Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 4, Pages 311-326

On the ergodic distribution of oscillating queueing systems

Mykola Bratiychuk1 and Andrzej Chydzinski2

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.


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/MM/1 system, where the interarrival distribution does not change and both service distributions are exponential. A numerical example is also given.