We study the derivation of macroscopic traffic models out of optimal speed and follow-the-leader particle dynamics as hydrodynamic limits of non-local Povzner-type kinetic equations. As a first step, we show that optimal speed vehicle dynamics produce a first order macroscopic model with non-local flux. Next, we show that non-local follow-the-leader vehicle dynamics have a universal macroscopic counterpart in the second order Aw-Rascle-Zhang traffic model, at least when the non-locality of the interactions is sufficiently small. Finally, we show that the same qualitative result holds also for a general class of follow-the-leader dynamics based on the headway of the vehicles rather than on their speed. We also investigate the correspondence between the solutions to particle models and their macroscopic limits by means of numerical simulations.
Macroscopic limits of non-local kinetic descriptions of vehicular traffic / Chiarello, Felisia Angela; Tosin, Andrea. - In: KINETIC AND RELATED MODELS. - ISSN 1937-5093. - STAMPA. - 16:4(2023), pp. 540-564. [10.3934/krm.2022038]
Macroscopic limits of non-local kinetic descriptions of vehicular traffic
Tosin, Andrea
2023
Abstract
We study the derivation of macroscopic traffic models out of optimal speed and follow-the-leader particle dynamics as hydrodynamic limits of non-local Povzner-type kinetic equations. As a first step, we show that optimal speed vehicle dynamics produce a first order macroscopic model with non-local flux. Next, we show that non-local follow-the-leader vehicle dynamics have a universal macroscopic counterpart in the second order Aw-Rascle-Zhang traffic model, at least when the non-locality of the interactions is sufficiently small. Finally, we show that the same qualitative result holds also for a general class of follow-the-leader dynamics based on the headway of the vehicles rather than on their speed. We also investigate the correspondence between the solutions to particle models and their macroscopic limits by means of numerical simulations.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2973521