Normal Inverse Gaussian Approximation for Arrival Time Difference in Flow-Induced Molecular Communications

TL;DR

This paper introduces a Normal Inverse Gaussian approximation for the distribution of arrival time differences in flow-induced molecular communications, improving accuracy over existing methods and providing practical tail probability estimates.

Contribution

It proposes a novel NIG distribution-based approximation for the difference of first hitting times, with derived asymptotic tail probability expressions.

Findings

NIG approximation closely matches exact numerical solutions.

The asymptotic tail probability outperforms existing approximations.

Numerical evaluations confirm the effectiveness of the proposed method.

Abstract

In this paper, we consider molecular communications in one-dimensional flow-induced diffusion channels with a perfectly absorbing receiver. In such channels, the random propagation delay until the molecules are absorbed follows an inverse Gaussian (IG) distribution and is referred to as first hitting time. Knowing the distribution for the difference of the first hitting times of two molecules is very important if the information is encoded by a limited set of molecules and the receiver exploits their arrival time and/or order. Hence, we propose a moment matching approximation by a normal inverse Gaussian (NIG) distribution and we derive an expression for the asymptotic tail probability. Numerical evaluations showed that the NIG approximation matches very well with the exact solution obtained by numerical convolution of the IG density functions. Moreover, the asymptotic tail probability outperforms state-of-the-art tail approximations.