A Hybrid Lagrangian Model based on the Aw Rascle Traffic Flow Model

A Hybrid Lagrangian Model based on the Aw-Rascle Traffic Flow Model S. Moutari ? M. Rascle ? Abstract In this paper, we propose a simple fully discrete hybrid model for vehicular traffic flow, for which both the macroscopic and the microscopic models are based on a Lagrangian discretization of the “Aw-Rascle” (AR) model [3]. This hybridization makes use of the relation between the AR macroscopic model and a Follow-the-Leader type model [15, 22], established in [2]. Moreover, in the hybrid model, the total variation in space of the velocity v is non-increasing, the total variation in space of the specific volume ? is bounded and the total variations in time of v and ? are bounded. Finally, we present some numerical simulations which confirm that the models' synchronization processes do not affect the waves propagation. Key words: Traffic flow, Hybrid model, Lagrangian discretiza- tion, Macroscopic model, Microscopic model, Total variation. AMS Subject Classification: 35L, 35L65. 1 Introduction Most of the vehicular traffic models are either macroscopic [3, 12, 18, 25, 30, 33, 34, 36, 37] or microscopic [15, 22]. When following a macroscopic approach, one focuses on global parameters such as traffic density or traffic flow.

• lagrangian discretization


• t1-wave


• fully discrete


• wnh ?


• discrete hybrid model


• traffic


• riemann problem


• volume ?


• hybrid model