On the Payne-Whitham Differential Model: Stability Constraints in One-Class and Two-Class Cases

This paper deals with the classic second order Payne-Whitham macroscopic model, commonly known as PW-Model, used to represent and forecast traffic conditions in a freeway. The results of the model may show a misbehavior similar to the instability of numerical solutions of partial differential equations. Since this model comes from a partial differential equation system, we use some stability rules to determine the conditions in order to avoid these errors in simulation. The work applies to the classic model, which considers a single class of vehicles, and to the two-class extension previously presented by the authors