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

Roland De Haan, Ahmad Al Hanbali*, Richard J. Boucherie, Jan Kees Van Ommeren

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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.

Original languageEnglish
Pages (from-to)32-60
Number of pages29
JournalAdvances in applied probability
Volume52
Issue number1
DOIs
Publication statusPublished - 1 Mar 2020

Keywords

  • Polling systems
  • Queueing
  • Transient analysis

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