The importance of power-tail distributions for modeling queueing systems

Power-tail distributions are those for which the reliability function is of the form x(-alpha) for large x. Although they look well behaved, they have the singular property that E(X-l) = infinity for all l greater than or equ al to alpha. Thus it is possible to have a distribution with an infinite va riance, or even an infinite mean. As pathological as these distributions se em to be, they occur everywhere in nature, from the CPU time used by jobs o n main-frame computers to sizes of files stored on discs, earthquakes, or e ven health insurance claims. Recently, traffic on the "electronic super hig hway" was revealed to be of this type, too. In this paper we first describe these distributions in detail and show thei r suitability to model self-similar behavior, e.g., of the traffic stated a bove. Then we show how these distributions can occur in computer system env ironments and develop a so-called truncated analytical model that in the li mit is power-tail. We study and compare the effects on system performance o f a GI/M/1 model both for the truncated and the limit case, and demonstrate the usefulness of these approaches particularly for Markov modeling with L AQT (Linear Algebraic Approach to Queueing Theory, Lipsky 1992) techniques.