Staggered Conservative Scheme for Simulating the Emergence of a Jamiton in a Phantom Traffic Jam

TLDR: The staggered conservative scheme applied on a staggered grid was implemented to solve the second-order Payne-Whitham equation and the shape and propagation speed of numerical jamitons are shown to confirm the analytical formulas.

Abstract: Traffic jams that appear without distinguishable reason is called phantom traffic jam. To study this phenomenon, macroscopic modelling using the second-order Payne-Whitham equation was adopted. In this article, the staggered conservative scheme applied on a staggered grid was implemented to solve the equation. Using this scheme, different behavior of a perturbed equilibrium solution was simulated; it might either decay or grow, depending on the critical threshold parameter. When unstable, a small perturbation was amplified into a local peak of high traffic density. This type of traveling wave is called a jamiton. On a circular road of a certain length and with a fixed number of vehicles, the growing process of these traveling jamiton waves was simulated. The shape and propagation speed of these numerical jamitons are shown to confirm the analytical formulas. A good understanding of this phenomenon may support decision-makers and engineers to determine the judicious selection of speed limits of a certain road section.