Two classes of time-inhomogeneous Markov chains: Analysis of the periodic case

Two classes of time-inhomogeneous Markov chains: Analysis of the periodic case

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Article ID: iaor20091350
Country: Netherlands
Volume: 160
Issue: 1
Start Page Number: 121
End Page Number: 137
Publication Date: Apr 2008
Journal: Annals of Operations Research
Authors: ,
Keywords: Matrix-analytic methods, M/G/1 queues, GI/M/1 queues
Abstract:

We consider the M/G/1 and GI/M/1 types of Markov chains for which their one step transitions depend on the times of the transitions. These types of Markov chains are encountered in several stochastic models, including queueing systems, dams, inventory systems, insurance risk models, etc. We show that for the cases when the time parameters are periodic the systems can be analyzed using some extensions of known results in the matrix-analytic methods literature. We have limited our examples to those relating to queueing systems to allow us a focus. An example application of the model to a real life problem is presented.

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