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Some explicit formulas and computational methods for infinite-server queues with phase-type arrivals

Published online by Cambridge University Press:  14 July 2016

V. Ramaswami  and
Marcel F. Neuts
V. Ramaswami*
Affiliation:
Drexel University
Marcel F. Neuts*
Affiliation:
University of Delaware
*
∗Postal address: Department of Mathematical Sciences, Drexel University, Philadelphia, PA 19104, U.S.A.
∗Postal address: Department of Mathematical Sciences, Drexel University, Philadelphia, PA 19104, U.S.A.
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Abstract

This paper discusses infinite-server queues with phase-type input. The problems of obtaining the transient and steady-state distributions and moments of the queue length are reduced to the solution of certain well-behaved systems of linear differential equations. Sample computations, provided with as many as ten phases, show that although (even the time-dependent) mean queue length is very insensitive to substantial random variability in the arrival process, the higher moments of the queue length are highly sensitive. These examples indicate that considerable caution should be exercised in using robustness results for such stochastic models.

Keywords

COMPUTATIONAL PROBABILITYINFINITE-SERVER QUEUEPHASE TYPE DISTRIBUTIONSINSENSITIVITY RESULTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 498 - 514
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Research supported by AFOSR–72–2350C at the Department of Statistics and Computer Science, University of Delaware.

This paper is based on Part II of the author's Ph. D. Thesis.

Research supported by AFOSR–77–3236 at the Department of Statistics and Computer Science, University of Delaware.

References

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