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 non-negligible. 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. 1

We present a time{parallel technique for the fast generation of self{similar tra c which is suitable for performance studies of Asynchronous Transfer Mode (ATM) networks. The technique is based on the well known result according to which the aggregation of a large number of heavy{tailed ON/OFF{ type renewal/reward processes asymptotically approximates a Fractional Gaussian Noise (FGN) process and, therefore, it possesses the characteristics of self{similarity and long{range dependence. The technique parallelizes both the generation of the individual renewal/reward processes as well as the merging of these processes in a per{time{slice manner. Results obtained from a message{passing implementation on a cluster of workstations con rm that it is possible to generate self{similar ATM tra c in real{ time for 155 Mbps (or even faster) links and that, furthermore, the technique achieves an almost linear speedup with respect to the number of available workstations. 1