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

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.