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

Qi-Ming He () and Attahiru Sule Alfa ()
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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

INFORMS Journal on Computing, 2018, vol. 30, issue 1, 1-10

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.

Keywords: Markov chains; order statistics; queues with multiple servers; reliability; phase-type distribution; Markovian arrival process (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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