Shock formation and traffic jam induced by a crossing in the 1D asymmetric exclusion model

Abstract

The asymmetric simple-exclusion model on two-crossing one-dimensional lattices is considered for studying shock formation and traffic jams induced by a crossing. The condition for shock formation is derived for car densities p₁ and p₂ of the first and second street. The phase diagram and the dependence of the traffic current on the car densities are shown. We compare the present result with that of a car accident. Also, we investigate the shock formation induced by both a crossing and a car accident. It is found that the dynamical transitions occur successively with increasing car density. The phase diagram is shown.