Approximating the mean waiting time in the GI/G/s queue

Approximating the mean waiting time in the GI/G/s queue

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Article ID: iaor19921557
Country: United Kingdom
Volume: 42
Issue: 11
Start Page Number: 959
End Page Number: 970
Publication Date: Nov 1991
Journal: Journal of the Operational Research Society
Authors:
Abstract:

The paper provides two distribution-dependent approximations for the mean waiting time in a GI/G/s queue. Both approximations are weighted combinations of the exact mean waiting times for the GI/M/s and M/D/s queues each of which has the same mean service time and traffic intensity as in the approximating GI/G/s queue. The weights in the approximations are expressed by the service-time c.d.f. and the first two moments of interarrival and service times. To examine the performance of the present approximations, they are numerically compared with exact solutions and previous two-moment approximations for various cases. Extensive numerical comparisons indicate that the relative percentage errors of the approximations are of the order of 5% in moderate traffic and 1% in heavy traffic, except for extreme cases.

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