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Stationary waiting-time distributions in the GI/PH/1 queue

Published online by Cambridge University Press:  14 July 2016

Marcel F. Neuts
Marcel F. Neuts*
Affiliation:
University of Delaware
*
∗Postal address: Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, U.S.A.
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Abstract

It is known that the stable GI/PH/1 queue has an embedded Markov chain whose invariant probability vector is matrix-geometric with a rate matrix R. In terms of the matrix R, the stationary waiting-time distributions at arrivals, at an arbitrary time point and until the customer's departure may be evaluated by solving finite, highly structured systems of linear differential equations with constant coefficients. Asymptotic results, useful in truncating the computations, are also obtained. The queue discipline is first-come, first-served.

Keywords

MATRIX-GEOMETRIC SOLUTIONSGI/PH/1 QUEUEWAITING-TIME DISTRIBUTIONSLINDLEY'S EQUATIONCOMPUTATIONAL PROBABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 901 - 912
Copyright
Copyright © Applied Probability Trust 1981 

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Footnotes

Research supported by the National Science Foundation under Grant No. ENG–7908351 and by the Air Force Office of Scientific Research under Grant No. AFOSR–77–3236.

References

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