The PH/PH/1 Multi-threshold Queue
Jan-Kees van Ommeren2014, Lecture Notes in Computer Science
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Abstract
We consider a P H/P H/1 queue in which a threshold policy determines the stage of the system. The arrival and service processes follow a Phase-Type (P H) distribution depending on the stage of the system. Each stage has both a lower and an upper threshold at which the stage of the system changes, and a new stage is chosen according to a prescribed distribution. This P H/P H/1 multi-threshold queue is modelled as a Level Dependent Quasi-Birth-and-Death process. An efficient algorithm is presented to obtain the stationary queue length vectors using Matrix Analytic methods.
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