faut management in I-over-DM networks: DM protection versus I reoration IEEE Journa on Seected Areas in Communications vo. 0 no. pp. -33 Jan. 00. [4] D. ofson T. Fjede and A. Koch Technoogies for a-optica waveength conversion in DDM networks The 4th acific Rim Conference on Lasers and Eectro- Optics vo. pp [5] M. Fre and T. Ndousse aveength conversion and ca connection probabiit in DM networks IEEE Transactions on Communications vo. 49 no. 0 pp Oct. 00. [6] Y. Luo and N. Ansari Reoration with waveength conversion in DM networks IEE Eectronics Letters Vo. 38 No. 6 pp Aug. 00. [7] M. Sridharan M.V. Saapaka and A. K. Somani A practica approach to operating survivabe DM networks IEEE Journa on Seected Areas in Communications vo. 0 no. pp Jan