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

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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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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada

    Attahiru Sule Alfa

  2. Department of Mathematics, Cleveland State University, Cleveland, OH, 44114-2214, USA

    Barbara Haas Margolius

Authors
  1. Attahiru Sule Alfa
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  2. Barbara Haas Margolius
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Correspondence to Attahiru Sule Alfa.

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Alfa, A.S., Margolius, B.H. Two classes of time-inhomogeneous Markov chains: Analysis of the periodic case. Ann Oper Res 160, 121–137 (2008). https://doi.org/10.1007/s10479-007-0300-3

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  • DOI: https://doi.org/10.1007/s10479-007-0300-3

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