A state-dependent polling model with k-limited service

Authors:
E. m. m. Winands;I. j. b. f. Adan;G. j. Van houtum;D. g. Down
Affiliations:
Department of mathematics, vu university, 1081 hv amsterdam, the netherlands e-mail: emm.winands@few.vu.nl;Department of mathematics and computer science, technische universiteit eindhoven, 5600 mb eindhoven, the netherlands e-mail: i.j.b.f.adan@tue.nl;Department of industrial engineering and innovation sciences, technische universiteit eindhoven, 5600 mb eindhoven, the netherlands e-mail: g.j.v.houtum@tue.nl;Department of computing and software, mcmaster university, hamilton, ontario l8s 4l7, canada e-mail: downd@mcmaster.ca
Venue:
Probability in the Engineering and Informational Sciences
Year:
2009

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Abstract

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.