Note sur les temps de service r\'esiduels dans les syst\`emes type M/G/c

TL;DR

This paper investigates the properties of residual service times and waiting probabilities in M/G/c queues, revealing their dependence on higher-order distribution characteristics to improve approximation accuracy.

Contribution

It provides new insights into the dependence of residual times on higher moments, aiding the development of more accurate queue performance approximations.

Findings

Residual service times depend on higher-order moments of service distribution

Properties of waiting probabilities are explored through numerical examples

Insights suggest avenues for improving M/G/c queue approximations

Abstract

Approximations for the mean performance indices for the M/G/c queue rely on the approximate computation of the probability that an arriving request has to wait for service and of the minimum of residual service times if all servers are found busy. Using numerical examples, we investigate properties of these two quantities. In particular, we show that the minimum of residual service times depends on higher order properties, beyond the first two moments, of the service time distribution. Improved knowledge of the properties of the two quantities studied in this paper provides insight into avenues for improving the accuracy of approximations for the M/G/c queue.