Symmetry Analysis for the 2D Aw-Rascle Traffic-Flow Model of Multi-Lane Motorways in the Euler and Lagrange Variables

A detailed symmetry analysis is performed for a microscopic model used to describe traffic flow in two-lane motorways. The traffic flow theory employed in this model is a two-dimensional extension of the Aw-Rascle theory. The flow parameters, including vehicle density, and vertical and horizontal velocities, are described by a system of first-order partial differential equations belonging to the family of hydrodynamic systems. This fluid-dynamics model is expressed in terms of the Euler and Lagrange variables. The admitted Lie point symmetries and the one-dimensional optimal system are determined for both sets of variables. It is found that the admitted symmetries for the two sets of variables form different Lie algebras, leading to distinct one-dimensional optimal systems. Finally, the Lie symmetries are utilized to derive new similarity closed-form solutions.

Automated summary

A detailed symmetry analysis is conducted for a microscopic model of traffic flow in two-lane motorways. The model is an extension of the Aw-Rascle theory and describes flow parameters using first-order partial differential equations. The model is expressed in terms of Euler and Lagrange variables, and different Lie algebras and optimal systems are found for each variable set. The Lie symmetries are then used to derive new closed-form solutions.