A non-Markovian queueing system with a variable number of channels

Hong-Tham T. Rosson, Jewgeni H. Dshalalow
2003 Journal of Applied Mathematics and Stochastic Analysis  
In this paper we study a queueing model of typeGI/M/m˜a/∞withmparallel 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
more » ... on 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.
doi:10.1155/s1048953303000297 fatcat:p4nv5x6c4zgq5pte23pn2422om