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On renewal processes relating to counter models: the case of phase-type interarrival times

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Edward P. C. Kao  and
Marion Spokony Smith
Edward P. C. Kao*
Affiliation:
University of Houston
Marion Spokony Smith*
Affiliation:
University of Houston
*
∗ Postal address for both authors: Department of Decision and Information Sciences, University of Houston, Houston, Texas 77204–6282, USA.
∗ Postal address for both authors: Department of Decision and Information Sciences, University of Houston, Houston, Texas 77204–6282, USA.
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Abstract

The Type I and Type II counter models of Pyke (1958) have many applications in applied probability: in reliability, queueing and inventory models, for example. In this paper, we study the case in which the interarrival time distribution is of phase type. For the two counter models, we derive the renewal functions of the related renewal processes and propose approaches for their computations.

Keywords

TYPE I AND II COUNTERSRENEWAL FUNCTIONS

MSC classification

Primary: 60K05: Renewal theory
Secondary: 60K10: Applications (reliability, demand theory, etc.) 60J05: Discrete-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 1 , March 1993 , pp. 175 - 183
Copyright
Copyright © Applied Probability Trust 1993 

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