Using the Imprecise-Computation Technique for ... - CiteSeerX

Appeared in Proc. of the Int'l Conf. on Parallel & Distributed Systems, Hsinchu, Taiwan, December 1994.

Using the Imprecise-Computation Technique for Congestion Control on a Real-Time Trac Switching Element V. Millan-Lopez c/ Narciso Serra 4, 7A 28007 Madrid Spain

W. Feng and J. W.-S. Liu Department of Computer Science University of Illinois at Urbana-Champaign Urbana, IL 61801

Abstract

This paper presents a congestion-control scheme based on the imprecise-computation technique [1] and shows that the scheme is eective in relieving network congestion due to uctuations in real-time trac. Section 2 discusses the applicability of the imprecisecomputation technique to congestion control and the network architecture based on this technique. Section 3 presents the scheduling policy. To assess the eectiveness of our congestion-control scheme, we present simulation results in Section 4. Finally, Section 5 summarizes our work and outlines future work.

The Broadband Integrated Services Digital Network provides communication services with dierent requirements, including real-time services such as voice and video. Real-time services are aected by the probabilistic behavior of such a network. In particular, when the network becomes congested, the end-to-end packet delay may exceed the maximum allowed. Fortunately, many real-time services are willing to trade service quality for information timeliness. The imprecisecomputation technique, in combination with layered coding schemes, makes this tradeo possible.

2 Congestion-Control Scheme

1 Introduction

A message containing related information, such as video frames, consists of a number of xed-size packets. To apply the imprecise-computation technique [1] to control congestion, we divide the packets in each message into two types: mandatory and optional. The mandatory packets carry the basic-quality portion of the message. When all mandatory packets over a connection are delivered in time, we achieve a reduced level of service quality which is acceptable to the end user. The optional packets carry the extra-quality portion, the additional information needed to achieve fullservice quality. Such a partition of packets can be achieved by using layered coding schemes [2]. Optional packets may be discarded, if necessary, so that the message and other messages can meet their deadlines. Our congestion-control scheme uses a two-level scheduling discipline | basic quality versus extra quality. This scheme provides dierent qualities of service to dierent trac classes based on a prioritybased scheduling policy. Several studies have shown that this two-level scheduling discipline is eective in handling overloads in multiprocessor systems and providing ow control in networks [3-5]. While these studies assume that task arrivals are random, our

Using the asynchronous transfer mode (ATM),

Broadband Integrated Services Digital Networks (B-

ISDNs) can provide real-time communication ser-

vices. These services have timing requirements, including end-to-end delay and delay jitter. End-to-end delay is the time interval between the time when a packet is generated by the source and the time when it is delivered to its destination. Delay jitter is the variation in the end-to-end delay. A packet misses its deadline if its end-to-end delay exceeds the maximum allowed value. The end user provides these requirements to the network during the connectionestablishment phase. A new connection is accepted only if there are enough resources to satisfy its requirements with a speci ed probability while still meeting the requirements of existing connections. Unfortunately, due to the non-deterministic behavior of trac sources, a good connection-acceptance strategy by itself cannot guarantee that all packets will meet their end-to-end delay requirement. Trac peaks can temporarily saturate a switching node, causing network congestion. A consequence of network congestion is the potential failure to meeting timing requirements. 1

study focuses on real-time messages whose arrivals are periodic. Switching elements are the basic components which make up a B-ISDN network. As a rst step towards evaluating our congestion-control scheme, we focus on the congestion local to a switching element. We assume that the switching element, shown in Figure 1, is non-blocking and output-queuing. In such a switching element, streams of trac bound to dierent outputs do not interfere with each other. This allows us to focus in on the trac bound to a single output link. Without loss of generality, we restrict our attention to the portion of the switching element consisting of one output buer and its corresponding transmission circuits and output link. We refer to this portion as the output system.

Switched Traffic from the Input Links

Imprecision Filter

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Figure 2: The Output System

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and the switch make up the constant part. Hereafter, we will ignore this part and focus on the variable part: packet delay through the output system | the interval of time between the instant when the rst byte of the packet enters the output system and the instant when its last byte is transmitted down the output link (i.e., queuing delay plus packet transmission time). The maximum allowed value for packet delay through the output system is the relative deadline of the packet. Video and voice packets (i.e., real-time packets) have nite relative deadlines. Data packets are considered to be non-real-time, and thus their relative deadlines are theoretically in nite; but we want data packets to have short delays on the average. When a connection is established, we assume that the end-to-end scheduling mechanism of the network derives the relative deadline of the packets at each switching element along the connection, based on the maximumallowed end-to-end delay on the connection. At each switching element, we assume that all packets in any trac class have the same relative deadline. This assumption allows us to consider each switching element in isolation. In practice, this assumption is restrictive since a packet may suer a short delay in a switching element and could therefore aord a longer delay in another switching element, and packets on a connection traversing a fewer number of switching elements can aord longer delays at each element. The scheduling policy for the output system is a non-preemptive one (since packet transmission should

TC

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LTC: Line Termination Circuit OB: Output Buffer TC: Transmission Circuit

Figure 1: An Output-Queuing Switching Element Figure 2 shows the structure of the output system [6]. There are three kinds of communication services: videotelephone, telephone, and data transference. Likewise, the output buer is split into three independent subbuers which share the same output link. Each subbuer stores packets of a dierent class: video, voice, and data. The video and voice subbuers are real-time subbuers while the data subbuer is non-real-time. The use of the transmission circuits and the output link by the packets in the subbuers is arbitrated by the scheduler. The imprecision lter is the component that implements the congestioncontrol scheme.

3 Scheduling Policy The delay of a packet through a switching element consists of a constant part and a variable part. The delays introduced by the input-line termination circuit 2

not be interrupted) based on a combination of the earliest-deadline- rst algorithm [7], a periodic-server scheme [8], and the imprecise-computation technique. Whenever the scheduler chooses to send real-time packets, the packet with the nearest absolute deadline among all packets in the real-time subbuers is transmitted. Con icts are resolved on a rst-come rst-serve (FCFS) basis. Since packets stored in a real-time subbuer all have the same relative deadline and are ordered by arrival time, it follows that they are also ordered by absolute deadline. Consequently, the earliest-deadline- rst algorithm is reduced to choosing the real-time subbuer whose rst available packet has the nearest absolute deadline and therefore can be implemented with negligible run-time overhead. Non-real-time packets in the data subbuer are transmitted on a FCFS basis. To reduce the delay of these packets, a periodic server [8] is used. A periodic server is de ned by its period and the percentage of bandwidth that it reserves for non-real-time packets. Given this percentage, the transmission rate of the link, and the period of the server, we can determine the maximum number of non-real-time trac packets that can be sent during each server period. Non-real-time packets are given higher priority than real-time packets within each server period until packets have been transmitted or until the data subbuer is empty. After that point, higher priority reverts to real-time packets until the next server period. To distinguish between mandatory and optional packets, the Cell Loss Priority (CLP) bit in the packet header can be used. When the output system becomes congested, the imprecision lter may discard optional packets before they enter the output buer. But once in the output buer, every packet is transmitted regardless of whether its deadline has been missed. There are two reasons for doing this: (1) keeping late packets relaxes the restrictive condition of having a relative deadline per class, and (2) letting the imprecision lter be the only source of packet loss allows us to isolate the eect of the imprecision mechanism on the quality of real-time communication services.

packets at an average bit rate of 1.28 Mbps and 30 frames per second [9]. Each telephone connection carries voice packets at an average bit rate of 25.175 kbps ( xed bit rate of 64 kbps when the subscriber is speaking) [10]. Each data-transference connection carries data packets at an average bit rate of 1 Mbps. The bit rates above do not include the overhead due to the header of ATM packets. The parameters used in our experiments are listed in Table 1. Trac load determines the number of connections that the output system supports. A trac load consists of a background load and a foreground load. Each experiment starts with a background load and then gradually adds connections, as part of the foreground load, until the link reaches full utilization. The background load has 20 videotelephone connections, 1000 telephone connections, and 13 data connection, which results in a total link utilization of 37.4%. The foreground load consists of videotelephone connections for a video-predominant trac load and telephone connections for a voice-predominant trac load. To model the worst-case behavior, connections in the foreground trac load are added in phase; that is, the rst packets of all connections arrive at the same time.

M

M

Trac

Parameters

Trac Load Relative Deadlines Imprecision Ratio Output System Congestion Threshold Reserved Bandwidth Periodic Server Period Table 1: Parameters for the Simulation Experiments The relative deadlines parameter, denoted by , is a pair of values in milliseconds | the relative deadlines of video and voice packets: = ( video voice). The imprecision ratio IR is the ratio of the number of mandatory packets to optional packets. The congestion threshold Th is the number of packets in the real-time subbuers above which the output system is said to be congested. The periodic server is de ned by its reserved bandwidth and period. We measure the performance of the output system by the miss ratio, loss ratio, and invalid ratio. Miss ratio is the fraction of packets that miss their deadlines, excluding discarded packets. Loss ratio is the fraction of packets that are discarded by the imprecision lter. Invalid ratio is the fraction of packets that are unusable by the receiver, which include late and RD

RD

RD

4 Simulation Experiments To evaluate the eectiveness of the imprecision lter, we simulated the output system using a trac model which assumes that all trac sources use variable bit-rate coding and that packet interarrival time distributions resemble real trac sources. Speci cally, each videotelephone connection carries video and voice 3

; RD

rst unstable region. The border point between the rst stable region and rst unstable region is the rst saturation point. While the curve for Th = 1 remains

discarded packets. This measure gives us the overall performance of the output system. We also recorded data on link utilization, subbuer occupancy levels, packet delay through the output system, and packetdelay jitter. Due to space limitations, none of the results on buer-occupancy levels and packet-delay jitters are presented here. They can be found in [11]. For all the results presented here, the 90% con dence intervals are negligibly small.

in the rst unstable region, the curves for nite values of Th reach their activation points and plateau again in the second stable region. Beyond a certain number of connections (i.e., the second saturation point), the delays increase again in their second unstable region. This pattern of stable and unstable regions of the output system is typical for nite values of . The mean delay for voice packets, as shown in Figure 6, is slightly higher than video packets because of the higher priorities of video packets due to their generally nearer absolute deadlines. It exhibits the same behavior as the mean delay for video packets as the number of connections increases [11]. Figure 7 shows the miss ratio of all packets in our base experiment with a video-predominant traf c load. For Th = 1, the miss ratio grows linearly with the number of connections. For nite values of Th, the shape of the curves depends strongly on the value of Th. The curves corresponding to Th = 500 and Th = 800 have the typical structure of two stable and two unstable regions. However, the curves for Th = 50 and Th = 300 do not have a rst unstable region; their rst stable region extends to their second saturation points. So, we can obtain very dierent miss-ratio behavior by simply changing the value of Th. This is particularly remarkable since the loss-ratio curves for dierent values of Th are very similar to each other (see Figure 4). Therefore, we conclude that it is possible to signi cantly improve the miss ratio at the expense of a slight increment in the loss ratio. Figure 8 shows the invalid ratio of all packets in our base experiment with a video-predominant trac load. By using a smaller congestion threshold, both the packet delay and the number of invalid packets can be kept small [11]. We repeated the base experiment using a voicepredominant trac load (BE;VoP). Unlike video predominance, we found that the eect of the imprecision mechanism is small. The reason for this dierence between video predominance and voice predominance lies in the structure of the trac. Videotelephone sources periodically generate frames of similar duration. Since the connections in the foreground load are in phase, the frames of all these connections are ready for transmission at the same time. This causes periodic peaks of trac that produce congestion and the consequent activation of the imprecision lter. On the other hand, for telephone connections, the cycles for speech and silence are not periodic and have difTh

4.1 Base Experiment Based on the work of [11, 12], we set the parameters for our base experiment (BE) to those listed in Table 2. When = 1, no packet is discarded, and hence the imprecision mechanism is not activated. Th

Relative Deadline Imprecision Ratio Reserved Bandwidth Periodic Server Period Congestion Threshold

(1,2) 1/1 10 10 f50, 300, 500, 800, 1g

Table 2: Parameters of the Base Experiment We rst ran the base experiment using a videopredominant trac load (BE;ViP). Figures 3 and 4 show the link utilization and loss ratio. The curves for nite values of Th coincide with that for Th = 1 until the loss ratio becomes signi cant (i.e., greater than 10?5, the resolution of the experiments). The number of connections at which this happens, for a given Th, is called the activation point. Beyond the activation points, the imprecision mechanism keeps link utilization relatively constant over a wide range of connections because the number of discarded packets nearly cancels the increase in trac oered to the output system. When nearly all optional packets are discarded, the imprecision mechanism can no longer cancel the increase in trac, and the utilization rises again quickly with the number of connections. Figure 4 shows that the loss ratio does not depend strongly on the congestion threshold Th. Figure 5 shows the mean delay of video packets in terms of packet slots; each slot is the transmission time of a packet. The mean packet delay is smaller for lower congestion thresholds. When the number of connections is low, packet delays are insensitive to increases in the number of connections. We call this at portion of the curves the rst stable region. As the number of connections grows, the delays increase rapidly in the 4

ferent durations. Thus, the trac is more uniformly distributed in time than videotelephone trac. As the number of connections increases, link utilization gets close to unity before the loss ratio begins to be signi cant. When it does, the imprecision mechanism cannot stabilize the system as it did when the videopredominant trac load was used. Consequently, all performance measures show only the rst stable and the rst unstable region [11].

of video packets that are sent before the voice packets decreases. Thus, the performance of voice packets is improved at the expense of video packets. Similarly, the invalid ratios also dier substantially from those obtained in the base experiment. In fact, the performance obtained by using the congestion threshold Th = 50 for RD = (0.5,1.0) is similar to that of Th = 300 for RD = (1.0,2.0). These results indicate that if we reduce the values of the relative deadlines, we must also lower the congestion threshold to attain the same performance in terms of the invalid ratio. Finally, in the experiment on the congestion threshold (ECT), Figure 9 shows the miss, loss, and invalid ratios for packets of all trac classes when RD = (1.0, 2.0). The loss ratio is a monotonically decreasing function of the congestion threshold because fewer packets are discarded when a higher congestion threshold is used. The miss ratio is a monotonically increasing function of the congestion threshold. It shows an extremely abrupt increase at = 350 because in this unstable region, a small variation in the number of connections causes a large increase in the subbuer occupancy levels and the packet delays. By slightly decreasing the congestion threshold, we cancel the slight increase in the number of connections that makes the output system enter its rst unstable region. The invalid ratio is determined by two opposing factors, the miss and loss ratios. As we can see in Figure 9, the invalid ratio reaches its minimum value for a congestion threshold of 200. The results of this experiment when RD = (0.5, 1.0) again lead us to conclude that when the relative deadlines are shorter, it is necessary to lower the congestion threshold to achieve the same performance in terms of the invalid ratio.

4.2 Experiments on System Parameters In a series of experiments, we changed each of the system parameters in turn while keeping the other parameters the same as in the base experiment. We rst changed the imprecision ratio of the trac sources to = 1 3. We found that the system behaves as expected. The link utilization for IR = 1/3 remains constant after the activation point for a wider range of connections than for IR = 1/1. This is due to the fact that more packets can be discarded when IR = 1/3. The change in the imprecision ratio does not affect the values of the mean packet delay in the second stable region, but it does produce a longer second stable region. This is a consequence of the extended at region of the link utilization. The results on the invalid ratio exhibit the same behavior as when IR = 1/1. Next, we repeated the base experiment but with the relative deadlines set to half their values, = (0.5, 1.0). Because the values of the relative deadlines do not aect the number of packets discarded by the imprecision lter, the loss ratio and the link utilization in this experiment are the same as in the base experiment. However, the packet delay for video and voice packets are noticeably dierent from those found in the base experiment. The mean delay of video packets is slightly longer for the shorter relative deadlines while for voice packets the opposite is true [11]. This phenomenon can be explained as follows: The values of the relative deadlines aect the way that real-time packets are scheduled since the earliest-deadline- rst algorithm is used. Suppose that a video packet and a voice packet have just arrived in empty buers. The video packet will be sent rst since its absolute deadline is sooner. Furthermore, subsequent video packets with absolute deadlines nearer than that of the voice packet will be sent rst. Since the ratio of the relative deadlines of video and voice packets is 1/2, all video packets arriving during an interval of time equal to a half of the relative deadline of the voice packet will be sent before the voice packet. It follows that when the relative deadlines are reduced, the number IR

=

Th

RD

5 Conclusions This paper presented the performance of a congestion-control scheme for an ATM-like switching element, based on the imprecise-computation technique and a priority-based scheduling scheme. Its objective is to reduce the number of packets which miss their deadlines under congestion conditions while guaranteeing a level of quality acceptable to the end users. The experimental results prove that our congestioncontrol scheme is eective. By discarding the optional packets under congestion, the system remains stable for a larger number of connections than if no packets were discarded. This number of connections is even larger if the trac load is bursty in nature. The con5

gestion threshold allows us to adjust the congestioncontrol scheme to the nature of the trac load. In general, lowering the congestion threshold achieves lower subbuer occupancy, lower packet delays, lower packet-delay jitters, and lower miss ratio. The cost for these bene ts is a higher loss ratio. Choosing an appropriate congestion threshold can greatly reduce the miss ratio at the expense of a little extra loss ratio. When the number of connections supported by the system is xed, the invalid ratio reaches a minimum for a certain congestion threshold. In the region around the minimum, the invalid ratio is fairly insensitive to the variation of the congestion threshold. In addition, by allowing a larger fraction of optional packets in messages, the system can support an increasing number of connections while still remaining stable but at the cost of a larger number of discarded packets and thus a reduction in the service quality. Two lines of future work are envisioned. First, we will extend the model of the switching element to the entire network, taking into account the interactions and dependencies among dierent switching elements. Second, we will study the complementary problem of using the imprecise-computation technique to develop a strategy for connection acceptance to the network.

[5] W. Zhao, J. W.-S. Liu, and S. Vrbsky. Imprecise scheduling in multiprocessor systems. In Proceedings of the 5th IEEE International Conference on Parallel and Distributed Computing Systems, September 1992. [6] J. M. Hyman, A. A. Lazar, and G. Paci ci. Real-time scheduling with quality of service constraints. IEEE Journal on Selected Areas in Communications, 9(7), September 1991. [7] C. L. Liu and J. W. Layland. Scheduling algorithms for multiprogramming in a hard realtime environment. Journal of the Association for Computing Machinery, 20(1):46{61, January 1979. [8] J. P. Lehoczky, L. Sha, and J. Strosnider. Enhancing aperiodic responsiveness in a hard-realtime environment. In Proceedings of 8th IEEE Real-Time Systems Symposium, pages 261{270, December 1987. [9] E. A. Fox. Advance in interactive digital multimedia system. IEEE Computer, pages 9{21, October 1991. [10] P. T. Brady. A statistical analysis of on-o patterns in 16 conversations. The Bell System Technical Journal, January 1968. [11] V. M. Millan-Lopez. A congestion control scheme for a real-time trac switching element using the imprecise computations technique. Master's thesis, Department of Computer Science, University of Illinois at Urbana-Champaign, 1993. [12] D. Ferrari. Client requirements for real-time communication services. Technical Report TR-90007, International Computer Science Institute, Berkeley, March 1990.

Acknowledgements This work was supported in part by ONR contract no. N00014-J-92-1146 and AFOSR contract no. F49620-93-1-0060.

References [1] J. W.-S. Liu, K.-J. Lin, W.-K. Shih, A. C.-S. Yu, J.-Y. Chung, and W. Zhao. Algorithms for scheduling imprecise computations. IEEE Computer, 24(5):58{68, May 1991. [2] Y.-Q. Zhang, W. W. Wu, K. S. Kim, R. L. Pickholtz, and J. Ramasastry. Variable-bit-rate video tranmission in the broadband-ISDN environment. IEEE, 1990. [3] T. Bially, B. Gold, and S. Sene. A technique for adaptive voice ow control in integrated packet networks. IEEE Transactions on Communications, COM-28(7):325{333, March 1980. [4] B. G. Kim and D. Towsley. Dynamic ow control protocols for packet-switching multiplexers serving real-time multipacket messages. IEEE Transactions on Communications, COM-34(4), April 1986.

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Figure 3: Link Utilization (BE;ViP).

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Figure 7: Miss Ratio for All Packets (BE;ViP).

Figure 4: Loss Ratio for All Packets (BE;ViP).

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Figure 8: Invalid Ratio for All Packets (BE;ViP).

Figure 5: Mean Delay of Video Packets (BE;ViP).

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Figure 9: Miss, Loss, and Invalid Ratios for All Packets (ECT;ViP;RD = (1.0, 2.0)).

Figure 6: Mean Delay of Voice Packets (BE;VoP). 7