Printed in the USA c©2003 by North Atlantic Science Publishing Company A NON-MARKOVIAN QUEUEING SYSTEM WITH A VARIABLE NUMBER OF CHANNELS

• Main Authors: Hong-tham T. Rosson, Jewgeni H. Dshalalow
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 2003
• Subjects: Multi-Channel Queue; Variable Number of Channels; Limiting Distribu- tion; Semi-Regenerative Process; Queueing Process; North Atlantic
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.526.6873; http://emis.maths.adelaide.edu.au/journals/HOA/JAMSA/Volume16_4/395.pdf

In this paper we study a queueing model of type GI/M/m̃a/ ∞ 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.