Optimal policies for a controlled queueing system with removable server under a random vacation circumstance

In this paper, we consider two stochastic models for a controlled single-server M/G/1 queueing system under a random vacation circumstance. The relevant expected costs are formulated under two control strategies and approximated by means of a familiar diffusion approximation method. Numerical calculations are devoted to examine the accuracy of the proposed approximation method. The results show that the diffusion approximation method is reasonably good for the performance evaluation on the typical queueing control systems, especially, for the M/M/1 single-server queue.