Toward a Time-Scale Based Framework for ABR Trac Management. Tamer Dag Ioannis Stavrakakis. 409 Dana Research Building, 360 Huntington Avenue

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1 Toward a Time-Scale Based Framework for ABR Trac Management Tamer Dag Ioannis Stavrakakis Electrical and Computer Engineering Department 409 Dana Research Building, 360 Huntington Avenue Northeastern University, Boston, MA ioannis@hilbert.cdsp.neu.edu Abstract This paper discusses some issues and possibilities for more eective ABR (Available Bit Rate) trac management which arise from a careful consideration of various time scales present in an ATM networking environment. Since the ABR applications will typically use the remaining resources after CBR (Constant Bit Rate) and VBR (Variable Bit Rate) applications have been accommodated, the ABR rate should be controlled through a feedback based ow control scheme to avoid excessive losses. It is well known that the increased propagation delay between the (controlled) ABR source and the network node leads to increased time horizons over which the source rate is based on outdated information, resulting in increased amount of bandwidth mismatch and, thus, cell losses. For this reason, the eectiveness of feedback based ow control schemes reduces with increased propagation delay. Besides the physical distance, some other system parameters - namely the network, ABR and VBR time scales - may also impact considerably on the eectiveness of feedback based ow control schemes. In this paper, the impact of these time scales is considered. In addition, a proactive feedback based ow control scheme is described, aiming to reduce the amount of bandwidth mismatch by generating early feedbacks. 1 Introduction The ABR service class [1] is intended for non-real time applications which can tolerate delay and will be supported - primarily - by using the remaining bandwidth left from VBR and CBR applications. Since the bandwidth availability for the ABR service class is time-varying due to the uctuations in the VBR/CBR trac, a feedback based ow control should be applied to control the rates of the ABR trac sources, in order to eciently utilize the available bandwidth and avoid losses. Two feedback based ow control approaches have been considered: the rate based [2], [3], [4] and the credit based [5], [6], [7]; an integration of these schemes has also been considered, [8]. The credit based ow control is implemented on a link by link and per virtual circuit (VC) basis. The sender associated with a VC receives credits from the corresponding receiver, reecting the amount of available buer space at the receiver. The sender can then transmit any number of cells up to its credit balance to avoid cell losses. This research is supported by the National Science Foundation under Grant NCR

2 In the rate based ow control, the sender is notied about congestion in the network with a feedback generated at the receiver or at any congested node. The sender adjusts its rate according to the received feedback and the control scheme in eect. Although the credit based ow control can handle both smooth and bursty trac (while the rate based ow control may not be very eective for bursty trac), it introduces an excessive amount of overhead and is expected to be expensive for a wide area network. For such reasons, the more exible rate based ow control has been adopted by the ATM Forum. Several trac control policies have been proposed for the rate based ow control, such as the Explicit Forward Congestion Indication (EFCI) [9], Backward Explicit Congestion Notication (BECN) [10], Proportional Rate Control Algorithm (PRCA) [11], Explicit Rate Feedback (ERF) [12] and Enhanced Proportional Rate Control Algorithm (EPRCA) [13]. Under the Non-Proactive Feedback based ow control (NPF) scheme considered in this paper, the ABR trac source is notied regarding the bandwidth availability at a network node through a feedback generated when the VBR/CBR source rate changes at that node. Assume that the forward and backward propagation delays are equal to T d and that the VBR/CBR source rate changes at time t 1, as shown in Figure 1. Because of the propagation delay, the ABR source will learn about the change in bandwidth availability at time t 1 +T d and the adjusted rate from the ABR source will reach the network access node at time t 1 + 2T d. Since the VBR rate change occurred at time t 1, a bandwidth mismatch will occur for a roundtrip propagation delay of 2T d. During this interval the link capacity is exceeded and cell losses may occur depending on the amount of available buers. Since the amount of bandwidth mismatch depends on the propagation delay, increased propagation delay reduces the eectiveness of feedback based ow control schemes. The impact of increased propagation delay on the eectiveness of feedback based ow control schemes has been studied in the past [14], [15], [16], [17]. In addition to the propagation delay, other system parameters may impact on the eectiveness of feedback based ow control schemes as well. In this paper, the impact of some system parameters - namely, the network, VBR and ABR time scales - will be investigated. rate overutilization underutilization total rate at the network access node ABR rate VBR/CBR rate t 1 t 1 + 2T d t 2 t 2 + 2T d time Figure 1: A bandwidth mismatch example under the NPF scheme The network time scale is dened to be the transmission time of a cell (slot). As the network time scale decreases, the propagation delay (measured in slots) increases. Thus, the decreased network time scale has a similar impact on a feedback based ow control schemes as the increased propagation delay. The frequency of change of the bandwidth availability would also impact signicantly on the 2

3 eectiveness of a feedback based ow control scheme. If over a given time interval the number of VBR/CBR source rate changes increases, then the number of initiated bandwidth mismatch cycles will typically increase as well. Since increased number of bandwidth mismatch cycles will increase the number of overutilization periods, more cell losses will be induced and the eectiveness of the feedback based ow control schemes will be reduced. The VBR time scale can be dened as the inverse of the frequency of the VBR source rate changes or the average time over which the VBR application maintains a constant rate. The VBR time scale will be employed in order to capture the impact of the frequency of bandwidth mismatch cycles on the eectiveness of feedback based ow control schemes. In addition to the network and VBR time scales, the cell transmission patterns of the ABR sources may also impact on the eectiveness of feedback based ow control schemes. It can be observed that between two ABR applications of the same rate, the one which transmits blocks of multiple cells every one of longer periods may utilize the resources better than the one which transmits one cell every one of shorter periods. The ABR time scale is dened here as the length of these periods and will describe the various transmission patterns considered in this paper. Since losses will typically occur only because of bandwidth mismatch, eliminating completely the bandwidth mismatch will reduce the losses to zero. Thus, if the bandwidth mismatch is eliminated, neither the network time scale nor the VBR time scale will impact on the eectiveness of feedback based ow control schemes. This elimination can be possible if the exact time instants of the VBR source rate changes are known at the network access node and the feedbacks are generated a roundtrip propagation delay before the rate changes occur. rate total rate at the network access node ABR rate VBR/CBR rate t 1-2T d t 1 t 2-2T d t 2 time Figure 2: A bandwidth mismatch example under the PF scheme Figure 2 illustrates the VBR and ABR source rates at the network access node under an early feedback transmission scheme. If the network access node knows that the VBR rate change will occur at time t 1, it can generate the feedback for the ABR source at time t 1? 2T d. Since a roundtrip propagation delay is necessary for the adjusted ABR source rate to return back to the network access node, the adjusted ABR source rate will arrive at the network access node at time t 1 and the bandwidth mismatch will be completely eliminated. For some VBR applications such as MPEG video applications, a xed cell rate may be maintained over well dened intervals, such as frames. If the resource management cells carry information about the rate associated with the next such interval, then early feedback generation can be possible. If these intervals are randomly distributed, the network access node could estimate the time of the rate changes and generate the feedback according to its estimated time of rate change. If a good estimator can be chosen, the 3

4 amount of bandwidth mismatch can still be reduced, reducing also the ABR cell losses. In this paper, the above briey described feedback based ow control scheme which aims to decrease amount of bandwidth mismatch by generating early feedbacks will be referred as the Proactive Feedback based ow control (PF) scheme. 2 Description of the System In order to simplify the study and facilitate the understanding of the impact of various time scales, a transmission link shared by one VBR source and one ABR source will be considered. The ABR trac source is away from the network access node and, thus, the propagation delay between the ABR source and the network access node is non-negligible. The distance between the VBR source and the network access node has no importance since no control is applied on the VBR source. The network access node is assumed to have a buer of capacity C to temporarily store the ABR source cells when the transmission link attends to the VBR trac. A queuing model of the network access node is shown in Figure 3. It is assumed that both trac sources may transmit at most one cell per slot, thus a buer with capacity 1 will be sucient for the VBR queue. Network access node VBR ABR d C Figure 3: A queuing model of the network access node 2.1 The ABR Trac Source The maximum allowable ABR source rate is determined by the current VBR source rate. If the latter is equal to r v, then the maximum allowable ABR source rate will be 1? r v?, where is a small positive number determined by the desirable load at the network access node. To achieve a rate close to its maximum allowable, the ABR source can transmit one cell per 1 T k slots where T k = d 1?r e and d()e denotes the smallest integer larger than (). In this paper, T v? k will be referred to as the fundamental ABR subframe. The same rate can also be achieved, if the ABR source transmits a block of B k cells per subframe of length B k T k, that is, if the ABR source employs a B k -order subframe, where B k 2 N. Thus, if B k = 1, the ABR source will employ the fundamental subframe T k to transmit at a rate equal to 1=T k. If B k > 1, the ABR source will employ a B k -order subframe to transmit at the same rate equal to 1=T k. Figure 4 shows examples of ABR cell transmission employing the fundamental and higher-order subframes. 4

5 T k B k =1 2Tk B k =2 ntk B k = n Figure 4: The ABR trac subframes Let T C(B k ; B k T k ) denote a transmission control policy according to which the ABR source transmits a batch with size B k at the beginning of a subframe of length B k T k. Let T C(T k ) = ft C(B k ; B k T k ); B k 1g denote the class of all T C(B k ; B k T k ) policies which implement the same transmission rate of 1=T k. This class of policies is characterized by the fundamental subframe of length T k. Let t k denote the beginning time instant of the k th subframe. At t k, a fundamental subframe T k (and the ABR rate) will be determined based on the current VBR rate. Any policy in T C(T k ) can be selected for the implementation of the ABR source rate of 1=T k. As long as the VBR rate remains constant, the same policy will be employed. That is, if T k+1 = T k then B k+1 = B k and T C(B k ; T k ) T C(B k+1 ; T k+1 ). However, if a VBR source rate change occurs, then the network access node calculates the new ABR fundamental subframe T k+1 and any policy in T C(T k+1 ) can be selected. The ABR time scale is dened as the length of the B k -order subframe used to transmit ABR cells. The impact of the ABR time scale on the eectiveness of a feedback based ow control scheme is investigated in this paper. 2.2 The VBR Trac Source For analysis tractability it will be assumed that the activity level of the VBR source changes at subframe boundaries. Let fs k g k1 be a 2-state underlying Markov chain with state space S = f0; 1g embedded at subframe boundaries ft k g k1 of length B k T k, where B k T k is determined by the perceived remaining capacity as indicated in the previous subsection. Let r v (s k ) denote the rate of the VBR source at the k th subframe where r v (1) > r v (0). The VBR cell arrival process is modeled as a Markov Modulated Bernoulli process. The probability of transmitting 1 (0) cell in a slot of the k th subframe is r v (s k ) (1? r v (s k )). Therefore, the number of VBR cell arrivals during a slot of the k th subframe, A(s k ), is given by, ( 1 with probability rv (s A(s k ) = k ) 0 with probability 1? r v (s k ) Let p s (s k ) denote the probability that S k changes at the end of the k th subframe, at the beginning of which it was in state s k. p s (s k ) will reect the average time over which VBR applications 5

6 maintain a constant rate (or VBR time scale). It is expected that the increased VBR time scale will increase the eectiveness of the feedback based ow control schemes. 3 Study of the System Details of the study of the loss performance of the queuing model of the system shown in Figure 3 may be found in [18]. Since the VBR trac is provided prioritized service and the maximum number of VBR cell arrivals per slot is 1, no VBR cell losses will occur. For this reason, the analysis will focus on the evaluation of ABR cell losses and the impact of the time scales considered in this paper will be evaluated based on the ABR cell loss probability. Let fs k ; Q k g k1 be a 2-dimensional process embedded at subframe boundaries ft k g k1 where Q k is a random variable describing the buer occupancy at t k and 0 q k C. S k completely determines the VBR arrival process. In order to determine the ABR arrival process at the network access node, both the current VBR source rate (r v (s k )) and whether the current ABR rate is based on the most recent feedback sent by the network access node or not (in other words, whether the feedback's impact is not pending or pending), are required. For this reason, the random variable J k is introduced describing the status of the impact of the feedback; J k is an indicator function which assumes the value of 1, if the impact of a feedback carrying a VBR source rate change is pending and 0 otherwise. Then, the ABR source rate at the network access node can be completely determined and it is equal to 1? r v (s k j k )? where denotes the modulo 2 addition. A Markov chain can be constructed to describe the evolution of the system under xed and non-zero roundtrip propagation delays. A simplifying assumption is made by assuming that the roundtrip propagation delay is random and geometrically distributed with mean 1 p f, measured in terms of subframes. Although it is possible that at any time, the impact of more than one feedbacks be pending, at most one pending feedback will be considered in order to simplify the analysis. This approximation will hold true if max sk fp s (s k )g p f ; that is, if the VBR source time scale is much larger than the propagation delay. Under the above assumptions, it is easy to establish that the stochastic process fs k ; J k ; Q k g embedded at subframe boundaries is a Markov chain with state space f(s k ; j k ; q k ) : 0 s k 1; 0 j k 1; 0 q k Cg. The ABR cell loss probability can be calculated using the average number of cells lost and arrived in a subframe fs k ; J k ; Q k g k1 in state (s k ; j k ; q k ) and taking the expectation over all possible states. Let LP, L(s k ; j k ; q k ) and M(s k ; j k ; q k ) denote the ABR cell loss probability, the average number of cells lost in a subframe and the average number of cells arrived in a subframe, respectively. Then, LP = Ef L(s k; j k ; q k ) M(s k ; j k ; q k ) g Details on the derivation of the ABR cell loss probability may be found in [18]. 6

7 4 An Attempt to Decrease the Amount of Bandwidth Mismatch: Early Feedback Generation As indicated previously, ABR cell losses are due to bandwidth mismatch and increased amount of bandwidth mismatch would reduce the eectiveness of feedback based ow control schemes. In this section, the PF scheme which attempts to reduce the bandwidth mismatch by generating early feedbacks is described. Under the PF scheme, the rate change instants of the VBR source are assumed to be known or be estimated and the feedbacks are generated in advance (2T d before the (estimated) VBR rate changes occur). Let X k denote the length of the time interval over which the VBR source maintains a constant rate. That is, X k = t k?t k?1, where t k denotes the time instant at which a VBR rate change occurs. Let ^X denote an estimator for X k. Under the PF scheme the transmission instant of the feedback depends on t k, X k, ^X and the roundtrip propagation delay 2Td. Let f k denote the time instant at which the k th feedback is transmitted. If X k > ^X? 2T d, the network access node transmits the feedback to the ABR source at time t k?1 + ^X? 2T d. If X k < ^X? 2T d, the feedback is transmitted at t k?1 + X k as under the NPF scheme. Therefore, f k = t k?1 + minfx k ; ^X? 2Td g Figure 5 illustrates an example of feedback transmission instants. Since X k?1 and X k+1 are greater than ^X?2T d, the feedbacks corresponding to these intervals are generated at t k?2 + ^X?2T d and t k + ^X? 2T d, respectively. Since X k < ^X? 2T d, the feedback corresponding to this interval is generated at time t k?1 + X k. Note that, because of the roundtrip propagation delay, the adjusted ABR rate reaches the network access node at f k + 2T d. Xk-1 Xk Xk+1 fk-1 fk fk+1 tk-2 tk-1 tk tk+1 X^ 2T d Figure 5: A realization of feedback transmission instants In order to compare the eectiveness of the PF scheme with that of the NPF scheme described in the previous section, the magnitude of the induced bandwidth mismatch under both schemes can be considered. Since the ABR cell losses are caused by the overutilization periods captured by the bandwidth mismatch, the expected bandwidth mismatch would reect the eciency of a feedback based ow control scheme in terms of the induced cell losses. Under the NPF scheme, the feedback is transmitted when a VBR rate change is detected, as described before. Thus, the induced bandwidth mismatch is always equal to the roundtrip propagation delay, 2T d. Thus, the expected value of the amount of induced bandwidth mismatch is 2T d. Let C N P F be equal to this amount, thus C N P F = 2T d. 7 X^ 2T d X^ 2T d

8 Let W P F be a random variable describing the amount of bandwidth mismatch under the PF scheme and let C P F = EfW P F g be its expected value. W P F is equal to, W P F = jt k? (f k + 2T d )j = jx k? minfx k ; ^X? 2T d g? 2T d j = 8 >< >: if X k ^X? 2Td if ^X? 2Td + 1 X k < ^X 2T d ^X? X k 0 if X k = ^X X k? ^X if X k > ^X Let f(x k ) denote the distribution of X k (the VBR time scale). An example distribution is shown in Figure 6. f( X ) k W = PF 2T d W < 2Td PF W > PF 2T d ^ X-2T d X^ ^ X+2T d X k Figure 6: An example distribution of X k If X k is in the region 1 X k ^X + 2T d, then the bandwidth mismatch is always equal to or less than the roundtrip propagation delay. Therefore, in this region W P F W N P F = 2T d. The only region in which the PF scheme may lead to larger bandwidth mismatch than the NPF scheme is X k > ^X + 2Td, since only in this region the bandwidth mismatch is greater than the roundtrip propagation delay. Therefore, the eectiveness of the PF scheme depends on the tail of the distribution of X k. If the selected estimator can decrease the probability of entering into this region while increasing the probability of entering into the low bandwidth mismatch region, the eectiveness of the PF scheme can be increased. Claim : If the maximum value of X k is nite (which would typically be the case), a value of ^X can always be found such that the PF scheme is at least as good as the NPF scheme, that is, C P F C N P F. Proof: Let X max denote the maximum value of X k. Since a bandwidth mismatch larger than 2T d may occur only in the region X k > ^X + 2Td, ^X can be chosen such that ^X + 2Td X max. In this case, X k ^X + 2Td and the bandwidth mismatch will never exceed 2T d. 8

9 5 Numerical Results 5.1 The Impact of Time Scales on the Feedback Based Flow Control Schemes In this subsection, the impact of various time scales (network, ABR and VBR) on the eectiveness of the NPF scheme is investigated by using the ABR cell loss probability derived in Section 3. Figure 7 illustrates the ABR cell loss probability as a function of p f for p s (0) = p s (1) = p s = 0:005; 0:001; 0:0005 and 0:0001. For this plot, the results are derived for VBR source rates r v (1) = 0:8 and r v (0) = 0:4 cells/slot and a buer with capacity 40. As the propagation delay decreases (p f increases), the amount of time that it takes for the ABR source to respond to the feedbacks generated at the network access node decreases. As a consequence, the amount of bandwidth mismatch (thus the overutilization periods) decreases, causing a decrease in the ABR cell loss probability. In addition to the propagation delay, the VBR time scale (1=p s ) also impacts on the ABR cell loss probability. When the VBR time scale decreases (p s increases), VBR source rate changes occur more frequently. Therefore, more bandwidth mismatch cycles are initiated resulting in more ABR cell losses. Note that, p s p f in order for the assumption of no multiple pending feedbacks to be reasonably accurate Cell Loss Probability ps= ps= ps= ps= Pf Figure 7: ABR cell loss probability vs. p f for various p s Figures 8 and 9, illustrate the ABR cell loss probability as a function of batch size B k for buer capacities of 10; 15; 20; 25 and 30. The distance between the ABR source and the network access node is assumed to be and 200 slots for Figure 8 and Figure 9, respectively. Since the VBR source rates are assumed to be r v (1) = 0:8 and r v (0) = 0:4, the fundamental subframe lengths are 2 and 6 slots. Thus, a B k -order subframe (ABR time scale) has lengths of 2B k and 6B k slots. For a xed value of buer capacity, it can be observed that the ABR cell loss probability initially decreases as B k (the ABR time scale) increases. This behavior is reversed when B k exceeds a threshold. Thus, for a given buer capacity, there is an optimal B k (or ABR time scale) that minimizes the induced ABR cell losses. The optimal B k also depends on the propagation delay. For example, the optimal B k for a buer capacity of 15 is equal to 8 in Figure 8 while it is equal to 2 in Figure 9. This trend may be attributed to the decreasing positive impact of a large ABR time scale for a decreased propagation delay. 9

10 10 2 C=10 Probability of Loss 10 3 C=15 C=20 C=25 C= Batch Size Figure 8: ABR cell loss probability vs. B k for various values of C for an average distance of slots 10 2 C= Probability of Loss 10 4 C=15 C= C=25 C= Batch Size Figure 9: ABR cell loss probability vs. B k for various values of C for an average distance of 200 slots 5.2 The ABR Cell Loss Probability under the PF Scheme In order to illustrate the eectiveness of the PF scheme in comparison to that of the NPF scheme, the expected amount of induced bandwidth mismatch is calculated under both schemes. In addition, simulation results for the induced loss probabilities are presented. Here it is assumed that the maximum length for X k is 100 slots. Figure 10 shows the expected amount of bandwidth mismatch for the PF and the NPF schemes when X k has a binomial distribution with parameters 100 and 0.5 (X k Bin(100; 0:5)). For this distribution, it turns out that the C P F reaches its minimum when ^X = 50 (the mean of the binomial distribution). Since the overutilization periods during bandwidth mismatch may induce cell losses, the latter are expected to increase as the amount of bandwidth mismatch increases. To illustrate this, some simulation results are presented next under the following system parameters: the buer capacity at the network access node is equal to 30; the VBR source rates are r v (1) = 0:8 and r v (0) = 0:4 10

11 50 45 C NPF C PF Estimator for X k Figure 10: Comparison of C N P F and C P F for X k Bin(100; 0:5) cells/slot and the corresponding ABR source rates are and 0.5 cells/slot. X~Bin(100,0.5) 10 4 PF with 2T d =30 NPF with 2T d =30 PF with 2T d =20 NPF with 2T d =20 ABR Cell Loss Probability Estimator for X k Figure 11: ABR Cell Loss Probability vs. ^X In Figure 11, the ABR cell loss probabilities for the PF scheme and NPF schemes are plotted as a function of the estimate ^X, for 2T d = 20 and 2T d = 30. As expected (from the results shown in Figure 10), the best estimator for X k is around the mean of the distribution. Once a good estimator for X k is chosen, there is a signicant gain in terms of losses. If ^X is close to Xmax, the loss probabilities under the PF scheme converge to those induced by the NPF schemes, since in this case the feedback is generated mostly at the instants of rate changes (as opposed to earlier). Also, the induced losses under the dierent propagation delays look very similar under the PF scheme when the chosen estimator is good. This is expected since the performance of the PF scheme when a good estimator is employed is mainly determined by the goodness of the estimator and not the propagation delay. 11

12 6 Some Concluding Comments This paper discusses some issues and possibilities for more eective ABR (Available Bit Rate) trac management which arise from a careful consideration of various time-scales present in an ATM networking environment. In the typical (WAN) ATM environment the propagation delay is expected to be large when measured in time slots (cell transmission times). For this reason, it is expected that the eectiveness of the feedback-based rate control mechanism will be compromised. A number of researchers have pointed to this problem and numerous studies have investigated the stability and performance of such mechanisms in the presence of non-zero propagation delays. By dening the network time scale to be equal to the cell transmission time (slot), it is clear that the propagation delay (measured in slots) increases as the network time scale decreases; the latter occurs when higher transmission rates are employed. The aforementioned studies have then basically investigated the impact of the network time scale on the eectiveness of feedback-based trac control schemes for ABR applications. The reduction of the eectiveness of the feedback-based ABR trac control as the network time scale decreases can be easily explained in terms of the increased mismatch between the ABR transmission rate and the available network capacity, due to the increasingly outdated feedback information. During the periods over which the available network capacity remains unchanged no feedback is generated and no rate/capacity mismatch occurs. Thus it is clear that the frequency of occurrence of this rate/capacity mismatch events impacts on the eectiveness of the feedback-based ABR trac control scheme. No matter how large the propagation delay (or small the network time scale), it will impact insignicantly on the performance of a feedback-based trac control scheme as long as the frequency of rate/capacity mismatch events is very low. Consequently, the frequency of change of the available capacity process seems to impact signicantly on the eectiveness of a feedback-based ABR trac control. The inverse of this frequency can be dened to be the time scale associated with the available capacity, or the time scale of the (aggregate) VBR (Variable Bit Rate) applications utilizing the networking resources. The impact of the VBR time scale is illustrated in this paper. In addition to determining the VBR time scale and assessing the level of anticipated performance, the idea of actively shaping the VBR time scale in order to improve the performance of the feedback-based ABR trac control is worth investigating. Such shaping would lead to a cooperative ABR/VBR trac management environment. For some VBR applications it may be possible to ensure that a xed cell rate is delivered over well dened intervals which may be xed -such as the frame associated with a video application- or provided to the network node. If -in additionresource management cells at the beginning of such intervals carry information about the rate associated with the next such interval then early feedback generation may be possible, minimizing signicantly the rate/capacity mismatch duration, as well at the magnitude of the rate mismatch. In addition, some VBR rate change prediction mechanisms may be considered in order to estimate the time of anticipated change and trigger an earlier feedback generation. Finally, earlier studies have suggested that, all other things being the same, lower rate ABR applications would utilize more eciently the remaining capacity than (fewer) higher rate ones. This may be attributed, at least in part, to the larger time scale (inverse of the rate) associated with the lower rate ABR sources. Furthermore it is observed that between two ABR applications of 12

13 the same rate, the one which transmits blocks of multiple cells every one of longer periods utilizes the resources better than the one which transmits one cell every one of shorter periods, as long as the receiving buer is suciently large. Clearly a larger time scale may be associated with the rate of the former ABR application. Such investigations are discussed in the paper, along with a proposal for a block-based ABR cell transfer by introducing a class of ABR cell transfer policies. References [1] ATM Forum, \Trac Management Specication Version 4.0", ATM Forum/ R10, Feb [2] F. Bonomi and R. Morris, \The Rate Based Flow Control Framework for the Available Bit Rate ATM Service", IEEE Network, pp , Mar./Apr [3] J. C. Bolet and A. Shankar, \Dynamical Behavior of Rate Based Flow Control Mechanism", ACM Comp. Commun Rev., pp , Apr [4] S. Liu et al., \Fairness in Closed Loop Rate Based Trac Control Schemes", ATM Forum/ , May [5] H. T. Kung and R. Morris, \Credit Based Flow Control for ATM Networks", IEEE Network, pp , Mar./Apr [6] H. T. Kung and K. Chang, \Receiver-Oriented Adaptive Buer Allocation in Credit-Based Flow Control for ATM Networks," INFOCOM'95, pp , [7] J. F. Ren and J. W. Mark, \Design and Analysis of a Credit Based Controller for Congestion Control in B-ISDN/ATM Networks," INFOCOM'95, pp , [8] K. K. Ramakrishnan and P. Newman, \Integration of Rate Based and Credit Schemes for ATM Flow Control", IEEE Network, pp , Mar./Apr [9] N. Yin and M. G. Hluchjy, \On Closed-Loop Rate Control for ATM Cell Relay Networks," INFOCOM'94, pp , Toronto, [10] R. Beraldi and S. Morano, \Selective BECN Schemes for Congestion Control of ABR trac in ATM LAN," ICC'96, pp , [11] A. Barnhart, \Baseline Performance Using PRCA Rate Control," ATM Forum/ , July [12] A. Charny et al., \Congestion Control with Explicit Rate Indications," ICC'95, pp , Seattle, [13] L. Roberts, \Enhanced PRCA," ATM Forum/ R1, Aug [14] Y. T. Wang and B. Sengupta, \Performance Analysis of a Feedback Congestion Control Policy Under non-negligible Propagation Delay," ACM SIGCOMM'91, pp , Sep [15] M. Abdelaziz and I. Stavrakakis, \Study of an Adaptive Rate Control Scheme Under Unequal Propagation Delays," ICC'95, pp , Seattle, [16] R. Pazhyannur and R. Agrawal, \Feedback Based Flow Control in ATM Networks with Multiple Propagation Delays," 1996 IEEE, pp

14 [17] T. Dag and I.Stavrakakis, \Study of the Impact of Network and Source Time Scales on Feedback Based Congestion Control," SPIE'96, Nov [18] T. Dag, I. Stavrakakis, \Evaluation of ABR Trac Management Under Various System Time Scales", Computer Networks and ISDN Systems, to appear. 14