Modelling and analysis of Markovian continuous flow systems with a finite buffer |
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Authors: | Bar?? Tan Stanley B Gershwin |
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Institution: | (1) Division for Industrial Engineering and Computer Science, Ecole des Mines de Saint Etienne, 158, Cours Fauriel, 42023 Saint-Etienne Cedex 2, France;(2) Discrete Optimization Laboratory, Omsk Branch of Sobolev Institute of Mathematics, Omsk, Russia;(3) Department of Mathematics, Omsk State University, Omsk, Russia |
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Abstract: | In this study, a Markovian fluid flow system with two stages separated by a finite buffer is considered. Fluid flow models
have been analyzed extensively to evaluate the performance of production, computer, and telecommunication systems. Recently,
we developed a methodology to analyze general Markovian continuous flow systems with a finite buffer. The flexibility of this
methodology allows us to analyze a wide range of systems by specifying the transition rates and the flow rates associated
with each state of each stage. In this study, in order to demonstrate the applicability of our methodology, we model and analyze
a range of models studied in the literature. The examples we analyze as special cases of our general model include systems
with phase-type failure and repair-time distributions, systems with machines that have multiple up and down states, and systems
with multiple unreliable machines in series or parallel in each stage. For each case, the Markovian model is developed, the
transition and flow rates are determined, and representative numerical results are obtained by using our methodology. |
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Keywords: | |
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