An M/G/1 Queue System with Single Working Vacation

This paper treats an M/G/1 queue with single working vacation.Whenever the system becomes empty at a service completion instant,the server goes for a single working vacation.In the working vacation,a customer is served at a lower speed.We derive the queue size distribution at a random epoch as well as a departure epoch under the steady state conditions.Further,we demonstrate the existence of the conditional stochastic decomposition property of the queue size at a departure epoch.We also derive some important performance measures of this model. Finally,several numerical examples are presented.