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

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

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.