Derivation of a first order traffic flow model of Lighthill-Whitham-Richards type. Issue 9 (2018)

• Record Type: Journal Article
• Authors: Burger, Michael; Göttlich, Simone; Jung, Thomas
• Is Part Of: IFAC-PapersOnLine. Volume 51:Issue 9(2018)
• Page Start: 49
• Page End: 54
• Publication Date: 2018
• Subjects: First order traffic models -- time delays -- delayed partial differential equations; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2018.07.009
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In this paper, we introduce a new type of macroscopic traffic model which, includes a delay term in the flux function. We start from a delayed microscopic model and use well-known techniques to derive a corresponding first order macroscopic traffic model. This leads to a delayed hyperbolic partial differential equation converging to the classical Lighthill-Whitham-Richards (LWR) model for diminishing delay. Furthermore, we present numerical results to show the impact of the delay, and to verify the new model we found. To do so, we adapt known methods to analyze the derived equations numerically.