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On the reversible counters system of Lampard
Published online by Cambridge University Press: 14 July 2016
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.
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- Copyright © Applied Probability Trust 1975
References
[1]
Lampard, D. G. (1968) A stochastic process whose successive intervals between events form a first order Markov chain. I.
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[2]
Kuczma, M. (1968) Functional equations in a single variable.
Polska Akademia Nauk Monografie Matematyczne
, Warszawa.Google Scholar
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