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Hitting times of Markov chains, with application to state-dependent queues

Published online by Cambridge University Press:  17 April 2009

R.L. Tweedie
R.L. Tweedie*
Affiliation:
Division of Mathematics and Statistics, CSIRO, Canberra, ACT.
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Abstract

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We present in this note a useful extension of the criteria given in a recent paper [Advances in Appl. Probability 8 (1976), 737–771] for the finiteness of hitting times and mean hitting times of a Markov chain on sets in its (general) state space. We illustrate our results by giving conditions for the finiteness of the mean number of customers in the busy period of a queue in which both the service-times and the arrival process may depend on the waiting time in the queue. Such conditions also suffice for the embedded waiting time chain to have a unique stationary distribution.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 17 , Issue 1 , August 1977 , pp. 97 - 107
Copyright
Copyright © Australian Mathematical Society 1977

References

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