Time-limited polling systems with batch arrivals and phase-type service times

Ahmad Al Hanbali, Roland de Haan, Richard J. Boucherie, Jan Kees van Ommeren*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


In this paper, we develop a general framework to analyze polling systems with either the autonomous-server or the time-limited service discipline. According to the autonomous-server discipline, the server continues servicing a queue for a certain period of time. According to the time-limited service discipline, the server continues servicing a queue for a certain period of time or until the queue becomes empty, whichever occurs first. We consider Poisson batch arrivals and phase-type service times. It is known that these disciplines do not satisfy the well-known branching property in polling systems. Therefore, hardly any exact results exist in the literature. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-lengths at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains.

Original languageEnglish
Pages (from-to)57-82
Number of pages26
JournalAnnals of Operations Research
Issue number1
StatePublished - Sep 2012
Externally publishedYes

Bibliographical note

Funding Information:
Acknowledgements We first would thank the reviewers for their valuable comments which helped to improve the paper. In the Netherlands, the 3 universities of technology have formed the 3TU.Federation. This article is the result of joint research in the 3TU.Centre of Competence NIRICT (Netherlands Institute for Research on ICT). The authors would also thank De Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) for their financial support.


  • Absorbing Markov chains
  • Autonomous server discipline
  • Iterative scheme
  • Matrix analytic solution
  • Performance analysis
  • Phase-type service times
  • Poisson batch arrivals
  • Polling system
  • Time limited discipline

ASJC Scopus subject areas

  • Decision Sciences (all)
  • Management Science and Operations Research


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