International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 1, Pages 189-194

A queueing system with a fixed accumulation level, random server capacity and capacity dependent service time

Jewgeni H. Dshalalow1 and Lotfi Tadj2

1Department of Applied Mathematics, Florida Institute of Technology, Melbourne 32901, FL, USA
2Department of Operations Research, Florida Institute of Technology, Melbourne 32901, FL, USA

Received 27 June 1991

Copyright © 1992 Jewgeni H. Dshalalow and Lotfi Tadj. 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.


This paper introduces a bulk queueing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at least r the server takes a batch of size r and processes it a random time arbitrarily distributed. If the queueing level is less than r the server idles until the queue accumulates r customers in total. Then the server capacity is generated by a random number equals the batch size taken for service which lasts an arbitrarily distributed time dependent on the batch size.

The objective of the paper is the stationary distribution of queueing process which is studied via semi-regenerative techniques. An ergodicity criterion for the process is established and an explicit formula for the generating function of the distribution is obtained.