Resource Allocation and Management in DiffServ Networks for IP Telephony

Transcription

1 esource Allocaton and Management n DffServ etworks for IP Telephony Maarten Büchl, Danny De Vleeschauwer, Jan Janssen, Anneles Van Moffaert, Gudo H. Pett Alcatel Bell, etwork Strategy Group Francs Wellesplen B-28 Antwerp, Belgum maarten.buchl@alcatel.be ABSTACT Ths paper dscusses resource allocaton and management n Dfferentated Servces (DffServ) networks, partcularly n the context of IP telephony. We assume that each node uses Weghted Far Queung (WFQ) schedulers n order to provde Qualty of Servce (QoS) to aggregates of traffc. All voce traffc destned for a certan output nterface s aggregated nto a sngle queue. When a voce flow traverses a node, ts packets are placed n ths queue; whch s draned at a certan rate, determned by a weght assocated wth that queue. Ths paper shows how to set ths weght such that the edge-router-to-edge-router queung delay n the DffServ network s statstcally bounded. The nodes are modeled as M/G/ queung systems and a heurstc formula s used to compute a quantle of the queung delay. Ths formula s compared wth results derved from smulatons. It s also shown how to use ths result to allocate the approprate resources n a DffServ network and how to update and process SVP messages at the edge of a DffServ network n an IntServ over DffServ scenaro. Keywords DffServ, WFQ, Voce over IP (VoIP), resource allocaton.. ITODUCTIO IP s currently one of the enablng technologes for mult-servce networks. These networks may, among other servces, provde telephony servces smlar to the current PTS. Because real-tme voce traffc has very strct delay requrements a certan Qualty of Servce (QoS) s requred n the network wth regard to bandwdth, delay and packet loss. One of the QoS archtectures ntroduced by the IETF s the Dfferentated Servces (DffServ) model []. In ths archtecture traffc requrng the same forwardng behavor s aggregated nto a sngle queue. For example, there may be separate queues for real-tme and data traffc. Packets are classfed based on ther DffServ Code Pont (DSCP) to put them nto the correct queue. However, a sngle queue for all real-tme (voce, vdeo) traffc s not lkely to be suffcent. In [5] t s shown that mxng voce and MPEG vdeo Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, or republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee. OSSDAV, June 25-26, 2, Port Jefferson, Y. Copyrght 2 ACM // $5.. traffc n the same queue has a serous mpact on the delay performance of the voce traffc. Hence, t s advantageous to put voce traffc n a dfferent queue from, for example, hghly varable vdeo traffc. A scheduler s needed n order to guarantee throughput and delay to the dfferent aggregate flows n the system. In [] the maxmum load of the voce queue s determned when a Head of Lne (HoL) prorty scheduler s used, whle adherng to a certan statstcal delay constrant. However, snce the HoL scheduler can completely starve the servce gven to the best-effort data queue we wll consder class-based Weghted Far Queung (WFQ). For WFQ the queung delay wll be larger than for HoL prorty schedulng but when WFQ s used the best-effort data queue s guaranteed a mnmum servce rate. Ths s because the voce queue s only served at a fracton of the lnk capacty as opposed to HoL where the complete lnk capacty s n prncple avalable for voce traffc. The queung delay s strongly mpacted by the weght assgned to the voce queue [5]. Dmensonng the bandwdth (.e. settng the weght) for the voce traffc s therefore of great concern. The dejtterng buffer at the recever has to compensate for the queung delay. When a statc dejtterng delay s used t should be chosen equal to the maxmum, or a quantle, of the queung delay. Ths paper focuses on (statstcal) delay guarantees for voce traffc snce telephony s a hghly delay-senstve applcaton. Adaptve codng s not consdered n ths paper snce t can result n a varable voce qualty, whch s not desrable n many cases. The contrbuton of ths paper s twofold. Frst, t s shown how to set the weghts of a WFQ scheduler n a DffServ router such that a certan delay bound s met. Secondly, t s shown how ths delay analyss can be appled n the context of IntServ/DffServ nterworkng scenaros [2] where SVP sgnalng s used to collect delay nformaton of the end-to-end path and to make resource reservatons. The rest of ths paper s organzed as follows. In secton 2 the model for the aggregated voce traffc s ntroduced. The consdered router archtecture s descrbed n secton 3. The analyss to calculate the queung delay s presented n secton 4. Smulaton results to verfy the formula are presented n secton 5. The obtaned formula s used n secton 6 to calculate the maxmum load for dfferent delay constrants. Secton 7 shows how these results can be appled for an IntServ/DffServ nterworkng scenaro where SVP s used for QoS sgnalng. Fnally, conclusons are drawn n secton 8.

2 2. VOICE TAFFIC MODEL When voce s transported over packet-based networks the analog voce s frst sampled (usually at 8 khz) and s then (lnearly) quanttzed. The next step s to encode ths dgtal voce sgnal. After encodng, one or more codewords are grouped and a packet header s attached. The packetzaton delay s defned as the tme to fll a packet wth voce codewords. The header of an IP packet conssts of IP/UDP/TP overhead and has a sze of 4 bytes (S OH =32 bt). Ths overhead makes that the bandwdth needed n the network s larger than the codec bt rate. The voce packet sze M s related to the bt rate of the codec cod, the header overhead S OH and the packetzaton delay T pack as follows M = ( cod T pack ) + S OH [bt] () In Table several standardzed codecs are lsted that may be good canddates for use n Voce over IP (VoIP) applcatons. The bt rate and the granularty are shown for each codec. The granularty s determned by the duraton of the voce sgnal nterval that s encoded n just one codeword. The packetzaton delay s always a multple of the granularty of the codec that s used. CODEC Btrate Granularty [kb/s] [ms] G G / 24 / 32 / 4.25 G / G G / GSM-F 3 2 Table : Bt rates and granularty of codecs The bt rate of the lsted codecs s fxed. Multrate codecs, e.g. the Adaptve Mult ate (AM) codec developed for the use n UMTS networks, are not consdered here. The packetzer (IP phone or gateway) has to choose a certan packetzaton delay. Ths wll result n a packet flow wth determnstc packet nterdeparture tmes and fxed packet szes. In [3][4] t s argued that an aggregate of Constant Bt ate (CB) voce flows s well modeled by a Posson process. Moreover, they also state that the superposton of (nearly) CB sources cannot become more bursty than a Posson process. Hence, a Posson arrval process assumpton s worst case wth respect to queung delay for an aggregate of CB voce flows. ote that t s assumed that the dfferent voce packet streams are not synchronzed such that packets do not all arrve at the same tme nstant at the router. Voce sources mght use Voce Actvty Detecton (VAD). In ths case voce packets are only sent durng the talk spurts. Durng the slence perods nothng or occasonally (when the characterstcs of the background nose change) some packets are sent. Voce sources that use VAD are much harder to characterze. However, n [9] a model for the speech pattern s presented for an average nteractve phone conversaton. It s an on-off model wth exponental dstrbuted length of the on- (speech) and off- (slence) perods. When several on-off sources are aggregated the resultng process depends on the consdered tme-scale [2]. Over small tme scales the process wll behave as a Posson process but over longer tme scales t wll become more bursty than a Posson process. The relevant tmescale of the arrval process (.e. whether t behaves as a Posson process or not) depends on the maxmum queung delay. In case the Posson assumpton holds, the analyss presented here can be appled. Determnng over whch tme scale such a Posson assumpton holds for an aggregate of on-off sources s a study on tself and beyond the scope of ths paper. 3. QUALITY OF SEVICE In ths paper we assume that the DffServ routers use WFQ schedulng to support QoS. Hence, all voce traffc destned for a certan output nterface s aggregated nto a sngle queue. Due to the tght delay constrants of telephony t s not recommended to mx voce and vdeo traffc. The delay wll ncrease sgnfcantly when voce traffc s mxed wth, for example, MPEG vdeo traffc [5][7]. In Fgure a system s shown wth queues for dfferent applcatons. Classfer Voce queue Vdeo queue Data queue φ voce φ φ data φ C φ vdeo Clnk φ C lnk WFQ lnk C lnk Fgure : Class Based Weghted Far Queung The classfer reads the DffServ code pont n the IP header to determne whether the packet should be put n the voce or n another queue. Each queue s assgned a weght φ such that a certan mnmum servce rate s guaranteed to that queue. Ths capacty assgned to voce traffc s denoted by C voce and s gven by C voce φvoce = C φ lnk Unused bandwdth wll be shared n a far manner among the backlogged queues. We assume however that there s always data to be processed n the other queues. Ths assumpton can be justfed by the fact that data sources are TCP controlled and wll always try to utlze the avalable bandwdth completely. In the next secton only the voce queue s consdered. The voce queue can be studed n solaton from the other queues because t s assgned a mnmum amount of guaranteed bandwdth that s ndependent of the traffc n the other queues of the system. Hence, wth B voce defned as the average bt rate of the aggregate of voce flows the load of the voce queue s gven by (2) Bvoce ρ = (3) φvoce Clnk φ

3 4. ED-TO-ED DELAY AALYSIS In order to provde IP telephony servces wth PST qualty t s very mportant to keep the mouth-to-ear delay wthn acceptable bounds. Ths delay conssts of several components that are dscussed n 4.. It s especally mportant to keep the queung delay under control snce t has to be compensated for n a dejtterng buffer. In 4.2 a method s ntroduced to calculate the queung delay n a DffServ network where WFQ schedulers are used. 4. Mouth-to-ear delay An mportant parameter for nteractve voce communcatons s the Mouth-to-Ear (M2E) delay. Ths s the tme between the moment the sendng party has spoken a word and the moment t s heard by the recevng party. The M2E delay conssts of a determnstc and a stochastc part. The determnstc part conssts of packetzaton T pack, seralzaton T ser, propagaton T prop, dejtterng T dejtter and other (encodng, decodng etc.) delays T oth. The stochastc part conssts of the queung delay of all traversed nodes. Although the queung delay s a stochastc quantty, we are only nterested n the maxmum queung delay,.e. the delay of the slowest possble packet, because f ths one arrves n tme for play-out, all others do too. For ths maxmum queung delay the absolute maxmum or a reasonable quantle (for nstance the 99% quantle) can be used snce ths s the fracton of packets that arrve n tme. Packets that arrve too late for play-out are consdered to be lost. Packet losses of % or lower are acceptable for voce (dependng on the type of codec and the use of packet loss concealment algorthms). Takng all delay components nto account, the mouth-to-ear delay can be wrtten as T ˆ = T ˆ 2 + T + T + T + T + T (4) m e queue dejtter pack prop An example of a delay dstrbuton s shown n Fgure 2. The tal dstrbuton of the delay s caused by the stochastc queung delay. ser oth s equal to the maxmum queung delay. However, t s questonable whether adaptve dejtterng algorthms can converge fast enough durng the typcal length of a phone call. 4.2 Queung delay It has been proven n [] that the worst case end-to-end queung delay n a network of WFQ schedulers s determnstcally bounded for (r, b) leaky bucket constrant flows, wth r the sustanable rate and b the maxmum burst sze. When the reserved rate n each node s equal or larger than r, the end-to-end queung delay s bounded by b M MTU D ˆ e2 e + ( ) + C (5) b M MTU C lnk reserved rate = maxmum burst sze lnk maxmum voce packet sze number of hops MTU at node Lnk capacty at node The frst term denotes the maxmum queung delay caused by a burst b. Ths term occurs only once because the burst has to be smoothed out just once. The second term denotes the maxmum queung delay n the consecutve nodes. The thrd term takes nto account the non-pre-emptveness of the system. In other words, a data packet may be n servce when a packet of the consdered flow s elgble for servce. However, the delay bound defned above apples only when per flow schedulng s used (.e. IntServ). In DffServ routers traffc wth the same codepont s aggregated n a sngle output queue and splt agan at the next node. Ths s llustrated n Fgure 3. Snce aggregaton takes place at each router, the arrvng traffc wll be bursty at each node. Hence, n the worst case the delay due to bursts occurs n each node on the end-to-end path. P [D>d] Mn. delay Sngle flow queung e.g. 99% quantle Dejtterng delay Delay (d) Fgure 2: Example of a delay dstrbuton The queung delay has to be compensated for n the dejtterng buffer of the recever. Hence, the dejtterng delay should be chosen equal to a quantle of the queung delay n order to prevent packets arrvng too late for play-out. Ths s the delay denoted by the arrow wth the capton dejtterng delay n Fgure 2. The packets wth a delay larger than the specfed quantle may be lost (dependng on the queung delay of the frst packet) because they wll arrve too late for play-out. Adaptve dejtterng algorthms also exst, they estmate the queung delay of the frst packet. When perfect adaptve dejtterng s used the queung and dejtterng delay of each packet Aggregate queung Fgure 3: End-to-end queung scenaros If the aggregated (voce) traffc s bounded by the traffc envelope (r, b ) at the output queue of each node the worst case queung delay s defned by (wth r ) b MTU Dˆ e2e + (6) C b = = lnk reserved rate at node maxmum burst sze at node

4 Due to the Posson assumpton we made for the aggregated voce traffc n secton 2 we model each DffServ node as a M/G/ queung system. A consequence of mxng the traffc as shown n Fgure 3 s that the arrvng traffc s not leaky bucket constrant. Because we consder constant bt rate voce sources we assume the arrval process s Posson. Hence, nstead of the delay caused by a maxmum burst sze at each node, Σ b /, we use a quantle (e.g. 99%) of the queung delay of M/G/ queues n tandem. Because we use a quantle, the delay bound becomes statstcal nstead of determnstc, and hence, s tghter. When a voce packet arrves at an empty queue the maxmum queung delay n the WFQ system s M/. Hence, ths delay has to be added for each node on the path. Fnally, the maxmum error between a WFQ and the Generalzed Processor Sharng (GPS) reference system has to be taken nto account, ths results n the followng (statstcal) delay bound M MTU Dˆ e e Dˆ 2 * M / G / + + (7) = Clnk Where the reserved rate s equal to C voce for all nodes and D ˆ * M / G / s a quantle of the end-to-end delay of M/G/ queues. ote that calculatng a quantle of the end-to-end queung delay provdes a much tghter bound than smply addng the delay quantles of each ndvdual node. For a cascade of M/G/ nodes the (-P) quantle of the delay can be approxmated wth a smple heurstc formula [3] Dˆ = µ + α( P) σ * M / G / (8) The mean µ and standard devaton σ of the total queung delay of a network of dentcal M/G/ nodes are respectvely 2 ρ E[ S ] µ = (9) 2( ρ) E[ S] σ = 2 E[ S ] ρ 2( ) E[ S] ρ 2 ρ E[ S ] + 3( ρ) E[ S] Where E[S] s the (average) servce tme of a packet n one node, n ths case equal to M/. The load ρ s defned n eq. (3). In case of dentcal nodes the factor α(p) can be calculated as E ( P) α ( P) = where E ( P) s the nverse of the Erlang tal dstrbuton of stages [8]. The fact that an Erlang dstrbuton s used should be no surprse. The tal dstrbuton of the delay of one node s approxmated by an exponental dstrbuton. The sum of dentcal exponental dstrbutons results n an Erlang dstrbuton of stages. Detals of the dervaton of eq. (8) can be found n [3]. The heurstc formula can be extended for heterogeneous nodes,.e. nodes wth a dfferent load ρ and reserved rate. However, the factor α(p) and the calculaton of µ and σ have to be modfed. Extendng the calculaton of α(p) for heterogeneous nodes s beyond the scope of ths paper. In the rest of the paper we consder, for llustratve purposes, voce packets wth a fxed sze. Therefore, the M/D/ model s used SIMULATIO In order to verfy the analyss of the prevous secton some smulatons have been done wth OPET smulaton software. 5. Smulaton scenaro and parameters The smulaton scenaro s depcted n Fgure 4. The WFQ system contans a voce and a data queue and s connected to an E3 lnk (34 Mb/s). The aggregate bt rate of the voce traffc s 2 Mb/s. The queue sze for voce s dmensoned such that no packet loss occurs. The smulaton has been done for a sngle hop. Posson source (2 Mb/s) TCP sources Voce queue Data queue WFQ 34 Mb/s Fgure 4: Smulaton scenaro In Table 2 the characterstcs of both the voce and data source are shown. The data sources are TCP controlled. Snce only one hop s consdered t wll be the bottleneck lnk for TCP. Hence, the data queue wll be almost always backlogged. Two TCP sources have been used. One wth short fle transfers and one wth very long fle transfers. Traffc Type Packet sze [byte] Packet rate [pkt/s] Bt rate [Mb/s] voce Posson data TCP Table 2: Traffc sources The smulaton has been repeated for dfferent weght settngs of the voce queue such that the capacty assgned to voce vared from 2. Mb/s to 3.9 Mb/s. Durng the smulaton the queung delay of each voce packet s collected. From these delay values a Tal Dstrbuton Functon (TDF) was constructed n order to determne the (- -3 )-quantle and a maxmum value. The smulated tme s 6 seconds (.e. 6*25 voce packets). 5.2 Smulaton results For each settng of the weght for the voce queue a TDF was constructed from the smulaton data. As an example, the TDF for weght settng of 2.2 Mb/s for voce s shown n Fgure 5. P[D<d] Delay [ms] Fgure 5: TDF of the queung delay

5 Three regons can be dstngushed n the TDF depcted n Fgure 5. The frst one s due to seralzaton delay of a 2 byte voce packet (.5 ms). The second regon, between.5 and.8 ms, s due to a data packet that s n servce. Ths s captured by the MTU term n eq. (7). The resdual servce tme of the data C lnk packet s unformly dstrbuted, and hence, there s a straght lne n the CDF. The thrd part, delay larger than.8 ms, s the delay due to contenton wth other voce packets. Ths delay component M s captured by the term D ˆ * M / G / + n eq. (7). For the dfferent smulatons the weght of the voce queue was vared such that the bt rate assgned to voce vared between 2. Mb/s and 3.9 Mb/s. Each smulaton has been repeated several tmes wth a dfferent seed for the random generator. From each smulaton the (- -3 )-quantle and the maxmum of the queung delay was determned. The dfferent obtaned values for the (- -3 )-quantle were averaged and from the maxmum values of each smulaton the largest value was taken. The smulaton results are presented n Fgure 6 together wth the theoretcal values calculated wth eq. (7). The load of the voce queue s defned by eq. (3) wth B voce =2 Mb/s and C lnk =34 Mb/s. queung delay [ms] Theoretcal (e-3 quantle) Smulaton (e-3 quantle) Smulaton (max. value) analyss s too pessmstc. However, t s always an upper bound n the consdered cases. For loads larger than 8% the bound s tghter. Hence, the analytc formula provdes an easy and effcent way to determne the weght for voce traffc n a WFQ system such that the queung delay requrement s met. 6. ESULTS Eqs. (7) and (8) can be appled to determne the maxmum tolerable load as a functon of the weght assgned to the voce queue under a certan delay constrant. In order to calculate ths maxmum load eq. (7) has to be nverted (numercally) wth respect to ρ,.e. the tolerable load has to be calculated as functon of a gven (-P)-quantle of D e2e. In Fgure 7 and 8 the maxmum tolerable load s shown as a functon of the fracton of the lnk capacty assgned to the voce queue for respectvely = and =8. These curves are made for a (- -3 )-quantle of 5 ms for the queung delay, a data MTU of 5 bytes and a fxed packet sze for voce of bytes. Curves are shown for lnk capactes C lnk up to 3 Mb/s. When the number of hops s ncreased the maxmum load of the voce queue decreases because the delay budget for queung has to be shared among more nodes. Load Weght 2 Mb/s 3 Mb/s 5 Mb/s Mb/s 3 Mb/s Fgure 7: Maxmum load as a functon of the weght for a queung delay bound of 5 ms (=) :HLJKWÃYLFHÃTXHXH Fgure 6: Smulaton results From the comparson n Fgure 6 t can be concluded that the calculated quantle gves an upper bound on the delay. Especally for lower loads t s too pessmstc. However, for hgh loads the calculated bound s tghter. Ths s also due to the larger confdence ntervals. The analyss and the smulaton dffer for two reasons. Frst, the delay measured n the smulaton s a drect quantle whle n eq. (7) only the frst term s a quantle and the other two terms are worst case. Hence, a calculated quantle wll always be somewhat hgher than the real value. Second, the data queue becomes empty sometmes (for example between two consecutve fle transfers). The extra avalable capacty s then assgned to the voce queue, whch wll result n a decrease of the effectve load. In the smulaton the data queue was empty for % of the tme. Ths wll result n a lower queung delay. Summarzng, the analytcal method to calculate the queung delay gves a reasonable delay approxmaton. For low loads the Load Weght Mb/s 5 Mb/s 2 Mb/s 3 Mb/s 5 Mb/s Fgure 8: Maxmum load as a functon of the weght for a delay bound of 5 ms (=8) The bt rate of the voce aggregate can be calculated wth the nverse of eq. (3) when the maxmum tolerable load and the weght assgned to the voce queue are known. When the bt rate of a sngle voce source s known the maxmum number of smultaneous calls can be determned.

6 As an example, we assume that all voce flows use 32 kb/s codecs (e.g. G.726) and use a packetzaton delay of 3 ms. Wth a IP/UDP/TP header of 4 bytes ths results n a gross bt rate of approxmately 43 kb/s and a packet sze of 6 bytes. The MTU of data traffc s assumed to be 5 bytes. In Fgure 9 and the maxmum number of calls s shown as a functon of the weght assgned to the voce queue n case of a lnk rate of Mb/s for respectvely = and =8. Curves are shown for dfferent delay bounds. Increasng the capacty reserved for voce ncreases the number of voce flows that can be supported. From Fgure 7 and 8 t s clear that ncreasng the weght wll also cause the maxmum tolerable load to ncrease. Ths results n curves (Fgure 9 and ) that ncrease more rapdly than just lnearly, especally for small delays. It can also be noted that t s very mportant to do strct Flow Admsson Control (FAC). The curves n Fgure 9 for the delay of 9 ms and 5 ms are very close to each other. Hence, ths mples that acceptng a few calls more n ths regon wll result n a drastc ncrease of the queung delay. Max number of calls Weght 2 ms 3 ms 5 ms 9 ms 5 ms lmt Fgure 9: Maxmum number of calls as a functon of the weght of the voce queue (lnk capacty Mb/s, =) Max number of calls Weght 5 ms 2 ms 3 ms lmt Fgure : Maxmum number of calls as a functon of the weght of the voce queue (lnk capacty Mb/s, =8) 7. VOICE OVE DIFFSEV ETWOKS Ths secton shows how the results obtaned n the prevous secton can be appled n the context of voce over DffServ networks. As an example we consder a DffServ network n an IntServ/DffServ nterworkng scenaro [2]. In ths case the DffServ network s treated as a sngle IntServ hop. Hence, when SVP s used for QoS sgnalng the edge routers of the DffServ network should be SVP aware. They also have to mantan perflow state nformaton snce SVP makes soft-state reservatons. Ths scenaro s depcted n Fgure. SVP PATH message SVP aware border router Flow admsson control esource management Update of C/D delay terms DffServ network SVP aware border router Fgure : DffServ network wth SVP aware edges The edge routers have to perform several functons. Frst, they have to update the SVP PATH message wth the approprate delay terms. The rate dependent delay term C should not be ncreased snce the delay n the DffServ network s not dependent on the rate of a sngle flow. The rate ndependent delay term D should be ncreased wth a quantle of the edge-to-edge delay. Ths delay can be calculated wth the method presented n ths paper. Second, the router has to perform resource management,.e. performng flow admsson control such that the traffc does not exceed the avalable resources n the network. Ths flow admsson control s done by acceptng or rejectng the SVP ESV message. In order to support voce over DffServ a few steps have to be taken. The frst one s to provson the network properly. Between each ngress and egress node a bt ppe has to be provsoned. The capacty of ths bt ppe should take delay and the call blockng probablty nto account. Ths can be done by usng the statstcs of the bt rate of voce traffc durng busy hour. Ths bt rate should be ncreased such that the blockng probablty s low enough by applyng the Erlang B formula for example. ow, a certan edge-to-edge delay has to be chosen for the bt ppe. By usng fgures lke Fgure 9 and the approprate weght that has to be set can be determned. Secondly, every edge routers should store the bt rate avalable for voce traffc and the queung delays to all other edge routers. The delay nformaton s requred to update the D term n the SVP PATH message and the capacty allocated for voce s needed n order to perform flow admsson control. When a SVP reservaton message s receved the flow admsson crteron s xy p + p C () Where p s the peak rate of the already accepted flows between the edge node x and y and p s the peak rate of the flow for whch the resources are requested. C xy s the capacty avalable for voce traffc (.e. equal to B voce n eq. (3)). ote that the reserved rate n the DffServ network (.e. C voce ) s larger than C xy n order to guarantee a certan maxmum queung delay and a certan blockng probablty (C xy =ρ C voce ). When the crteron of () cannot be satsfed, the SVP reservaton request should be rejected.

7 8. COCLUSIOS In ths paper the maxmum load of a voce queue n a WFQ system was determned under a certan delay constrant. Ths was done by modelng each node as a M/G/ queung system. The formula to calculate the worst case queung delay n a WFQ system was extended by usng a heurstc formula to calculate a quantle of the queung delay over dentcal nodes. Ths results n a much tghter delay bound for two reasons. Frst, the bound s statstcal and not worst case. Secondly, a quantle s calculated from the delay dstrbuton over nodes nstead of addng the delay quantle of each node. The formula was compared wth results from smulatons. The calculated delay quantle s hgher than the one obtaned from smulaton. However, the bound becomes better for larger loads of the voce queue. The analytcal method presented n ths paper provdes a tool to allocate (.e. assgnng the correct weght to the voce queue) the approprate resources for voce traffc n order to guarantee a certan delay bound. Ths can, for example, be used n a DffServ/IntServ nterworkng scenaro. In ths case the edge routers of the DffServ cloud are SVP-aware and bt ppes are provsoned between the ngress and egress nodes. When SVP PATH messages are receved the rate ndependent delay term D should be updated wth a quantle (e.g. 99%) of the edge-to-edge queung delay. Ths delay value can be calculated wth the method presented n ths paper. The rate-dependent delay term C should not be modfed. When a certan bt ppe between an ngress and an egress node s saturated t wll start rejectng SVP reservaton requests. Future work wll nclude the extenson of the heurstc formula for the heterogeneous scenaro,.e. non-dentcal nodes. Ths nvolves modfcaton of the factor α(p) n eq. (8) and the calculaton of µ and σ. However, once the formula has been extended the method presented here n ths paper can stll be used. 9. ACKOWLEDGEMETS Ths work was carred out wthn the framework of the project LIMSO, sponsored by the Flemsh nsttute for the promoton of scentfc and technologcal research n the ndustry (IWT). We would lke to thank Stefaan De Cnodder for provdng the necessary smulaton models.. EFEECES [] S. Blake, D. Black, M. Carlson, E. Daves, Z. Wang and W. Wess, An Archtecture for Dfferentated Servce, FC 2475, December 998. [2] Y. Bernet et al., A Framework for Integrated Servces Operaton over Dffserv etworks, FC 2998, ovember 2. [3] T. Bonald, A. Proutère and J.W. oberts, Statstcal Performance Guarantees for Streamng Flows usng Expedted Forwardng, Proceedngs of IFOCOM 2, Volume 2, pp. 4-2, Anchorage (AL), USA, Aprl 2. [4] F. Brchet, L. Massoulé, J.W. oberts, Stochastc Orderng and the oton of eglgble CDV, Proceedngs of ITC 5 (Washngton), pp , Washngton, June 997. [5] M.J.C. Büchl, D. De Vleeschauwer, J. Janssen, A. Van Moffaert, G.H. Pett, On the Effcency of Voce over Integrated Servces usng Guaranteed Servce, Proceedngs of the 2 nd IP-Telephony Workshop (IPTEL 2), pp. 6-3, ew York Cty (Y), 2-3 Aprl 2. [6]. G. Garoppo, S. Gordano, S. ccoln and F. usso, A Smulaton Analyss of Aggregaton Strateges n a WF 2 Q+ Schedulers etwork, Proceedngs of the 2 nd IP Telephony workshop (IPTEL 2), pp. 2-7, ew York Cty (US), 2-3 aprl 2. [7] M.J. Karam and F.A. Tobag, Analyss of the Delay and Jtter of Voce Traffc Over the Internet, Proceedngs of IFOCOM 2, Volume 2, pp , Anchorage (AL), USA, Aprl 2. [8] L. Klenrock, Queueng Systems, Volume I: Theory, John Wley & Sons, 975. [9] H.H. Lee and C.K. Un, A Study of On-Off Characterstcs of Conversatonal Speech, IEEE Transactons on Communcatons, vol. COM-34, o. 6, pp , June 986. [] M. Mandjes, K. van der Wal,. Kooj, H. Bastaansen, End-to-end Delay models for Interactve Servces on a Large-Scale IP etwork, Proceedngs of the 7th workshop on performance modellng and evaluaton of ATM & IP networks (IFIP99), 28-3 June 999. [] A.K. Parekh and.g. Gallager, A Generalzed Processor Sharng Approach to Flow Control n Integrated Servces etworks: The Multple ode Case, IEEE/ACM Transactons on etworkng Volume 2 r. 2, pp. 37-5, Aprl 994. [2] K. Srram and W. Whtt, Characterzng Superposton Arrval Processes n Packet Multplexers for Voce and Data, IEEE journal on selected areas n communcatons, vol. SAC-4, o. 6, pp , September 986. [3] D. De Vleeschauwer, G.H. Pett, S. Wttevrongel, B. Steyaert, H.Bruneel, An Accurate Closed-Form Formula to Calculate the Dejtterng Delay n Packetsed Voce Transport, Proceedngs of the IFIP-TC6 /European Commsson Internatonal Conference ETWOKIG 2, pp , Pars (France), 4-9 May 2.