Mathematical Modelling of Traffic Flows

Tong Li ()
Additional contact information
Tong Li: University of Iowa, Department of Mathematics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 695-704 from Springer

Abstract: Abstract We are concerned with mathematical modeHng of of traffic flow. In particular, well-posedness theory of various nonequilibrium continuum models of traffic flow are established. One such a model is an inhomogeneous traffic flow model which allows road situation changes. The road situation changes arise naturally from obstacles, curvature, number of lanes, speed limit and others. Our proposed inhomogeneous model is a system of nonlinear hyperbolic equations in which the flux and the source terms depend on the space variable. We show the global existence of solutions and their convergence to a solution of the equilibrium equation as the relaxation time goes to zero. Furthermore, a traffic flow model with a nonconcave fundamental diagram is studied. The model is a system of nonconcave hyperbolic conservation laws with relaxation. A nonconcave fundamental diagram is observed in real traffic flow. Other more realistic traffic flow models are discussed.

Keywords: Traffic Flow; Global Existence; Entropy Solution; Equilibrium Curve; Inhomogeneous Model (search for similar items in EconPapers)
Date: 2003
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_65

Ordering information: This item can be ordered from
http://www.springer.com/9783642557118

DOI: 10.1007/978-3-642-55711-8_65

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().