具有定时与随机时间闸门机制的两队列轮循模型

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

中文关键词:  轮循服务  空竭服务  定时机制  随机时间闸门机制.

英文关键词:polling  exhaustive  Timer  Randomly-Timed Gated.

中文摘要:

      本文考虑了具有定时与随机时间闸门机制的两队列轮循模型.在$Q_1$,设置一个定时机制$T^{(1)}$:当服务员到达$Q_1$时,发现为空时,启动一个定时机制.定时机制期满时,如果有顾客到达,忙期开始且按照$Q_1$空竭服务原理服务;然而如果无顾客到达,服务员不再等待,转移到$Q_2$.在$Q_2$,设置一个随机时间机制 :无论服务员何时到达$Q_2$,指数时间$T^{(2)}$启动.$T^{(2)}$期满时,如果服务完所有顾客,服务员立即离开;否则服务员只完成$T^{(2)}$内到达的工作然后离开.假定Poisson到达,一般服务时间和转移时间分布.获得了在到达时刻队长的概率母函数,平均循环长度及工作量的Laplace变换.

英文摘要:

      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.