Hitting times of Markov chains, with application to state-dependent queues
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 t...
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| Veröffentlicht in: | Bulletin of the Australian Mathematical Society 1977-08, Vol.17 (1), p.97-107 |
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| container_title | Bulletin of the Australian Mathematical Society |
| container_volume | 17 |
| creator | Tweedie, R.L. |
| description | 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. |
| doi_str_mv | 10.1017/S0004972700025508 |
| format | Article |
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Austral. Math. Soc</addtitle><date>1977-08</date><risdate>1977</risdate><volume>17</volume><issue>1</issue><spage>97</spage><epage>107</epage><pages>97-107</pages><issn>0004-9727</issn><eissn>1755-1633</eissn><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.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S0004972700025508</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Bulletin of the Australian Mathematical Society, 1977-08, Vol.17 (1), p.97-107 |
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| language | eng |
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| source | EZB-FREE-00999 freely available EZB journals; Cambridge University Press Journals Complete |
| title | Hitting times of Markov chains, with application to state-dependent queues |
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