Arrival modelling for molecular communication via diffusion

The arrival of molecules in molecular communication via diffusion obeys, by its nature, the binomial distribution, considering the hitting probability as the success probability. It is, however, hard to work with the binomial cumulative distribution function (CDF) when considering consecutively sent symbols as it is necessary to add the distribution. Therefore, in the literature, two approximations of the binomial distribution are used. In the present reported work, the Gaussian and Poisson approximations of the binomial model of the molecule arrival process have been analysed. Considering the distance and the number of emitted molecules, the regions in which the Poisson or Gaussian model is better in terms of root mean squared error of CDFs are investigated and the regions using numerical simulations are confirmed.