A MARKOV chain model of a polling system with parameter regeneration

Details A MARKOV chain model of a polling system with parameter regeneration A MARKOV chain model of a polling system with parameter regeneration

2007-01-08

arxiv.org/abs/math/0701226v2

Annals of Applied Probability 2007, Vol. 17, No. 5,6, 1447-1473

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/105051607000000212 the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051607000000212

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.

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