Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 3, Pages 203-210

A single-server queue with random accumulation level

Jewgeni H. Dshalalow

Department of Applied Mathematics, Florida Institute of Technology, Melbourne 32901, FL, USA

Received 1 March 1991; Revised 1 June 1991

Copyright © 1991 Jewgeni H. Dshalalow. 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 queueing system. Upon completion of a previous service, the server can take a group of random size from customers that are available. Or, the server can wait until the queue attains a desired level. The author establishes an ergodicity criterion for both the queueing process with continuous time parameter and the imbedded process. Under this criterion, the author obtains explicit formulas for the stationary distributions of both processes by using semi-regenerative techniques.