Stability of macroscopic traffic flow modeling through wavefront expansion

In this paper, second-order macroscopic vehicle traffic flow models are discussed from the perspective of their capability to reproduce stable and unstable traffic flow behaviors observed in real traffic. To achieve this goal, a nonlinear traffic flow stability criterion is derived using a wavefront expansion technique. Qualitative relationships between traffic flow stability and model parameters are derived for an entire class of second-order macroscopic traffic flow models. The stability criterion is illustrated by numerical results using the CLAWPACK package for the well-known Payne-Whitham (PW) model. The newly derived stability results are consistent with previously reported results obtained using both microscopic models and approximate linearization methods. Moreover, the stability criteria derived in this paper can provide more refined information regarding the propagation of traffic flow perturbations and shock waves in second-order models than previously established methodologies.