Operating characteristic analysis on the M[x]/G/1 system with a variant vacation policy and balking

This paper studies the operating characteristics of an M[x]/G/1 queueing system under a variant vacation policy, where the server leaves for a vacation as soon as the system is empty. The server takes at most J vacations repeatedly until at least one customer is found waiting in the queue when the server returns from a vacation. If the server is busy or on vacation, an arriving batch balks (refuses to join) the system with probability 1 − b. We derive the system size distribution at different points in time, as well as the waiting time distribution in the queue. Finally, important system characteristics are derived along with some numerical illustration.