A Dstrbuted Algorthm for Least Constranng Slot Allocaton n MPLS Optcal TDM Networks Hassan Zeneddne and Gregor V. Bochmann, Unversty of Ottawa, Ottawa, ON-K1N 6N5 Abstract - In ths paper, we propose a dstrbuted approach for the least constranng slot allocaton scheme n all-optcal TDM networks (LC) that was ntroduced n a prevous work. The drvng force behnd our proposal s the employment of the LC scheme n a GMPLS context. After descrbng the basc data model and messagng parameters, we focus on defnng an effcent LC resource status update scheme, whch s essental to acheve compatblty wth GMPLS perodc lnk state update standards. Bascally, we reduce the rate of resource status updates from once per call to once per few calls, and measure the mpact on network performance. I. INTRODUCTION In a prevous work [1], we proposed the least constranng slot (LC) schedulng scheme as a novel slot reservaton approach n all-optcal TDM mesh networks wthout bufferng [2,3], whch are synchronzed on slots wthout synchronzaton of frame boundares. Thus, a tme slced traffc segment that travels a route consstng of several lnks may be carred by slots that have dfferent postons wthn the frames on the respectve lnks. LC reduces call blockng n these networks to an optmal rate close to what can be acheved wth full bufferng. The constrant n LC s the number of fxed routes that mght use a tme slot at a gven pont n tme. The algorthm selects the least constranng slots on the route, hence the name least constranng slot. Comparng ts performance to the frst ft (FF) approach [2], and FF wth optcal tmeslot nterchangers (OTSI) [4], the LC approach provded a performance gan close to the FF approach wth OTSI, but at a reduced complexty close to FF wthout OTSI. The reported gan was consstent under unform and non-unform traffc dstrbuton. In addton, we found that the LC approach outperformed the least loaded (LL) approach n mult-fber envronments [5]. Thus, LC proved to have an edge over LL, snce the former s not restrcted to mult-fbers networks as s the latter. As a general concluson of our prevous study, the LC approach provded close to optmum performance n optcal TDM networks wth no bufferng. In ths paper, we propose a dstrbuted soluton for the least constranng slot reservaton scheme. Our am s to employ LC n a Generalzed MPLS context [6]. We defne the nodal database and basc parameters to be added to GMPLS reservaton and sgnalng messages. To comply wth GMPLS perodc lnk state updates, we ntend to reduce the LC resource status update rate to a level that matches GMPLS standards and stll mantans close to optmum performance. In the subsequent sectons, we revew the LC algorthm and descrbe the elements of our dstrbuted scheme and how t comples wth GMPLS. Before concludng ths work, we dscuss the effect of reducng the rate of resource status updates on the network performance. II. LC ALLOCATION SCHEME Before descrbng the basc steps of the LC approach, we should clarfy the nomenclature used n [1] to provde a better understandng of the presented concepts. Route, route-slot and lnk-slot are essental concepts used n descrbng the LC approach. A network route s a seres of undrectonal lnks nterconnected through ntermedate nodes from a gven source node to a gven destnaton node. Two routes are consdered ntersectng f they have at least one lnk n common. A node transmts data nto a lnk n the form of repeatng frames of N equal tmeslots. Due to lnk propagaton delay, frame algnment s not preserved along the route. Consderng lnk AB, a traffc segment forwarded on a gven tmeslot at egress node A mght be ntercepted on a dfferent tmeslot at ngress node B. Thus, a tmeslot s better dentfed wth reference to a lnk; we use the term lnk-slot AB x to descrbe tmeslot x on lnk AB. There s no need to menton the correspondng wavelength snce only one wavelength plane s consdered n ths study. Formally speakng, a lnk-slot s a tmeslot on a lnk wth reference to the local clock of ts egress node. In general, a transmtted traffc segment from source node S to destnaton node D travels through dfferent lnks along a fxed route, and hence occupes a seres of dfferent lnk-slots. For nstance, f A and B are two ntermedate nodes between S and D, a seres of lnk-slots would be descrbed as SA x AB y BD z. Knowng the delay of each lnk, an ntermedate lnkslot UV corresponds to a source lnk-slot SA accordng to the general rule = ( + d SU ) mod N, where d SU s the total delay of all lnks from node S to node U. Thus, knowng the fxed route between a source-destnaton par and all assocated lnk delays, we can easly derve the entre seres of lnk-slots for a gven lnk-slot at the source. In ths case, we descrbe the seres SA x AB y BD z wth the smple notaton SD x, whch we call a route-slot. The upper bar s essental to dfferentate t from a lnk-slot. A route-slot SDx s consdered avalable f all ts consttuent lnk-slots are
avalable; otherwse, SDx s unavalable. In a sngle fber envronment, a lnk-slot s avalable f t s not reserved. On the other hand, n a mult-fber case, a lnk-slot s avalable f t s free for at least one of the lnk fbers. To make our approach generc, we develop t based on a mult-fber envronment, and apply t to a sngle-fber network as a specal case. The exercse of allocatng resources, for a communcaton request, from node S to D s to fnd and reserve an avalable route-slot SDx along a fxed route, whch s assumed to be gven. A. Defntons If a lnk-slot XY s part of a route-slot SD, we wrte: ( d ) mod N XY n SD,where = + SX. (1) Consderng M fbers per lnk, we defne the lnk-slot avalablty Α XY, an nteger between 0 and M, to be the number of fbers on whch XY s free. If Α XY s equal to zero, then XY s unavalable. Furthermore, we defne the avalablty Α of a route-slot to be equal to the mnmum SD avalablty Α XY among ts consttuent lnk-slots, ( Α ) Α = MIN XY. (2) SD XY n SD Knowng the assocated fxed route of each sourcedestnaton par, we derve the set Ω of all possble route-slots n the network. We defne Ω XY to be a subset of Ω consstng of all route-slots that contan lnk-slot XY. Ω XY = { SD Ω XY n SD }. (3) We further defne Ω' XY to be a subset of Ω XY of all route-slots whose avalabltes are equal to Α XY. { SD Ω XY Α = Α XY SD XY = } consstng Ω '. (4) The purpose of Ω' XY s to dentfy all route-slots whose avalabltes are decremented when XY s reserved. We desgnate the constrant of lnk-slot XY to be the sum of the avalabltes of all route-slots belongng to Ω. W XY = Α. (5) SD SD Ω XY XY In a sngle fber envronment, Α becomes a bnary SD varable showng whether the route-slot s avalable (1) or not (0); and hence, WXY would reflect the number of avalable route-slots contanng XY. In other words, t ndcates the number of routes that can potentally use the desgnated lnkslot. Last, we defne the constrant of a route-slot to be equal to the total constrant of all ts consttuent lnk-slots: W = W. (6) SD XY nsd XY B. Allocaton Prncple It s essental to reserve a lnk-slot whch has the lowest nterference wth other ntersectng route-slots,.e. havng the lowest constrant. Ths keeps more avalable route-slots n the network, hence mprovng the blockng rate for subsequent communcaton requests. Thus, the route-slot that has the lowest constrant W would be the best choce on a gven SD route between S and D. In ths case, only a mnmal number of route-slots n the network become unavalable when servng a gven call. C. Constrant Update After dentfyng the best route-slot, all consttuent lnkslots are reserved. Consequently, the constrant of each lnkslot n each route-slot n Ω' XY s modfed accordng to the algorthm, shown n Fg. 1. foreach XY WXY foreach n : = W SD XY f do 1 RTn Ω' XY do RT SD n foreach UV k n RTn do WUV : = W 1 k UV k Fg. 1: Constrant update algorthm By defnton (4), Ω' XY contans all route-slots whose avalabltes are decremented due to a reservaton of XY. For nstance, when reservng XY n a sngle fber envronment, all route-slots n Ω' XY become unavalable, and accordngly, ther avalabltes flp from 1 to 0. Therefore, the constrant of ther consttuent lnk-slots must be decremented snce a lnk-slot constrant s the sum of the avalablty of the ntersectng route-slots. Fnally, the same algorthm s repeated when freeng resources, but the constrants are ncreased nstead.
III. DISTRIBUTED APPROACH Amng to make the LC scheme applcable n a GMPLS context, we should defne a dstrbuted algorthm that blends well wth GMPLS protocols. In GMPLS, each node has a database and exchanges lnk state nformaton va update messages based on the Open Shortest Path Frst (OSPF) [7] or Intermedate System to Intermedate System (IS-IS) routng protocols [8]. For connecton reservaton, GMPLS uses the Resource Reservaton Protocol wth Traffc Engneerng (RSVP-TE) [9] or the Constrant-Based Routng Label Dstrbuton Protocol (CR-LDP) [10]. Both reservaton protocols requre two phases: label request phase ssued by the source node and label response phase ssued by the destnaton. The dstrbuted LC approach requres three maor components: a database schema at each node, a reservaton protocol, and a lnk state update protocol. A. Node Database Each node n a network employng the dstrbuted LC approach mantans a database contanng basc nformaton essental for the decentralzed reservaton process. Bascally, for each outgong lnk XY at a node X, two lsts must be mantaned: Lnks Info Lst (LIL) and Lnk-Slots Info Lst (LSIL). LIL has entres for each lnk n the network that shares a route wth XY. A LIL s entry correspondng to lnk UV has the followng structure: Total delay d n tmeslot unt between nodes U and X. f U s upstream from X, the delay s a postve nteger; otherwse, the delay s a negatve. Common Route-Slots Lst (CRSL) contanng entres for all route-slots that have lnk XY and UV n ther paths. Each CRSL s entry stores the route-slot s avalablty and a set of consttuent lnk-slot ds. LSIL has an entry for each lnk-slot on XY, whch contans the followng data: Avalablty Constrant B. Reservaton process Although the am s to extend the exstng RSVP-TE or CR-LDP protocols, we defne a new set of messages that can be ntegrated later wth the correspondng messages n these protocols ust to avod lengthy techncal dscussons that go beyond the scope of ths paper. The dstrbuted LC approach uses the followng messages durng the slot reservaton process: Request (REQ): t contans source and destnaton node ds, the cumulatve delay, and a route-slot nformaton lst (RSIL) whch has the same structure as an LSIL. The content of the REQ can be ntegrated wth RSVP Path message. Response (REP): t contans source and destnaton node ds, a selected route-slot, the cumulatve delay, and a lnk-slot avalablty lst (LSAL) ndexed by lnk-slot. The LSAL contans the avalabltes for a selecton of lnk-slots. These parameters can be ntegrated wth RSVP Resv message. Release (REL): t contans destnaton node d, and a lnk-slot. It can be ntegrated wth RSVP Resv Teardown message. Negatve Acknowledgment (NACK): t s used to nform the source of a dened request. Ths acknowledgment can be realzed by usng RSVP Path Error message. Durng a reservaton process, the followng steps are performed: 1. The source node sends a REQ to the destnaton on a predetermned route. It ntally sets the REQ s RSIL to the outgong lnk s LSIL. 2. An ntermedate node receves the request message, and performs the followng steps before forwardng the receved message to the next node on the route:. Identfy matchng lnk-slots on the outgong lnk by usng the cumulatve delay n the REQ.. Add the lnk-slot constrants n the outgong lnk s LSIL to the correspondng route-slot constrants n REQ s RSIL.. Set the avalablty n each entry of the RSIL to the avalablty of ts correspondng lnk-slot only f the latter value s less than the former. v. Add the correspondng delay d n the LIL to the cumulatve delay n the REQ. 3. When a destnaton node receves the REQ, t sends a REP to the source node after settng the REP s route-slot feld to the lowest weghed route-slot n the REQ s RSIL. It also sets the REP s cumulatve delay to the REQ s cumulatve delay. 4. When an ntermedate node receves the REP, t does the followng before forwardng the receved REP to the next node on the reverse route to the source.. Deduct the correspondng delay d n the LIL from the REP s cumulatve delay.. Identfy and lock the lnk-slot that matches the selected route-slot by referrng to the cumulatve delay.. Insert the avalablty of the correspondng lnk-slot to the REP s LSAL When the REP message reaches the source node, the node starts transmttng on the reserved route-slot. After completng the communcaton process, the source sends a REL message towards the destnaton to free all resources, whch were locked for servng the communcaton request. A request for communcaton can be reected ether durng the REQ phase or the REP phase. If no matchng resource s avalable durng a REQ phase, the REQ message s dropped and a NACK s sent back to the source. In ths case, the connecton s consdered blocked. On the other hand, f two REPs on two ntersectng routes requre the same avalable lnk-slot on the ntersecton lnk, the correspondng ntermedate node locks ths lnk-slot to the frst arrvng REP and drops the late one. It sends a NACK to the source of the
dropped REP and a REL to ts destnaton n order to free the locked resources. In ths case, the connecton s not consdered blocked snce the source node can retry wth another REQ. Further detals on the reecton scenaros durng the REQ and REP phases can be found n [11]. C. Resource Status Update Wth every establshed or released connecton, the constrants and avalabltes of correspondng resources change across the network. Therefore, a resource status update scheme s requred to keep the databases of all nodes up to date. An update scheme can be nstant or perodc. An nstant update s broadcasted by the source node upon routeslot s reservaton or release. On the other hand, a perodc update s frequently broadcast by all nodes lke the OSPF lnk state update mechansm. In both update schemes, we employ an update message (UPD) smlar to the OSPF Update message. However, we append an LSAL as an extra parameter. Whle smulatng rregulartes and errors n the centralzed scheme, we explctly forced our smulated algorthm to skp the constrant update module for n successve calls before executng t at the 1 rst call after n. We notced that network performance remaned close to optmum for relatvely large n. It bascally means that one resource status update every t perod of tme could mantan close to optmum performance and sgnfcantly reduce the assocated sgnalng cost. Instant Resource Status Update The followng steps occur durng an nstant resource status update process: 1. The source node notfes all nodes n the network about the reservaton of lnk-slots by broadcastng a UPD message contanng the LSAL that was orgnally carred by the REP. 2. Each node recevng the notfcaton performs the followng steps for each reserved lnk-slot n the LSAL:. Identfy the outgong lnk that shares a common route wth the reserved lnk-slot f any, by referrng to the LIL.. Identfy the correspondng local lnk-slot by usng the total delay from the reserved lnk s upstream node to ths local node.. Identfy the route-slot onng the reserved lnk-slot wth the correspondng local lnk-slot. Ths can be acheved by referrng to the CRSL. v. If the avalablty of the route-slot dentfed n the CRSL s equal to the avalablty of the reserved lnkslot, reduce the route-slot avalablty and the constrant of the correspondng local lnk-slot. Perodc Resource Status Update In order to mplement a perodc resource status update, the followng steps are essental: 1. At a fxed tme nterval t, every node n the network comples an LSAL and appends t to a UPD message before broadcastng t to the network. A compled LSAL contans only lnk-slots avalabltes whose values have changed snce the prevous notfcaton. 2. Each node recevng the notfcaton performs the followng steps for each lnk-slot n the LSAL:. Process the frst 3 steps of the nstant update case.. If recevng the frst notfcaton for a partcular routeslot after the down perod t, set the avalablty of the route-slot dentfed n the CRSL to the avalablty of the consdered lnk-slot. Otherwse, execute ths step only f the lnk-slot s avalablty s the lowest of both values. Dependng on the resultng change n the route-slot avalablty, the constrant of the correspondng local lnk-slot should change accordngly. If s postve, ncrease the lnk-slot constrant by ; otherwse, decrease t by. IV. SIMULATION RESULTS In ths secton, we dscuss the performance of the dstrbuted LC approach under varous status update rates. Our observatons are based on smulaton results plotted wth 95% confdence ntervals. The smulaton experments are based on the 14-nodes 21- lnk NSFNET network topology [12]. A lnk between two nodes conssts of dual undrectonal fbres wth a fxed capacty of 10 tmeslot channels per fbre. Fxed shortest path routng s used to derve paths between all source destnaton pars. Each path serves up to 10 concurrent connectons at the granularty of a transmsson channel,.e. one tmeslot per lnk along the path. Each smulaton s repeated for 30 runs. Calls arrve accordng to a Posson process, and lasts for an exponentally dstrbuted perod. We study our scheme under two dfferent traffc dstrbutons among source-destnaton pars, unform and non-unform. In the unform traffc case, every par s chosen at random wth equal constrant and hence havng the same traffc load n Erlang (mean arrval rate mean holdng tme). In the non-unform case, source-destnaton pars have dfferent constrants to acheve non-unform traffc dstrbuton. Fg. 2 shows the performance of the LC approach for dfferent status update rates. Best performance s obtaned for nstant updates, that s, an update after each accepted or termnated call. In the case that an update s only done after 10 5 new accepted calls, we obtan what we call degraded performance ; ths performance s approxmately one half of the best-performance level that s attaned wth nstant updates. Performance remans at that degraded level even f we ncrease the update rate to once per 10 2 calls arrvng to the network. However, f the update rate s once per 10 calls, we obtan best performance as n the case of nstant updates. As a generalzaton, we consder that the performance s unaffected f the update rate s greater than or equal to λ/α where λ s the call nter-arrval rate, and α s a coeffcent
related to the network sze whch s close to 10 for the NFSNET. Fg. 3 s a chart that shows samples of blockng probablty collected over several short perods of 10 calls each. To reduce statstcal varatons caused by samplng over short perods, the same smulaton s repeated 10000 tmes wth a hgh load of 120 Erlang. The employed status update rate s once per 500 calls after an ntal perod (not shown n the dagram) of nstant updates. We notce an ntal transton perod of gradual performance degradaton reflected n the early samples. The transton s from the best-performance level to the degraded performance level. The frst couple of samplngs are close to the best performance rate of 0.027. If we average out the statstcal varatons after the transton perod, the worst performance rate seems to stablze at a fxed level of 0.035 on average. The chart also shows that subsequent (sngle) status updates do not reproduce the best performance rate observed earler. To dscuss these results further, we defne the followng: - ω t : s the lst of all recorded route-slots constrants n the network. The constrant values are based on lnk-slot constrants that are recorded n nodal databases. - ώ t : s the lst of all actual route-slots constrants n the network. The constrant values are based on actual lnkslot constrants that are not recorded n nodal databases. - Low(SD, ω t ): s a functon that returns the route-slot on route SD that has the lowest constrant accordng to ω t. In the case of nstant updates, ω t should always be equal to ώ t at any tme t;.e. ω t = ώ t, and hence Low(SD, ω t ) = Low(SD, ώ t ) for all routes at any pont n tme. Ths equaton s essental for a perfect route-slot allocaton pattern and best network performance. Startng from a perfect LC allocaton pattern and stoppng all further updates, ω t and ώ t would break tes after the frst allocated or de-allocated call; and ω t s sad to be outdated. However, the equaton Low(SD, ω t ) = Low(SD, ώ t ) mght stll hold for a maorty of routes durng the frst few allocated or deallocated calls. As long as ths equaton holds for the routes at whch all subsequent calls arrve, the system would allocate the same route-slots that would be chosen n the case of nstant updates. Thus, the perfect LC route-slots allocaton pattern n the network s mantaned, and hence best performance s preserved. As soon as a call arrves at a route SD where Low(SD, ω t ) Low(SD, ώ t ), the resultng allocaton pattern becomes mperfect; and hence performance starts to degrade. The length of the best performance perod precedng the degraded performance s gven by α/λ. Note that α depends on the probablty P/n(n-1); where n s the number of nodes n the network, and P s the probablty of havng Low(SD, ω t ) Low(SD, ώ t ) for a gven route SD (note that n(n-1) s the number of routes n the network). P s relatvely small durng the frst few calls and ncreases gradually wth every allocated or de-allocated call as each route-slot affects the constrants of ts ntersectng route-slots. Durng the best performance perod, the constrants n ώ t wll always be based on a perfect LC allocaton pattern. As a result, f (sngle) updates occur at a perod shorter than or equal to the best performance perod, ω t wll always be based on a perfect LC pattern; best performance s contnually mantaned. On the other hand, f (sngle) updates occur at a longer perod, ω t wll most lkely be based on an mperfect allocaton pattern leadng to degradaton of performance. Regardless of the update rate, network performance s at the degraded level as long as the update nterval s longer than the best-performance perod. Note that f the route-slot allocaton pattern becomes mperfect t reflects an mperfect ώ t. After an update, ώ t gets coped to ω t whch would emphasze the pattern s mperfecton. Thus, further updates emphasze rather than fx mperfecton; and hence, the rrelevance of update rates to the performance degradaton level s now clear. Although the route-slot allocaton pattern s mperfect, the performance level s stll better than the performance level of the FF approach. Note that an outdated ω t stll mposes an order that the system follows when allocatng route-slots. Ths order s the result of the most recent LC update. It actually gves dfferent prortes to the route-slots n all routes accordng to the constrants collected by the last update. Note that the resultng prorty order for dfferent routes s not arbtrary but rather synchronzed based on the LC update. Ths synchronzaton between dfferent routes s the essence behnd the degraded performance level whch s better than the worst case scenaro of the FF approach. As an analogy, a synchronzed traffc lght system based on an outdated traffc pattern would stll manage traffc better than a chaotc arbtrary system. In a mult-fbers envronment, an mperfect route-slot allocatons pattern can stll produce a performance smlar to what s obtaned wth a perfect pattern (see Fg. 4). The mproved performance of an mperfect pattern n a multfbers envronment s manly due to the addtonal number of fbers. Although P n a mult-fbers envronment s smaller than n the sngle fber case, t does not ustfy the dfference n performance. Its effect wll be lmted to slghtly ncreasng the perfecton perod. Regardless of ths perod, the pattern would eventually become mperfect after few calls wthout updates. However, the prorty order that remans n effect stll produces close to optmal performance as shown n Fg. 4. Therefore, we conclude that network performance metrcs resultng from mperfect and perfect allocaton patterns converge as an effect of extra fbers. V. CONCLUSION In a prevous work, we proposed the least constranng slot reservaton approach (LC) for all-optcal TDM networks. In ths paper, we desgned a dstrbuted LC scheme n an attempt
to make t applcable n GMPLS networks. After specfyng the node database, we defned new parameters that need to be added to the RSVP-TE or CR-LDP messages. In addton, we developed two dfferent resource status update schemes: nstant and perodc. The maor challenge was to ncorporate the LC resource status update nto GMPLS, whch reles on OSPF or IS-IS lnk state update mechansms. Snce GMPLS reles on global perodc updates, we have to skp a number of calls before nvokng the LC resource updates. We showed by smulaton that an update rate greater than or equal to λ/α mantans close to optmal performance; where λ s the call nter-arrval rate, and α s a coeffcent related to the network sze whch s close to 10 n NFSNET. For lower update rates, performance degrades to a fxed level but does not converge to the worst performance level reported wth the frst ft (FF) approach; hence, stoppng all subsequent updates throughout the network lfetme after a bref perod of nstant updates produces a performance level as good as any update rate less than λ/α. In mult-fber envronments, the update reducton has no sgnfcant effect on performance regardless of the rate. In ths case, stoppng the nstant updates at an early stage of the network operaton does not affect performance, and hence the assocated sgnalng bandwdth s spared. As a general concluson, the dstrbuted LC scheme produces a close to optmal performance n a GMPLS optcal TDM network after slghtly extendng the reservaton protocol and not changng the rate of lnk state updates. REFERENCES [1] H. Zeneddne and G. V. Bochmann, Least Constraned Slot Allocaton n Optcal TDM Networks, Proc. IEEE Wreless and Optcal Communcatons Networks, July 2007, pp. 1-5. [2] J. M. Yates, J. P. R. Lacey, and D. Evertt, Blockng n multwavelength TDM networks, Telecommuncaton Systems Journal, vol. 12, no. 1, pp. 1-19, August 1999. [3] H. Zang, J. P. Jue, and J. Mukheree, Photonc Slot Routng n All- Optcal WDM Mesh Networks, Proc. IEEE Globecom '99, Ro de Janero, Brazl, December 1999. [4] H. Zeneddne, P. He, and G. V. Bochmann, Optmzaton Analyss of Optcal Tme Slot Interchanges n All-Optcal Network, Proc. IASTED Wreless and Optcal Communcatons, July 2006, pp. 207-212. [5] B. Wen, R. Shena, and K. Svalngam, Routng, Wavelength and Tme- Slot Assgnment Algorthms for Wavelength-Routed Optcal WDM/TDM Networks, Journal of Lghtwave Technology, vol. 23, No. 9, September 2005. [6] A. Baneree, et al., Generalzed multprotocol label swtchng: An Overvew of Routng and Management Enhancements, IEEE Commun. Mag. (2001) 144 150. [7] J. Moy, OSPF Verson 2, STD 54, RFC 2328, Aprl 1998. [8] D. Oran, OSI IS-IS Intra-doman Routng Protocol, RFC 1142, February 1990. [9] D. Awduche, L. Berger, D. Gan, T. L, V. Srnvasan, and G. Swallow, RSVP-TE: Extensons to RSVP for LSP Tunnels, RFC 3209, December 2001. [10] B. Jamouss et al., Constrant-Based LSP Setup usng LDP, RFC 3212, January 2002. [11] X. Yuan, R. Gupta, and R. Melhem, Dstrbuted Control n Optcal WDM Networks, IEEE Conf. on Mltary Communcatons, McLean, VA, October 1996. [12] B. Mukheree, Optcal WDM Networks, Brkhauser, 2006. Blockng probablty Blockng probablty 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 Load (Erlang) 30 35 40 45 50 80 120 1.E+02 1.E+01 1.E+00 FF 1.00E+05 Fg. 2: LC performance for dfferent update rates (once per 1E+x calls) Blockng Probablty 0.045 0.04 0.035 0.03 0.025 Tme (unt of 10 calls) 1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 Fg 3: LC performance measured every 10 calls load s 120 Erlang (update rate s once every 500 calls) 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 Load (Erlang) 100 150 200 250 300 350 1.E+05 1.E+01 1.E+00 FF Fg. 4: LC performance for dfferent update rates (once per 1E+x calls) n a 3-fbers network