Size Expansions of Mean Field Approximation: Transient and Steady-State Analysis

Abstract : Mean field approximation is a powerful tool to study the performance of large stochastic systems that is known to be exact as the system's size N goes to infinity. Recently, it has been shown that, when one wants to compute expected performance metric in steady-state, this approximation can be made more accurate by adding a term V /N to the original approximation. This is called a refined mean field approximation in [21]. In this paper, we improve this result in two directions. First, we show how to obtain the same result for the transient regime. Second, we provide a further refinement by expanding the term in 1/N 2 (both for transient and steady-state regime). Our derivations are inspired by moment-closure approximation, a popular technique in theoretical biochemistry. We provide a number of examples that show: (1) that this new approximation is usable in practice for systems with up to a few tens of dimensions, and (2) that it accurately captures the transient and steady state behavior of such systems.
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https://hal.inria.fr/hal-01891632
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Submitted on : Tuesday, October 9, 2018 - 6:00:47 PM
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Nicolas Gast, Luca Bortolussi, Mirco Tribastone. Size Expansions of Mean Field Approximation: Transient and Steady-State Analysis. Performance Evaluation, Elsevier, In press, pp.1-15. ⟨hal-01891632⟩

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