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

TL;DR

This paper presents an exactly solvable model of two-way traffic flow using asymmetric 2-channel exclusion processes, revealing phase transitions and detailed statistical properties of traffic jams.

Contribution

It introduces a novel exactly solvable model for two-way traffic flow with interchannel interactions and derives explicit expressions for key traffic statistics.

Findings

Traffic jam occurs at a critical interchannel interaction, indicating a first-order phase transition.

Exact formulas for velocities, current, and density correlations are obtained.

Cars form a weakly bound state in the jammed phase.

Abstract

We study completely asymmetric 2-channel exclusion processes in 1 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 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 one. When the interchannel interaction reaches a critical value, 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 in one lane being distance $R$ apart, provided there is a finite density of cars on the other lane, and show the two cars form a weakly bound state in the jammed phase.