ANALYSIS OF TRANSIENT LOSS PERFORMANCE IMPACT OF LONG-RANGE DEPENDENCE IN NETWORK TRAFFIC in VS .NET

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ANALYSIS OF TRANSIENT LOSS PERFORMANCE IMPACT OF LONG-RANGE DEPENDENCE IN NETWORK TRAFFIC
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GUANG-LIANG LI AND VICTOR O. K. LI
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Department of Electrical & Electronic Engineering, The University of Hong Kong, Pokfulam, Hong Kong, China
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INTRODUCTION
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To support multimedia applications, high-speed networks must be able to provide quality-of-service (QoS) guarantees for connections with drastically different traf c characteristics. Some of the characteristics fall beyond the conventional framework of Markov traf c modeling. For instance, recent studies have demonstrated convincingly that there exists long-range dependence or self-similarity in packet video, which is an important traf c component in high-speed networks. Essentially, longrange dependence cannot be captured by Markov traf c models. Although longrange dependence in network traf c has been widely recognized [1, 2, 4, 8, 11, 15, 17, 18], QoS impact of long-range dependence is still an open issue. For example, there are different opinions regarding whether Markov traf c models can still be used to predict loss performance in the presence of long-range dependence. This and other related issues are also discussed in 12 of this book. QoS guarantee for long-range dependent (LRD) traf c is the topic of s 16 and 19 as well. The issue of congestion control for self-similar traf c is addressed in 18.
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Self-Similar Network Traf c and Performance Evaluation, Edited by Kihong Park and Walter Willinger ISBN 0-471-31974-0 Copyright # 2000 by John Wiley & Sons, Inc.
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TRANSIENT LOSS PERFORMANCE IMPACT OF LRD IN NETWORK TRAFFIC
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In this chapter, we present an analysis of transient loss performance impact of long-range dependence in network traf c. This work is only the rst step of our exploration. But we hope that it will still be helpful for understanding loss performance impact of long-range dependence in the transient state, although much further work needs to be done in the future. A different transient analysis in the context of capacity planning and recovery time is given in 17. In general, the transient analysis of queueing models is very challenging. A transient solution to a queueing model is a function of a time index, either continuous or discrete, de ned over an in nite range. It is very dif cult to nd an explicit, closed-form solution if the system is not Markovian. For a Markov model, the probabilistic evolution of the system state is governed by the Chapman Kolmogorov equation. In the presence of long-range dependence, the model is essentially non-Markovian. So the Chapman Kolmogorov equation does not hold anymore. Due to this and other dif culties involved in transient analysis, most of the existing work on QoS impact of long-range dependence is limited to asymptotic analysis in the steady state [4, 6, 9, 10, 15 17] (see also s 4 10 in this volume). Although certain insights have been gained through investigation carried out in steady-state, we feel that it is still necessary to extend the investigation beyond the region of steady-state. First, due to the high variability caused by long-range dependence, the convergence of an LRD traf c process toward steady-state can be very slow. In contrast, Markov traf c processes converge to steady-state exponentially fast. Consequently, for a link carrying LRD traf c, the discrepany between steady-state performance and transient performance can be more signi cant, compared with the situations in which traf c can be modeled by Markov processes. Second, to guarantee QoS for traf c with the high variability caused by long-range dependence, dynamic and adaptive resource allocation may be necessary to account for the effect of the current system state. Performance analysis based on the steady state may not be appropriate for this purpose, since in steady-state, any initial effect will disappear eventually. Because steady-state performance may differ from transient performance signi cantly for LRD traf c, the image regarding loss behavior of LRD traf c in the transient state still largely remains vague. In this chapter, an approach different from conventional transient analysis is used, which allows us to investigate the transient performance impact of long-range dependence in traf c without rst seeking a closed-form transient solution. That is, we limit our analysis to some short period of time, and even to a single state of a traf c process. The reasons for us to adopt this approach are as follows. First, it is relatively easy, and may also be suf cient, to consider transient solutions de ned only for a relatively short time period, since a short time period may actually cover the time span in which we are interested for transient performance analysis. A large time span may be less interesting from a point of view of transient analysis, since the difference between the steady state and the transient state may diminish signi cantly after a long time has elapsed. Second, if the arrival process is renewal type, then the behavior of the system is probabilistically periodic. So it may be suf cient to focus only on a ``typical'' probabilistic period to study the transient performance of the
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