Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 4, Pages 375-395
doi:10.1155/S1048953303000297
A non-Markovian queueing system with a variable number of channels
1Florida Institute of Technology, Operations Research Program, Melbourne 32901, FL, USA
2Florida Institute of Technology, Department of Mathematical Sciences, Melbourne 32901, FL, USA
Received 1 March 2002; Revised 1 August 2003
Copyright © 2003 Hong-Tham T. Rosson and 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
In this paper we study a queueing model of type GI/M/m˜a/∞ with m parallel channels, some of which may suspend their service at specified random moments of time. Whether or not this phenomenon occurs depends on the queue length. The queueing process, which we target, turns out to be semi-regenerative, and we fully explore this utilizing semi-regenerative techniques. This is contrary to the more traditional supplementary variable approach and the less popular approach of combination semi-regenerative and supplementary variable technique. We pass to the limiting distribution of the continuous time parameter process through the embedded Markov chain for which we find the invariant probability measure. All formulas are analytically tractable.