On the Statistics of Reaction-Diffusion Simulations for Molecular Communication

TL;DR

This paper compares microscopic, mesoscopic, and hybrid simulation models for molecular reaction-diffusion systems in molecular communication, analyzing their statistical properties and the accuracy of common approximations.

Contribution

It provides a detailed comparison of different simulation approaches and evaluates the validity of Poisson and Gaussian approximations in molecular communication contexts.

Findings

Microscopic and mesoscopic models show different statistical behaviors.

Poisson and Gaussian approximations vary in accuracy depending on conditions.

Hybrid models can effectively combine features of both approaches.

Abstract

A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular diffusion, are well understood. However, the coupling of multiple interactions can impede closed-form analysis, such that simulations are required to determine the statistics. This paper compares the statistics of molecular reaction-diffusion simulation models from the perspective of molecular communication systems. Microscopic methods track the location and state of every molecule, whereas mesoscopic methods partition the environment into virtual containers that hold molecules. The properties of each model are described and compared with a hybrid of both models. Simulation results also assess the accuracy of Poisson and Gaussian approximations of the underlying Binomial statistics.