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Abstract: We consider a polling model with multiple stations, each with Poissonarrivals and a queue of infinite capacity. The service regime is exhaustive andthere is Jacksonian feedback of served customers. What is new here is that whenthe server comes to a station it chooses the service rate and the feedbackparameters at random; these remain valid during the whole stay of the server atthat station. We give criteria for recurrence, transience and existence of the$s$th moment of the return time to the empty state for this model. This papergeneralizes the model, when only two stations accept arriving jobs, which wasconsidered in Ann. Appl. Probab. 17 2007 1447-1473. Our results are statedin terms of Lyapunov exponents for random matrices. From the recurrencecriteria it can be seen that the polling model with parameter regeneration canexhibit the unusual phenomenon of null recurrence over a thick region ofparameter space.



Autor: Iain MacPhee, Mikhail Menshikov, Dimitri Petritis, Serguei Popov

Fuente: https://arxiv.org/







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