Kinetic theory methods are applied in this paper to model the dynamics of vehicular traffic. The basic idea is to consider each vehicular-driver system as a single part, or micro-system, of a large complex system, in order to capture the heterogeneous behavior of all the micro-systems that compose the overall system. The evolution of the system is ruled by nonlinearly additive interactions described by stochastic games. A qualitative analysis for the proposed model with discrete states is developed, showing well-posedness of the related Cauchy problem for the spatially homogeneous case and for the spatially nonhomogeneous case, the latter with periodic boundary conditions. Numerical simulations are also performed, with the aim to show how the model proposed is able to reproduce empirical data and to show emerging behavior as the formation of clusters. Keywords: Traffic flow; empirical data; heterogeneity; nonlinearity; Cauchy problem. AMS Subject Classification: 35L50, 35L65, 90B20

Towards the modeling of vehicular traffic as complex system: a kinetic theory approach / Bellouquid, Abdelghani; DE ANGELIS, Elena; L., Fermo. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - STAMPA. - 22:Suppl. 1: 1140003(2012), pp. 1140003-1-1140003-35.

Towards the modeling of vehicular traffic as complex system: a kinetic theory approach

BELLOUQUID, ABDELGHANI;DE ANGELIS, Elena;
2012

Abstract

Kinetic theory methods are applied in this paper to model the dynamics of vehicular traffic. The basic idea is to consider each vehicular-driver system as a single part, or micro-system, of a large complex system, in order to capture the heterogeneous behavior of all the micro-systems that compose the overall system. The evolution of the system is ruled by nonlinearly additive interactions described by stochastic games. A qualitative analysis for the proposed model with discrete states is developed, showing well-posedness of the related Cauchy problem for the spatially homogeneous case and for the spatially nonhomogeneous case, the latter with periodic boundary conditions. Numerical simulations are also performed, with the aim to show how the model proposed is able to reproduce empirical data and to show emerging behavior as the formation of clusters. Keywords: Traffic flow; empirical data; heterogeneity; nonlinearity; Cauchy problem. AMS Subject Classification: 35L50, 35L65, 90B20
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2495938
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo