Comprehensive performance model of differentiated service with token bucket marker

Transcription

1 Comrehensive erformance model of differentiated service with token bcket marker H. S and M. Atiqzzaman Abstract: Differentiated services (DiffServ) networks se two tye of roters: edge roters mark the acket headers according to their service rofile while the core roters imlement qee management to rovide service differentiation between ackets according to information in their acket headers. Most revios stdies on the erformance of DiffServ have considered either the effect of the edge marking scheme or the effect of core qee management on the throght of TCP alications. To stdy the combined effect of marking at the edge roter and qee management at the core roter on the erformance of DiffServ the athors roose a simle model that takes into consideration the committed information rate and maximm allowed brst size of the marker in addition to the nmber of flows in an aggregate rond tri time and the robability of a acket droing at the core network. Observations from the model are resented and simlations were erformed to validate the accracy of the model. The model shows that the erformance of DiffServ is largely flow-based rather than desired-aggregate-based and the DiffServ network sffers from nfairness isses. 1 Introdction The Internet has sccessflly rovided a worldwide data commnication service for the ast few decades. However it does not rovide any qality of service (QoS) garantee to alications. Emerging new service tyes sch as real-time adio/video alications demand QoS sort from the Internet. The differentiated services (DiffServ) network [1] is crrently being develoed by IETF to rovide coarsegrained QoS to Internet alications. Instead of roviding a garantee to individal flows which may case scalability roblems DiffServ rovides statistical QoS to a few redefined service classes over a long time scale. In a DiffServ network a service sbscriber first sets a service rofile with an Internet service rovider (ISP) regarding the desired tye of service. At the ingress of the DiffServ network edge roters classify all ackets assing throgh them into several redefined service classes and mark the ackets with different dro recedences (sch as in/ot ackets) [1] according to the sbscriber s service rofile. The traffic that conforms to the service rofile are marked with low dro riority and will receive better service while the nonconformant art of the traffic are marked with high dro riority and receive a best effort service. The token bcket marker is one of the most commonly sed markers in edge roters. Variants of the token bcket marker [ 3] were roosed to mark ackets with mltidro riorities. Service differentiation of ackets is rovided by core roters by sing an active qee r IEE 003 IEE Proceedings online no doi: /i-com: Paer first received 5th Aril and in revised form 11th December 00 H. S is with the School of Comting Armstrong Atlantic State University Savannah Georgia USA M. Atiqzzaman is with the School of Comter Science University of Oklahoma Norman OK USA management scheme [4] sch as RED with in and ot (RIO) [5] according to the reassigned service classes and dro recedences carried in the acket headers. Althogh Diffserv overcomes the scalability roblem fond in revios roosals to rovide QoS to Internet alications the extent to which the service goals of DiffServ can be achieved is still ncertain. Many recent research reslts have shown that the service goals romised by the DiffServ network are not likely to be achieved in many sitations [6 7] de to the TCP congestion control algorithm [8] which was develoed for the best effort service and has no knowledge abot the riorities of ackets. It is well known that for a long-lived TCP flow nder the assmtion of constant rond-tri time (RTT) and low to medim eriodic acket losses the TCP congestion control window (CND) follows a saw-tooth like attern. Based on this assmtion Mathis et al. [9] described the behavior of a single TCP flow by B ¼ ðmssþc ffiffiffi ð1þ ðrtt Þ where MSS is the maximm segment size RTT is the rond-tri time is the robability of acket loss in the network and c is a constant. Under the assmtion that acket losses are eriodic and the destination acknowledges every acket c is eqal to 3=. This model catres only the congestion avoidance hase of the TCP congestion control algorithm [8]. Padhye et al. [10] develoed a more accrate model by considering both congestion avoidance and retransmissions cased by time ot. Althogh the reslt of the latter is more accrate the reslt is not as intitive as the former one. Yeom and Reddy [11] have extended Padhye s work to evalate the erformance of a DiffServ network while Baines et al. [6] have extended Mathis s work to model a DiffServ network. Their reslts and conclsions were similar. Althogh the effect of the committed information IEE Proc.-Commn. Vol. 150 No. 5 October

2 rate (CIR) was considered in both aers [11 6] eitherof them considered the effect of the marker settings on the erformance of DiffServ. As a basic bilding block of the DiffServ roosal markers lay an imortant role in achieving the service goals of DiffServ [1]. Research on DiffServ markers [7 1] has shown that the choice of markers and their settings have a significant effect on the erformance of DiffServ. In this aer we incororate the effect of token bcket marker settings in or roosed model. e develo a simle yet accrate DiffServ erformance model that incororates the two reqired arameters of a token bcket marker viz. the CIR and maximm allowed brst size (B). In contrast to revios stdies or roosed model integrates the effect of token bcket marker settings acket droing robabilities in the core network and the nmber of flows in a traffic aggregate. e focs on modelling the erformance of a DiffServ network with a token bcket marker in the resence of mltile flows in an aggregate. Based on or roosed model and simlations we find that the erformance of a DiffServ with a token bcket marker nder TCP congestion control algorithm is flow based rather than the desired aggregate based. This leads to nfairness roblems among sorces having different nmber of flows er aggregate. Proosed model e first describe the assmtions and notation sed in or model..1 Assmtions In this aer we assme that the loss in the DiffServ network is low to medim and is eriodic. Periodic loss means that whenever the TCP congestion control window reaches some maximm window size a acket loss occrs. e also assme constant rond-tri times for ackets. It is well known [8 9] that nder these assmtions the TCP congestion control window follows a erfect saw-tooth like attern as shown in Fig. 1. Althogh this assmtion may not be tre in the real world simlation reslts in Section 3 show good accordance with reslts from the model and or roosed model is simle and intitive. It shold be noted that this assmtion has also been sed and validated by revios researchers [6 9]. (measred in ackets) Fig. 1 CND AS / CS transmitting cycle / ot ackets in ackets e also assme all TCP flows from a sorce go to the same destination (i.e. all flows belonging to an aggregate Congestion window in largely over-rovisioned network exerience the same RTT and have the same MSS. Under this assmtion all flows in an aggregate will share the network resorce fairly and will enconter the same loss. The bandwidth achieved by an aggregate emitting n flows with different RTT and MSS has been shown [6 9] to be given by X n ðmss i Þc ffiffiffiffi ðrtt Þ i¼1 i i where n is the nmber of flows from a sorce i is the acket dro robability in the network for the ith flow and c ¼ 3= for eriodic loss. Therefore nder or assmtion of all flows having the same RTT and MSS the bandwidth of an aggregate is given by B ¼ c ffiffiffi ðþ ðrtt Þ. Notations e se the following notation in or model. Flow connection: a flow or connection means a TCP connection going from a TCP sorce to a TCP destination. There may be mltile flows or connections going from a sorce to a destination Aggregate: aggregate refers to the collection of all flows/ connections going from the same TCP sorce to the same TCP destination CND: the TCP congestion window size measred in ackets : maximm congestion window size measred in ackets (see Fig. 1) for a TCP connection. e assme that whenever CND ¼ a acket loss occrs and CND is redced to / after which CND increases by one segment er RTT. It will therefore take / time nits for CND to reach again B: achieved bandwidth in bytes er second (byte/s). This reresents the average bandwidth achieved by an aggregate MSS: maximm segment size in bytes AS: average congestion window size of a TCP connection measred in ackets. It is defined as the average vale of the congestion window size and reflects the average bandwidth obtained by a TCP flow. It can therefore be exressed as (B)(RTT)/MSS for an aggregate with single flow. From Fig. 1 it can also be exressed as (3/4). Therefore AS ¼ ðb ÞðRTT Þ MSS ¼ 3 4 ð3þ Transmitting cycle: a cycle dring which CND goes from / to (see Fig. 1). In each cycle there are (/) +(1/)(/) ¼ (3/8) ackets being transmitted. Also we know that there are 1/ ackets being transmitted in one cycle de to the eriodic loss assmtion [6]. Sowe obtain sffiffiffiffiffiffi 8 ¼ ð4þ 3 CIR: committed information rate in bytes er second is the desired bandwidth of an aggregate. It is also sed as the token arrival rate of the token bcket marker 348 IEE Proc.-Commn. Vol. 150 No. 5 October 003

3 CS: committed window size for a TCP flow in ackets which is defined as CS ¼ ðcirþðrtt Þ ð5þ MSS for an aggregate with single flow. It is the eqivalent of CIR in TCP congestion control window diagrams P MIn P MOt : in and ot ackets marking robabilities resectively. They reresent the robability that an in or ot acket will be marked by the token bcket marker. For the in / ot acket marking scheme P MIn ¼ 1 P MOt B: token bcket size measred in bytes B : token bcket size measred in ackets i.e. B ¼ B ð6þ MSS i o : in and ot acket droing robability resectively in the core network. They can be measred by many network tools : total acket loss robability in the core network. This incldes loss of both low and high riority ackets. The total ackets loss robability in the core network can be exressed as ¼ðP MIn Þ i þðp MOt Þ o ¼ i þ P MOt ð o i Þ ð7þ Maximm effective token bcket size: minimm of the maximm ossible accmlated tokens in one transmitting cycle and the token bcket size. Since we assme that the network resorce is fairly shared among all flows in an aggregate therefore for an aggregate with n flows (3) (5) and (6) can be rewritten for individal flows as AS ¼ ðb ÞðRTT Þ ¼ 3 4 CS ¼ ðcirþðrtt Þ B ¼ B ð8þ ð9þ ð10þ.3 Model The main task in develoing or model is to exress the acket loss robabilities P MIn and P MOt as a fnction of CIR and B i.e. finding the relationshi between the acket loss robability and the token bcket arameters. To hel s find this relationshis we divide the congestion window into for regions deending on the vale of CS in Fig. 1. (i) Region CSo/: By sbstitting (8) and (9) into it we can exress CIR forthisregion asciro(b)/3. This corresonds to a network that is largely over-rovisioned with the total CIR mch less than the available bandwidth. e call this network largely over rovisioned. (ii) Region /rcsras: Again with the hel of (8) and (9) we find that this bondary condition is eqivalent to (B)/3rCIRrB. Clearly the network is oerating almost at its fll caacity. e call it a nearly rovisioned network. (iii) Region ASrCSr4(AS)/3: For this region BrCIRr4(B)/3. The level of network rovisioning is slightly higher than the available bandwidth; we call it a slightly nder rovisioned network. (iv) Region CS44(AS)/3: we have CIR44(B)/3 which means that the network is largely nder rovisioned. e call it a largely nder-rovisioned network. e will now derive or model for all these for regions..3.1 Largely over-rovisioned network (CSo /): As shown in Fig. 1 de to the fact that CS is less than / (the minimm window size) in this regision it is easy to see that the token bcket is always emty nder revios assmtions (recall that token arrival rate at the marker is sally set to CIR). So in this region the token bcket size setting B does not have any effect on the achieved bandwidth and all ackets above CS will be marked as ot ackets. Note that the robability that a acket is marked as an ot acket is given by the ratio of all ackets marked as ot sent dring a cycle to the total nmber of ackets sent dring that cycle. Therefore the robability of a acket being marked as ot in this region is (see Fig. 1 for reference) P MOt ¼ ð3=8þð Þ ðcsþð =Þ ð3=8þð Þ ¼1 4ðCSÞ ð11þ 3ð Þ Sbstitting this together with (4) into (7) and solving for 1= ffiffiffi we obtain (note that we only need the ositive root) 1 ffiffiffi ¼ CS o i þ c o sffi CS o i þ 1 ð1þ c o o where c ¼ 3=. Sbstitting this together with (9) into () and after simlification we obtain B ¼ CIR o i þ o s ffiffiffi CIR o i þ c ð13þ o ðrtt Þ o Note that in this region the droing robability of in ackets in the DiffServ core is very small becase of the low network load. If we assme i ¼ 0 we can simlify (13) to sffiffiffi B ¼ CIR þ CIR þ c ð14þ ðrtt Þ o.3. Nearly rovisioned network (/rcsr AS): In this region for each cycle if the window size is less than the CS all ackets will be marked as in ackets and tokens can be accmlated in the token bcket for ftre sage. However if the window size is greater than CS we assme that all the committed art of the traffic will be marked as in ackets. If there are enogh tokens accmlated in the bcket the excess ackets will be marked as in ackets; otherwise they will be marked as IEE Proc.-Commn. Vol. 150 No. 5 October

4 ot ackets. Therefore the setting of B has an effect on B in this region. Note that dring a transmitting cycle tokens can only be accmlated in the bcket if CNDoCS. Therefore the maximm ossible accmlated tokens for a cycle can be given by (1/)(CS /) asshowninfig..ifb Z(1/)(CS /) the excess bcket size (B (1/)(CS /) )has no effect on the reslt. e frther sbdivide this region into two small regions deending on the vale of B. (measred in ackets) Fig. CND AS CS / bcket size B maximm effective bcket size Case 1: 0rB r(1/) (CS /) : In this region the robability of ackets being marked as ot ackets is given by the ratio of ackets exceeding CS B and the total amont of transmitted ackets in a cycle i.e. P MOt ¼ ð1=þð CSÞ B ð3=8þ ð15þ Using similar techniqe as in Section.3.1 we can obtain B as: B ¼ ðcirþ þ b v 3 B ðrtt Þ b t 4 iðcirþ b ð o i Þ þ / ot ackets in ackets ffiffi RTT bð o i Þ ð16þ where a ¼ 8=3 and b ¼ (i )/( o i )+a. In this region it is still reasonable to assme that i ¼ 0. Sbstitting it into (16) we obtain a rather intitive eqation B ¼ 3 4 ðcirþþ v ffiffiffiffiffi " 3 B # 4 ðrtt Þ þ t ð17þ ðrtt Þ o The above eqation will be discssed frther in Section 4. Case : B 4(1/)(CS /) : Using similar reasoning as in case 1 above in this sbregion regardless of the size of B the effective bcket size is (1/)(CS /) ackets; therefore the robability of a acket being marked as Ot is 1 P MOt ¼ ð CSÞ 1 ðcs Þ ð3=8þ ð18þ Congestion window in nearly-rovisioned network! 3 5 As before we can obtain the B as B ¼ CIR o i þ o sffiffiffiffiffi CIR o i þ c o ðrtt Þ o ð19þ.3.3 Slightly nder-rovisioned network (AS rcsr(4/3)as): AsshowninFig.3wealsodivide this region into two sbregions deending on the vale of B. (measred in ackets) Fig. 3 CND CS AS / Case 1: 0rB r(1/)( CS) : In this region the robability of ackets being marked as ot ackets is the ratio of ackets exceeding CS B and the total amont of transmitted ackets in one cycle i.e. 1 P MOt ¼ ð CSÞ B ð3=8þ ð0þ Using similar techniqe as sed in Section.3.1 we can obtain B as B ¼ ðcirþ þ b v 3 B ðrtt Þ b t 4 iðcirþ b ð o i Þ þ / bcket size B ot ackets in ackets ffi ðrtt Þ bð o i Þ ð1þ where a ¼ 8=3 and b ¼ i /( o i )+a. In contrast to earlier cases in this region we cannot assme that i ¼ 0 becase the loss robability of in ackets is large. Case : B 4(1/)( CS) : For this sbregion all ackets will be marked as in ackets. Therefore the robability of ackets being marked as ot is P MOt ¼ 0 ðþ so ¼ i. In this case neither CIR nor B has any effect on achieved bandwidth; the network is indeed a best effort network. The B is (see ()) B ¼ c ffiffiffiffi ð3þ ðrtt Þ.3.4 Largely nder-rovisioned network (CS 4(4/3)(AS)): For this region all ackets will be i maximm effective bcket size Congestion window in slightly nder-rovisioned network! IEE Proc.-Commn. Vol. 150 No. 5 October 003

5 marked as in ackets as shown in Fig. 4. The robability of ackets being marked as ot is P MOt ¼ 0 so ¼ i for this case. Neither CIR nor B has any effect on the achieved bandwidth; the network is indeed a best effort network. The B is given by (see ()) B ¼ c ffiffiffiffi ð4þ ðrtt Þ (measred in ackets) Fig. 4 CND CS AS / This is the same formla sed in modelling the crrent best effort network [9] i.e. the DiffServ network losses it ability to rovide service differentiation. 3 Simlation validation and reslts In this Section we will se simlation to validate the accracy of or model. A set of simlations have been erformed sing the NS- network simlator [13] with a DiffServ atch from the Nortel Networks (which is now art of the NS- ackage). Figre 5 shows the simlation toology sed in this stdy. There are two TCP sorces: one sends traffic from sorce 0 to destination 0 the other sends traffic from sorce 1 to destination 1 which we call aggregate 0 and aggregate 1 resectively. E0 E1 E are edge roters. E0 and E1 are resonsible for monitoring and marking traffic aggregate 0 and 1 resectively. Both of them se a token bcket marker to mark the traffic. Token arrival rates are set to their CIRs resectively while the token bcket size is set to bytes for both markers. Choosing the above vale of the bcket size ensres that the network goes throgh all the cases mentioned in Section.3 when CIR varies between 1 Mbyte/s and 13 Mbyte/s. S0 S1 Fig. 5 / in ackets In Fig. 5 C1 is the core roter which imlements the RIO scheme. e se the notation {x y z} toreresent minimm threshold maximm threshold and weight arameter resectively of a RED qee [4]. The setting i Congestion window in largely nder-rovisioned network E0 E1 Simlation toology C1 10 Mbyte/s E D0 D1 of the RIO roter is { } and { } for the ot and in ackets resectively for the given set of reslts. e se SACK TCP [14] becase it hels to kee the TCP oerating in the congestion avoidance hase even with a higher loss rate. Also in this stdy all TCP flows are long lived FTP alications with MSS ¼ 1500 bytes and RTT ¼ 40 ms. In the rest of this Section we resent reslts for two cases: single flow and mltile flow deending on whether an aggregate has one or mltile flows. 3.1 Single flow case In this simlation each aggregate has only one flow. The CIR for aggregate 1 is fixed at 1 Mbyte/s while the CIR for aggregate 0 increases from 1 Mbyte/s to 13 Mbyte/s. This corresonds to the network going from over-rovision to nder-rovision. Figre 6 shows the achieved bandwidth against CIR for this simlation. In addition to the measred bandwidth and the estimated bandwidth from or roosed model for both aggregates we have inclded information regarding CIR of aggregate 0 and /3 and 4/3 of measred bandwidth for aggregate 0 in the Figre to ease the nderstanding. To hel the reader to associate the simlation reslts with or roosed model given in Section.3 we divide Fig. 6 into six regions (R1 R6) deending on the relationshi between CIR B and B. achieved bandwidth (x 10 6 ) est. B for aggr. 0 mea. B for aggr. 0 est. B for aggr. 1 mea. B for aggr. 1 CIR for aggr. 0 /3 of mea. B for aggr.0 4/3 of mea. B for aggr.0 R1 R R3 R4 R5 R CIR of aggregate 0 (x 10 6 ) Fig. 6 Achieved bandwidth against CIR of aggregate 0 in single flow case Aggregate 0: For aggregate 0 we divide Fig. 6 into six regions as below. Region R1: In this region CIR of aggregate 0 is between 1 and 4 Mbyte/s. e can see that CIR is less than two-thirds of the measred bandwidth. The estimated bandwidth is calclated sing (13). Althogh the reslts from simlation and model differ slightly they are close. Region R: For this region 4oCIRr5.5 Mbyte/s. B is greater than the maximm effective token bcket size and the estimated bandwidth is calclated sing (19). The simlation and modelling reslts are close. Region R3: ith 5.5oCIRr7.4 Mbyte/s the network is near rovisioned and B is less than maximm effective token bcket size. Eqation (16) has been sed to calclate the estimated bandwidth. The reslts from simlation and model are very close. This means that by taking B into consideration or model gives a very good estimation of the achievable bandwidth in a DiffServ network. IEE Proc.-Commn. Vol. 150 No. 5 October

6 Region R4: For 7.4oCIRr10.4 Mbyte/s model and simlation reslts begin to diverge slowly becase some of the modelling assmtions (for examle the low to medim acket droing robability assmtion) no longer hold. This corresonds to a slightly nder-rovisioned network with a small token bcket case. As CIR increases the amont of traffic aroaches the limit of the bottleneck link and the droing robability increases. Regions R5 and R6: For CIR410.4 Mbyte/s both the estimated and measred bandwidth sto increasing. This corresonds to either the slightly nder-rovisioned network with a large token bcket case or the largely nderrovisioned case. In these two regions the network load exceed its caacity all ackets are in ackets and the network looses its ability to rovide service differentiation Aggregate 1: From Fig. 6 we can see that even at a rather high level of congestion aggregate 1 still achieves its service rate even thogh aggregate 0 does not achieve its contracted rate. It indicates that DiffServ network favors small service rofile sbscribers. This cases an nfairness roblem as will be discssed in Section Mltile flows case In this simlation aggregates 0 and 1 have for and one flows resectively. The CIR for aggregate 1 is still fixed at 1 Mbyte/s while CIR for aggregate 0 increases from 1 Mbyte/s to 13 Mbyte/s. Therefor the network goes from over-rovisioned to nder rovisioned. Figre 7 shows the achieved bandwidth against CIR of aggregate 0 for this simlation. achieved bandwidth (x 10 6 ) est. B for aggr. 0 mea. B for aggr. 0 est. B for aggr. 1 mea. B for aggr. 1 CIR for aggr. 0 /3 of mea. B for aggr. 0 4/3 of mea. B for aggr CIR of aggregate 0 (x 10 6 ) Fig. 7 Achieved Bandwidth lotted against CIR of aggregate 0 in the mltile flows case As in the single flow case reslts from simlation and model are close to each other even at a rather high load. This roves the validity of or roosed model. It shold be noted that when CIRs of aggregate 0 and 1 are all 1 Mbyte/s the bandwidth gained by aggregate 0 is abot for times that gained by aggregate 1. Clearly this is becase of the fact that aggregate 0 has for flows while aggregate 1 has only one. This indicates that the erformance of DiffServ is flow based rather than aggregate based for a largely over-rovisioned network. 4 Observation Several simlations with different sets of RIO arameters and token bcket settings were rn. The reslts of these simlations were similar to those given in Section 3. These simlations validate the accracy of or model. In choosing the combined arameter settings we shold try to make sre that the modelling assmtions made in Section.1 are still valid otherwise the reslts from simlation and model may not be comarable. e now resent some observations based on the roosed model. Observation 1: For largely over-rovisioned network all aggregates can achieve their rofiles and the excess bandwidth is shared among aggregates deending on the nmber of flows in the aggregates MSS RTT etc. This can be exlained by (14) which is coied here for easy reference. In this case we assme that i ¼ 0. sffiffiffi B ¼ CIR þ CIR þ c ð5þ ðrtt Þ o e see that for a largely overrovisioned network each aggregate can achieve its service rate CIR. Theterm c=ðrtt Þ o reflects the amont of excess bandwidth that will be obtained by an aggregate. Clearly an aggregate with more flows (higher vale of n)willbeableto gain more excess bandwidth. For the same vales of RTT and MSS the excess bandwidth is eqally shared among all the flows (considering all the aggregates) instead of aggregates. Simlation of mltile flows case (see Section 3.) verified this observation where at CIR ¼ 1 Mbyte/s for aggregate 0 with the same RTT and MSS the excess bandwidth obtained by aggregate 0 (with for flows) is abot for times that of aggregate 1 (with only one flow). Becase the service charge in a DiffServ network is alied to aggregates rather than flows this creates nfairness among the sbscribers. Sbscribers aying the same charge shold eqally share the excess bandwidth regardless of the nmber of flows in their aggregates. Observation : For a near rovisioned network with a small token bcket size abot three qarters of the CIR is not sensitive to the arameter settings the other art deends on arameter settings sch as B RTT acket loss robability etc. This is drawn from (17). Here we still assme that the acket droing robability of in ackets is small. Eqation (17) is coied here for easy reference v ffiffiffiffiffi B ¼ 3 4 CIR þ 3 " B # 4 ðrtt Þ þ t ð6þ ðrtt Þ o For all aggregates having the same settings aggregates with more flows will acqire more of the excess bandwidth. This eqation also shows that only 3/4 of the sorce s desired service rate is garanteed; the rest deends on the arameter settings. So there is a ossibility that an aggregate with small nmber of flows will not be able to achieve its service rate while an aggregate with a large nmber of flows will receive more bandwidth than its sbscrition. This cases an nfairness roblem. In this region increasing B will slightly increase the achieved bandwidth. Observation 3: There is a trade-off between the token bcket size (B) and the robability of acket droing. Once B exceeds some threshold an aggregate can not get any more bandwidth by frther increasing B. As discssed in Section.3. there is a maximm ossible accmlative token threshold for each congestion 35 IEE Proc.-Commn. 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7 avoidance cycle. Once B reaches this threshold any frther increase in B does not have any effect on the achieved bandwidth. Note that the token bcket size is indeed the maximm allowed brst size. As B increases the traffic becomes more brsty and increases the robability of acket droing at the core roter which in trn leads to a redction in the achieved bandwidth. There is therefore a balance between the setting of B and the robability of acket dro in the core network. This agrees with the simlation reslts in [7]. Observation 4: The erformance of DiffServ is flow-based rather than the desired-aggregate-based. ith same settings an aggregate with more flows acqires more bandwidth than the one with fewer flows. The excess bandwidth is distribted in roortion to the nmber of flows in an aggregate instead of CIRs of that aggregate. This is evidenced in (5) and (6). An aggregate with more flows will acqire more excess bandwidth than aggregates with fewer flows and the excess bandwidth is shared among flows rather than aggregates. As discssed in observation 1 this is not the desired behavior. The nderlying reason for this is that the excess bandwidth is acqired by sending ot ackets. hile the rate of sending in ackets is aggregate-based the rate of sending ot ackets is largely flow based. All these ot ackets exerience the same best effort service casing the excess bandwidth to be shared among flows instead of aggregates. Observation 5: For a slightly nder-rovisioned network with a relative large B or a largely nder rovisioned network the DiffServ network loses its ability to rovide service differentiation de to the fact that all ackets are in ackets. The DiffServ network redces to a best effort network. Large sbscribers lose their services garantee however the small service sbscribers may still be able to achieve their services. For a DiffServ network oerated in this sitation all the romises of the DiffServ are broken. All ackets are in ackets and receive the same service that is similar to what in the crrent internet. It is clear that a well rovisioned network is the recondition for service differentiation. 5 Conclsion e have roosed a new comrehensive model that nlike revios models takes the two main comonents of a DiffServ network; the marker at the edge network and the qee at the core network; into consideration. The effect of flows is also considered in the model. e derived an intitive relationshi among the achieved bandwidth and the CIR maximm brst size or token bcket size B dro robability of in/ot ackets nmber of flows in aggregates and the RTT. Simlations have been erformed to validate the accracy of or model. Reslts from or model roved to be very close to reslts from simlation for both single flow and mltile flow cases. Several observations were made based on or model. Or model can hel network engineers to nderstand the behavior of a DiffServ network. To alleviate the nfairness roblem of DiffServ we strongly believe that new mechanisms sch as aggregate based markers have to be added to the DiffServ site to imrove the network erformance. 6 References 1 Blake S. Black D. Carlson M. Davies E. ang Z. and eiss.: An architectre for differentiated services. RFC 475 December 1998 Heinanen J. and Gerin R.: A two rate three color marker. RFC 698 Setember Heinanen J. and Gerin R.: A single rate three color marker. RFC 697 Setember Floyd S. and Jacobson V.: Random early detection gateways for congestion avoidance ACM/IEEE Trans. Netw (4) Clark D. and Fang.: Exlicit allocation of best effort acket delivery service IEEE/ACM Trans. Netw (4) Baines M. Nandy B. Pieda P. Seddigh N. and Devetsikiotis M.: Using TCP models to nderstand bandwidth assrance in a differentiated services network. Nortel Technical Reort Jly Yeom I. and Narasimha Reddy A.L.: Realizing throght garantees in a differentiated services network. Proc. ICMCS Florence Italy 7 11 Jne 1994 Vol Jacobson V. and Karels M.J.: Congestion avoidance and control. Proc. SIGCOMM 88 Stanford CA USA Agst Mathis M. Semke J. Mahdavi J. and Ott T.: The macroscoic behavior of the TCP congestion avoidance algorithm Comt. Commn. Rev (1) Padhye J. Firoi V. Towsley D. and Krose J.: Modeling TCP throght: A simle model and its emirical validation. SIG- COMM 98 Vancover BC Canada Setember Yeom I. and Narasimha Reddy A.L.: Modeling TCP behavior in a differentiated services network. Texas A&MTechnical Reort May Feng. Kandlr D.D. Saha D. and Shin K.G.: Adative acket marking for roviding differentiated services in the internet. Proc. Int. Conf. on Network rotocols Astin TX USA October Network simlator (ns-). University of California at Berkeley CA USA available via htt:// Mathis M. and Mahdavi J.: Forward acknowledgement: refining TCP congestion control. Proc. SIGCOMM 96 Stanford CA USA Agst IEE Proc.-Commn. Vol. 150 No. 5 October