Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 4, Pages 311-326
doi:10.1155/S104895330300025X
On the ergodic distribution of oscillating queueing systems
1Silesian University of Technology, Institute of Mathematics, Kaszubska 23, Gliwice 44-100, Poland
2Silesian University of Technology, Institute of Computer Sciences, Akademicka 16, Gliwice 44-100, Poland
Received 1 April 2002; Revised 1 March 2003
Copyright © 2003 Mykola Bratiychuk and Andrzej Chydzinski. 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
This paper examines a new class of queueing systems and proves a theorem on the existence of the ergodic distribution of the number of customers in such a system. An ergodic distribution is computed explicitly for the special case of a G/M−M/1 system, where the interarrival distribution does not change and both service distributions are exponential. A numerical example is also given.