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On the reversible counters system of Lampard

Published online by Cambridge University Press:  14 July 2016

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

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.

Type
Short Communications
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, 648668.Google Scholar
[2] Kuczma, M. (1968) Functional equations in a single variable. Polska Akademia Nauk Monografie Matematyczne , Warszawa.Google Scholar