Efficient Bandwidth Sharing in Bus-Based Optical Access Networks

Transcription

1 Effcent Banwth harng n Bus-Base Optcal Access Networs Anre-Luc Beylot, Nzar Bouaballah an Guy Pujolle LIP6, Unversty of Pars 6, 8 rue u Captane cott, F-755 Pars, France nzar.bouaballah, guy.pujolle@lp6.fr ENEEIHT - IRIT/TeA Lab., rue C. Camchel, BP7, F-37 Toulouse Anre-Luc.Beylot@enseeht.fr Abstract. Pacet-base optcal access rng s becomng a promsng soluton n metropoltan networs. Its performance epens manly on how optcal resource sharng taes place among the fferent competng access noes. In such a networ farness ssues are lely to arse between upstream an ownstream noes competng to access a common ata channel. Ths paper proves a new protocol calle TCARD (Traffc Control Archtecture usng Remote Descrptors), base on a preventve reservaton scheme, to allevate the farness problems. The reservaton process conssts n forcng the upstream noes to ensure enough avalable banwth for ownstream noes transmsson purpose. Moreover, we evelop analytcal moels n orer to assess the access elay when TCARD s enable. The analytcal an smulaton results show how the propose soluton allevates the performance egraaton an the resource sub-utlzaton whle achevng farness among bus noes. Introucton Over the last ecae, networs have been wtnessng a perpetual growth n ata traffc. Ths shft, rven prmarly by the prolferaton of nternet, has create a rsng eman for robust networs, wth ncreasngly hgh-ln capacty an noe throughput. Due to the new ncumbent challenges, the operators are progressvely mgratng towar optcal core networs tang avantage of the tremenous transmsson capacty offere by the optcal technology. Thans to the mplementaton of wavelength vson multplexng (WDM) n core networs, the relentless nee for more capacty may have been satsfe. However, at the bounares of bacbone networs, especally at metropoltan an local area networs (MAN/LAN), an effcent soluton for transportng an swtchng huge amounts of ata stll nees to be foun. The man goals of next-generaton metropoltan networs are to prove hghspee transmssons an the ntegraton of varous servces (e.g., ata, voce, an veo) over larger geographc areas. In ths regar, three major enablng factors are entfe as crucal for the evoluton process of metropoltan networs archtecture: optcs, pacet swtchng, an protocol convergence. To eal wth the new requrements of next-generaton metro networs, a new archtecture name the ual bus optcal rng networ (DBORN) has been propose.

2 The DBORN archtecture wll be escrbe n ths artcle, but for more etale nformaton the reaer s nvte to refer to []. The performance of such networs epens manly on how optcal resource sharng taes place among the fferent competng access noes. Thus, both collson-free transmsson an far sharng of the common banwth among rng noes must be ensure. A meum access control (MAC) protocol s neee to avo collsons on the nvual WDM channels share among competng noes. The propose MAC protocol must conser the case of nonslotte WDM rngs. However, even though the MAC protocol enables collsonfree transmsson over the share meum, t oes not aress the nherent farness ssue, whch s pronounce n the case of share meum networs. In fact, snce several source noes share a common channel, one noe may grab all the avalable banwth, an possbly starve the ownstream noes competng to access the same channel. Protocols at varous levels (such as MAC or CAC Call Amsson Control) must be ntrouce to ensure goo utlzaton of the transmsson resources an to allevate farness problems. In general, farness control mechansms lmt the transmsson of upstream noes n an attempt to eep enough banwth for ownstream statons []. Although these schemes may be effcent n the case of slotte WDM rngs, yet, they o not perform well n the case of asynchronous transmsson base archtectures le DBORN. We presente n [3] analytcal moels an smulaton results that llustrate the aforementone ssue. Inee, we notce that sharng the common banwth farly but arbtrarly among bus noes, le n slotte WDM rng, oesn t resolve the farness problem wthn asynchronous system. In ths regar, we emonstrate n [4] the nherent lmtatons of the toen bucet access rate-base algorthm once apple to asynchronous transmsson bus-base networs. As a result, we suggest n ths paper a novel control traffc protocol that ams to solve the farness ssue. The propose soluton, the so-calle TCARD (Traffc Control Archtecture usng Remote Descrptors) an presente brefly n [4], s base on a preventve mechansm when grantng access to the resource,.e. free banwth s reserve by each noe accorng to the traffc requrements of ts ownstream partners. In ths context, analytcal moels are evelope n an attempt to prove explct formulas that express the mean access elay of each noe of the bus-base optcal access networ when TCARD s consere. The remanng parts of ths paper are organze as follows. ecton emphaszes the MAC context nclung a escrpton of the rng networ along wth ts man features. Then, secton 3 proves a etale escrpton of the propose control mechansm TCARD. Analytcal moels for evaluatng the access elay performance of each rng noe, when TCARD s consere, are evelope n secton 4. Then, secton 5 valates the accuracy of the propose moels by comparng the analytcal results wth that obtane by means of smulatons. Furthermore we emonstrate how TCARD can acheve farness an mproves the networ performances. Fnally, conclusons are rawn n secton 6. Networ Archtecture an MAC Desgn Ths secton escrbes the DBORN archtecture an the propose MAC protocol.

3 to/from core networs hub noe to/from access networs rng noe ncomng transt fram es < etecton wnow > ae frame upstream/ wrtng bus fber rop opt. coupler passve optcal rng noe a Transparent Transt FDL opt. spltter opt. DMux photooe vo etecton unt FD L fber M AC logc Tx AD D Rx Rx Tx Ph (photooe) PD U s ownstream/ reang bus Burst Moe Transmtter & Recevers Opt. CMA/ CA nput buffer Fg.. Overvew of DBORN networ an noe archtecture Fg.. chema of the CMA/CA base MAC of DBORN. DBORN Archtecture DBORN can be escrbe as a unrectonal fber splt nto ownstream an upstream channels spectrally sjont (.e. on fferent wavelengths). The ownstream bus, ntate at the hub noe, s a meum share for reang purposes, whle the upstream bus, ntate n the rng noes, s a multple access-wrtng meum. Note that all the transmssons n the rng are performe between the hub an the rng noes. Therefore, n the ownstream recton, DBORN s a pont-to-multpont networ, an n the upstream recton t s a multpont-to-pont networ. Let us conser N noes place n the unrectonal rng, as shown n Fg.. Each noe serves one or more access networs. Wth regar to the recton from the access networs to the feeer rng, the rng noe plays the role of a concentrator. Buffere pacets are transmtte along the upstream bus towar the hub. In fact, pacets travel along the rng wthout any electro-optc converson at ntermeate noes. Thus we eal wth the optcal transparency property of the transt traffc through ntermeate rng noes. The hub termnates upstream wavelengths an electroncally processes the pacets. Accorng to ts estnaton, a pacet s forware ether nto the bacbone or through the ownstream bus to reach the rng noes whch are beng estne. In the latter case, the rng noe pcs up a copy of the ownstream sgnal, orgnatng from the hub, by vrtue of a spltter n orer to recover ts corresponng pacets. Once splt, the man sgnal s no more processe at the noe level an t contnues ts path to serve the other rng noes, snce a wavelength channel coul be share n recepton by several noes. However, the rng noe termnatng the cope channel, electroncally processes the ata pacets contane theren, an elvers them to users.. MAC Desgn In terms of logcal performance, the man ssue s relate to the collson-free pacet nserton on a share wrtng bus. nce the path n transt remans transparent an

4 passve (nether an actve optcal evce nor electronc converson are employe to hanle transt frames), no pacet s roppe once transmtte on the rng. Hence, traffc control mechansms are requre at the electronc ege of the rng noes to avo collson wth transt traffc urng ts own ata emsson. In a fxe-slotte rng system wth fxe pacet sze, vo (.e., slot) fllng can be carre out mmeately upon etecton, snce the vo uraton s a multple of the fxe pacet sze uraton. The etecte vo s therefore guarantee to prove a mnmum uraton of one fxe pacet length. However, n nonslotte rng systems wth varable pacet length an arbtrary vo uraton, t s very lely that a collson wll occur f a pacet s mmeately transmtte upon etecton of a vo s ege. To meet these requrements, each rng noe must retan the upstream traffc flow wthn the optcal layer whle montorng the meum actvty. o, as shown n Fg., each rng noe frst uses an optcal spltter to separate the ncomng sgnal nto two entcal parts: the man transt sgnal an ts copy use for control purposes. Wth regar to the control part, as n [5], low bt rate photooes (ph) typcally 55 MHzare use to montor the actvty of the upstream wavelengths. Once a free state of the meum s etecte, the MAC unt measures the sze of the progressng vo. To o so, a Fber Delay Lne (FDL) s ntrouce on the transt path to elay the upstream flow by one maxmum frame uraton augmente by the MAC processng tme. The length of the FDL s slghtly larger than the Maxmum Transmsson Unt (MTU) sze allowe wthn the networ, n orer to prove the MAC unt wth suffcent tme to lsten an to measure the meum occupancy. The rng noe wll begn njectng a pacet to fll the vo only f the null pero s large enough (.e. at least equal to the sze of the pacet to be nserte). Unelvere ata wll reman buffere n the electronc memory of the rng noe untl a suffcent vo space s etecte. Ths way, collson free pacet nserton on the upstream bus from the a port s ensure. However, conserng only ths basc mechansm, Hea Of the Lne (HOL) blocng an farness ssues arse. A rect result woul be performance egraaton for rng noes that are close to the hub noe on the upstream bus. Atonal flow control mechansms must be thus consere, both at the MAC layer an at the upper layers of ege noes. 3 The Propose Protocol: TCARD To regulate the transmsson of a noe, we can use the TB rate-base control scheme put nto acton n the case of slotte WDM rng. However, as emonstrate n [4], ths same mechansm presents several lmtatons when ealng wth the farness problem n the case of asynchronous transmsson. We showe n [4] that even f the traffc source by upstream noes, whch s regulate by the TB shaper, oes not volate the negotate throughput, t causes unacceptable pacet elay to ownstream noes sharng the same channel. Certanly, thans to TB algorthm the free banwth (state n bt/s) allocate to each noe s theoretcally suffcent to hanle ts traffc. However the man ssue pertans to the napproprate strbuton of the free banwth. Ths s manly ue to the lac of

5 organzaton urng the emsson process n the networ. In fact, the msmatch, between the le pero strbuton resultng from the upstream noes utlzaton of the meum an the pacets sze strbuton of the ownstream noe, often leas to banwth waste as well as farness problems wth regar to resource access. To cope wth the aforementone factors, we suggest a new preventve control mechansm that forces a noe to conform to ts allocate banwth, an t also prevents the ranom vson of the resource capacty. Let us conser N noes sharng a common unrectonal channel travelng to the hub an let us conser th more specfcally the noe of the bus. Unle the TB algorthm whch s base on th the noe traffc escrptor, the TCARD algorthm reles on the specfcaton of the aggregate traffc source at the ownstream noes (,.., N). The TCARD mechansm s base on the strbuton an the gatherng of remote nformaton (escrptors) relatve to the traffc requrements contracte by ownstream rng noes sharng the same resource. For each rng noe (,.., N), the aggregate escrptor reflects the traffc nees of ts ownstream neghbors. Ths nformaton s then use to constran the access of the noe to the meum. The basc operaton of such a scheme s smple. To escrbe t, let us conser an ant-toen pool at the noe where ant-toens are generate at fxe tme ntervals that correspon to the specfe average rate of the aggregate ownstream traffc. Unle TB scheme where each toen represents the permsson to transmt one bt, each TCARD ant-toen prevents the noe from transmsson on a etecte le pero for a fxe amount of tme. Ths le pero of sze s reserve for ownstream noes. Followng ths reservaton, an ant-toen s remove from the ant-toen pool. Pacets arrvng to the noe enter frst to the nput buffer. Thans to the MAC protocol, the noe lstens an measures the vo uraton present n the meum. If the etecte null pero s smaller than,.e. the ant-toen cannot be place, the vo coul be use by the noe for ts own usage purpose as long as the cumulatve sze of frames to be sent s smaller than the current vo sze. If the etecte null pero s equal or greater than, t s use manly for the release of one ant-toen f the ant-toen pool s not empty, otherwse the vo can be use by the noe for transmsson. The arrval of an ant-toen to the pool urng the transmsson of a pacet oes not preempt the emsson process. The ant-toen has to wat the pacet servce completon n orer to be serve. Hence, the man ea behn TCARD les n the preservaton of banwth (represente by vos) by upstream noes n orer to satsfy ownstream noes requrements. However, organze an sensble reservaton schemes must be apple to fully beneft from the protocol effcency. A basc rule conssts n avong ranom vson of the resource leang to naequacy between the le pero length an the pacet sze strbutons. Inee, n orer to guarantee for a ownstream noe the ablty to transmt pacets of maxmum sze, the length of a reserve vo (whch consumes one ant-toen) must be at least equal to the MTU sze. On the other han, the maxmum length of an le pero that can be reserve s lmte by the FDL length aopte n the MAC esgn. As stpulate earler, the FDL length use s slghtly larger than the MTU sze allowe on the networ. Therefore, to fulfll the

6 aforementone requrements the uraton that has to be aopte must be equal to the tme requre to transmt the MTU on the share meum. 4 Approxmate Analytcal Moels of TCARD In ths secton, we propose a frst analyss of the TCARD mechansm. Our am s to assess the mean watng tme E [ W] at each noe (,.., N) when TCARD s enable. To acheve ths am, we wll prmarly conser the frst noe. Furthermore, the analyss s extene to the followng rng noes. 4. Analyss of the Frst Noe The frst noe can be moele by an MD/G/ queue wth non-preemptve prorty. In fact, the worloa for the frst queue conssts of two classes of job: the ant-toens, whch represent the hgher prorty class, an the ata flows (.e. pacets). Ant-toens arrve to each noe accorng to a etermnstc process wth an arrval rate an requre a fxe servce tme. On the other se, pacets arrve accorng to a Posson process wth rate λ an requre a general servce tme. Recall that the objectve s to etermne the average watng tme of the lower prorty class jobs. Ths analyss s qute complcate so we propose an accurate approxmaton of the watng tme of the frst noe. In ths stuy, the queue server can be n one of two states: free or busy. The server s busy whenever an ant-toen or a pacet s present n the system, otherwse the server s free. Let us conser a pacet #j enterng the queue. Two cases are to be stngushe: a. When the pacet arrves, t s the only job of the lower prorty class. The pacet transmsson begns as soon as there are no hgher prorty jobs (anttoens) remanng n the queue. Hence the servce tme of the pacet can be emulate as follows:. If the queue server has gone n a free state snce the latest pacet transmsson (.e. pacet #j-), the emulate servce tme nclues the resual servce tme of the eventual ant-toen alreay present n the server when the pacet #j arrves. o pacet #j may tae a watng tme (set up tme) before ts transmsson can start. Note that at most one anttoen may be present n ths case, snce the ant-toen generaton rate s lower than the meum throughput. The emulate servce tme gets over as soon as there are no ant-toens remanng n the queue snce the begnnng of pacet #j transmsson.. The queue server s always n a busy state snce the pacet #j- has been successfully transmtte. In other wors, the emulate servce of pacet #j- s not yet complete. Once ths servce s complete (.e. there s no more ant-toens n the queue) the pacet #j s taen mmeately nto servce. In ths case there s no watng tme or set up tme. Inee, the emulate

7 servce of pacet #j begns once the pacet #j transmsson starts an gets over as soon as there are no ant-toens n the queue. b. In the secon case, the pacet arrves whle other pacets are stll present n the system. The pacet #j has to wat ts turn to be serve. When the servce of pacet #j- s complete, the pacet #j s taen nto servce mmeately. In ths case, the emulate servce tme retans the same expresson as n the case a- an there s not a set up tme. Henceforth both cases wll be aggregate n the remaner of ths stuy. In summary, ths moel behaves as an M/G/ queue wth a set up tme [6]. For ths moel, we frst erve the emulate servce tme strbuton as escrbe above. Moreover, we obtan the mean watng tme. 4.. Emulate ervce Tme Wth Possble Non Null et Up Tme It correspons to the case a-. As explane earler, the pacet #j has to wat urng the resual servce tme of the eventual ant-toen stll present n the system. Then pacet #j s transmtte. In ths case, the emulate servce of pacet #j- s alreay complete. Thus the system s empty of customers when pacet #j arrves even f the server may be occupe by the last generate ant-toen. Let T enote the arrval tme of the pacet #j. Due to the memoryless property of Posson arrvals, we conser that the arrval tme A of the last generate ant-toen s unformly strbute over T, T where s the generaton rate of ant-toens. Two cases can be stngushe: Case : A < T,.e. the last generate ant-toen has alreay left the system when the pacet #j arrves. The set up tme s thus null. The pacet #j transmsson begns mmeately (at X T ) an wll fnsh at tme X j, where j s the transmsson tme of pacet #j. The followng anttoen wll arrve at tme A A. If X j < A, then the noe can transmt a new pacet at tme X j. Hence the servce tme of the pacet #j s smply j an the setup tme s equal to. If X j A, the ant-toen wll be sent just after the eparture of the pacet #j, urng the tme pero X, X ]. The next anttoen wll arrve at tme A [ j j A. The analyss s terate untl X j < A where A A. In ths case, the set-up tme s zero an the emulate servce tme equals to j.

8 Case : A > T,.e. the last arrve ant-toen s stll n the system when the pacet #j arrves. The pacet #j has to wat at least urng the tme pero [ T, A ] before ts transmsson starts. Ths wll consttute the set-up tme of the system. As <, the last arrve ant-toen wll leave the queue before the arrval of the followng one. Inee, A < A A. Thus, the pacet #j wll enter the server at tme X A an wll be transmtte urng the tme pero X, X ]. Then, one falls own n the same stuy as n the frst [ j case wth X A nstea of X T. Hence the servce tme s gven by the expresson: j X T where X j < A, X j ( ) > A an wth A A () The set up tme s X T n ths case. 4.. Emulate ervce Tme Wth Null et Up Tme We refer here to the cases a- an b. As state before, the servce tme expresson remans the same n both cases. When the pacet #j arrves, the emulate servce of pacet #j- s not yet complete. Thus the system s not empty of customers when pacet #j arrves. The set up tme s zero. The emulate servce tme starts at X as soon as there s no ant-toen n the system snce the arrval of pacet #j. Hence, the last ant-toen arrve at A wth X < A < X. We assume that the arrval of the last ant-toen s unformly strbute between X X,. The pacet #j wll be emtte urng the tme pero X, X ]. If urng ths [ j transmsson pero, the followng ant-toen arrves ( A A < X j ), t wll be serve at tme X j an wll leave the server at tme X. In a smlar way as prevously, ths operaton s terate n orer to erve the emulate servce tme of a pacet #j.

9 4..3 The Mean Watng Tme for the Frst Noe The frst noe s then analyze as an M/G/ queue wth set-up tme [6]. Let C (resp. C ) enote the emulate servce tme when the system s empty (.e. case a-) (resp. not empty,.e. cases a- an b) at arrval epochs. Let π, be the probablty that a pacet arrves whle the system s empty of customers. It can be shown that: The mean emulate servce tme [ C] equal to: E λe[ C] [ ] λe[ C ] π () λ E (nclung set-up tmes) s consequently [ C] π E[ C ] ( π ) E[ ] (3) C The mean response tme can be expresse as follows: E [ R] π [ ] λe[ C ] ( λe[ C ]) The mean watng tme s thus equal to: λ [ ] E[ C ] ( λe[ C ]) (4) [ W ] E[ R] E[ C] π E (5) Where s the average resual servce tme of the eventual ant-toen present n the server when a pacet arrves whle the system s empty. Dfferent pacet length strbutons can be consere. In the present wor, we conser pacets of varable length (5, 5 an 5 bytes) more or less representatve of the peas n pacet sze strbuton n Ethernet. The total traffc volume comprses 5% of 5 Bytes, 4% of 5 Bytes an % of 5 Bytes pacets sze. Let p be the probablty of the fferent pacet szes an the corresponng emsson tme. The transmsson tme of an ant-toen s chosen equal to the emsson tme of the longest pacets. For each type of pacets, we get the probablty ensty functon of C, (nex refers to pacets of length ): f ( x) δ ( x ( ( ) )) δ ( x ( )) C, (6) where δ enote the Delta Drac functon an.

10 Whch yels to: [ ] ( ) ( ) ( ) [ ] ( ) ( ) ( ),, (7) In a smlar way, the probablty ensty functon of C, s gven by: ( ) ( ) ( ) { },, < < x x x f x f C C (8) The frst two moments of those servce tmes are then equal to: [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] p p p p,,,, (9) 4. Analyss of the Followng Noes The analytcal moel escrbe so far hanles the frst noe case. However, t can be easly extene to the followng rng noes wthout major mofcatons but stll approxmatons have to be accounte for. To acheve ths am, we assume that the avalable banwth receve by each noe s equal to the banwth reserve by upstream noes ue to the ant-toens. Thus the server spee D of each noe s consere equal to: D wth > () Afterwars, we can recursvely apply exactly the same metho presente n secton Performance Evaluaton In ths secton, we evaluate the performance of the propose farness control protocol. We conser a rng of 8 noes sharng the same wavelength that runs at Gbt/s. Each

11 noe receves traffc from the access networs to be forware towar the hub at a mean rate of, Gbt/s. Thus the traffc source by all the rng noes represents 8% of the wavelength capacty. The pacets arrve accorng to a Posson process. The arrval rate of the pacets at each noe s the same n orer to hghlght the farness ssues. In ths secton we assess the access elay an the pacet loss rate (PLR) at each rng noe. As explane before, the ant-toen generaton at each noe wthn TCARD s confgure to reflect the average amount of traffc expecte at ownstream noes. Moreover, the banwth reserve for ownstream noes use purpose s representatve of vos of 5 bytes n orer to comply wth pacets of maxmum sze. For nstance, the TCARD ant-toens are generate at the frst noe at a rate of 9 (, 7 ) /(5 8) ant-toens/s. We frst compare the performance of each rng noe whether TCARD s enable or not. Then, we evaluate the accuracy of the propose analytcal moel by comparng ts results wth those obtane from smulatons carre out usng networ smulator. Fgure 3 epcts the average access elay experence by pacets arrvng to each noe. Results hghlght the farness ssue alreay scusse. We pont out that the performance egraaton, when TCARD s sable, s not ue to the meum saturaton snce the channel occupancy s below 7 %. Ths s manly ue to the lac of organzaton urng the emsson process n the networ. In fact, the msmatch, between the le pero strbuton resultng from the upstream noes utlzaton of the meum an the pacets sze strbuton of the ownstream noe, often leas to banwth waste as well as farness problems wth regar to resource access. Recall that the nput loa s 8%. Ths fference s smply ue to the pacet loss resultng from buffer overflow of ownstream noes. On the other han, TCARD enables farness an better use of the resource by sharng effcently the banwth between competng noes. The mean access elay s aroun 6 µs for all the noes. We notce that the performance of the ownstream noes when gong closer to the hub s not affecte by the upstream noes. In aton, smulatons show that TCARD mproves the resource utlzaton, whch ncreases from 7% to 8%. We pont out however that the elay recore at upstream noes s slghtly ncrease, wth respect to the case where no farness control mechansm s Mean access elay (µs),e6,e5,e4,e3,e,e,e,e Noes TCARD-Anal TCARD sable TCARD-mul Fg. 3. Mean access elay of the eghtnoe bus wth varable-pacet sze traffc Pacet loss rate,9,8,7,6,5,4,3,, TCARD sable TCARD Noes Fg. 4. Pacet loss rate of the eght-noe bus wth varable-pacet sze traffc

12 apple, but stll remans below 7 µs. Ths s because TCARD algorthm mposes more constrants on upstream noes n orer to preserve usable banwth for ownstream ones. The analytcal results of access elay when TCARD s enable reveal a perfect match wth the smulaton results: analytcal results practcally conce wth the smulaton results. o, the approxmate analytcal moels can acheve hgh accuracy. Fgure 4 epcts the PLR at each rng noe. The capacty of the electronc buffer at each noe s set to Mbytes. As expecte, when TCARD s sable, pacet loss occurs more an more when approachng the hub ue to the noe buffer overflow. Inee, ownstream noes o not fn sutable le pero to transmt ther pacets. In partcular, the loss rate regstere at noe 8 s above 99% n the absence of any control mechansm. In contrast, wth TCARD, no pacet loss s recore n the networ. In ths case TCARD never ncurs loss ue to ts effcent share of banwth among noes. 6 Concluson Ths paper proves the analyss of share bus networ s behavor wth asynchronous transmsson. We analyze the system performance n terms of access elay requre by each noe to nject a pacet on the share meum. The analyss results showe that farness ssues are lely to arse between upstream an ownstream noes. To allevate the farness problem, we suggeste a new protocol, calle TCARD, base on a preventve reservaton scheme. We evelope analytcal moels n orer to assess the access elay at each noe when TCARD s enable. The propose moels are proven to be hghly accurate by comparson wth smulaton results. The analytcal an smulaton results showe how the propose soluton allevates the performance egraaton an the resource sub-utlzaton whle achevng farness among bus noes. References. N. Le auze et al.: A novel, low cost optcal pacet metropoltan rng archtecture. Proc. of ECOC ', Amsteram, Netherlans, Vol. 4 (October ) M. A. Marsan, A. Banco, E. Leonar, F. Ner, an. Tonolo: Metarng Farness Control chemes n All-Optcal WDM Rngs. Proc. of INFOCOM '97, Kobe, Japan, vol. (Aprl 997) N. Bouaballah, A. L. Beylot, G. Pujolle: Farness Issues n Bus-Base Optcal Access Networs. Proc. of Networng '4, Athens, (May 4) 4. N. Bouanallah et al.: Resolvng the Farness Issue n Bus-Base Optcal Access Networs. IEEommun. Mag., vol. 4, no., (Nov. 4) pp R. Gauno et al.: RINGO: a WDM Rng Optcal Pacet Networ Demonstrator. Proc. of ECOC ', Amsteram, Netherlans, Vol. 4 (eptember ) H. Taag: Queueng Analyss Vol I: Vacaton an Prorty ystems Part I. North Hollan (99)