M/G/1 Queue with Two Stage Heterogeneous Service and Compulsory Deterministic Server Vacations

We analyze a single server vacation queue with Poisson arrivals, two stages of heterogeneous service with different (arbitrary) service time distributions subject to deterministic vacation of constant duration . After the first stage service, the server must provide the second stage service. We assume that after completion of second stage service, the server may decide to take a vacation of fixed length . The time dependent probability generating functions using supplementary variable technique have been obtained in terms of their Laplace transforms and the corresponding steady state results are also obtained explicitly.