Using quantile estimates in simulating Internet queues with Pareto service times

Abstract

It is readily apparent how important the Internet is to modern life. The exponential growth in its use requires good tools for analyzing congestion. Much has been written recently asserting that classical queueing models assuming Poisson arrivals or exponential service cannot be used for the accurate study of congestion in major portions of the Internet. Internet traffic data indicate that heavy-tailed distributions (e.g., Pareto) serve as better models in many situations for packet service lengths. But these distributions may not possess closed-form analytic Laplace transforms; hence, much of standard queueing theory cannot be used. Simulating such queues becomes essential; however, previous research pointed out difficulties in obtaining the usual moment performance measures such as mean wait in queue. In this paper, we investigate using quantile estimates of waiting times (e.g., median instead of mean), which appear to be considerably more efficient when service times are Pareto.