Stability analysis of parallel server systems under longest queue first |
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Authors: | Golshid Baharian Tolga Tezcan |
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Institution: | 1.Industrial and Enterprise Systems Eng.,University of Illinois at Urbana-Champaign,Urbana,USA;2.Simon Graduate School of Business,University of Rochester,Rochester,USA |
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Abstract: | We consider the stability of parallel server systems under the longest queue first (LQF) rule. We show that when the underlying
graph of a parallel server system is a tree, the standard nominal traffic condition is sufficient for the stability of that
system under LQF when interarrival and service times have general distributions. Then we consider a special parallel server
system, which is known as the X-model, whose underlying graph is not a tree. We provide additional “drift” conditions for
the stability and transience of these queueing systems with exponential interarrival and service times. Drift conditions depend
in general on the stationary distribution of an induced Markov chain that is derived from the underlying queueing system.
We illustrate our results with examples and simulation experiments. We also demonstrate that the stability of the LQF depends
on the tie-breaking rule used and that it can be unstable even under arbitrary low loads. |
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Keywords: | |
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