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

  • Roland De Haan (a1), Ahmad Al Hanbali (a2), Richard J. Boucherie (a3) and Jan-Kees Van Ommeren (a3)

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.

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Copyright

Corresponding author

*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: ahmad.alhanbali@kfupm.edu.sa
***Postal address: Department of Stochastic Operations Research, University of Twente, The Netherlands.

References

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Keywords

MSC classification

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

  • Roland De Haan (a1), Ahmad Al Hanbali (a2), Richard J. Boucherie (a3) and Jan-Kees Van Ommeren (a3)

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