Kink Solution in a Fluid Model of Traffic Flows

TL;DR

This paper analyzes traffic jams in a fluid traffic model, presenting an analytic scaling solution near the critical point and validating it through simulations, enhancing understanding of traffic flow dynamics.

Contribution

It introduces an analytic scaling solution for traffic jams near the bifurcation point and confirms its validity with simulation data.

Findings

Analytic solution accurately describes traffic jam behavior near critical point

Simulation results agree with the theoretical scaling solution

Provides insights into traffic flow phase transitions

Abstract

Traffic jam in a fluid model of traffic flows proposed by Kerner and Konh\"auser (B. S. Kerner and P. Konh\"auser, Phys. Rev. E 52 (1995), 5574.) is analyzed. An analytic scaling solution is presented near the critical point of the hetero-clinic bifurcation. The validity of the solution has been confirmed from the comparison with the simulation of the model.