Approximations in the Multi-Server Queue with Hyper-exponential Inter-arrival Times and Exponential Service Times

Abstract

Approximate formulae are developed and evaluated in this paper for the equilibrium queue-size and queueing-time distributions in the multi-server system with hyper-exponential inter-arrival and exponential service times. The derivation of the formulae is based on a combination of heuristic arguments, analytical considerations and sensitivity analyses on numerical results. The degree of approximation achieved depends on the particular formula used and on the values of the various parameters involved. The relative percentage errors incurred seem, however, to be reasonably small for most practical purposes.