A note on workload control for an under-utilized server of M/G/1 system

In this note, we study the issue of adjusting the workload of an under-utilized server in a queueing system. Using an M/G/1 model with server vacations of two types, we can effectively control the workload level of the server. The server vacations are time periods that the server does not serve the queue. Type 1 vacations represent durations of supplementary non-queue jobs assigned to the server. Type 2 vacations represent the non-productive period for the server such as idle time. With a two threshold policy, we demonstrated that the server's workload can be effectively controlled. A simple procedure for determining the conditionally optimal policy is proposed. Numerical examples are presented to illustrate the use of the procedure.