Study of M/G/1 Feedback Queue with Deterministic Server Vacations

摘要

We study a single server queue with Poisson input, kstages of general hetrogeneous services and deterministic vacations of constant duration. The server provides service to customers one by one on a first come first served basis. After complicating k~(th) stage of service, a customer may leave the system or may opt to repeat the service in which case this customer rejoins the queue. Further just after completion of a customer's k~(th) stage of service, the server may take a vacation of random length or may opt to continue staying in the system to serve next customer. We find the time probability generating function in terms of Laplace transforms and derive explicitly the corresponding steady state results.