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Transient analysis for exponential time-limited polling models under the preemptive repeat random policy

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  29 April 2020

Roland De Haan ,
Ahmad Al Hanbali ,
Richard J. Boucherie  and
Jan-Kees Van Ommeren
Roland De Haan*
Affiliation:
CQM
Ahmad Al Hanbali*
Affiliation:
King Fahd University of Petroleum and Minerals
Richard J. Boucherie*
Affiliation:
University of Twente
Jan-Kees Van Ommeren*
Affiliation:
University of Twente
*
*Postal address: CQM, The Netherlands
**Corresponding author. Postal address: Department of Systems Engineering, College of Computer Science and Engineering, King Fahd University of Petroleum and Minerals, PO Box 5063, Dhahran 31261, Kingdom of Saudi Arabia. Email address: [email protected]
***Postal address: Department of Stochastic Operations Research, University of Twente, The Netherlands.
***Postal address: Department of Stochastic Operations Research, University of Twente, The Netherlands.
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Abstract

Polling systems are queueing systems consisting of multiple queues served by a single server. In this paper we analyze two types of preemptive time-limited polling systems, the so-called pure and exhaustive time-limited disciplines. In particular, we derive a direct relation for the evolution of the joint queue length during the course of a server visit. The analysis of the pure time-limited discipline builds on and extends several known results for the transient analysis of an M/G/1 queue. For the analysis of the exhaustive discipline we derive several new results for the transient analysis of the M/G/1 queue during a busy period. The final expressions for both types of polling systems that we obtain generalize previous results by incorporating customer routeing, generalized service times, batch arrivals, and Markovian polling of the server.

Keywords

Queueingpolling systemstransient analysis

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 1 , March 2020 , pp. 32 - 60
Copyright
© Applied Probability Trust 2020

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