POLLING SYSTEMS WITH PARAMETER REGENERATION, THE GENERAL CASE

Author(s)

MacPhee, Iain ^[1] ; Menshikov, Mikhail ^[1] ; Petritis, Dimitri ^{[2, 3]} ; Popov, Serguei ^[4]

Affiliation

^[1] Univ Durham, Dept Math, Durham DH1 3LE - England

^[2] Univ Rennes 1, Inst Rech Math, F-35042 Rennes - France

^[3] CNRS, UMR 6625, F-35042 Rennes - France

^[4] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil

• Document type: Journal article
• Source: ANNALS OF APPLIED PROBABILITY; v. 18, n. 6, p. 2131-2155, DEC 2008.
• Web of Science Citations: 3

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. (AU)

• FAPESP's process: 04/07276-2 - Stochastic Modelling of Interacting Systems
• Grantee: Luiz Renato Gonçalves Fontes
• Support type: Research Projects - Thematic Grants
• FAPESP's process: 04/13610-2 - Mikhail Menshikov | Durham University - United Kingdom
• Grantee: Serguei Popov
• Support type: Research Grants - Visiting Researcher Grant - International