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Regeneration in tandem queues with multiserver stations

Published online by Cambridge University Press:  14 July 2016

Karl Sigman
Karl Sigman*
Affiliation:
Columbia University
*
∗Postal address: Department of Industrial Engineering and Operations Research, Mudd Building, Columbia University, New York, NY 10027, USA.
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Abstract

A tandem queue with a FIFO multiserver system at each stage, i.i.d. service times and a renewal process of external arrivals is shown to be regenerative by modeling it as a Harris-ergodic Markov chain. In addition, some explicit regeneration points are found. This generalizes the results of Nummelin (1981) in which a single server system is at each stage and the result of Charlot et al. (1978) in which the FIFO GI/GI/c queue is modeled as a Harris chain. In preparing for our result, we study the random assignment queue and use it to give a new proof of Harris ergodicity of the FIFO queue.

Keywords

RANDOM ASSIGNMENTFIFOHARRIS ERGODIC MARKOV CHAIN
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 391 - 403
Copyright
Copyright © Applied Probability Trust 1988 

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