Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 4, Pages 359-384

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

David C. R. Muh1,2

1Department of Operations Research, Florida Institute of Technology, Melbourne 32901, FL, USA
21767 Brookside St. N.E., Palm Bay 32907, FL, USA

Received 1 June 1993; Revised 1 October 1993

Copyright © 1993 David C. R. Muh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 NR and NR, are studied.

The author finds explicitly the probability generating function of the stationary distribution of the queueing process and gives numerical examples.