Modeling 3-D diffusion using queueing networks

The objective of this paper is to propose and then validate a new method for simulating molecular diffusion in a 3-D environment. Diffusion governing principles of Brownian motion have been discovered by Einstein and Smoluchowski. In a classical approach, diffusion is modeled using partial differential equations. However, solving those, even using numerical methods is usually time consuming, particularly in the case of an inhomogeneous environment. In this paper, we propose to use queueing networks to model diffusion of molecules as governed by Fick’s law. The proposed model has been validated using the Kolmogorov-Smirnov test to compare results obtained from a simulation with theoretical standard deviations resulting from Einstein-Smoluchowski’s approach.