Microscopic selection of solutions to scalar conservation laws with discontinuous flux in the context of vehicular traffic

In the context of road traffic modeling we consider a scalar hyperbolic conservation law with the flux (fundamental diagram) which is discontinuous at x=0, featuring variable velocity limitation. The flow maximization criterion for selection of a unique admissible weak solution is generally admitted in the literature, however justification for its use can be traced back to the irrelevant vanishing viscosity approximation. We seek to assess the use of this criterion on the basis of modeling proper to the traffic context. We start from a first order microscopic follow-the-leader (FTL) model deduced from basic interaction rules between cars. We run numerical simulations of FTL model with large number of agents on truncated Riemann data, and observe convergence to the flow-maximizing Riemann solver. As an obstacle towards rigorous convergence analysis, we point out the lack of order-preservation of the FTL semigroup. © Springer Nature Switzerland AG 2020.

Авторы
Andreianov B. 1, 2 , Rosini M.D.3, 4
Сборник материалов конференции
Издательство
Springer New York LLC
Язык
Английский
Страницы
113-135
Статус
Опубликовано
Том
325
Год
2020
Организации
  • 1 Institut Denis Poisson (CNRS UMR7013), Université de Tours, Université d’Orléans, Parc Grandmont, Tours, 37200, France
  • 2 Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
  • 3 Department of Mathematics and Computer Science, University of Ferrara, Ferrara, I-44121, Italy
  • 4 Instytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, pl. Marii Curie-Skłodowskiej 1, Lublin, 20-031, Poland
Ключевые слова
Conservation laws; Discontinuous flux; First order follow-the-leader model; Follow-the-leader semigroup; Order-preservation; Point constraint on the flux; Riemann solvers; Traffic flow
Дата создания
02.11.2020
Дата изменения
02.11.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/65578/