Two queues with random time-limited polling

摘要

In this paper, we analyse a single server polling model withtwo queues. Customers arrive at the two queues according to two independentPoisson processes. There is a single server that serves both queues withgenerally distributed service times. The server spends an exponentially distributedamount of time in each queue. After the completion of this residingtime, the server instantaneously switches to the other queue, i.e., there is noswitch-over time. For this polling model we derive the steady-state marginalworkload distribution, as well as heavy traffic and heavy tail asymptotic results.Furthermore, we also calculate the joint queue length distribution forthe special case of exponentially distributed service times using singularperturbation analysis.