Nonlinear Analysis in the Aw-Rascle Anticipation Model of Traffic Flow

In this paper, the Aw–Rascle anticipation (ARA) model is discussed from the perspective of the capability to reproduce nonlinear traffic flow behaviors observed in real traffic. For this purpose, a nonlinear traffic flow stability criterion is derived by using a wavefront expansion technique. The result of the nonlinear stability analysis can be used not only to judge the stability evolution of an initial traffic state but also to determine the pressure term in the ARA model. The KdV equation is derived from the ARA model added by the viscous term with the use of the reduction perturbation method. The soliton solution can be analytically obtained from the perturbed KdV equation only near the neutral stability line. Weighted essentially nonoscillatory schemes are employed to simulate the KdV soliton. The numerical results confirm the analytical KdV soliton solution.

[1]  R D Kuhne,et al.  FREEWAY SPEED DISTRIBUTION AND ACCELERATION NOISE : CALCULATIONS FROM A STOCHASTIC CONTINUUM THEORY AND COMPARISION WITH MEASUREMENTS , 1987 .

[2]  P Berg,et al.  On-ramp simulations and solitary waves of a car-following model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Axel Klar,et al.  Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models , 2002, SIAM J. Appl. Math..

[4]  L. Chambers.  Linear and Nonlinear Waves , 2000, The Mathematical Gazette.

[5]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.