Hitting times of Markov chains, with application to state-dependent queues
- 1 August 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 17 (1) , 97-107
- https://doi.org/10.1017/s0004972700025508
Abstract
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.Keywords
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