Approximations for the GI / G / c queue

Abstract

In this paper, we give good-quality approximations for multiserver queues with general service-time distributions. For the interarrival-time distribution we consider hyperexponential distributions and mixtures of Erlang distributions with the same scale parameters. We give an algorithm to compute various operating characteristics such as the delay probability and the mean queue length. The approximations are obtained by making assumptions regarding the residual service times of services in progress at service completion epochs, whereas the arrival process is modelled exactly. As the operating characteristics are far more sensitive to changes in the parameters of the arrival process, the latter is very important. The quality of the approximations is extensively tested by using the exact results of more than 2000 cases. In heavy traffic the average relative error is up to 1% and in moderate traffic about 4%.

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