Reduced systems in Markov chains and their applications in queueing theory |
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Authors: | Ram Lal U Narayan Bhat |
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Institution: | (1) Department of Management Science, California State University, 92634 Fullerton, CA, USA;(2) Department of Statistics, Southern Methodist University, 75275 Dallas, TX, USA |
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Abstract: | A reduced system is a smaller system derived in the process of analyzing a larger system. While solving for steady-state probabilities of a Markov chain, generally the solution can be found by first solving a reduced system of equations which is obtained by appropriately partitioning the transition probability matrix. In this paper, we catagorize reduced systems as standard and nonstandard and explore the existence of reduced systems and their properties relative to the original system. We also discuss first passage probabilities and means for the standard reduced system relative to the original system. These properties are illustrated while determining the steady-state probabilities and first passage time characteristics of a queueing system. |
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Keywords: | Markov chains reduced systems steady-state probabilities queueing theory first passage times |
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