M/G/1 Queue with Two-Stage Heterogeneous Service Compulsory Server Vacation and Random Breakdowns

We analyze a single server queue with Poisson arrivals, two stages of heterogeneous service with different (arbitrary) service time distributions subject to random breakdowns and compulsory server vacations with general (arbitrary) vacation periods. After first-stage service the server must provide the second stage service. However, after the completion of each second stage service, the server will take compulsory vacation. The system may breakdown at random and repair time follow exponential distribution. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been obtained explicitly. Also the average number of customers in the queue and the average waiting time are derived. Mathematics Subject Classification: 60K25, 60K30