Interpolation approximations for the mean waiting time in a multi-server queue

Interpolation approximations for the mean waiting time in a multi-server queue

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Article ID: iaor19932435
Country: Japan
Volume: 35
Issue: 1
Start Page Number: 77
End Page Number: 92
Publication Date: Mar 1992
Journal: Journal of the Operations Research Society of Japan
Authors:
Keywords: statistics: regression
Abstract:

This paper gives numerical validation of a couple of interpolation approximations for the mean waiting time in a GI/G/s queue, which are provided by a unified approach similar to that in Kimura. Both approximations are represented as certain combinations of the mean waiting times for the GI/M/s and GI/D/s queues in which the arrival processes and the mean service times are the same as in the approximating GI/G/s queue. To let these approximations be more tractable, the paper further provides simple interpolation approximations for the mean waiting times in GI/M/s and GI/D/s queues with low variable interarrival times. The quality of the approximations is tested by comparing them with exact solutions and previous two-moment approximations for a variety of cases. Extensive numerical comparisons indicate that the present approximations are more accurate than the two-moment approximations and that the relative percentage errors are in the order of 5% in moderate traffic and in the order of 1% in heavy traffic.

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