On a single server queue with two-stage heterogeneous service and deterministic server vacations

We analyse a single server queue with Poisson arrivals, two stages of heterogeneous service with different general (arbitrary) service time distributions and binomial schedule server vacations with deterministic (constant) vacation periods. After first-stage service the server must provide stage service. However, after the second stage service, he may take a vacation or may decide to stay on in the system. For convenience, we designate our model as M/G(1); G(2)/D/1 queue. We obtain steady state probability generating function of the queue length for various states of the server. Results for some particular cases of interest such as M/Ek1; Ek2/D/1, M/M1; M2/D/1, M/Ek/D/1 and M/G(1); G(2)/1 have been obtained from the main results and some known results including M/Ek/1 and M/G/1 have been derived as particular cases of our particular cases.