Computing stationary queueing-time distributions of \(GI/D/1\) and \(GI/D/c\) queues. (English) Zbl 0757.60093

Summary: 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 \(E_ m/D/1\) and \(HE_ 2/D/1\). 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, et cetera.


60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
Full Text: DOI


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