Journal of Applied Mathematics and Stochastic Analysis
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 Λ, 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.
David C. R. Muh, “A bulk queueing system under N-policy with bilevel service delay discipline and start-up time,” Journal of Applied Mathematics and Stochastic Analysis, vol. 6, no. 4, pp. 359-384, 1993. doi:10.1155/S1048953393000309