Transient solution of a finite-capacity M/Ga’,b/1 queueing system

In this article the authors consider a single-server, bulk-service queueing system in which the waiting room is of finite capacity. Arrival process is Poisson and all the arrivals taking place when the waiting room is full are lost. The service times are generally distributed independent random variables and the distribution is dependent on the batch size being served. Using renewal theory, the authors derive the time-dependent solution for the system-size probabilities at arbitrary time points. Also they give expressions for the distribution of virtual waiting time in the queue at any time t.