Two-way traffic flow: Exactly solvable model of traffic jam

Abstract

We study completely asymmetric two-channel exclusion processes in one dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars in the other lane. Particularly, we consider in detail the system with a finite density of cars on one lane and a single car on the other. When the interchannel interaction reaches a critical value, a traffic jam occurs, which turns out to be of first-order phase transition. We derive exact expressions for the average velocities, the current, the density profile and the k-point density correlation functions. We also obtain the exact probability of two cars being in one lane of distance R apart, provided there is a finite density of cars on the other lane, and show that the two cars form a weakly bound state in the jammed phase.