| Two-Queue Polling Model with a Timer and a Randomly-Timed Gated Mechanism |
| Received:July 12, 2007 Revised:May 21, 2008 |
| Key Words:
polling exhaustive Timer Randomly-Timed Gated.
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| Fund Project:the National Natural Science Foundation of China (No.10726063); Leading Academic Discipline Program, 211 Project for Minzu University of China (the 3rd phaze, No.021211030312). |
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| Abstract: |
| In this paper, we consider two-queue polling model with a Timer and a Randomly-Timed Gated (RTG) mechanism. At queue $Q_1$, we employ a Timer $T^{(1)}$: whenever the server polls queue $Q_1$ 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 $Q_1$, the server does not wait any more and switches back to queue $Q_2$. At queue $Q_2$, we operate a RTG mechanism $T^{(2)}$, that is, whenever the server reenters queue $Q_2$, an exponential time $T^{(2)}$ is activated. If the server empties the queue before $T^{(2)}$, it immediately leaves for queue $Q_1$. 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.04.019 |
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