Hitting times of Markov chains, with application to state-dependent queues-Reference-Cited by-同舟云学术

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

Published:1977-08 Issue:1 Volume:17 Page:97-107
ISSN:0004-9727
Container-title:Bulletin of the Australian Mathematical Society
language:en
Short-container-title:Bull. Austral. Math. Soc.

Author:

Tweedie R.L.

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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference11 articles.

1. [11] Tweedie R.L. , Westcott M. , “First-passage times in skip-free processes”, submitted.

2. Criteria for classifying general Markov chains

3. [4] Laslett G.M. , Pollard D.B. , Tweedie R.L. , “Techniques for establishing ergodic and recurrence properties of continuous-valued Markov chains”, submitted.

4. [8] Tuominen Pekka and Tweedie Richard L. , “Markov chains with continuous components”, submitted.

5. On the Stochastic Matrices Associated with Certain Queuing Processes

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