Asymmetric exclusion process for modeling of information flow

In this paper we investigate the dynamics of totally asymmetric exclusion process (TASEPs) on a one-dimensional lattice with long-range hopping and parallel update. The model is inspired by information traffic over networks. Compared to other TASEP models, particles in our model will firstly try to hop to the last site with a probability q. The probability q may reflect network reliability or available bandwidth. A mean-field approach is developed to deal with the long-range hopping. Theoretical calculations for stationary particle currents, density profiles and a phase diagram have been obtained. There are two possible stationary phases (LD and HD) in the system, corresponding to free flow and jammed flow, respectively. Interestingly, bulk density in the LD phase tends to zero, while in the HD phase it is the same as that of the normal TASEP. The LD and HD phase regions are obtained numerically. The steady-state currents and density profiles obtained from computer simulations show a very good agreement with theoretical predictions. The model and theoretical results may provide a better understanding of information traffic flow over networks.