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Space Reduction for a Class of Multidimensional Markov Chains: A Summary and Some Applications

Author

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  • Qi-Ming He

    (Departments of Industrial and Systems Engineering and Computer Science and Software Engineering, Auburn University, Auburn, Alabama 36849)

  • Attahiru Sule Alfa

    (Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada; Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria 0002, South Africa)

Abstract

In this paper, we present examples of a class of Markov chains that occur frequently, but whose associated matrices are a challenge to construct efficiently. These are Markov chains that arise as a result of several identical Markov chains running in parallel. Specifically for the cases considered, both the infinitesimal generator matrix for the continuous case, and more so the transition probability matrix for the discrete equivalent, are complex to construct effectively and efficiently. We summarize the algorithms for constructing the associated matrices and present examples of applications, ranging from special queueing problems to reliability issues and order statistics. MATLAB subroutines are provided in an online supplement for the implementation of the algorithms.

Suggested Citation

  • Qi-Ming He & Attahiru Sule Alfa, 2018. "Space Reduction for a Class of Multidimensional Markov Chains: A Summary and Some Applications," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 1-10, February.
    • Handle: RePEc:inm:orijoc:v:30:y:2018:i:1:p:1-10
    DOI: 10.1287/ijoc.2017.0759
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    References listed on IDEAS

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    1. Che Kim & Vilena Mushko & Alexander Dudin, 2012. "Computation of the steady state distribution for multi-server retrial queues with phase type service process," Annals of Operations Research, Springer, vol. 201(1), pages 307-323, December.
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    Cited by:

    1. Dudin, A.N. & Dudin, S.A. & Dudina, O.S. & Samouylov, K.E., 2018. "Analysis of queueing model with processor sharing discipline and customers impatience," Operations Research Perspectives, Elsevier, vol. 5(C), pages 245-255.

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