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

Ahmad Hanbali (), Roland Haan (), Richard Boucherie () and Jan-Kees Ommeren ()

Annals of Operations Research, 2012, vol. 198, issue 1, 57-82

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. Copyright The Author(s) 2012

Keywords: Absorbing Markov chains; Matrix analytic solution; Polling system; Autonomous server discipline; Time limited discipline; Poisson batch arrivals; Phase-type service times; Iterative scheme; Performance analysis (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10479-011-0846-y

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