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.
In this paper we present an approximation for the GI /G /m queue with Coxian interarrival times and service times. The approximation is based on aggregation of the exact state description of both the arrival and service process. This substantially reduces the state space of the QBD describing the GI /G /m queue. The QBD can then be solved efficiently by the matrix geometric method, yielding an approximation for the complete steady-state distribution. Comparison with simulation shows that the approximation produces accurate results.
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