Resurrection of "Second Order" Models of Traffic Flow

TLDR

Earlier second‑order traffic flow models, modeled after gas dynamics, exhibit nonphysical behavior due to an unrealistic pressure space‑derivative dependence, as noted by Daganzo (1995). The authors introduce a new second‑order traffic flow model. The model replaces the problematic space derivative in the momentum equation with a convective derivative, thereby eliminating the nonphysical effects. This simple modification resolves the inconsistencies of prior models and enables the new model to predict instabilities near vacuum for very light traffic.

Abstract

We introduce a new "second order" model of traffic flow. As noted in [C. Daganzo, Requiem for second-order fluid with approximation to traffic flow, Transportation Res. Part B, 29 (1995), pp. 277--286], the previous "second order" models, i.e., models with two equations (mass and "momentum"), lead to nonphysical effects, probably because they try to mimic the gas dynamics equations, with an unrealistic dependence on the acceleration with respect to the space derivative of the "pressure." We simply replace this space derivative with a convective derivative, and we show that this very simple repair completely resolves the inconsistencies of these models. Moreover, our model nicely predicts instabilities near the vacuum, i.e., for very light traffic.