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On the stationary waiting-time distribution in the GI/G/1 queue, I: Transform methods and almost-phase-type distributions

Published online by Cambridge University Press:  01 July 2016

Teunis J. Ott
Teunis J. Ott*
Affiliation:
Bell Communications Research
*
∗ Postal address: Bell Communications Research, 435 South Street, Morristown, NJ 07960-1961, USA.
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Abstract

This paper establishes a link between the Wiener–Hopf factorization and the phase-type method for studying the GI/G/1 queue. Using the Wiener–Hopf factorization, infinite-matrix type results are established for the GI/G/1 queue. An iterative numerical procedure (‘Levinson&s method’) based on these results is described. This method does not always converge. For the situation where either the interarrival times or the service times are of the so-called almost phase type (APH) an alternative, probabilistic derivation of the same results is given. This alternative derivation shows that in the APH situation Levinson&s method converges, converges essentially monotonically, and converges to the correct values.

The algorithm has been coded and examples of numerical results are included.

Keywords

SINGLE-SERVER QUEUENUMERICAL METHODSPHASE-TYPE METHODSWIENER-HOPFALMOST PHASE TYPEGENERALIZED PHASE TYPE

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 1 , March 1987 , pp. 240 - 265
Copyright
Copyright © Applied Probability Trust 1987 

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