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Uniformization: Basics, extensions and applications
یکنواخت سازی: پایه ها، بسط ها و کاربردها-2018 Uniformization, also referred to as randomization, is a well-known performance evaluation technique to model and analyse continuous-time Markov chains via an easier to performance measures via iteration of the one-step transition matrix of the discrete-time Markov chain. The number of iterations has a Poisson distribution with rate dominating the maximum exit rate from the states of the continuous-time Markov chain. This paper contains an expository presentation of uniformization techniques to increase awareness and to provide a formal and intuitive justification of several exact and approximate extensions, including:
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exact uniformization for reward models,
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exact uniformization for time-inhomogeneous rates,
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a numerical comparison with simple time-discretization,
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approximate uniformization for unbounded transition rates, and
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exact uniformization for continuous state variables for non-exponential networks.
Furthermore, several of these results are numerically illustrated for a processor sharing web server tandem model of practical interest.
keywords: Uniformization |Randomization |Time discretization |Time inhomogeneous |Cumulative reward model |Web server tandem model |
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