Modeling Two-Windows TCP Behavior in Internet Differentiated Services Networks

Transcription

1 Modeling Two-Windows TCP Behavior in Internet Differentiated Services Networks Jianhua He, Zongkai Yang, Zhen Fan, Zuoyin Tang Department of Electronics and Information HuaZhong University of Science and Technology, Wuhan, China 4374 Abstract An important issue on Assured Services within Differentiated Services (DiffServ) architecture is that bandwidth guarantee for larger profile flows is broken in the existence of numerous small profile flows. Although strict and accurate admission control mechanisms can improve the performance of bandwidth guarantee, it s difficult to deploy the mechanisms and the cost is also very high. And another issue on fair share of excess bandwidth is not touched at all. Whereas a modified TCP, named two-windows TCP, is proposed to address those issue. The protocol is shown to be effective by simulations. But its effectiveness is not validated theoretically and for general network configurations. Thus in this paper, an analytical model is developed to calculate the steady state throughput achieved by an individual two-windows TCP flows in a DiffServ network. The model characterizes two-windows TCP throughput as a function of contract rate, loss rates of In and Out packets and round-trip time. Extensive simulations validate the analytical model. The performance of two-windows TCP is also compared with that of traditional TCP on the performance of bandwidth guarantee and fair share of unsubscribed bandwidth. To quantify the degree of fair share of excess bandwidth, a performance metric called Fairness Index is introduced. It s shown that two-windows TCP is much better than traditional TCP on bandwidth guarantee and fair share of excess bandwidth. And the performance of two-windows TCP is robust to a wide range of bandwidth subscriptions and RIO ( RED with In and Out ) parameters configurations. Thus it will leverage the burden of admission control mechanism and promote practical deployment of Differentiated Services. I. INTRODUCTION Differentiated Services (DiffServ) architecture receives extensive research interests and is regarded as the most promising solution for the issues of quality of service (QoS) encountered in today s IP networks [][]. It relies on packet tagging and lightweight router support to provide Premium Services (PS) and Assured Services (AS) that extend beyond besteffort services (BE) [][]. In DiffServ architecture, a source specifies a service class (e.g., PS, AS, or BE) and a service profile, which indicates the amount of traffic that the sender negotiates with the service provider to send its packets in the specified class. In particular, the class of AS is designed to give the customers the assurance of a minimum throughput (or rate) during congestion, and allows flows to consume the remaining bandwidth in a fair manner when the network load is low. Thus two major performance metrics for Assured Services to be considered are bandwidth guarantee and fair share of excess bandwidth. Throughput assurance means that each flow should receive its subscribed bandwidth in average. Fair sharing of excess (or unsubscribed) bandwidth means that excess network bandwidth should be evenly shared among AS and BE flows. But simulations reported in [] [] reveal that the quality of Assured Services is affected by many factors, such as network bandwidth, service subscription and so on. And several recent studies [] [3] show that flows with relatively higher bandwidth reservations may achieve lower throughput than subscribed while flows with smaller reservations may realize throughput higher than their. The intrinsic reason is that TCP is originally designed for best-effort services. The achievable TCP throughput is closely related to packet loss rate in the networks. As in the profile of AS, packets from TCP flows with different bandwidth reservations are classified into In (profile) and Out (profile), average packets loss rates of In and Out packets are similar for TCP flows passing the same path. And the loss of an Out packet will decrease the congestion window by half. Then in the case of bandwidth reservation rate being high, packet loss rate of Out packets will be high and has significant impact on the overall TCP throughput. Thus TCP flows with higher bandwidth reservation is more difficult to be guaranteed. To improve the performance of Assured Services on bandwidth guarantee and fairness, various approaches have been proposed by employing strict admission control schemes in the side of networks and introducing transport protocols [4] [5]. While it s hard to implement strict and effective admission control schemes in the cases of bursty network traffic and with inaccurate network information, those issues on bandwidth guarantee and fairness are not likely to be fundamentally solved unless plenty of network bandwidth are provided, which will significantly degrade bandwidth utilization. One the other hand, a modified TCP protocol, named two-windows TCP, is more reasonable and practical [4]. The motivation of the protocol is that while service quality is almost impossible or extremely expensive to be guaranteed only by considerable network designs and managements, it may be significantly improved with combined efforts from both networks and end users. In two-windows TCP, each flow will try to get the subscribed bandwidth, in addition of competing fairly for excess bandwidth. The impact of Out packet losses will not affect the competition of subscribed bandwidth. Thus the fairness issue in AS is well solved even in the case of under-provisioned network. Simulation results also show that bandwidth subscribed by the users are well guaranteed [4]. However, the performance of two-windows TCP is not analytically evaluated, which is important to understand its effectiveness over DiffServ networks in common network conditions. It s the motivation of the paper to propose an analytical model for two-windowstcp, to examine the potential of wide deployment of the protocol over DiffServ networks.

2 Although there are already wide studies on steady-state analytical models for TCP protocols [6] [7], few works investigate TCP behavior in DiffServ networks [8] [9]. In this paper, a conventional analytical approach for calculating TCP throughput is extended to evaluate the performance of the modified TCP protocol under different network situations. The contributions of the work are modelling two-windows TCP analytically, understanding the effectiveness and limitations of the protocol on improving the quality of Assured Services on throughput assurance and fair share of excess bandwidth, which is important for the practical deployment of Differentiated Services. The rest of this paper is organized as follows. Section II surveys the Assured Services architecture and RIO ( RED with In/Out ) mechanism Section III presents the analytical model of two-windows TCP. Section IV presents the simulation results. Section V concludes the paper. II. BACKGROUND In the Assured Services architecture, marking mechanism and queue management are two major components Packet marking mechanism, which includes meters and markers, is implemented in edge routers. It classifies packets as in-profile (In) or out-of-profile (Out) according to service contracts before those packets enter the network. The most commonly used marker algorithms are token bucket (TB) and time sliding window (TSW) The queue management mechanism is used at core routers to differentiate and forward packets based on marking tags and service classes in the packets. Among all the router mechanism proposed for Assured Services, RIO mechanism receives the most attention []. In brief, RIO can be viewed as the combination of two RED instances with different dropping probabilities. Two sets of RED parameters, (minth in/maxth in /maxp in) and (minth out /maxth out/maxp out) are used for In packets and Out packets, respectively. More details on the parameters can be found in []. To improve the quality of Assured Services on bandwidth guarantee, a two-windows TCP is proposed in two-windows TCP [4]. In the protocol, the congestion window ( in the unit of packet), denoted by cwnd, is consisted of two parts. The first part is reserved window, denoted by rwnd. The other is excess bandwidth window, denoted by ewnd. The congestion window is the sum of rwnd and cwnd, cwnd = rwnd + ewnd. Both reserved window and excess bandwidth window response to packets dropping as the congestion window of traditional TCP protocols does. But reserved window only responses to dropping of In packets, and it is limited below value determined by the bandwidth subscription of the flow. Reserved window is introduced in order to protect the reserved rate of flows. Whereas excess bandwidth window responsing to dropping of both Inand Out packets, Out packets are used to compete for the excess bandwidth. When an Out packet is dropped, the modified TCP will not reduce rwnd, such that the reserved rate is reserved. But when an In packet is dropped, which indicates that the network is over-subscribed, then both rwnd and ewnd are reduced. The two-windows TCP congestion avoidance algorithm is shown in Fig.. In the figure, RTT is defined as average round-trip time of TCP connections, and pkt size is defined as average size of packets. Furthermore, some mechanisms to discriminate the losses of In and Out packets for two-windows TCP are also proposed in [4]. For simplicity, those mechanisms are not taken into account in the analytical model and simulations in this paper. : After every packet loss detected : if (Out packet loss) { 3: rwnd = RTT reserved rate/pkt size; 4: if (rwnd < cwnd) { 5: ewnd = cwnd rwnd; 6: cwnd = rwnd + ewnd/; 7: } 8: } 9: else { // In packet loss : cwnd = cwnd/; : } Fig.. Two-windows TCP congestion avoidance algorithm Before presenting the analytical model, some assumptions are made as follows.. The marker is ideal, which means that every packet is marked as In when cwnd rwnd; a packet is marked as In with the probability rwnd/cwnd, when cwnd > rwnd.. The sender always has data to send. 3. The receiver window is never reached. 4. One packet is acknowledged by one ACK. 5. There is no ACK drop. 6. Loss ratio of In packet is much less than that of Out. 7. Contribution of packet loss to throughput is negligible. Similar assumption has been made for modelling TCP throughput in [9]. It clear that a TCP flow s sending rate averaged in each RTT interval is cwnd pkt size/rtt, which is in the unit of bit per second. Furthermore, a new

3 3 variable R, called maximum reservation window, is introduced. It is defined as, R = contract rate pkt size III. ANALYTICAL MODEL In this paper, steady-state TCP throughput is defined as, B = RTT. () Total number of packets sent pkt size. () Total transmission time When network bandwidth is over-subscribed, it s clear that there will be little excess bandwidth for TCP flows to be shared. Then the throughput achieved by a TCP flow is mainly determined by the bandwidth it subscribes. Thus the complexity of modelling two-windows TCP is under the condition of bandwidth under-subscribed, In this section, we will only consider calculating the throughput of two-windows TCP in the case of bandwidth under-subscribed. cwnd W'() W() β() W() W(k) W(M) W'()... RTT recovery-period W'(k) β() W'(M) β(μ) β(κ) Out-period Out-period Out-period In-period time Fig.. Illustration of packet transmission in two-windows TCP model The evolution of transmission window of two-windows TCP is simply illustrated in Fig.. When two-windows TCP is under a steady state, the evolution is periodic and it is consisted of identical periods called In-periods, which is defined as the interval between two consecutive In packet drops. Moreover, an In-period is consisted of so called mini-period, including a recovery-period and some Out-periods. Similar to In-period, an Out-period is defined as the interval between two consecutive Out packet drops. Without loss of generality, we assume there are M + mini-periods in an In-period. Among the M + mini-periods, the first mini-period is a recovery-period, whereas other M mini periods are Out-period. As the In-periods are independently identical distribution (i.i.d.) process, the steady state throughput of two-windows TCP can be calculated by analyzing only one of In-periods. With the above illustration on the evolution of congestion window, we define the following variables which is related to only one In-period. N in : number of transmitted packets that are marked as In in the In-period; N: number of transmitted packets of both In and Out packets in the In-period; T : duration of the In-period; W (k): initial window size in the kth mini-period in the In-period; W (k): final window size before Out packets are lost in the kth mini-period in the In-period; X(k): number of RTT in the kth mini-period; N o (k): number of Out packets transmitted in the kth mini-period; N i (k): number of In packets transmitted in the kth mini-period; N(k): number of transmitted packets of both In and Out packets in the kth mini-period; β(k): number of packets sent in the last RTT in the kth mini-period.

4 4 Based on the above definitions, the steady state throughput can be expressed as B = E[N] pkt size. (3) E[T ] As W (k), k =,,, M are i.i.d. variables, we have E[W ] = E[W (k)], k =,,, M. In the phase of congestion recovery, the congestion window will increase one for every RTT. Thus we have From Fig., we also have the following formula for Out-periods, W (k) = W (k ) And W () is a fast recovery window, Combining (4) and (5) yields X(k) = W (k) W (k) = W (k) = W (k) + X(k), k =,,, M. (4) W (k ) R { = W (k ) + R, k =,,, M. (5) E[W ()] = E[W ]. (6) W (k ) + R W (k), k =,,, M. W () W (), k = Now let s consider (3) and (7). To get the value of B, we need to know the value of E[T ] and E[N]. The duration of an In-period can be expressed as, T = X(k) + )RT T (8) k=o And in the In-period, the total number of transmitted packets is (7) N = = N(k) k= k= [W (k) + W (k)]x(k) (9) From (8), (9) and (7), it s clear that if the variables E[M] and E[W ] are known, then we are able to get the value of the steady state bandwidth. Thus we will calculate E[W ] and E[M] in subsection III-A and III-B respectively, with which the throughput will be achieved in subsection III-C. A. Calculation of E[W ] The calculation of E[W ] is simply described as follows. A formula on E[W ] and E[N(k)] is derived from Fig.. And another formula on E[W ] and E[N(k)] is derived from the definition of E[N(k)]. Based on those two formulas, we are able to get the value of E[W ]. Considering the k-th Out-period in Fig., the number of successfully transmitted packets is Then, using (7), we get N(k) = X(k) l= [W (k) + l] + β(k). () N(k) = [W (k) + W (k ) + R ] [W (k) W (k ) R] + β(k), () 8 Assume that β(k) is uniformly distributed between to W (k), and X(k) and W (k) are i.i.d. random variables [9]. Then we have E[β] = E[W ]. ()

5 5 Thus, from (), we have the mean of N(k) E[N(k)] = (E[W ] R) (3E[W ] + R ) + E[β]. (3) 8 On the other hand, N(k) can be viewed as the sum of In packets and Out packets transmitted before the Out Packet loss, and the packets transmitted in the RTT right after the Out packet loss in the kth out-period. Then the mean of N(k) is given by N(k) = N o (k) + N i (k) + β[k]. (4) E[N(k)] = E[N o (k)] + E[N i (k)] + E[β]. (5) Define p out as the probability of an Out packet being dropped. It s assumed that there will be /p out Out packets transmitted during an Out-period, E[N o (k)] = p out. (6) When an Out packet is dropped, only ewnd is halved and sending rate R is guaranteed. Thus the number of In packets transmitted in the kth Out-period is N i (k) = R X(k). (7) Replace X(k) with that in (7), we get And the mean of N i (k) is calculated as N i (k) = R [W (k) W (k ) + R ]. (8) E[N i (k)] = R E[W ] R. (9) Substituting (6) and (9) to (5), and using (3), we obtain The above equation yields B. Calculation of E[M] 3 8 E [W ] ( 3 4 R + 4 ) E[W ] + (3 8 R + 4 R ) =. () p out E[W ] = + 3R p out. () 3 In this subsection, we will analyze the number of In packets transmitted in an In-period and then calculate E[M]. The calculation will be derived for two kinds of network conditions. The number of In packets transmitted during an In-period is given by N in = N i () + N i (k). () Consider an In-period in Fig.. In the case of R W (), after an In packet drop, the sending rate remains above the contract rate. In the case of R > W (), as a result of an In packet drop, the sending rate will fall below the reservation rate. During the recovery-period, the number of In packets successfully transmitted is N i () = X() In the rest time of the In-period, the number of transmitted In packets is l= k= min[r, W () + l], (3) N i (k) = k= = R X(k) k= R [W (k) k= W (k ) + R ]. (4)

6 6 When R E[W ]/, using (3), (4) and (), we can get the mean of N in E[N in ] = R {E[W ] + E[M](E[W ] R)}. (5) Define p in as the probability that an In packet is dropped. It s assumed that there will be /p in In packets transmitted during the In-period, E[N in ] = p in. (6) From (5) and (6), we have E[M] = Similarly, when R > E[W ]/, from (3), (4) and (), we have the mean of N in R p in E[W ] E[W ] R. (7) E[N in ] = R E[M] (E[W ] R) + R (E[M] R) + (E[M] + R ) (R E[W ]). (8) 8 From (5) and (8), we also get E[M] = In summary, the mean of M is as follows E[M] = C. Calculation of steadystatethroughput 4R (E[W ] R) ( 8 + E [W ] E[W ] 8R E[W ] + 4R + 4R). (9) p in R p in E[M] E[M] R, R E[M]/ 4R (E[W ] R) ( 8 + E [W ] E[W ] 8R E[W ] + 4R + 4R), p in R > E[M/] In the previous subsections, we have calculated E[W ] and E[M]. Now, we will calculate E[T ], E[N] and then get the value of B by (3). The time of an In-period is given by T = The number of packets transmitted during an In-period is given by k= (3) (X(k) + ) RTT. (3) k= N = N(k) = [W (k) + W (k)] X(k). (3) k= After algebraic manipulations, we get the mean of T And the mean of N is E[T ] = {E[M] (E[W ] R + ) + E[W ] + } RTT. (33) E[N] = 8 {3(E[M] + ) E [W ] + E[W ] (E[M] R E[M] + ) R E[M] + R E[M]}. (34) Substituting E[T ] and E[N] into (3), we get the steady state throughput B = {3(E[M] + ) E [W ] + E[W ] (E[M] R E[M] + ) R E[M] + R E[M]} pkt size. (35) 4{E[M] (E[W ] R + ) + E[W ] + } RTT In the case of loss ratio of In packet being zero, (35) becomes B = {3E [W ] + ( R) E[W ] R + R} pkt size. (36) 4(E[W ] R + ) RTT

7 7 If reserved bandwidth of a two-windows TCP flow is equal to zero, then the operation of that flow is the same as that of a traditional best-effort TCP flow. From () we get, and Finally we get E[W ] = B = 4 + sqrt + P out, (37) 3 E[N(k)]pkt size (E[X(k)] + )RTT. (38) B = ( 3 8 E[W ] + 4 )E[W ]pkt size ( E[W ] + )RTT. (39) After comparison, it s found that (39) is the same as formula () in [4] in the case of R =. Thus the analytical model proposed in the paper is compatible to that for traditional TCP protocol. A. Simulation design IV. SIMULATION RESULTS In this section, two sets of simulations in Network Simulator (version ) [] are conducted to validate the proposed analytical model. As the loss rate of In packets will be mainly affected by bandwidth subscription, three levels of bandwidth subscription are investigated in the first set of simulations: (a) less than 6% of the bottleneck link bandwidth is subscribed; (b) between 6% and 9% of the bottleneck link bandwidth is subscribed; (c) more than 9% of the bottleneck link bandwidth is subscribed. Then under one of the bandwidth subscriptions, the impact of RIO parameters configuration on the robustness of the bandwidth guarantee and fairness performance is investigated in the second set of simulations. S D S. 3ms. D S9 R 5Mbps,3ms R 5Mbps,3ms S9 S3 D3 Fig. 3. Simulation model For all simulations a simple dumb-bell network topology is used, which is shown in Fig. 3. The capacity of the link from an end host to the router is set to 5 Mbps.???marking algorithms??? RIO queues are deployed in both R and R. There are thirty TCP flows sharing a congested link between routers R and R. Individual TCP flows are long-lived FTP applications that transmit MSS sized (5 bytes) packets. Flows are configured into five groups. Flows to 5 are in the first group. The rwnd of those flows is fixed and is set to 8; rwnd of flows 6 to is set to 36; rwnd of flows to 5 and flows 6 to are set to 54 and 7, respectively; rwnd of the last ten flows (flow to 3) are set to, which means those flows are best-effort TCP flows. In all of the simulations, the maximum reservation window R for each group of flows is fixed. whereas the bottleneck bandwidth, loss ratio of Out and In packets are changeable. If the bandwidth of the bottleneck link is set to different values, then there will be different subscription levels in the bottleneck link. In the simulations, an extra module is added between R and R, which randomly discard In packets with a probability Pin e. The first purpose of introducing the module is to simulate the In packet drop in the real network environments. In simple simulated networks In packets are seldom dropped by routers due to the inaccurate admission control. Thus introducing a module of packet dropping will make the loss of In packets controllable. The second purpose is to facilitate the validation of the analytical model proposed in the paper. In the simulations, for each level of bandwidth subscriptions, Pin e is set to different values. At the end of each simulation, p in and p out for each flow are calculated and recorded. With the recorded p in and p out, the analytical throughput can be calculated with formula (35) and compared to the simulation results.

8 8 B. Simulation Results and Analysis B. Different bandwidth subscriptions Extensive simulations are carried out to get the steady state throughput of flows under the conditions of different bandwidth subscriptions. In the first set of simulations, the RIO parameters are set as follows, minth in/maxth in/maxp in: 5/4/. minth out/maxth out/maxp out: 7//.5 Each simulation lasts 5 seconds. To avoid oscillation at the starting period, the first 6 seconds of simulation data are discarded. Typical analytical and simulated throughput of both two-windows TCP flows are plotted in Fig. 4, compared with simulation results for the traditional TCP flows. Although the impact of P in e on service quality are widely investigated, results are presented in the figure for P in e being,. and.5 respectively. In Fig. 4(a), (c) and (e), plotted are the simulated throughput of the flows using traditional TCP flows, with the capacity of the bottleneck link being set to Mbps, 5Mbps and 35Mbps respectively. In Fig. 4(b), (d) and (f), plotted are the analytical and simulated throughput of flows using two-windows TCP. In all sub-figures, the line marked with indicate the bandwidths that should be guaranteed for flows when those flows subscribe bandwidth. From Fig. 4, the following conclusions are observed.. In all the simulated network conditions with different bottleneck link capability and dropping rate of In packets, the steady state throughput of two-windows TCP flows achieved by the analytical model matches very well with that achieved by simulations. Thus the analytical model is very accurate and is effective for wide range of network conditions.. In a wide range of network conditions, the bandwidth subscribed by two-windows TCP flows is well guaranteed; while the bandwidth subscribed by traditional TCP flows is not, especially when the bandwidth of bottleneck link is almost over-subscribed. 3. More important is that the unsubscribed bandwidth in the bottleneck link is almost fairly assigned among the twowindows TCP flows. But it s not the case for the traditional TCP flows. To make a comparison on the fair assignment of unsubscribed bandwidth among two-windows TCP flows and traditional TCP flows, we introduce a new performance metric, fairness index. It s denoted by FI and can be calculated by the following formula, n i= F I = (E i E) ne, (4) where E is the average excess bandwidth assigned to a flow; E i is the achieved bandwidth minus rate for the ith flows (E i is allowed to be minus); n is the number of flows competing the bandwidth of the bottleneck link. It can be induced that the lower the fair index, the better the performance of the system on fairly assigning unsubscribed bandwidth. Based on the above definition, we get the fairness indexes for those flows using traditional TCP and twowindows TCP flows. The values are presented in Table I. It s clear that the fair indexes for traditional TCP flows are several ten times that for two-windows TCP. TABLE I Fairness index for traditional TCP and two-windows TCP type M 5M 35M original TCP two-windows TCP B. Impact of RIO parameters configuration As described previously, RIO mechanism is an important component to enable differentiated services. But the configuration of RIO parameters is very complex and there is no general configurations recommended for RIO parameters. Thus in this subsection, we investigate the impact of RIO parameters configuration on the performance of Assurance Services. Three kinds of RIO parameters configurations are investigated, including Non-overlapping, 5%overlapping and %overlapping, which is shown in Fig. 5. The RIO parameters corresponding to those configurations are listed in Table II. Typical analytical and simulated throughput of two-windows TCP flows are shown in Table III with different RIO parameters configurations. In the simulations, the capacity of the bottleneck link is 5 Mbps and Pin e is set to.. From results presented in Table III, it is shown that the accuracy of the analytical model of two-windows TCP is not affected by the configurations of RIO parameters. And the bandwidth for two-windows TCP flows are well guaranteed for the considered RIO parameter configurations.

9 9 TABLE II RIO parameters used in the simulations. non-overlapping 5%overlapping %overlapping minth in/maxth in/maxp in 5/4/. /4/. 7/4/. minth out/maxth out/maxp out 7//.5 /3/.5 7/4/. TABLE III Analytical and measured bandwidth with different RIO configurations. (predicted bandwidth/measured bandwidth) (Mbps) No. non-overlapping 5%overlapping %overlapping G.4/.47.43/.43.4/.4 G.693/.78.7/ /.759 G3.98/.6.4/.9.3/.7 G4./.4.4/.6.4/.???G-G4???,??? new simulations are required??? The achieved bandwidth of two-windows TCP and original TCP flows are also compared. In the analysis and simulations, the bottleneck bandwidth is 5Mbps and Pin e is set to.. The RIO parameters are configured in the non-overlapping style. Typical results are presented in Table IV. TABLE IV Comparison of throughput of two-windows TCP and original TCP (Mbps) Contracted BW two-windows TCP Computed Measured original TCP V. CONCLUSIONS Two-windows TCP is proposed recently to address the issues of bandwidth guarantee and fairness for Assured Services in DiffServed networks. In this paper, an analytical model is proposed to evaluate the steady state throughput of twowindows TCP in DiffServed networks. The accuracy of the analytical model is validated by simulations over a wide range of network scenarios. Analytical results also show that two-windows TCP is effective on improving the performance of Assured Services on fairness and bandwidth guarantee, which will leverage the burden of admission control. The performance of the protocol is observed to be robust to bandwidth subscription and RIO parameter configurations. The work presented in this paper is valuable on understanding the performance of two-windows TCP in complex network environments and promoting the deployment of Differentiated Services. References [] S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, An architecture for differentiated services, Network Working Group, RFC475, Dec [] J. Heinanen and F. Baker, Assured forwarding PHB group, Network Working Group, RFC597, June 999. [3] J. Ibanez and K. Nichols, Preliminary simulation evaluation of an assured service, IETF draft, Aug [4] I. Yeom and A. L. N. Reddy, Realizing throughput guarantees in a differentiated services network, in Proc. ICMCS, pp , June 999. [5] W. H. Park and S. Bahk, A modified RIO algorithm that alleviates the bandwidth skew problem in Internet Differentiated Service, in IEEE ICC, June. [6] J. Padhye, V. Firoiu, D. Towsley, and J. Kurose, Modeling TCP throughput: A simple model and its empirical validation, in Proc. ACM SIGCOMM, pp , 998. [7] M. Mathis, J. Semke, J. Mahdavi, and T. Ott, The macroscopic behavior of the TCP congestion avoidance algorithm, in Comput. Commun. Rev., vol.7, No. 3, pp. 67-8, July 997. [8] M. Baines, N. Seddigh, B. Nandy, P. Pieda, and M. Devetsikiotis, Using TCP model to understand bandwidth assurance in a differentiated services network, IPS, Nov.. [9] I. Yeom and A. L. N. Reddy, Modeling TCP Behavior in a Differentiated Services Network, in IEEE/ACM Trans. on Networking, pp , Feb.. [] D. D. Clark and W. Fang, Explicit allocation of best-effort packet delivery service, in IEEE/ACM Trans. on Networking, Vol.6, No.4, pp , Aug [] Univ. of California at Berkeley. (997) Network Simulator v. (ns-). [Online]. Available:

10 pin_e=e-4,m pin=,e pin_e=e-4,m pin=e-4,e. pin_e=5e-4,e (a) Bandwidth = M, original TCP (b) Bandwidth=M, two-windows TCP pin_e=e-4,m pin=,e pin_e=e-4,m pin=e-4,e. pin_e=5e-4,e (c) Bandwidth=5M, original TCP (d) Bandwidth=5M, two-windows TCP pin_e=e-4,m pin=,e.5 pin_e=e-4,m pin=e-4,e pin_e=5e-4,e.5.5 (e) Bandwidth=35M, original TCP (f) Bandwidth=35M, two-windows TCP Fig. 4. Steady state throughput of traditional TCP and two-windows TCP. Symbol M corresponds to simulation results; symbol E corresponds to analytical results.

11 Drop probability.5. maxp_out maxp_in Drop probability.5. maxp_out maxp_in Average queue length 3 4 Average queue length (a) non-overlapping (b) 5%overlapping Drop probability. maxp_out=maxp_in 7 4 Average queue length (c) %overlapping Fig. 5. Illustration of three RIO parameters configurations