A bulk queueing system under N-policy with bilevel service delay discipline and start-up time

The author studies the queueing process in a single-server, bulk arrival and batch service queueing system with a compound Poisson input, bilevel service delay discipline, start-up time, and a fixed accumulation level with control operating policy. It is assumed that when the queue length falls below a predefined level r (¸≥1), the system, with server capacity R, immediately stops service until the queue length reaches or exceeds the second predefined accumulation level N(¸≥r). Two cases, with N•R and N≥R, are studied. The author finds explicitly the probability generating function of the stationary distribution of the queueing process and gives numerical examples.