具有N-策略休假的M/G/1排队的随机分解与最优策略

Stochastic Decomposition and Optimal Policy of the M/G/1 Queue with the N-policy and Server Vacations

本文利用向量Markov过程方法,研究了具有N-策略休假且休假时间为一般分布的M/G/1排队,它的两种特殊情况分别是具有多重休假的M/G/1排队和具有N-策略控制的M/G/1排队。我们得到了这个排队系统稳态时的队长分布,证明了它的稳态队长存在随机分解。然后讨论了当休假时间服从指数分布时的最优策略问题。

In this paper, we analyse an M/G/1 queue with the N-policy and server vacations by means of the vector Markov process method. This model includes the M/G/1 queue with the N-policy and the M/G/1 queuewith vacations as its special cases. We obtain the queue length of this queueing system in the steady-state, and prove the queue length exists stochastic decomposition property. Finally, we discuss the problem of optimal policy when the vacation time is exponentially distributed.