A state-dependent polling model with k-limited service

E.M.M. Winands, I.J.B.F. Adan, G.J. van Houtum, D.G. Down

Research output: Contribution to JournalArticleAcademicpeer-review


We consider a two-queue model with state-dependent setups, in which a single server alternately serves the two queues. The high-priority queue is served exhaustively, whereas the low-priority queue is served according to the k-limited strategy. A setup at a queue is incurred only if there are customers waiting at the polled queue. We obtain the transforms of the queue length and sojourn time distributions under the assumption of Poisson arrivals, generally distributed service times, and generally distributed setup times. The interest for this model is fueled by an application in the field of logistics. It is shown how the results of this analysis can be applied in the evaluation of a stochastic two-item single-capacity production system. From these results we can conclude that significant cost reductions are possible by bounding the production runs of the low-priority item, which indicates the potential of the k-limited service discipline as priority rule in production environments. © Cambridge University Press 2009.
Original languageEnglish
Pages (from-to)385-408
JournalProbability in the Engineering and Informational Sciences
Issue number02
Publication statusPublished - 2009


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