Analysis of the M/G/1 queueing system with randomized control of T-policy

In this paper, we consider the queueing system with randomized control of T-policy. Whenever the busy period ends, the server is turned off and takes multiple vacations whose interval is fixed time T with probability p or stays on and waits for arriving customers with probability (1−p). We introduce the cost function and determine the optimal combination of (p,T) to minimize the average cost per unit time.