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COMPUTATIONAL ANALYSIS OF STATIONARY WAITING-TIME DISTRIBUTIONS OF GIX/R/1 AND GIX/D/1 QUEUES

Published online by Cambridge University Press:  01 January 2005

Mohan L. Chaudhry ,
Dae W. Choi  and
Kyung C. Chae
Mohan L. Chaudhry
Affiliation:
Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario K7K 7B4, Canada, E-mail: chaudhry-ml@rmc.ca
Dae W. Choi
Affiliation:
Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, Yuseong, Daejeon 305-701, Korea, E-mail: cdw@kaist.ac.kr
Kyung C. Chae
Affiliation:
Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, Yuseong, Daejeon 305-701, Korea, E-mail: kcchae@kaist.ac.kr
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Abstract

In this article, we obtain, in a unified way, a closed-form analytic expression, in terms of roots of the so-called characteristic equation of the stationary waiting-time distribution for the GIX/R/1 queue, where R denotes the class of distributions whose Laplace–Stieltjes transforms are rational functions (ratios of a polynomial of degree at most n to a polynomial of degree n). The analysis is not restricted to generalized distributions with phases such as Coxian-n (Cn) but also covers nonphase-type distributions such as deterministic (D). In the latter case, we get approximate results. Numerical results are presented only for (1) the first two moments of waiting time and (2) the probability that waiting time is zero. It is expected that the results obtained from the present study should prove to be useful not only for practitioners but also for queuing theorists who would like to test the accuracies of inequalities, bounds, or approximations.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 1 , January 2005 , pp. 121 - 140
Copyright
© 2005 Cambridge University Press

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References

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