HAL : hal-00260810, version 1

DOI : 10.1214/08-AAP519

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The Annals of Applied Probability 18, 6 (2008) 2131-2155

Polling systems with parameter regeneration, the general case

Iain Macphee 1, Mikhail Menshikov 1, Dimitri Petritis 2, Serguei Popov 3

(01/12/2008)

We consider a polling model with multiple stations, each with Poisson arrivals and a queue of infinite capacity. The service regime is exhaustive and there is Jacksonian feedback of served customers. What is new here is that when the server comes to a station it chooses the service rate and the feedback parameters at random; these remain valid during the whole stay of the server at that 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 paper generalizes the model when only two stations accept arriving jobs which was considered in~\cite{MMPP}. Our results are stated in terms of Lyapunov exponents for random matrices. From the recurrence criteria it can be seen that the polling model with parameter regeneration can exhibit the unusual phenomenon of null recurrence over a thick region of parameter space.

1 :	Department of Mathematics
	University of Durham
2 :	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II
3 :	Instituto de Matematica
	Universidade de São Paulo

Équipe de recherche : Théorie ergodique

Domaine

:

Mathématiques/Probabilités

Mots Clés : Polling system – parameter regeneration – stability – time-inhomogeneous Markov chains – recurrence – Lyapunov functions – random matrices

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Contributeur : Dimitri Petritis <>

Soumis le : Mercredi 5 Mars 2008, 11:53:34

Dernière modification le : Mercredi 4 Mars 2009, 15:28:15