Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 3, Pages 203-210
doi:10.1155/S1048953391000163
A single-server queue with random accumulation level
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.
Abstract
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.