A Refined Mean Field Approximation

@article{Gast2017ARM,
  title={A Refined Mean Field Approximation},
  author={Nicolas Gast and Benny Van Houdt},
  journal={Proceedings of the ACM on Measurement and Analysis of Computing Systems},
  year={2017},
  volume={1},
  pages={1 - 28}
}
  • Nicolas Gast, B. V. Houdt
  • Published 19 December 2017
  • Computer Science
  • Proceedings of the ACM on Measurement and Analysis of Computing Systems
Mean field models are a popular means to approximate large and complex stochastic models that can be represented as N interacting objects. Recently it was shown that under very general conditions the steady-state expectation of any performance functional converges at rate O(1/N) to its mean field approximation. In this paper we establish a result that expresses the constant associated with this 1/N term. This constant can be computed easily as it is expressed in terms of the Jacobian and… 
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Size Expansions of Mean Field Approximation: Transient and Steady-State Analysis
TLDR
This paper shows how to obtain the same result for the transient regime and provides a further refinement by expanding the term in 1/N2 (both for transient and steady-state regime) and provides examples that show this new approximation is usable in practice for systems with up to a few tens of dimensions.
Refining Mean-field Approximations by Dynamic State Truncation
TLDR
A new method is presented that couples the master equation governing the evolution of the probability distribution of a truncation of the original state space with a mean-field approximation of a time-inhomogeneous population process that dynamically shifts the truncation across the whole state space and provides a result of asymptotic correctness in the limit when the truncations covers the state space.
Refining Mean-field Approximations by Dynamic State Truncation
TLDR
A new method is presented that couples the master equation governing the evolution of the probability distribution of a truncation of the original state space with a mean-field approximation of a time-inhomogeneous population process that dynamically shifts the truncation across the whole state space and provides a result of asymptotic correctness in the limit when the truncations covers the state space.
Size expansions of mean field approximation: Transient and steady-state analysis
A refined mean field approximation of synchronous discrete-time population models
A Refined Mean Field Approximation for Synchronous Population Processes
TLDR
It is shown that, similarly to the asynchronous case, the mean field approximation of a synchronous population can be refined by a term in 1/N, and holds for finite time-horizon and steady-state.
Mean Field and Refined Mean Field Approximations for Heterogeneous Systems
TLDR
An interaction model is defined that allows obtaining asymptotic convergence results for stochastic systems with heterogeneous object behavior, and it is shown that for moderate system sizes the refined mean field approximation tends to be more accurate than simulations for any reasonable simulation time.
A Refined Mean Field Approximation
TLDR
This paper focuses on mean field theory, a very popular approximation method used to study the behavior of stochastic models used to assess the performance of computer systems for many decades.
A Refined Mean Field Approximation
  • Nicolas Gast, B. Van Houdt
  • Computer Science
    Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems
  • 2018
TLDR
This paper focuses on mean field theory, a very popular approximation method used to study the behavior of stochastic models used to assess the performance of computer (and other) systems for many decades.
A Refined Mean Field Approximation
TLDR
This paper focuses on mean field theory, a very popular approximation method used to study the behavior of stochastic models used to assess the performance of computer systems for many decades.
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A Refined Mean Field Approximation
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