Queues as Harris recurrent Markov chains
- Karl Sigman
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We present a framework for representing a queue at arrival epochs as a Harris recurrent Markov chain (HRMC). The input to the queue is a marked point process governed by a HRMC and the queue dynamics are formulated by a general recursion. Such inputs include the cases of i.i.d, regenerative, Markov modulated, Markov renewal and the output from some queues as well. Since a HRMC is regenerative, the queue inherits the regenerative structure. As examples, we consider split & match, tandem, G/G/c and more general skip forward networks. In the case of i.i.d. input, we show the existence of regeneration points for a Jackson type open network having general service and interarrivai time distributions.
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- Queues as Harris recurrent Markov chains
Volume 3, Issue 2 , pp 179-198
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- Kluwer Academic Publishers
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- discrete time
- Harris recurrent Markov chains
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- Karl Sigman (1)
- Author Affiliations
- 1. Department of Industrial Engineering and Operations Research, Columbia University, Mudd Building, 10027, New York, NY, USA