OPTIMAL SERVER TIME MANAGEMENT IN A SINGLE SERVER QUEUE

This paper considers an optimal server time management of a single server queue with -policy in which the server is under vacation until the realization of a random variable . When is realized, the server takes all waiting customers as a batch for service. After the batch service completion, the server shifts to a single service if there is any waiting customer and become idle when the system becomes empty. Such types of models deal with a very important class of real life congestion situations encountered in day-to-day as well as industrial scenario. The problem is to find a policy for selecting the service rate which maximizes the expected net profit per cycle in an M/M/1/K queue. Steady-state solutions and various performance measures are derived and obtained the optimal service rate numerically.