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Two queues with random time-limited polling

Saxena M., Boxma O., Kapodistria S., Núñez-Queija R.

Probability and Mathematical Statistics

2017

Vol. 37, Fasc. 2

257--289

In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues with generally distributed service times. The server spends an exponentially distributed amount of time in each queue. After the completion of this residing time, the server instantaneously switches to the other queue, i.e., there is no switch-over time. For this polling model we derive the steady-state marginal workload distribution, as well as heavy traffic and heavy tail asymptotic results. Furthermore, we also calculate the joint queue length distribution for the special case of exponentially distributed service times using singular perturbation analysis.

Uniform moderate deviations of functional empirical processes of Markov chains

Guillin A.

Probability and Mathematical Statistics

2000

Vol. 20, Fasc. 2

237--260

We obtain uniform (in time) moderate deviations for the functional empirical process of a general state space Markov chain under the geometric ergodicity assumption, and a regularity condition for the initial measure, by the regeneration split chain method. Our results deal both with bounded and unbounded class of functions.