Space Reduction for a Class of Multidimensional Markov Chains: A Summary and Some Applications
| Autor: | Qi-Ming He, Attahiru Sule Alfa |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematical optimization
021103 operations research Theoretical computer science Markov kernel Markov chain 0211 other engineering and technologies General Engineering Markov process 02 engineering and technology 01 natural sciences Uniformization (probability theory) Continuous-time Markov chain 010104 statistics & probability symbols.namesake Matrix analytic method symbols Markov property Examples of Markov chains 0101 mathematics Mathematics |
| Zdroj: | INFORMS Journal on Computing. 30:1-10 |
| ISSN: | 1526-5528 1091-9856 |
| DOI: | 10.1287/ijoc.2017.0759 |
| Popis: | 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. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0759 . |
| Databáze: | OpenAIRE |
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