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

Recent evidence suggests that some characteristics of computer and telecommunications systems may be well described using heavy tailed distributions — distributions whose tail declines like a power law, which means that the probability of extremely large observations is nonnegligible. 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 designers 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 simulations; these properties make simulation stability hard to achieve. In this paper we explore the difficulty of achieving stability in such simulations, using tools from the theory of stable distributions. We show that such simulations exhibit two characteristics related to stability: slow convergence 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 discuss methods for simulating such systems while explicitly incorporating time scale as a parameter.