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

Ahmad Al Hanbali, Roland de Haan, Richardus J. Boucherie, Jan C.W. van Ommeren

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)
20 Downloads (Pure)

Abstract

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
Volume198
Issue number1
DOIs
Publication statusPublished - Sep 2012

Fingerprint

Batch
Polling
Queue
Servicing
Kernel
Markov chain

Keywords

  • EWI-21585
  • Autonomous server discipline
  • Time limited discipline
  • Matrix analytic solution
  • Absorbing Markov chains
  • Phase-type service times
  • Poisson batch arrivals
  • Polling system
  • Performance analysis
  • Iterative scheme
  • METIS-275145
  • IR-76967

Cite this

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title = "Time-limited polling systems with batch arrivals and phase-type service times",
abstract = "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.",
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Time-limited polling systems with batch arrivals and phase-type service times. / Al Hanbali, Ahmad; de Haan, Roland; Boucherie, Richardus J.; van Ommeren, Jan C.W.

In: Annals of operations research, Vol. 198, No. 1, 09.2012, p. 57-82.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - van Ommeren, Jan C.W.

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