Hitting times of Markov chains, with application to state-dependent queues
1977 ◽
Vol 17
(1)
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pp. 97-107
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Keyword(s):
The Mean
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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.
2008 ◽
Vol 2008
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pp. 1-20
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1976 ◽
Vol 8
(04)
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pp. 737-771
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Keyword(s):
2018 ◽
Vol 28
(1)
◽
pp. 141-154
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1975 ◽
Vol 12
(04)
◽
pp. 744-752
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Keyword(s):