Abstract
The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) k-limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue polling system is decomposed into single-queue vacation systems with k-limited service and state-dependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrix-analytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out to be accurate, robust and computationally efficient.
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This research is supported by the Technology Foundation STW, applied science division of NWO and the technology programme of the Dutch Ministry of Economic Affairs.
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van Vuuren, M., Winands, E.M.M. Iterative approximation of k-limited polling systems. Queueing Syst 55, 161–178 (2007). https://doi.org/10.1007/s11134-007-9010-4
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DOI: https://doi.org/10.1007/s11134-007-9010-4