rmf tool - A library to Compute (Refined) Mean Field Approximation(s)

Abstract

Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as systems of interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or large-scale data centers, for which mean field approximation gives very accurate estimates of the transient or steady-state behaviors. In a series of recent papers [9, 7], a new and more accurate approximation, called the refined mean field approximation is presented. Yet, computing this new approximation can be cumbersome. The purpose of this paper is to present a tool, called rmf tool, that takes the description of a mean field model, and can numerically compute its mean field approximations and refinement.

Analysis of the Refined Mean-Field Approximation for the 802.11 Protocol Model

“…The main contribution of this article is to investigate the accuracy of the refined meanfield approximation of the model presented in [4]. To this end, we used the rmf tool [6], which is a tool that takes the description of a stochastic model and computes numerically not only its mean-field approximations but also its refined mean-field approximation. Our results show that the accuracy of the refined mean field is much better than that of the mean-field approximation, especially when the number of objects is small.…”

“…However, in more complicated models, it is required to compute this constant using numerical software. In this work, we used the rmf tool [6] to compute this constant.…”

“…Likewise, in the following figures, we plot in blue the curves that represent the mean-field approximation and the dynamics of the stochastic process when the state is 0, i.e, for x 0 ; in orange, we represent state 1, i.e., x 1 ; in green state 2, i.e., x 2 ; in red state 3, i.e., x 3 , and finally, in violet state 4, i.e., x 4 . All the figures of this section have been obtained using the command plot_ODE_vs_simulation of the rmf tool [6].…”

“…We computed numerically the mean of X N i for different values of N, and we aimed to compare the obtained values with the mean-field approximation (mf) and the refined mean-field approximation (rmf) at the steady state. These values were obtained using the command compare_refinedMF of the rmf tool [6]. The results we obtained are presented in Table 1.…”

“…In the following tables (see Tables 2-4), we represent the results we obtained using the command compare_refinedMF of the rmf tool [6]. These tables show that the properties observed for D = 5 still hold when D = 15.…”