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On the reversible counters system of Lampard

Published online by Cambridge University Press:  14 July 2016

R. M. Phatarfod
R. M. Phatarfod*
Affiliation:
Monash University, Clayton, Australia
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Abstract

The paper considers some properties of the reversible counters system of Lampard [1]. Lampard considers the properties of the process imbedded at the epochs when the counter receiving pulses from the ‘down’ process reaches zero. We consider here the time-dependent and stationary distributions of the original process. Their derivation gives rise to some interesting functional equations, besides being useful for studying queues with Markov-dependent inter-arrival or service times.

Keywords

REVERSIBLE COUNTERSSTATIONARY DISTRIBUTIONTIME-DEPENDENT DISTRIBUTIONFUNCTIONAL EQUATIONSMARKOV-DEPENDENT QUEUES
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 639 - 646
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Lampard, D. G. (1968) A stochastic process whose successive intervals between events form a first order Markov chain. I. J. Appl. Prob. 5, 648–668.Google Scholar
[2] Kuczma, M. (1968) Functional equations in a single variable. Polska Akademia Nauk Monografie Matematyczne , Warszawa.Google Scholar