Large estimations for characteristics of asyncronous inhomogeneous exclusion process with open boundaries

A model based on a totally asymmetric exclusion process on a one-dimensional lattice with open boundaries is considered. In time intervals such that the leftmost site is vacant, particles arrive. Any particle belongs to one of the types characterized by rates of particle attempts to move to the neighbor nearest site to the right or to depart the system from the rightmost site. An algorithm for compiling a system of equations for stationary probabilities of process states is presented. The knowledge of the stationary distribution allows one to calculate the probability of occupancy for any site (particle flow density in the site), the particle flow velocity in the site, and the particle flow rate along the lattice. For a particular case, it is established that, in this case, the density, velocity, and particle flow rate take the same value as for a homogeneous process, in which the particle hop rates are the same as the harmonic average of different type particles hop rates in the inhomogeneous process. The process under consideration can be used as a model of a traffic flow, in which particles correspond to vehicles with different velocity characteristics, or a model of statistical physics, in which particles correspond to molecules or elementary particles, or a model of an infocommunication network.