On a vacation queue with instantaneous customer loss

The paper studies an M/M/1 queueing system with variable batch-size arrivals and single exponential departures. The system is subject to time-homogeneous server vacations. In addition, a variable bulk customer loss of j units occurs with probability π_j (j = 0, 1, 2, 3,.. . M) where Σ π_j = 1 , at an instant when a vacation starts. The vacation times follow a general probability distribution. The probability generating functions of the number in the system have been determined and some particular cases of interest have been discussed. Finally some steady state results have been derived.