Iain MacPhee, Mikhail Menshikov, Dimitri Petritis, Serguei Popov
Published 2007-01-08, updated 2007-10-29Version 2
We study a model of a polling system, that is, a collection of $d$ queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is mapped to a mathematically equivalent model of a random walk with random choice of transition probabilities, a model which is of independent interest. All our results are obtained using methods from the constructive theory of Markov chains. We determine conditions for the existence of polynomial moments of hitting times for the random walk. An unusual phenomenon of thickness of the region of null recurrence for both the random walk and the queueing model is also proved.
Comments: Published in at http://dx.doi.org/10.1214/105051607000000212 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Applied Probability 2007, Vol. 17, No. 5,6, 1447-1473
Polling systems with parameter regeneration, the general case
Queue lengths and workloads in polling systems
Random walk on graphs with regular resistance and volume growth
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