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December 2008 Polling systems with parameter regeneration, the general case
Iain MacPhee, Mikhail Menshikov, Dimitri Petritis, Serguei Popov
Ann. Appl. Probab. 18(6): 2131-2155 (December 2008). DOI: 10.1214/08-AAP519

Abstract

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 sth 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 [Ann. Appl. Probab. 17 (2007) 1447–1473]. 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.

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Iain MacPhee. Mikhail Menshikov. Dimitri Petritis. Serguei Popov. "Polling systems with parameter regeneration, the general case." Ann. Appl. Probab. 18 (6) 2131 - 2155, December 2008. https://doi.org/10.1214/08-AAP519

Information

Published: December 2008
First available in Project Euclid: 26 November 2008

zbMATH: 1154.60351
MathSciNet: MR2473652
Digital Object Identifier: 10.1214/08-AAP519

Subjects:
Primary: 60J10, 60K25
Secondary: 60G42, 90B22

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.18 • No. 6 • December 2008
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