A Simple Cell Scheduling Mechanism for ATM Networks

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(1)A Simple Cell Scheduling Mechanism for ATM Networks Ming-Chi Lee, Tsung-Chun Chen, Hsin-Tai Yang, and Shie-Jue Lee Department of Electrical Engineering National Sun Yat-Sen University Kaohsiung 804, Taiwan E-mail: fmcleej nomadj styangj [email protected]. ABSTRACT Carry-Over Round Robin(CORR) is a simple mechanism for scheduling cells in asynchronous transfer mode networks. It is competitive with much more complex scheduling disciplines in terms of performance, especially in operational simplicity. However, CORR makes some extra design to maintain a maximum frame size, which leads to an unfair allocation of bandwidth and increases complexity of operations. In this paper, we propose a modi

(2) ed scheme to simplify CORR. We provide a mathematicalanalysis and show that this scheme achieves better performance than CORR.. 1 INTRODUCTION Integrated services networks are required to support a variety of applications with a wide range of Quality of Service(QoS) requirements. At a switch node in high-speed networks, hundreds of thousands of sessions belonging to di erent services interact with each other and contend for the same output link. Scheduling [1, 2] is a discipline that allocates the sequence in which the packets of di erent sessions are sent. The design of a trac scheduling algorithm involves tradeo among its delay, complexity of implementation, and fairness. Concerning the delay and fairness, Packet by Packet Generalized Processor Sharing (PGPS) is considered an ideal scheduling algorithm and achieves nearly perfect performance [3]. However, PGPS requires O(N) work per packet, where N is the number of ows that are currently active at the switch node. Several approaches were proposed to reduce the complexity of PGPS [4, 5, 6]. They exhibit desirable performance characteristics compared with PGPS and achieve high network utilization. All of the protocols mentioned above, called Flow Timestamps schedulers, have in common the requirement of transmitting packets in a priority order according to timestamps. Since maintaining a sorted priority queue [7, 8] introduces significant overhead, these algorithms are dicult to implement with a large number of active sessions at high speed. This. work was supported by the National Science Council. under the grant NSC-89-2213-E-110-010.. Another class of category based on frame-based [9] or round-robin [10] usually has O(1) time complexity. Although they perform a little worse than Flow Timestamp schedulers in delay and fairness, these algorithms are simple and ecient in a high-speed network. In general, frame-based schedulers are nonwork-conserving and waste network bandwidth. Round-robin schedulers usually su er from poor delay performance. CarryOver Round Robin is essentially a frame-based scheduler. However, it is work-conserving and yields low delay independent of the number of connections.. 2 CORR ALGORITHM CORR is a variation of the frame-based scheduling discipline in ATM networks [11]. It divides the time line into cycles of maximum length T . At the time of admission, each connection Ci is allocated a rate Ri expressed in cells per cycle. Unlike simple round-robin schemes, where Ri has to be an integer, CORR allows Ri to be any real number. Although Ri can be real in CORR, the actual number of slots allocated to a connection in a cycle is still an integer. The debits and credit due to imperfect allocation are carried over into the next cycle. The CORR scheduler (see Figure 1) consists of three asynchronous events | Initialize, Enqueue, and Dispatch. The event Initialize is invoked when a connection is admitted. If a connection is admissible, it simply adds the connection to the connection list fC g. Note that the connection list must be in the decreasing order of Ri ; bRic, i.e., the fraction part of Ri. Intuitively, arranging connections in a decreasing order of the fractional part of Ri can make sure that the connections with higher fraction requirement are served earlier. Let us walk through an example(as shown in Figure 2) referred to [11]. Consider a system with cycle length T=4 cells serving three connections, C1; C2, and C3, with R1 = 2; R2=1.5, and R3=0.5, respectively. For ease of exposition, assume that all the three connections are backlogged starting from the beginning of the system busy period. In the major cycle of the

(3) rst cycle, CORR allocates C1 ; C2 , and C3; bR1c = 2; bR2c = 1, and bR3c = 0 slots, respectively. Hence, at the beginning of the

(4) rst minor cycle, r1 = 0:0; r2 = 0:5, and r3 = 0:5. The only slot left for the minor cycle.

(5) Constants. T:Cycle length. Ri:Slots allocated to Ci. Variables. fC g:Set of all connections. t:Slots left in current cycle ni :Number of cells in Ci ri :Current slot allocation of Ci. Events Initialize(Ci);/*Invoked at connection setup time*/ add Ci to fC g; ni. 0; ri. 0;. Enqueue();/*Invoked at cell arrival time*/. ni = ni + 1; add cell to connection queue; Dispatch();/*Invoked at the beginning of a system busy period*/ 8C: : ri 0; while not end of busy period do t T 1. Major Cycle: for all Ci 2 fC g do /* From head to tail*/ ri min(ni; ri + Ri );xi min(t; bric); t t ; xi ; ri ri ; xi; ni ni ; xi; dispatchxi cells from connection queue Ci;. end for. 2. Minor cycle: for all Ci 2 fC g do /*From head to tail*/ xi min(t; drie); t t ; xi ; ri ri ; xi; ni ni ; xi; dispatch xi cells from connection queue Ci;. end for end while. Figure 1: CORR algorithm. goes to C2. Consequently, at the end of the

(6) rst cycle, r1 = 0:0; r2 = ;0:5, and r3 = 0:5. The adjusted requirements for the second cycle are r1 = r1 + R1 = 0:0 + 2:0 = 2:0 r2 = r2 + R2 = ;0:5 + 1:5 = 1:0 r3 = r3 + R3 = 0:5 + 0:5 = 1:0 Since all the ri's are integers, they are all satis

(7) ed in the major cycle of the second cycle. The main attraction of CORR is its simplicity, which is regarded as the most important criterion for the selection of an algorithm for use in a real system. Nevertheless, we believe CORR should be simpli

(8) ed due to several reasons as follows. 1. The sorted connection list increases the complexity of implementation. Although CORR still maintains O(1) work per cell, it will probably drive up the cost of routers. 2. A CORR scheduler makes at most two passes through the connection list in each cycle{one during the major cycle and the other during the minor. Figure 2: An example of CORR. cycle. Thus CORR performs twice the number of operations performed by a round-robin scheduler in the worst case. If we combine the two subcycles into one, or eliminate either of them successfully, the algorithm will be more ecient. 3. CORR allows ri to be negative. It implies that some connections getting a slot in the minor cycle would exceed their allocated quotas. Hence, the allocation of bandwidth is a little unfair. In fact, the drawbacks of CORR mentioned above come from maintaining the maximum frame size. In order to derive the worst-case end-to-end delay, a maximum frame length is helpful at the beginning. However, it doesn't mean such a step is necessary. In the next section, we will present a modi

(9) ed scheme to simplify CORR. Also, we will show that the scheme proposed has a similar delay bound and better fairness.. 3 THE MODIFIED SCHEME The minor cycles in CORR allow ri to be negative. It has been proved that ri 0 at the beginning of each cycle. After updating ri to ri + Ri, the number of cells dispatched during one cycle is smaller than T. Combined with the sorted connection list, CORR guarantees that the bandwidth allocated to each frame never exceeds T. Under this condition, the worst-case delay encountered by the ith cell in a CORR scheduler can be derived. A detailed proof can be found in [12] and [11]. The basic idea of our modifying CORR is to reduce operations. Now, assume we erase the minor cycle of the Dispatch event in CORR. Then a much larger frame with a probably in

(10) nite length may be generated. Since a larger frame leads to a larger delay, a similar bound after modifying CORR seems dicult to derive. Thus the key to simplify CORR is to derive a delay bound without a maximum frame size. Let us consider the similar example presented in the previous section. However, at this time there are no minor cycles (as shown in Figure 2). Let cycle length.

(11) Figure 4: The un

(12) xed cycle length of our scheme.. Figure 3: An example of our algorithm. T =4 and R1 = 2; R2 = 1:5, and R3 = 0:5. Observe that from time t0 to t2 , the scheduler dispatches 8 cells during this interval. r1 = r2 = r3 = 0 at the beginning of Cycle 1 and the end of Cycle 2. That is almost the same as CORR. Observe that in time interval (t1; t2 ), cells allocated in Cycle 2 are 5. r1 = 0:0; r2 = 0:5, and r3 = 0:5 at the beginning of Cycle 2. r1 = r2 = r3 = 0 at the end of Cycle 2. Cycle 2 is allowed to send one more cell than T. Note that ri = 1 at the beginning of Cycle 2. We generalize our observations as follows. 1. If we don't consider the initial values of ri (or assume all ri are set to zero), the following expression holds (the situation is shown in Figure 4). ;. n X1 k =0. Ck . ;. n X1. T = nT. k =0. That is the case we observe at t0 :C1 = 3 is smaller than the ideal length T and C1 + C2 = 8 is equal to the ideal length 2T. 2. If we consider the initial values of ri, the above inequality becomes ;. n X1 k =0. Ck nT +. ;. N X1 i=0. ri. This case is like the observation at t0 . C2 = 5 T + ri = 5. Now we solve the problem of the maximum frame size. The delay without minor cycles is at most N T plus ri . So we can follow the steps used by CORR to analyze the delay performance. It is clear that the operational complexity of CORR can be reduced. The sorted connection list and the minor cycle are not necessary for deriving the delay bound. Thus we propose another scheduling algorithm as shown in Figure 5. The main di erence between CORR mechanism and ours is that we erase the minor cycle in the new scheme. Hence each ri becomes a non-negative number and connection list doesn't have to be sorted anymore. The. Constants Ri:Slots allocated to Ci . Variables. fC g:Set of all connections. ni :Number of cells in Ci ri:Current slot allocation of Ci. Events Initialize(Ci);/*Invoked at connection setup time*/ add Ci to fC g; ni. 0; ri. 0;. Enqueue();/*Invoked at cell arrival time*/. ni = ni + 1; add cell to connection queue; Dispatch();/*Invoked at the beginning of a system busy period*/ 8Ci :: ri 0; while not end of busy period do for all Ci 2 fC g do /* From head to tail*/ ri min(ni; ri + Ri); ri ri ; bri c; ni ni ; bri c; dispatch bric cells from connection queue Ci;. end for end while. Figure 5: The modi

(13) ed algorithm. number of the basic operations such as +, -, *, / is approximately reduced half as many as CORR. In the next section, we analyze the fairness properties and delay performance of the new scheme. Then we compare with CORR and typically Flow-Timestamp methods. The results show that, albeit its simplicity, this scheme outperforms CORR in terms of fairness. As long as the frame size T close to 1, the performance of delay and fairness is also similar to Flow-Timestamp methods.. 4 MATHEMATICAL ANALYSIS A.Fairness In a work-conserving server, when the system is not fully loaded, the spare capacity can be used by the busy connections (a connection is busy if its queue is nonempty) to achieve better performance. One of the important performance metrics of a work-conserving server is the fairness. Here the fairess means how fair.

(14) the server is in distributing the excess capacity among the active connections. In this section, we analyze the fairness property of our scheduling algorithm and compare with CORR. Formally, if Ri is the reserved rate of ow i and sendi (t1; t2) is the aggregate service (in cells) received by it in the interval [t1; t2], then an allocation is fair for any intervals [t1; t2] in which both ows i and j are backlogged. That is, send (t1; t2 ) = send (t1; t2) Ri Rj This is an idealized de

(15) nition of fairness as it assumes that ows can be served in in

(16) nitesimally divisible units. The objective of fair scheduling algorithms is to ensure that

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(19) sendi (t1 ; t2) sendj (t1 ; t2)

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(32) H(i; j) Ri Rj for all intervals [t1; t2], then H(i; j) 2cl ( R1 + R1 ) i j where H(i; j) is a function of the property of ows i and j, c denotes the capacity of the output channel, and l denotes the cell length in bits. The function H(i; j) is referred to as fairness measure. Like CORR, we assume that our sampling points coincide with the beginning of the allocation cycles only. Now, when a connection is busy during the cycles (c1; c2) , the amount of services received is sendi (c1 ; c2) = b(c2 ; c1)Ri + i c where i is the initial value of the counter at the beginning of cycles. Note that i has to be nonnegative and smaller than 1. In the following, we let 1 )Ri + i c Wi (c1 ; c2) = b(c2 ; cR i Thus, j. i. jWi (c2 ; c1) ; Wj (c2 ; c1)j

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(36) b(c2 ;cR1 )iRi +i c ; b(c2 ;cR1 )jRj +j c

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(42) (c2 ;c1 )RRii +i ;xi ; (c2 ;c1 )RRjj +j ;xj

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(48) iR;ixi + xjR;jj

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(50) 0 xi; xj < 1 In the worst case, jWi (c2 ; c1 ) ; Wj (c2 ; c1)j R1 + R1 i j. Under the same scenario, it has been proved that in a CORR scheduler the following equation holds at all times. jWi (c2 ; c1) ; Wj (c2 ; c1 )j R2 + R2 i j Clearly, the fairness measure of CORR is within two times that of our scheme. B. Delay in single node The delay su ered by any cell in a scheduler is the di erence between its arrival time at and departure time from the system. The arrival time of a cell can be obtained from the trac envelope associated with the connection it belongs to and is determined by the shaping mechanism used. In the rest of the section, we derive delay bound for arrival function characterized by the composite leaky bucket. Let's consider a composite leaky bucket consisting of n component leaky bucket (bi ; i); i = 1; 2; 3:::; n. It has been proven in [13] that the departure time of the ith cell from the composite shaper, denoted by a(i), is a(i) = where. Pn+1 k =1. (i ; bk + 1)k [U(i ; Bk ) ; U(i ; Bk;1)]; i = 0; 1; :::; 1. 8 > > > > <. 1. k=0. bk k ;bk+1 k+1 Bk = > b k ;k+1 c k = 1; 2; :::;n > > > 0 k = n+1 :. and. 8 > <. 0 x<0 U(x) = > 1 x 0 :. We regard a(i) as the arrival time of the ith cell at the network entry point. Now we have to derive the departure time of the ith cell. Assume a connection enters a busy period at time = 0. Let d(i) be the latest time by which the ith cell departs the system. It's dicult to know the exact time when the cells exit. To capture the worst case, we assume that all cells served during a cycle leave at the end of cycle. Now, if cell i departs at the end of the Lth cycle from the beginning of the connection busy period, the number of slots allocated by the scheduler is L R + , and the number of slots consumed is i + 1(assuming packet number starts from 0). As a result, LR+;i 1 Since is between 0 and 1, in the worst case, = 0.Thus we get L 1 R+ i.

(51) From the above inequality and noting that L is an integer and d(i) = L T , we get N ;1 X d(i) = cl 1 R+ i T + cl rk k =0. . . Now we can compute the delay bound from the di erence between d(i) and a(i). It has been proven in [11] that the maximum delay encountered by any cell is at most as large as the delay su ered by cell Bj (with composite leaky bucket) and a(Bj ) can be derived as follows. 1 < a(Bj ) = (Bj ; bj + 1)tj when t1 < R T tj +1 j Therefore, the delay bound is Delay d(Bj ) ; a(Bj ) = +. PN ;1 k =0. rk when. 1. tj. l. < < R T. Bj +1 R. m. T ; (Bj ; bj + 1)tj. 1 tj +1. ak (i) in the above theorem. That becomes ak (i) = 1max fa (j)+j =l =max ( j i 1 l :::l =i 1. n X. ak (i) = 1max fa (j)+ j =l1 lmax ( Sh (lh ; lh+1 ))g j i 1 2 :::lk =i h=1 where n is the number of switch nodes between the source and the destination.. The theorem presented above is very broad in the sense that it does not assume any speci

(52) c arrival pattern of scheduling discipline. It means that if the ith cell never encounters any queuing in the system, its departure time can be computed as the sum of its arrival time into the system and its service time at di erent nodes. If the ith cell encounters queuing in the system, its departure time may potentially depend on the arrival time of any cell that entered the system before it. A detailed description of the theorem can be found in [11]. However, computing exact service time of different cells at each node is quite dicult. Fortunately, computing the worst case bound on departure time and the worst case delay for speci

(53) c service discipline and arrival patterns is not that dicult. Thus we can replace the service time Sh (:) at nodes h = 1; 2; :::n with the worst case service time Sw (:) in the expression for. h=1. Sw (lh ; lh+1 ))g. N ;1 X l (l l h+1 ; lh ) + 1 Sw (lh ; lh+1 ) = c T+c rk R k =0. . . Also, Pn. l h=1 Sw (lh ; lh+1 ) = c. Pn l. +c. cl. PNh. Pn. h. h=1. h=1. r. . R. . 1c n + nR;1 T + cl Pn;1 PNh h=1. h. (lh. +1 ;lh )+1 R. i. +1 ;lh )+1. (lh. l. Pn. h k =1 k. h=1. + 1 T + cl ;. ln+1 l1 +1 R. i. Pn. h=1. T + cl. m. T. PNh. r. h k =1 k. PNn. r. n k =1 k. r. h k =1 k. ;1 PNh rh 1c n + nR;1 T + Sw (l1 ; ln+1 ) + cl Pnh=1 k =1 k n;1 l Pn;1 PNh 1 c n + R T + Sw (j; i) + c h=1 k=1 rkh . Theorem: For any node k and for any cell i, the following holds:. k. Recall that we have computed the worst case service time d(i). Now we can derive the end-to-end delay bound by replacing. + cl. C. Delay in multi-nodes Consider a connection traversing n switching nodes between source and destination. Let's denote by ak (i) the arrival time of the ith cell of the connection at node k. The service time of the ith cell at node k is denoted by sk (i). The service time of cells p ; q at node k is Sk (p; q). Assume the propagation delay between nodes is zero. Then the departure time of cell i from node k is ak+1(i). A theorem in [12] is descirbed as follows.. 2. n X. . (l1 = j and ln+1 = i) Hence, the end to end delay bound is ak(i) ; a1(i). h. i. Delay(i) cl n + nR;w1 T + max1j ifa1 (j) + Sw (j; i)g + cl. Pn;1 PNh h=1. r ; a1(i). h k =1 k. D. Comparison with CORR Now we compare the performance with CORR(as shown in Table 1). As we expect, the fairness of our scheme is better than that of CORR since the counter value ri is limited to be nonnegative. The worst case complexity is still O(1), the same as CORR. However, CORR has two subcycles in a frame. Thus CORR has nearly as twice the number of operations as our scheme. The worst case end to end delay of these two schedulers seems similar. So we assume all rkh = 1 and each node has the same number of connections N. Therefore, the di erence in maximum delay that a cell may incur employing CORR and our scheme is DCORR (i) ; DOU RS (i). ;1 N ;1 rh ) = cl ( nR;w1 T ; nh=1 k =0 k = cl ( nR;w1 T ; N(n ; 1)) = cl (n ; 1)( RTw ; N) P. P. Observe that the maximum delay of cells of a connection in our scheme is smaller than in CORR if.

(54) Fair End to End Delay Complexity. CORR Our approach 2 1 2 + + R1j Rj h i Ri h i Ri l n;1 l n;1 c n + 2 Rw T + max1j ifa1 (j)+ c n + Rw T + max1j i fa1 (j)+ P ;1 PNh h Sw (j; i)g ; a1 (i) Sw (j; i)g + cl nh=1 k =1 rk ; a1 (i) O(1) O(1) Table 1: Comparison with CORR.. Rw < T=N. In other words, a connection of CORR has a smaller delay if Rw > T=N. Since T=N is the average rate of all connections in full load, we can expect that half of connections would have reserved rate smaller than T=N. That is, half of them have a smaller delay than CORR if the system employs our scheme. Thus, the delay performance of our algorithm is not worse than CORR. However, this algorithm has a better fairness and lower operational complexity. E. Comparison with Flow-Timestamps As mentioned earlier, the schedulers based on computing timestamps are the best of breed. Although it is hard to implement in high-speed networks, they are still very attractive. The author of CORR has compared with SCFQ and PGPS, two typically owtimestamp schedulers, in terms of fairness and delay. It seems CORR is competitive with them. However, this comparison is not suitable due to the di erent trac models and de

(55) nitions. For example, CORR uses the begging of allocation cycles (c1; c2) instead of real time(t1; t2) to derive fairness measure. Then CORR compared fairness with SCFQ directly. In fact, the fairness measure should have two properties|longterm fairness and short-term fairness. The long-term fairness implies fair allocation of bandwidth and the short-term fairness implies the size of trac burst of a connection. Unfortunately, to derive the fairness measure using cycles instead of real time does not have the short-term fairness property. The scheduler may produce a large burst during any cycle even though the distribution of bandwidth is fair at the end of this cycle. This situation may occur in any frame-based but not in ow-timestamps schedulers. However, we can not see such a property in mathematical analysis as we derive fairness measure like CORR. Therefore, we provide another analysis similar to ow-timestamps and compare with them in Table 2. As expected, ow-timestamps schedulers always perform better except complexity. The larger the frame size is, the worse ` the delay and fairness are. Fortunately, our scheduler is designed for asynchronous transfer mode networks. Since the cell length is

(56) xed in ATM networks, the frame size can be reduced to a minimum as small as 48 bytes(one cell length). Then the performance is very similar to any ow-timestamps scheduler as shown in Table 3. However, it is not ef

(57) cient if the frame size T is 1. The overhead of each pass through the connection list is high. It may lead. to a bottleneck in the system as well as sorting in the ow-timestamps schedulers.. 5 CONCLUSION In this paper, we have proposed a modi

(58) ed scheme of CORR algorithm, which is a variation of framebased scheduling discipline in ATM networks. We also have shown that our algorithm improves the fairness of CORR and reduces the operational complexity. In addition to CORR, we provided another analysis to compare with ow-timestamps schedulers. The result shows that our scheme performs as well as SCFQ and PGPS if the frame size is limited to one cell length. However, the implementation of ours is much easier. Like the scheduling mechanisms with high complexity of implementation, the frame size limited to 1 may cause a serious bottleneck in high-speed networks. We believe the problem can be solved if the frame size is dynamically adjusted. When the trac load is light, the smaller frame size limits the burst to be small. When the trac load is heavy, the larger frame size leads to a lower average delay than SCFQ and PGPS. Although a larger burst is produced in heavy trac load, our scheduler is still simpler and more ecient than SCFQ and PGPS.. References. [1] S. Iatrou and S. I., \A dynamic regulation and scheduling scheme for real-time trac management," IEEE/ACM Trans. Networking, vol. 8, pp. 60{70, February 2000. [2] S. D., Z. H., and J. Bennett, \Implementing scheduling algorithms in high-speed networks," IEEE J. Select. Areas Commun., vol. 17, pp. 1145 {1158, June 1999. [3] K. Parekh and R. G. Gallager, \A generalized processor sharing approach to ow control in integrated services network: The single node case," in Proc. IEEE INFOCOM'92, vol. 2, pp. 915{924, May 1992. [4] P. Goyal, V. H. M., and C. H., \Start-time fair queuing:A scheduling algorithm for integrated services network," IEEE/ACM Trans. Networking, vol. 5, pp. 690{704, 1997. [5] J. A. Cobb, M. G. Gouda, and A. El-Nahas, \Time-shift scheduling-fair scheduling of ows in.

(59) CORR 1 1 Fair Ri + Rj 1 l l End to End Delay R C + C PGPS 1 l l R C + (N ; 1) C SCFQ Complexity O(logN) or O(N) l c. . Our approach 2T + R1i + R1j ;1 lT l R + 1 C + (N ; 1) C l c. . O(1). Table 2: Comparison with Flow-Timestamps. CORR 1 1 Fair Ri + Rj 1 l l End to End Delay R C + C PGPS l 1 l R C + (N ; 1) C SCFQ Complexity O(logN) or O(N) l c. . Our approach 2 + R1i + R1j ;1 l l R + 1 C + (N ; 1) C l c. O(1). Table 3: Comparison with Flow-Timestamps.. [6]. [7]. [8]. [9] [10] [11]. [12] [13]. high-speed networks," IEEE/ACM Trans. Networking, vol. 6, pp. 274 {285, June 1998. L. Zhang, \Virtualclock: A new trac control algorithm for packet switching networks," ACM trans. Comput. Syst., vol. 9, pp. 101{124, May 1991. D. Stiliadis and V. A., \Ecient fair queuing algorithms for packet-switched networks," IEEE/ACM Trans. Networking, vol. 6, pp. 175{ 185, April 1998. D. Stiliadis and V. A., \Rate-proportional Servers: A design methodology for fair queuing algorithms," IEEE/ACM Trans. Networking, vol. 6, April 1998. G. S. J., \A framing strategy for connection management," in Proc. SIGCOMM'90, 1990. M. Shreedhar and G. Vaghese, \Ecient fair queuing using de

(60) cit round robin," IEEE/ACM Trans. Networking, vol. 4, pp. 375{385, June 1996. D. Saha, S. Mukherjee, and S. Tripathi, \Carryover round robin: A simple cell scheduling mechanism for ATM networks," IEEE/ACM Trans. Networking, vol. 6, pp. 779{796, December 1998. D. Saha, Supporting distributed multimedia applications on ATM networks. PhD thesis, Univ. Maryland, 1995. S. Raghavan and S. Tripathi, Networked multimedia systems. Prentice Hall, 1998..

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