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Monotonicity and stability of periodic polling models. (English) Zbl 0789.60092
Summary: This paper deals with the stability of periodic polling models with a mixture of service policies. Customers arrive according to independent Poisson processes. The service times and the switchover times are independent with general distributions. A necessary and sufficient condition for the stability of such polling systems is established. The proof is based on the stochastic monotonicity of the state process at the polling instants. The stability of only a subset of the queues is also analyzed and, in case of heavy traffic, the order of explosion of the queues is given. The results are valid for a model with set-up times, and also when there is a local priority rule at the queues.

MSC:
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
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