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

*(English)*Zbl 1006.90021Summary: We analyze 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 the second 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 \(M/E_{k_1}\), \(E_{k_2}/D/1\), \(M/M_1\), \(M_2/D/1\), \(M/E_k/D/1\) and \(M/G_1\), \(G_2/1\) have been obtained from the main results and some known results including \(M/E_k/1\) and \(M/G/1\) have been derived as particular cases of our particular cases.