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

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  • M. L. Chaudhry

Abstract

This article gives closed‐form analytic expressions as well as the exact computational analysis of stationary queueing‐time distribution for the GI/D/I 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, et cetera. © 1992 John Wiley & Sons, Inc.

Suggested Citation

  • M. L. Chaudhry, 1992. "Computing stationary queueing‐time distributions of GI/D/1 and GI/D/c queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(7), pages 975-996, December.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:7:p:975-996
    DOI: 10.1002/1520-6750(199212)39:73.0.CO;2-X
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    1. Mohan L. Chaudhry & Carl M. Harris & William G. Marchal, 1990. "Robustness of Rootfinding in Single-Server Queueing Models," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 273-286, August.
    2. Toshikazu Kimura, 1986. "A Two-Moment Approximation for the Mean Waiting Time in the GI/G/s Queue," Management Science, INFORMS, vol. 32(6), pages 751-763, June.
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