GI/M/1 Queue with Server Vacations

A queueing model with server vacations is studied in which it is assumed that the interarrival time has a general distribution, the service-time distribution is exponential and vacations are independently and indentically distributed with a general distribution. Using the embedded Markov chain technique, the equilibrium probability distributions of system size have been obtained at pre-arrival and at random epochs separately. Finally, the distribution of waiting time of a customer in the queue (excluding service) has been derived.