Second-order macroscopic traffic models

Second-order macroscopic traffic flow models introduce a second dynamic equation compared to first-order models, i.e. the equation describing the dynamics of the mean speed of vehicles. Second-order models were introduced in the 70s as continuous models, the earliest one being the so-called Payne–Whitham model. Some critiques arose on this class of models, focusing in particular on the dissimilarity between the flow of vehicles and the flow of molecules in fluids or gases. This criticism encouraged new developments of second-order models, leading to the model proposed by Aw and Rascle, and a similar model developed independently by Zhang. A discrete version of second-order models has been elaborated in the 90s, known as METANET. This discrete model, conceived both for freeway stretches and for networks, is very widespread in the engineering field and particularly suitable for prediction and control purposes.