Studying an overload system using rotation |
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Authors: | Yiqiang Q. Zhao Attahiru Sule Alfa |
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Affiliation: | (1) School of Mathematics and Statistics, Carleton University, K1S 5B6 Ottawa, Ontario, Canada;(2) Department of Industrial and Manufacturing Systems Engineering, University of Windsor, N9B 3P4 Windsor, Ontario, Canada |
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Abstract: | For a finite Markov chain, by rotating the transition matrix by 180°, or relabelling the states, one can define a new Markov chain. This Markov chain in fact is the imbedded Markov chain of an inverse process. Duality properties about this Markov chain sometimes are not difficult to obtain. Similarly, one can discuss an infinite Markov chain with states 0,±1,±2,…, However, many applications involve transition matrices with various boundary modifications where rotation cannot directly apply. After introducing some duality properties for a boundary-free or finite Markov chain, we will mainly focus on some interesting application problems and show how to use the duality from rotation to these problems. The research of Y.Q. Zhao is supported by NSERC (Grant No. 4452) and that of A.S. Alfa by NSERC (Grant No. OGP0006584). |
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Keywords: | Duality rotation boundaries overloaded |
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