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Computing stationary queueing‐time distributions of GI/D /1 and GI / D /c queues
Author(s) -
Chaudhry M. L.
Publication year - 1992
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(199212)39:7<975::aid-nav3220390708>3.0.co;2-x
Subject(s) - queueing theory , bulk queue , mean value analysis , burke's theorem , layered queueing network , mathematics , queue , computer science , discrete mathematics , fork–join queue , queue management system , statistics , computer network
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 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. © 1992 John Wiley & Sons, Inc.