Performance Evaluation of an Optical Packet Scheduling Switch

Transcription

1 Performnce Evluton of n Optcl Pcket Schedulng Swtch Kyrkos Vlchos, memer IEEE, Kyrk Seklou nd Emmnuel Vrvrgos Reserch Acdemc Computer echnology Insttute, RA-CI, Unversty of Ptrs, GR-26500, RIO, Ptrs, Greece, eml: kvlchos@ced.uptrs.gr Astrct In ths pper performnce nlyss of the pcket schedulng swtch s presented. he schedulng swtch uses seres of feed forwrd delys nterconnected wth elementry optcl swtches. hs seres of progrmmle dely locks consttute n optcl uffer of depth, whose purpose s to dely/re-rrnge ncomng pckets tht request the sme outgong lnk so s to resolve or reduce pcket contenton. Performnce results hve een otned for rndom Bernoull trffc, Preto trffc, s well s for smooth trffc wth n upper ound of nherent urstness. Keywords-component; optcl pcket swtchng, urst trffc, pcket schedulng, Preto, optcl networks I. INRODUCION Severl nnovtve pcket swtch rchtectures hve een proposed so fr, ncludng swtches wth re-crcultng loops [], the Stggerng swtch [2], the Swtch wth Lrge Optcl Buffers (SLOB) [3], the Wvelength Routng Swtch nd the Brodcst (WRS) nd Select Swtch (BSS) [4]. However, work on new rchtecturl concepts, node s performnce, nd ntellgent control hve lgged ehnd progress n trnsmsson speeds. Swtches wth recrcultng loops were the frst optcl pcket swtches to ddress the hgh ndwdth nd ufferng ssues []. hs soluton however ncreses swtch lock complety, snce for n NN swtch wth L dely lnes for ufferng, nsted of n NN, n (N+L)(N+L) spce swtch s requred [5]. he Stggerng swtch ws the frst optcl swtch desgned to truly emulte n output-uffered swtch [2]. Although very promsng nd nfluentl, ths desgn ehts unnecessry pcket delys nd unstsfctory pcket loss chrcterstcs for ursty trffc. Reducton of the pcket loss rte for ursty trffc s cheved y cscdng mny smll output-uffered swtches, consequently ncresng costs, to rrve t lrger uffer depth. he SLOB s n emple of such desgn [3]. Renud et l [4] detled two WDM shred output-uffered pcket swtchng rchtectures, nmely the WRS nd the BSS swtch, tht were developed through the ACS KEOPS (Keys to Optcl Pcket Swtchng) project. he WRS s two-stge swtch tht frst uffers conflctng pckets efore routng them to ther desred output, where tunle wvelength converter s used to route pckets to the pproprte dely lne nd output port respectvely. he BSS rchtecture s one of the few proposed rchtectures tht cn esly provde multcstng. In ddton, t cn e used s the uldng lock n mult-stge swtch, to llow for modulr growth, up to severl hundreds of swtch I/Os. In ths pper, we nlyze the performnce of the optcl pcket schedulng swtch [6] for rndom Bernoull trffc, Preto trffc, s well s for constrned nd unconstrned ursty trffc ptterns. he schedulng swtch uses seres of feed forwrd delys nterconnected wth optcl swtches to resolve nternlly pcket contenton, nd t s gurnteed to e lossless when certn smoothness property holds. In ths pper we nvestgte the pcket loss performnce of the swtch when ths smoothness property does not hold. he nlyss crred out shows tht the schedulng swtch ehts very low pcket loss rto for rndom Bernoull trffc, whle t llows lossless communctons for sessons tht re suject to n upper ound of urstness, herenfter clled (n,) smoothness property. he remnder of the pper s orgnzed s follows. Secton II presents the schedulng swtch rchtecture nd the (n,) smoothness property. Secton III presents performnce evluton results, whle Secton IV concludes the pper nd proposes some future work. II. SWICH ARCHIECURES AND SMOOHED RAFFIC MODEL he schedulng swtch hs een desgned to provde lossless communcton for sessons tht hve certn urstness property or cn e trnsformed to sessons wth such property, tolertng the correspondng dely. It conssts of schedulng unt wth k nput/output ports, nd kk nonlockng spce swtch, s shown n Fgure. Ech rnch delys the ncomng pckets, ssgnng pckets to outgong slots resolvng contenton nd mntnng pcket orderng for the sme outgong lnk. he prolem of schedulng pckets through rnch of dely locks to vod collsons s prolem of routng permutton etween nputs nd outputs n the equvlent Benes network, where non-overlppng pths n the network correspond to collson-free trnsmsson through the dely locks [6]. Ech dely rnch consst of 2m- dely locks, where m log. s ssumed to e power of 2 nd corresponds to the mmum numer of sequentl pckets from ll ncomng lnks tht request the sme output nd cn e served wth no contenton. he th lock conssts of three-stte (or two 22) optcl swtch nd three fer dely pths, correspondng to delys equl to 0, 2 nd 2 + pcket slots. o ensure tht the pckets n the ncomng frme cn e ssgned to ny slot n hs work ws supported n prt y EC v the e-photon/one project

2 Fgure : he Schedulng Swtch rchtecture, consstng of the Scheduler (k nputs) nd kk spce swtch. he Scheduler comprses of k rnches, ech wth 2log2- dely locks. he -th dely lock conssts of one three-stte swtch nd three dely lnes of length 0, 2 nd 2+ pcket slots. the outgong frme, the ltter must strt t lest (3)/2-2 fter the ncomng frme egns. Such n nput queung scheme cn e vewed s mplementng n optcl pcket uffer of depth [7]. One of the mjor dvntges of the schedulng pcket swtch s ts modulr ufferng scheme desgn tht cn e esly epnded to ccommodte more urstness n the trffc (n wy smlr to the wy electronc uffers cn e epnded n conventonl electronc swtch). he cost of the swtch, when mesured n terms of the elementry swtchng elements t requres, grows only logrthmclly wth. A correspondng trffc model tht cn gurntee lossless communcton must e sed on the forementoned ufferng scheme. o ths end, we ssume tht the tme s on lnk s dvded nto pcket slots of equl length nd every slots re vrtully grouped to form frme. hs concept s llustrted n Fgure 2. Pckets re grouped n -sze frmes efore enterng the swtch, whle frme ntegrty s mntned t the output s well. A sesson s sd to hve the (n,)- smoothness property t node f t most n pckets of the sesson rrve t tht node durng frme of sze. A sesson cn esly e trnsformed to hve the (n,) smoothness property t the ngress pont of the network whle ths property cn e preserved throughout network consstng of schedulng swtches, due to frme ntegrty mntennce. We let n j e the numer of pckets tht rrve durng frme over ncomng lnk nd hve to e trnsmtted on lnk j, nd k the numer of ncomng (nd outgong) lnks of node. If the connecton nd flow control protocols used gurntee tht the numer of pckets whch requre the sme outgong lnk j n frme s less thn or equl to the frme sze,.e., lrger s the flelty grnulrty n ssgnng rtes to sessons. For emple f ech lnk n network hs cpcty C nd sesson hs the (n,)-smoothness property, then ths sesson wll hve n verge rte of t most nc/, mplyng tht cpcty cn only e llocted n dscrete multples of C/. It s mportnt to note tht ths s not crcut swtched dt, ut nsted, ths s pcket swtchng wth ult-n flow control to ensure lossless trnsmsson. Pckets from prtculr source do not rrve n the sme slot nd the numer of pckets tht rrve per frme s not constnt, ut s ounded y n. III. SCHEDULING SWICH PERFORMANCE In ths secton, we present results on the pcket loss performnce of the schedulng swtch for rndom Bernoull trffc, for ursty trffc sed on truncted Preto pcket dstruton model, s well s for (n, trffc ) smooth trffc wth prmeter trffc dfferent thn the correspondng prmeter used n the swtch desgn. For the forementoned cse studes, the schedulng swtch s consdered s pcket swtch wth k nput uffers, ech wth vlle pcket slots. Regrdng our frst trffc scenro, we ssume tht pckets rrve t ech swtch nput ccordng to noml process, nd ther destntons re unformly dstruted over ll output ports. In relty, trffc s much more ursty thn tht; more specfclly, Internet nd voce trffc hve een shown to e etter modeled y Preto nd eponentlly dstruted sttstcs, respectvely. he model of ndependent Bernoull processes s the smplest model tht cn e consdered, resultng n trctle nlyss, whle stll yeldng n k n, j for ll j {,2,..k }. () then ll of the ncomng pckets cn e ssgned slots n the requred outgong lnks so tht no pckets re dropped. Both wt-for-reservton nd tell-nd-go protocols cn e used to ensure tht ths property s met. he frme sze s n mportnt prmeter nd cn e vewed s mesure of the trffc urstness llowed. he lrger s, the less constrned (more ursty) s the ncomng trffc llowed to e, nd the Fgure 2: Incomng nd outgong frmes t node. Pckets rrvng n prtculr frme of n ncomng lnk tht wnt to use the sme outgong lnk re sent over the sme frme of the outgong lnk.

3 pprecton of swtch performnce. More ursty models for the trffc wll e consdered lter. Assumng tht pckets rrve ndependently t ech ncomng slot wth prolty p, then the prolty of hvng pckets rrvls durng the k slots of the k ncomng frmes requestng the sme output j, j k, nd ssumng unformly dstruted destntons s: P[ X k p p ] k k k (2) he pcket loss rto cn then e esly clculted s: PLR k k k P[ X ] ) p k p k k!! ( k ) p k p k ) p p! k k p k ) In otnng ths equton, we used the fct tht the swtch mntns frme ntegrty nd tht f more thn pckets rrve durng the k ncomng frmes hedng for output j, the ecess pckets re lost. Fgure 3() nd () show the pcket loss rto s functon of lnk utlzton for schedulng swtch wth k2 nd k4 nput/output ports, whle s vred from 2 to 024. From Fgure 3, t cn e seen tht the pcket loss rto s very low for vlues of hgher thn 32 nd p < 0.8. he prmeter cn lso e vewed s mesure of the uffer sze vlle per nput. he ufferng tht cn e ccomplshed wth the schedulng swtch s consderly hgher thn the ufferng tht cn e ccomplshed wth other swtch rchtectures tht use e.g. fer dely lnes [4],[5], for the sme mplementton cost, ecuse of the logrthmc dependence of the complety of the schedulng swtch on. Although the schedulng swtch s qute comple requrng the ntegrton of numerous elementry swtches, however mprovement n ts rchtecture wth stte-of the rt, ll-optcl technologes cn downsze ts cost nd complety [8]. We eleve tht the schedulng swtch rchtecture, where ufferng s ccomplshed usng logrthmc numer of elementry 22 optcl swtches, offers fesle wy to desgn modulr, hgh cpcty ll-optcl uffers tht cn tke dvntge of sttstcl multpleng. hs s more cler n Fgure 4() nd () tht dsply, for gven utlzton fctor, the wy the pcket loss rto vres wth. From these fgures, t cn e seen tht the loss rto drops very fst s ncreses. Even wth 00% utlzton (p), PLR cn e very smll when s of the order of 024 or lrger. Incresng y fctor of 2 requres the ddton of two dely locks nd thus four 22 swtches per (3) Fgure 3: Pcket loss rto for () k2 nd () k4 for noml pcket trffc nd unformly dstruted destntons swtch port. he modulrty of the schedulng rchtecture desgn llows us to ncrese the throughout or e le to ccommodte more ursty trffc for gven PLR wth only moderte ncrese n the complety nd the cost of the swtch. In our second cse study, we ssume tht the ncomng trffc oeys the (n,) smoothness property, ut wth prmeter hgher thn the one the schedulng swtch hs een desgned to tolerte. More specfclly, we ssume tht the prmeter of the trffc, denoted y trffc, s n nteger multple of the correspondng prmeter of the swtch, denoted y swtch. he rto trffc / swtch cn e treted s n nde of the trffc urstness n Schedulng-swtch sed optcl network. he lnk utlzton s ssumed to e equl to p, menng tht the totl numer of pckets rrvng over ll nputs n n ncomng frme of sze trffc tht request the sme outgong lnk j s: k n, j p trffc for ll outputs j. he poston of the pckets of n (n, trffc ) smooth sesson wthn n ncomng frme s ssumed to e dstruted unformly mong ll slots of the ncomng frme of sze trffc. he prolty of hvng pckets wthn the swtch frst slots Fgure 4: Pcket loss rto versus for () k2 nd () k4 nd for utlzton p {0., 0.2, }. For p, pcket loss rto s nd 0-3, when 2 0 for k2 nd k4 respectvely.

4 of the k ncomng frmes s: () P k swtch ktrffc k ptrffc ktrffc ptrffc swtch (4) From Eq. (4) we cn esly derve the correspondng pcket loss rto: PLR ptrffc swtch k swtch ktrffc k p ktrffc p trffc p trffc swtch ( ) swtch (5) In the ove pcket loss rto clculton, we hve used the fct tht the p trffc pckets tht rrve per ncomng frme nd request output j re evenly dstruted wthn the frme of sze ktrffc trffc, nd cn rrve n ny of the possle ptrffc comntons. If more thn swtch pckets rrve durng the frst k swtch ncomng slots, the ecess pckets wll e dropped. Fgure 5 nd dsply the loss prolty curves for k 2 nd k 4. In these fgures, fed vlues of swtch equl to 2 nd 6 hve een consdered, whle trffc s vred to nteger multples of the forementoned swtch vlues. It s worth notng tht Eq. (5) s vld only for p trffc > swtch, whle for p trffc swtch or trffc swtch, the pcket loss rto s zero for ny utlzton fctor p. From oth fgures t cn e seen tht when trffc / swtch ncreses (eyond 2), the pcket loss rto decreses. hs s prmrly due to the urstness vergng s result of the numerous possle pcket dstrutons wthn trffc frme. In the thrd trffc model we consder, we nvestgte the performnce of the schedulng swtch under hevy-tled truncted Preto dstruton, whch s consdered y mny reserchers s good model for urst trffc n rel networks. In our model, pckets rrve n ursts (ON perods), whch re seprted y dle perods (OFF perods). o generte Pretodstruted sequence of ON perods, one cn generte Pretodstruted sequence of urst (pcket trn) szes, followed y Preto-dstruted dle tmes. he mnmum urst sze s correspondng to sngle pcket rrvl. he formul to generte Preto dstruton s: X PAREO, where s unformly dstruted vlue n the rnge (0, ], s the mnmum non-zero vlue of X PAREO, denoted y on nd off for () Fgure 5: Pcket loss rto for () swtch2 nd () swtch 6, versus the trffc / swtch rto for k2 nd k4 schedulng swtch nd utlzton p {0.25, 0.5, 0.75, }. trffc s vred from 2 swtch to 2 0. the pcket trn nd dle perod respectvely nd the tl nde or shpe prmeter of the Preto dstruton. However computer smultons usng the ove formul generte truncted Preto dstruton, ecuse of the dscreet vlue. On the contrry, ny true Preto dstruton of suffcently lrge length wll hve vlues tht eceed the rnge generted y computer smultons. o ths end, snce the men sze of the truncted Preto dstruton dffers from the men sze of true one, the queston tht rses s whch s the mnmum possle dle perod so tht on verge the truncted Preto dstruton yelds lnk utlzton fctor of p. In order to defne off, we hve ssumed, frst fed length pckets nd secondly dle perods to e equl to n nteger multple of sngle fed length- pcket. o ths end, y epressng the utlzton fctor p s the men sze of ON perod over men sze of ON nd OFF perods: ON perod p (6) ON perod + OFF perod, clcultng the men vlue of the truncted Preto m dstruton, whch does not eceed the vlue X Preto, mn s shown elow:

5 E( ) m X Preto f ( ) d X m Preto d + mn nd susttutng eq. (7) to (6), the mnmum dle perod s functon of lnk utlzton cn e derved [9]: off off on on mn on off (8) on mn off off p In the ove equtons, f() s the prolty densty functon of the Preto dstruton, mn s the smllest non-zero vlue of tht s unformly dstruted n (0,], nd α on, α off re the tl ndces for the pcket trn nd dle perod sze respectvely. It s worth notcng here tht our ntenton ws to generte trffc lod eng very close to the specfed lod wth ll comntons of on, nd off. After defnng off, we performed computer smultons for k 2 nd k 4 schedulng swtch wth α on.7, α off,2 nd X mn 0-4. Fgure 6 show the correspondng loss rto results for є [2 64]. Agn pcket destntons were evenly dstruted. In our smulton, we hve selected α on to e lrger tht α off, snce n rel trffc, the prolty of hvng etremely lrge OFF perod s hgher then the prolty of hvng etremely lrge ON perods. From Fgure 6, t cn e seen tht the schedulng swtch loss rtos, n the cse of Preto dstruton dffer sgnfcntly from the ones shown n Fgure 3 for rndom Bernoull trffc. hs s more evdent for smll vlues nd s ttruted to the ursty nture of the Preto dstruton. More specfclly, snce the men sze of the ON perods, ~2.4, s close to then durng n ON perod, ll slots of the frme re flled, ndependent of the resultng worklod. hs results n ncresed pcket loss rtos nd especlly n the cse of 2, t cn e noted tht loss vres slghtly for ll p. hs s due to the fct tht s smller thn the men vlue of ON perods. Nevertheless, s ncreses, pcket loss rto drops fst nd for vlues hgher thn 32, n cceptle loss rto of 0-6 for p < 0.6 s otned. IV. CONCLUSIONS In ths pper, we hve nlyzed the performnce of the schedulng swtch under vrety of models for the ncomng trffc. he schedulng swtch s gurnteed to e lossless when the ncomng trffc hs the so-clled (n,) smoothness property. We hve evluted the swtch performnce, when ths property does not hold for three dfferent trffc models nmely, Bernoull model, truncted Preto model, nd model where trffc s constrned ut wth smoothness prmeter dfferent thn the one used n the swtch desgn. In future communcton, the dely mprments t the network ngress pont due to the (n,) smoothness property enforcement wll e nvestgted nd sutle edge router rchtecture wll e proposed. (7) Pcket Loss Rto Pcket Loss Rto,E+00,E-0,E-02,E-03,E-04,E-05,E-06,E-07,E-08,E-09,E+00,E-0,E-02,E-03,E-04,E-05,E-06,E-07,E-08,E ,2 0,4 0,6 0,8 Lnk Utlzton ,2 0,4 0,6 0,8 Lnk Utlzton Fgure 6: Pcket loss rto for () k2 nd () k4 versus lnk utlzton for є [2 64]. Pcket rrvls nd dle perods follow truncted Preto dstruton wth tl nde of.7 nd.2 respectvely. REFERENCES [] A. Hung nd S. Knuer, Strlght: A wdend dgtl swtch, n Proc. IEEE Glol elecommun. Conf. (GLOBECOM 84) vol., pp. 2 5, Nov. 984 [2] Z. Hs, he Stggerng swtch: An electronclly controlled optcl pcket swtch, J. Lghtwve echnol., vol., pp , 993. [3] D. Hunter et l., SLOB: A swtch wth lrge optcl uffers for pcket swtchng, J. Lghtwve echnol., Vol. 6, pp , 998. [4] M. Renud et l. Network nd system concepts for optcl pcket swtchng, IEEE Commun. Mg., vol. 35, pp , Apr [5] K. Vlchos, I.. Monroy, A.M.J. Koonen, C. Peucheret nd P. Jeppesen SOLAS: Swtchng echnologes for Optcl Lel Sgnls, IEEE Communctons Mgzne, vol. 4, no., pp , Novemer [6] J.P. Lng, E.A. Vrvrgos nd D.J. Blumenthl, he lmd scheduler: A multwvelength schedulng swtch, IEEE J. of Lghtw. echn., vol.8, no.8, pp , [7] I. Chlmtc et l. CORD: Contenton Resoluton y Dely Lnes, IEEE Journl on Selected Ares n Communctons, vol. 4, no. 5, pp , June 996. [8] G. heophlopoulos et l. An lterntve mplementton technque for the schedulng swtch rchtecture, ccepted for pulcton n IEEE J. of Lghtw. echn. [9] G. Krmer, On genertng self-smlr trffc usng pseudo-preto dstruton echncl ref, Deprtment of Computer Scence, Unversty of Clforn, Dvs. < /ppers/self_sm.pdf> () ()