Before revision:  The aim of this work is  to propose a fully stochastic  model describing the main characteristics of a multiple channel system , in which ion movement is coupled with a Poisson--Nernst--Planck equation . Exclusion forces are considered and different nondimensionalization procedure, supported by numerical simulation, are discussed. Both cases of nano and micro channels are considered .
After revision:  The aim of this work is to propose a fully stochastic model describing the main characteristics of a multiple channel system , in which ion movement is coupled with a Poisson--Nernst--Planck equation . Exclusion forces are considered and different nondimensionalization procedure, supported by numerical simulations. The specific features of both cases of micro and nano channels have been have been taken in due consideration with particular attention to the latter case in order to show that it is necessary to consider inside the channels a discrete and stochastic model for ions movement .