M/G/1 QUEUE WITH COMPULSORY VACATION AND THREE PHASE REPAIRS

We study a single server M/G/1 queueing system with Poisson input subject to compulsory server vacation and random breakdowns. The server provides service to all arriving customers on a first come first served basis and service times follow general distribution. However after the completion of each service the server will take compulsory vacation. The system may breakdown at random and it must be send to repair process immediately. Further the repair process involves three phases of repairs with different general repair time distributions. The supplementary variable technique is applied to find explicitly probability generating function of the number in the system