Mathematical Problems in Engineering
Volume 3 (1998), Issue 6, Pages 539-554

On a bulk queueing system with impatient customers

Lotfi Tadj, Lakdere Benkherouf, and Lakhdar Aggoun

Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 9 March 1997

Copyright © 1998 Lotfi Tadj et al. 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.


We consider a bulk arrival, bulk service queueing system. Customers are served in batches of r units if the queue length is not less than r. Otherwise, the server delays the service until the number of units in the queue reaches or exceeds level r. We assume that unserved customers may get impatient and leave the system. An ergodicity condition and steady-state probabilities are derived. Various system characteristics are also computed.