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In this paper, we consider molecular communications in one-dimensionalflow-induced diffusion channels with a perfectly absorbing receiver. In suchchannels, the random propagation delay until the molecules are absorbed followsan inverse Gaussian (IG) distribution and is referred to as first hitting time.Knowing the distribution for the difference of the first hitting times of twomolecules is very important if the information is encoded by a limited set ofmolecules and the receiver exploits their arrival time and/or order. Hence, wepropose 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 withthe exact solution obtained by numerical convolution of the IG densityfunctions. Moreover, the asymptotic tail probability outperformsstate-of-the-art tail approximations.

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