Computing stationary queueing-time distributions of GI/D/1 and GI/D/c queues

Computing stationary queueing-time distributions of GI/D/1 and GI/D/c queues

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Article ID: iaor19931218
Country: United States
Volume: 39
Issue: 7
Start Page Number: 975
End Page Number: 996
Publication Date: Dec 1992
Journal: Naval Research Logistics
Authors:
Abstract:

This article gives closed-form analytic expressions as well as the exact computational analysis of stationary queueing-time distribution for the GI/D/1 queue. By exploiting the relationship between the distributions of queueing times of GI/D/1 and GI/D/c queues, the computational analysis of the queueing-time distribution of GI/D/c queue is also done. Numerical results are presented for (i) the first two moments of queueing time and (ii) the probability that queueing time is zero. Also, comments are made regarding the graphs of the distribution functions for particular cases of Em/D/1 and HE2/D/1. Some further properties such as computing the pre- and postdeparture probabilities for GI/D/1 are also discussed. The results discussed here should prove to be useful to practitioners and queueing theorists dealing with inequalities, bounds, etcetera.

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