TWO QUEUES WITH RANDOM TIME-LIMITED POLLING
Mayank Saxena
Onno Boxma
Stella Kapodistria
Rudesindo Núńez Queija
Abstract: 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.
2010 AMS Mathematics Subject Classification: Primary: 68M20; Secondary:
90B22.
Keywords and phrases: Polling model, workload decomposition, heavy traffic, heavy
tail asymptotics, singular perturbation analysis, time-scale separation, geometric
ergodicity.