Abstract
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.