Micro-Macro Limit of a Nonlocal Generalized Aw-Rascle Type Model
Felisia Angela Chiarello, Jan Friedrich, Paola Goatin, Simone Göttlich
Abstract
We introduce a Follow-the-Leader approximation of a nonlocal generalized Aw--Rascle--Zhang (GARZ) model for traffic flow. We prove the convergence to weak solutions of the corresponding macroscopic equations deriving $L^\infty$ and BV estimates. We also provide numerical simulations illustrating the micro-macro convergence and we numerically investigate the nonlocal to local limit for both the microscopic and macroscopic models.
Topics & Concepts
Limit (mathematics)MacroConvergence (economics)Type (biology)MathematicsFlow (mathematics)Applied mathematicsStatistical physicsMathematical analysisPhysicsGeometryComputer scienceEconomicsBiologyProgramming languageEcologyEconomic growthTraffic control and managementTransportation Planning and OptimizationStochastic processes and financial applications