Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-25T17:05:17.304Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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