Buffer Dumping Management for High Speed Routers

Transcription

1 Buffer Dumpng Management for Hgh Speed Routers Carolne Fayet, André-Luc Beylot IT, 9 rue Charles Fourer, 90 Evry Cedex, France carolne.fayet@nt-evry.fr, Groupe des Ecoles des Télécommuncatons ESEEIHT,, rue C. Camchel BP7, 307, Toulouse Cedex 7, France andre-luc.beylot@enseeht.fr, IRIT/TeSA Lab. Abstract To transport nformaton wth performance guarantees expressed n terms of delay, bounded delay varaton, mnmum pacet loss, the archtecture of multggabt and terabt networs today desgned n optcal technology requres the use of hgh speed electrcal/optcal routers and swtches. These nterfaces need to manage effcently the QoS, n partcular they have to guaranty a short delay n the queues. Ths paper presents an effcent soluton to optmze buffer dumpng allowng to reduce sgnfcantly the delay or losses caused by buffer overflow. To hghlght the proposed archtecture we have analyzed ts performance compared wth dfferent confguratons of pollng scheme. Keywords: buffer management, hgh-speed routers, QoS, performance analyss.. Introducton Routers mplementng QoS functonaltes requres some specfctes. They need logcal processes for the dfferent traffcs receved, requrng many algorthms and also the avalablty of several queues for each output nterface. A router mang use of QoS functons needs to propose the followng processes: classfcaton, polcng and marng, queung and schedulng. Frst the classfcaton of pacets, n order to determne ts output nterface and whch queue nowng ts characterstcs. We now that the classfcaton may be done by nformatons contaned nsde the pacet. Concernng the DffServ model, the IETF has defned the DFCP feld (Dfferentated Servce Code-Pont) allowng to obtan 64 dfferent values for a pacet. Secondly polcng and marng, to determne f the ncomng traffc s conform to the foreseen servce contract wth a provder for example. In the negatve, the pacet may be dscarded or tagged. Classfcaton of ncomng pacets and control of traffc have been done to choce the approprate queue, but n order to obtan an optmal process of traffcs, t s mandatory to mantan a mnmum occupancy of these queues. Loaded buffers presents two man drawbacs: they lmt the avalablty of tang account of traffc burst whch s a frequent phenomenon, moreover they ncrease the process delay nsde the router causng an end to end delay often unacceptable. In order to reduce the queues length one way s to nvte the transmtter to lmt ts throughput. In ths nd of approach, t s necessary to reman that the congeston avodance mechansm s just valuable for the mean tme. An example can be done n frame relay usng a bt BEC (Bacward Explct Congeston otfcaton), and FEC (Forward Explct Congeston otfcaton). These bts nvte the transmtter or the recever to lmt the flow. In the precse case of frame relay networs nterconnectng routers the man problem consst to fnd routers able to understand these FEC and BEC bts n order to react consequently. Ths thrd step named queung s composed, as explan prevously, of congeston control and of an effcent dumpng of the buffers of the routers. Concernng the short tme only approprated mechansms related to the queues management of the used equpment wll be effcent. Our wor focus on ths pont. The last step s the schedulng, allowng to gve the prorty to the approprate traffc. Hgh speed buffer dumpng s the purpose of ths paper. More precsely we propose a new desgn allowng to optmze the buffer dumpng of the routers. A more detaled presentaton of the proposed archtecture s

2 descrbed n []. Tradtonally the buffers are empted by means of a pollng process, descrbed n secton, where all the queues are scanned and served sequentally even though for empty queues. The man drawbac of processng empty queues result n a useless waste of tme. The process pollng used for many ATM swtches correspond to ths descrpton [] [3]. We fnd n the lterature an mproved soluton for routers consderng a reduced servce tme for empty queues. We propose a mechansm descrbed n secton 3 whch offers two advantages, frstly a very effcent and smple soluton by allowng the pollng process to gnore empty buffers, secondly lowerng the watng tme n nonempty queues. We present, n secton 4, a performance analyss of ths proposed soluton, compared wth the ATM-le pollng and the classcal pollng scheme. We have focused on the pollng process n order to overcome the weaness of ths scheme. The followng secton presents two confguratons of pollng process most often used.. Pollng processes The pollng process s the most common server model [4]. The system conssts of sequentally scannng queues and the server cyclcally vstng all the queues as shown n fgure. When vstng queue then queue, the changeover tme s not equal to zero. Moreover, when vstng queue, the server spends a sgnfcant amount of tme even though t s empty [5]. As a consequence of ths system the pollng process s very effcent when every queue s non-empty and n case of unform traffc. Unfortunately, ths system whch scans all the queues does not tae account of empty queues whch s a common case n the presence of traffc mbalances and of nonunform traffc. Consequently we observe a waste of tme due to the changeover tme and the scannng of these empty queues, especally n case of unbalanced traffc. Two dfferent cases have to be consdered. Frstly the ATM-le pollng where, as prevously explaned all the nput queues are scanned and served wth a constant cycle tme even f there are empty. Secondly, the classcal pollng often studed n the lterature n whch all the nput queues are scanned and served even f there are empty, but n ths case the servce tme concernng empty queues corresponds to a reduced constant swtch-over tme. Unfortunately the tme devoted to empty queues beng not equal to zero, t ncreases the watng procedure for prorty nformaton and obvously s a very bad soluton for the probablty of losng nformaton. Fgure : Pollng Process System Havng descrbed the drawbacs of these processes we propose n the followng secton a new desgn allowng to effcently ncrease the performance of the buffer dumpng. 3. Archtecture of the buffer dumpng management The speed requrements put on broadband swtches or routers mpose a wred soluton. A wred sequencer usng dgtal crcuts n a very hgh-speed technology avalable on the maret today provdes ths hardware soluton. We consder the problem of multplexng nput lns to a sngle output. The stuaton occurs nsde swtchng fabrcs, hgh-speed routers or when matrces are nterconnected n multstage swtches. Most often (ths s the case when multplexng for concentraton) the sum of the speeds on each nput ln exceeds the capacty of the output ln, so that bufferng s compulsory [7-8]. Ths amounts to consder nput lns, whch feed nput buffers. An overvew of the global structure s shown n fgure. The proposed swtchng mechansm s composed of a bus and a regster RI. Ths Data Bus wll receve sequentally an

3 ncomng nformaton from the nput regsters. An ncomng data located at the head of the elected queue s transferred to the bus, whch carres t to the regster RI where t s stored, watng to be processed -.e., redrected to the allocated output port. The flterng of the ncomng data s processed by means of very hgh-speed 3-state outputs. Each nput owns ts proper wred state machne whose role s frstly to control the presence or not of the nformaton n the assocate regster, then eventually ts prorty level and also the state of the other nputs. A decson s then taen enablng one nput regster among to be loaded on the bus. Ths shows a constant nteracton between the dfferent computer blocs. As opposed to classcal pollng schemes, here empty buffers are gnored. Classcally, an empty buffer sends an empty nformaton or cell whch s overwrtten later on. Therefore, non-empty buffers are vsted more often, ncreasng sgnfcantly the performance of such a system. PF: Prorty Functon of Queue PI: Presence of Informaton n the queue Loadng Prorty Functon PF Reset PI Cloc Int Data regster Wred State Machne PI Loadng Prorty Functon PF Reset PI Cloc Int Data Bus Data regster Wred State Machne Fgure : Bloc dagram of buffer dumpng 3. Descrpton of an Input Bloc PI Regster RI Loadng Prorty Functon Reset PI Data regster Wred State Machne A selected nput has a two part structure: - The data part, ncludng the nput data regster and the 3-state outputs flterng the loadng on the bus. - The Local Control Unt, ncludng the wred state machne whose role s to manage the dfferent states and functons of the correspondng nput, and the loadng prorty functon allowng loadng data on the bus. Cloc Int PF PI 3. Dversty of System functonaltes The man advantage of a such structure s to be adaptable to dfferent nds of processes. Whatever the type of traffc, empty nputs are not taen nto account. Therefore, they do not slacen the process. Consequently we have a gan n tme, ncreasng sgnfcantly the performance of such a system. The elementary choce s a sequental servce scannng the nputs from the left to the rght or the nverse. It wll be possble to ntroduce a management of several level prortes per nput f requred. The cloc frequency s fxed by hardware and must be ndependent of the number of unts. The cloc frequency s 00 Mhz, n order to be n adequacy wth the maret. 4. Performance Analyss Pollng systems have been extensvely studed durng the last forty years. Many analyss were proposed [4-6] and more recently [] for nstance. In the present paper, we wll analyze and compare dfferent confguratons. A generc model wth queues wth nfnte watng rooms served n cyclc order by a sngle server. Pacets arrve to the queues accordng to a Posson process wth rates λ, λ, L, λ. The pollng server has no ntalzaton tme. The servce tmes of pacets at queue are constant wth mean ( ) b and second moment b b. All the consdered confguratons, presented n the prevous parts corresponds to a E-lmted servce (lmted from an exhaustve vewpont) wth a maxmum of pacet served n a gven cycle. In order to consder unbalanced traffc patterns, we wll consder that one nput port has a hgher nput rate λ a λ where a s a coeffcent of asymmetry and λ λ corresponds to the global nput rate.

4 On the other nput ports, the nput load s λ λ a The followng solutons are consdered : ATM-le pollng : Ths frst soluton conssts on consderng that all the nput queues are polled and served even f there are empty. Ths soluton have been extensvely studed n the ATM context for whch perodc arrvals are consdered and for whch a constant cycle tme s mplemented wth a duraton equal to the mnmal nterarrval duraton. The servce tme c wll correspond to a constant swtch-over tme wth mean s plus the servce tme b (a servce tme wll be consdered even f the nput queue s empty), c s b. Its ( ) second moment s smply equal to c Classcal pollng : c In ths soluton, all the nput queues are polled even f there are empty. In ths case, the servce tme s equal to zero and a constant swtch-over tme wth mean s and ( ) second moment s s consdered. s Optmzed Pollng : Ths soluton corresponds to our optmzed dumpng management. Only non-empty queues are polled n a gven cycle. For nonempty queues, the swtch-over tme s constant wth the same parameters as those of the classcal pollng. As the ntalzaton process duraton s neglected, as long as the system remans empty no cycle are to be consdered. In a gven cycle, at least one pacet s served, only non-empty queues are polled. 4. Analyss of the «ATM-le» pollng The analyss of the frst case can be done through a M G queue analyss. Each nput queue can be studed ndependently (a cycle wll have a constant duraton). If a pacet arrves n a non empty queue, ts servce tme S (long servce tme) wll be equal to the duraton of a cycle, c c If the queue s empty, as Posson arrvals are consdered, ts servce tme S 0 (short servce tme) wll be unformly dstrbuted between c and c c. Let V (resp. B) denote the number of pacets whch arrves n a queue durng a long servce tme (resp. short servce tme) (ndex s omtted). Let V ( z) (resp. ( z) B ) be the z-transform assocated to r.v. V (resp. B). Let q ~ be the number of pacets n the queue at steady state and ( z) Q ts z- transform. By wrtng Chapman-Kolmogorov equatons and by summng over all the values of the number of pacets n the queue, one can fnd Q ( z) π 0 ( V ( z) zb( z) ) V ( z) z () where π 0 s the steady state probablty for the queue to be empty. Let E [ S] be the mean servce tme. As, π 0 λ E[ S] and E[ S] π 0E[ S0 ] ( π 0 ) E[ S] we obtan λe[ S] [ S ] λ E[ S ] π 0 λe 0 In order to determne the mean number of pacets n the queue E [ q ~ ], we can evaluate the dervatve of those z-transforms. Let B V ( ) ( ) ( ) ( ) d B dz d V dz ( z) ( z) z z and. By consderng the dervatve of () and usng L Hosptal rule, one can fnd : ( ) ( ( ) ) ( ( ) ) ( ) ( ~ B B B V ) ( ) E q π 0 ( ( ) ( )) ( ) V V ( ) ( )

5 The parameters easly be found : ( ) ( ) B and ( c ) ( ) ( ) V can ( ) λ B ( ) ( c c ) ( ) ( ) (! c ) V λc The mean response tme can be obtan by usng Lttle s result : E [ R ] E λ [ q~ ] 4. Analyss of the «classcal» pollng soluton In the second case, the methods proposed n [9] and [0] can be appled as follows. Let C denote the tme between two consecutve vsts to server. E [ C ] s ndependent of, as long as the system s E C wth stable wth a common value s E [ C] () where s s the mean swtch-over tme and the total server utlzaton. For the classcal pollng scheme, we obtan s C s Let and C C λ b E W be the mean watng tme of queue. It has been shown that n the - lmted case (only a smplfed verson of these expressons s presented snce the servce tmes and the swtch-over tmes are constant) ( λ E[ C] ) E[ W ] A E[ C] (3) where β A wth β b ( ) s E C λ Approxmated methods were proposed to derve parameters E [ W ]. In the present paper, we mplemented the methods ntated by [9] and [0]. It conssts on consderng a tagged customer. Its mean watng tme s equal to the mean resdual tme untl the server next vsts queue, E[ θ ], plus the mean tme necessary to serve the customers whch are present n queue when the customer arrves. An approxmate formula can be appled : E W E λ E C [ θ ] One method conssts on approxmatng E[ θ ] by a common value E [ θ ] whch leads to a soluton of () [0]. The second one [9] conssts on consderng that E ( C ) E( ) E( C ) E( θ ) b, θ b, j where E( C ) b,. β s 4.3 Analyss of the optmzed pollng 4.3. Introducton For the optmzed pollng scheme, t s more convenent to nclude the swtch-over tme for non-empty queues n ther servce tme whch leads to a null swtch-over tme. s O O j 0 and λ O ( b s ) The analyss of the Optmzed Dumpng soluton s consequently more complcated because equaton () can not be appled. evertheless, a smple result can be appled to the whole system. The global mean response tme and the global mean watng are those of an M D queue wth servce tme d b s because no swtch over tme s lost. The dfference between the actual system and the equvalent M D queue comes from the fact that n the proposed soluton, the pollng system may lead to a non-fifo schedulng algorthm even f the schedulng s FIFO for each nput queue. The mean watng tme s consequently equal to λd E [ W ] (4) ( ) whch s the mean watng tme when the traffc s balanced.

6 [ W ] E[ W ] E[ W ] E (5) where ndex refers to the frst queue and ndex to the other ones. The mean response tme n all ths analyss s smply equal to the mean watng tme plus the servce tme d. It s a lower bound of the mean response tme for the heavly loaded nput queue and an upper bound of the mean response tme for the other queues. Ths s due to the fact that the mean length of the frst queue s larger than the other ones and consequently some pacets of the other queues may overtae pacets of the frst queue Upper bound of the response tme of the frst queue As the arrval processes are of Posson type, the mean number of pacets n the whole systems at arrval epochs are the same for all the nput queues : E [ L] ( ) ( ) Let us consder a pacet p whch arrves n the frst queue. As ths queue s heavly loaded, the number of pacets n the other queues may be lower than the number of pacets n the frst queue. Consequently, most of the pacets that are n the system when pacet p arrves wll leave the system before p. In the worst case, all the pacets that enter all the other queues when p s watng wll also be served before p. It leads to : [ W ] E [ W ] E [ W ] E Fnally, E [ W ] E W ( ) d λ Usng (4), t leads to a lower bound of the mean watng tme of the other queues : λ d [ W ] ( ) λ E[ W ] λe[ W ] λ E (6) Lower bound of the response tme of the frst queue The bound provded by (5) may be qute low especally when the nput load s hgh. Another bound can be obtaned by consderng that the frst queue s never empty and by analyzng the other queues. The system can be analyzed le a symmetrc -lmted pollng systems wth a constant swtch-over tme s d. Equaton () and (3) leads to d E [ C] wth and λ E[ C] E W wth A ( ) A E[ C] ( ) d ( ) ( ) d E[ C] λ whch can be smplfed as follows : d ( ) E W λd λd Usng (4), we fnally derve : [ W ] ( ) λ E[ W ] λe[ W ] λ E (7) 5 Results In ths part, we wll present the valdaton of the models and the nterest of the proposed schedulng method. The followng numercal values are consdered : The number of nput ports s set to 8. s, b, In the followng fgures, the mean response tmes wll be expressed n number of cloc tme perods and the nput rate n number of pacets per cloc tme perod. Fgures 3 and 4 correspond to the valdaton of the model for the Dumpng Method mechansm. In fgure 3 (resp. fgure 4), we represented the mean response tme of the frst nput port (resp. the other nput ports) as a functon the nput load wth a coeffcent of asymmetry a5.

7 R curves correspond to the mean response tme n the symmetrc traffc case, R- (resp. R) to the lower bound (resp. upper bound). SIMUL results were obtaned usng dscrete event smulatons. 0 the dscrete event smulaton results, BOXMA and WAG curves to the applcaton of the Boxma [0] and Wang [9] approxmatons. It s shown that the approxmatons lead to accurate estmatons of the performance crtera when the nput load s not too hgh. In ths confguraton, the mean response tme qucly ncreases wth the nput load especally for the frst nput port ,05 0,0 0,5 0,0 0,5 0,30 Fgure 3. Mean Response Tme as a functon of the nput load, frst nput port Dumpng Mechansm, a5 R R- SIMUL R ,05 0,07 0,09 0, 0,3 0,5 SIMUL BOXMA WAG R R- SIMUL R Fgure 5. Mean Response Tme as a functon of the nput load, frst nput port Classcal Pollng, a ,05 0,0 0,5 0,0 0,5 0,30 Fgure 4. Mean Response Tme as a functon of the nput load, other nput ports Dumpng Mechansm, a ,05 0,0 0,5 0,0 0,5 0,30 SIMUL BOXMA WAG It s shown that the model leads to a good estmaton of the mean response tme. The lower bound of the mean response tme for the frst nput port s really accurate even wth hgh nput rate. The dfference between smulaton results and ths bound s about % to %. The upper bound s also really good, the dfference s about 5%. When the nput load s low, the bound gven by the mean response tme of the symmetrc system s qute good. For the other nput ports, the bounds are also accurate ; the dfference between the smulaton results and the bounds are about 0%. In fgures 5 and 6, we represented the same performance crtera n the classcal pollng confguraton. SIMUL curves correspond to Fgure 6. Mean Response Tme as a functon of the nput load, other nput ports Classcal Pollng, a5 In the followng fgures, we fnally compare the results obtaned wth the ATM-le pollng (exact results), the classcal pollng (Smulaton results) and the optmzed pollng (Smulaton results). When parameter a s equal to 5, the ATMle soluton s not stable for the frst nput queue. It s shown that the optmzed dumpng mechansm leads to really good performance results even when compared wth the classcal pollng mechansm especally for the frst nput port.

8 ,05 0,0 0,5 0,0 0,5 0,30 SIMUL-OPTI SIMUL-CLASS Fgure 7. Comparson of the dfferent mechansms. Mean Response Tme as a functon of the nput load, a5, heavly loaded nput port 5 5. Concluson In ths paper, we proposed a new buffer dumpng management mechansm for hgh speed routers. It conssts on allowng the pollng process to gnore empty buffers. Analytcal models were proposed to compare ths soluton to classcal pollng schemes. It has been shown, especally when consderng unbalanced traffc patterns, that ths mechansm mproves the global performance of the system. Prospectve wors deal wth the comparson wth other pollng dscplnes (gated or K-lmted []) and the evaluaton of the pacet loss probablty ,05 0,0 0,5 0,0 0,5 0,30 Fgure 8. Comparson of the dfferent mechansms. Mean Response Tme as a functon of the nput load, a5, other nput ports. We fnally compared the dfferent mechansms n the symmetrc traffc case, for whch we can derve exact analytcal results for all the proposed confguratons. It s shown that the optmzed pollng mechansm leads to a great mprovement of the system. The mean response tme s lower for both heavy and low traffc. The mprovement ncreases wth the nput load. 70,00 60,00 50,00 40,00 30,00 0,00 0,00 SIMUL-OPTI SIMUL-CLASS EXACT-ATM-Le EXACT-OPTI EXACT-CLASS EXACT-ATM-le References [] C. Fayet, Buffer Management for Rng ode n the DAVID Metro etwor, submtted to LC 003. [] S. Bush, R. Crucshan, D. Bachar, F. Huang, Swtchng to ATM-The fore Runner ASX etwor World- Feb [3] Catalyst 8500 Campus Swtch Router Seres, Whte paper, Csco Systems, 998. [4] H. Taag, Analyss of Pollng Systems, Cambrdge MIT Press, 986. [5] S. Borst, Pollng Systems, Ph.D. Thess, CWI, The etherlands, 994. [6] H. Levy, M. Sd, Pollng Systems: applcatons, modelng and optmzaton, IEEE Transactons on Communcatons, Vol. 38, 0, October 990, pp [7] M. Karol, M. Hluchyj, S. Morgan, Input versus output queueng on a space dvson pacet swtch, IEEE Trans. Commun. 35 (987) [8] M. Hluchyj, M. Karol, Queueng n hgh performance pacet swtchng, IEEE J. Selected Areas Communcatons 6 (988) [9] S.W. Furman, Y.T. Wang, Mean Watng Tme Approxmatons of Cyclc Servce Systems wth Lmted Servce, Performance 87, pp , Elsever Scence. [0] O.J. Boxma, B. Mester, Watng-tme approxmatons for cyclc-servce systems wth swtch-over tmes, Performance Evaluaton, Vol. 4, pp. 54-6, 986. []. T. Tedjanto, on Exhaustve Polces n Pollng Systems and Vacaton Models: Qualtatve and Approxmate Approach, Ph.D Thess, Unversty of Maryland, 990. [] T.L. Olsen, R.D. van der Me, Perodc pollng systems n heavy-traffc: dstrbuton of the delay. Journal of Appled Probablty 40, -, 003 0,00 0,05 0,0 0,5 0,0 0,5 0,30 Fgure 9. Mean Response Tme as a functon of the nput load, symmetrc traffc case.