Interpolation Approximations for M/G/infinity Arrival Processes
Abstract
We present an approximate analysis of a discrete-time queue with correlated arrival processes of the so-called M | G | infinity 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 | infinity 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1999
- Accession Number
- ADA442652
Entities
People
- Armand M. Makowski
- Konstantinos P. Tsoukatos
Organizations
- University of Maryland