Interpolation Approximations for M/G/infinity Arrival Processes

Abstract

Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. AbstractWe present an approximate analysis of a discrete-time queue with correlated arrival processes of the so-called M |G|∞ type. The proposed heuristic approximations are developed around asymptotic results in the heavy and light traffic regimes. Investigation of the system behavior in light traffic quantifies the differences between the gradual M |G|∞ inputs and the point arrivals of a classical GI|GI|1 queue. In heavy traffic, salient features are effectively captured by the exponential distribution and the Mittag-Leffler special function, under short-and long-range dependence respectively. By interpolating between the heavy and light traffic extremes we derive approximations to the queue size distribution, applicable to all traffic intensities. We examine the accuracy of these expressions and discuss possible extensions of our results in several numerical examples.