Long-lasting transient conditions in simulations with heavy-tailed workloads

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Abstract
Recent evidence suggests that some characteristics of com- puter and telecommunications systems may be well de- scribed using heavy tailed distributions — distributions whose tail declines like a power law, which means that the probability of extremely large observations is non-negli- gible. For example, such distributions have been found to describe the lengths of bursts in network traffic and the sizes of files in some systems. As a result, system design- ers are increasingly interested in employing heavy-tailed distributions in simulation workloads. Unfortunately, these distributions have properties considerably different from the kinds of distributions more commonly used in simu- lations; these properties make simulation stability hard to achieve. In this paper we explore the difficulty of achiev- ing stability in such simulations, using tools from the the- ory of stable distributions. We show that such simulations exhibit two characteristics related to stability: slow con- vergence to steady state, and high variability at steady state. As a result, we argue that such simulations must be treated as effectively always in a transient condition. One way to address this problem is to introduce the notion of time scale as a parameter of the simulation, and we dis- cuss methods for simulating such systems while explicitly incorporating time scale as a parameter.

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