A Framework for the Analysis of a General M/G/1 Queue with Variable Server Vacations

The systematic growth of vacation queueing model in recent part is described in this paper .An M/G/1 queue with probability association is also analyzed in this paper. A two phase service queueing system with multiple server vacation is the subject matter. Service to customer starts with a batch mode service in the phase-I followed by individual mode service in phase – II. Each customer may or may not balk on the arrival at the queue. As soon as the system becomes empty, the server starts taking sequence of different distributed vacations. The number of Poisson arrivals during the time interval is distributed as the forward recurrence time of vacation and the number of customers present in the standard M/G/1 queueing system is random. Based on the numerical values of service rate and mean system time is analyzed in a graphical manner.