Analysis of Transient Loss Performance Impact of Long‐Range Dependence in Network Traffic
LI Guang-liang, Victor O. K. Li · 2000
To support multimedia applications, high-speed networks must be able to provide quality-of-service (QoS) guarantees for connections with drastically different traffic characteristics. In this chapter, we present an analysis of transient loss performance impact of long-range dependence in network traffic. This work is only the first 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. 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 traffic without first 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 traffic process. We introduce a framework for traffic modeling that captures the essential property of long-range dependence. Within this framework, traffic is modeled by multistate, fluid-type stochastic processes. When such a process is in a given state, the underlying traffic source generates traffic at a constant rate. The time spent by the process in a state is a random variable. For the purpose of this chapter, we let the distribution of the random variable be arbitrary. As a result, we can construct Markov and LRD traffic models as we wish. Then we define loss performance measures in the transient state. We compare transient loss performance between the traditional Markov models and the LRD models. To keep the comparison reasonable, for the Markov and LRD models, except for the distributions of the times spent by the traffic processes in their respective states, we let all other traffic parameters be the same. By doing so, the difference in loss behavior between Markov and LRD traffic is only due to the modeling assumption on the underlying traffic process. We then compare transient loss of Markov and LRD traffic for two cases. In the first case, we assume that both traffic processes are in the same state with the same initial condition characterized by the amount of traffic left in the system when the processes enter the state. In the second case, we consider two-state Markov and LRD fluids. To examine whether it is appropriate to predict loss performance computed according to Markov models in steady state for LRD traffic, we show how to compute steady-state limits of transient loss measures for general two-state fluids, and compare transient loss against loss in steady state. We discuss the impact of long-range dependence in network traffic, based on the analytical and numerical results obtained. We conclude this chapter with a summary of the findings of our study, and a brief discussion on the challenge posed by transient performance guarantee in the presence of long-range dependence and some extension of this work.