Solitons in a macroscopic traffic model

Abstract

The steady behavior in the macroscopic Kerner and Konhäuser (1993, 1994, 1997) traffic model in a closed circuit, is studied numerically to see the time evolution of perturbations around the homogeneous steady case[9]. The simulation shows that after a transient time interval, the perturbation develops a traveling wave structure with the characteristics associated to a typical soliton in nonlinear partial differential equations. In traffic flow, the formation of solitons indicate the permanent presence of jams along the road. The solitons characteristics depend on the fundamental diagram and the specific values in the viscosity and the velocity variance introduced in the model. The nonlinearity and dissipation in the model cause the propagation of the traveling wave, Drazin (1990)[3].