Polling systems with parameter regeneration, the general case
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 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 [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.
Keywords
Cite
@article{arxiv.0803.0625,
title = {Polling systems with parameter regeneration, the general case},
author = {Iain MacPhee and Mikhail Menshikov and Dimitri Petritis and Serguei Popov},
journal= {arXiv preprint arXiv:0803.0625},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/08-AAP519 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)