Two-Queue Polling Model with a Timer and a Randomly-Timed Gated Mechanism

摘要

In this paper, we consider two-queue polling model with a Timer and a RandomlyTimed Gated (RTG) mechanism. At queue Q1, we employ a Timer T(1): whenever the server polls queue Q1 and finds it empty, it activates a Timer. If a customer arrives before the Timer expires, a busy period starts in accordance with exhaustive service discipline. However, if the Timer is shorter than the interarrival time to queue Q1, the server does not wait any more and switches back to queue Q2. At queue Q2, we operate a RTG mechanism T(2), that is, whenever the server reenters queue Q2, an exponential time T(2) is activated. If the server empties the queue before T(2), it immediately leaves for queue Q1. Otherwise, the server completes all the work accumulated up to time T(2) and leaves. Under the assumption of Poisson arrivals, general service and switchover time distributions, we obtain probability generating function (PGF) of the queue lengths at polling instant and mean cycle length and Laplace Stieltjes transform (LST) of the workload.