Asymmetric exclusion process with next-nearest-neighbor interaction: Some comments on traffic flow and a nonequilibrium reentrance transition

We study the steady-state behavior of a driven nonequilibrium lattice gas o f hard-core particles with next-nearest-neighbor interaction. We calculate the exact stationary distribution of the periodic system and for a particul ar line in the phase diagram of the system with open boundaries where parti cles can enter and leave the system. For repulsive interactions the dynamic s can be interpreted as a two-speed model for traffic flow. The exact stati onary distribution of the periodic continuous-time system turns out to coin cide with that of the asymmetric exclusion process (ASEP) with discrete-tim e parallel update. However, unlike in the (single-speed) ASEP, the exact do w diagram for the two-speed model resembles in some important features the flow diagram of real traffic. The stationary phase diagram of the open syst em obtained from Monte Carlo simulations can be understood in terms of a sh ock moving through the system and an overfeeding effect at the boundaries, thus confirming theoretical predictions of a recently developed general the ory of boundary-induced phase transitions. In the case of attractive intera ction we observe an unexpected reentrance transition due to boundary effect s.