A rigorous treatment of a follow-the-leader traffic model with traffic lights present

SIAM Journal on Applied Mathematics

Volumn 63, Issue 1, 2002, Pages 149-168

  Argall, Brenna ^a   Cheleshkin, Eugene ^a   Greenberg, J M ^a   Hinde, Colin ^a   Lin, Pei Jen ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Conservation laws; Follow the leader; Relaxation models; Traffic flow

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; HIGHWAY TRAFFIC CONTROL; INTEGRATION; TRAFFIC SURVEYS;

CONSERVATION LAWS; FOLLOW THE LEADER TRAFFIC MODEL; RELAXATION MODELS; TRAFFIC FLOW; TRAFFIC LIGHTS;

MATHEMATICAL MODELS;

EID: 0036706323     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139901391215     Document Type: Article

References (9)

1. J.M. Greenberg, Extensions and amplifications of a traffic model of Aw and Rascle, SIAM J. Appl. Math., 62 (2001), pp. 729-745.
2. A. Aw and M. Rascle, Resurrection of "second order" models of traffic flow, SIAM J. Appl. Math., 60 (2000), pp. 916-938.
3. A. Aw, A. Klar, T. Materne, and M. Rascle, Derivation of continuum traffic flow models from microscopic follow-the-leader models, SIAM J. Appl. Math., to appear.
4. M.J. Lighthill and G.B. Whitham, On kinematic waves. I: Flood movement in long rivers, Proc. Roy. Soc. London Ser. A 229 (1955), pp. 281-316.
5. M.J. Lighthill and G.D. Whitham, On kinematic waves. II: A theory of traffic flow on long crowded roads, Proc. Roy. Soc. London Ser. A, 229 (1955), pp. 317-345.
6. P.I. Richards, Shock waves on the highway, Oper. Res., 4 (156), pp. 42-51.
7. G.B. Whitham, Linear and Nonlinear Waves, Pure and Applied Mathematics, Wiley-Interscience, New York, 1974.
8. R. Rotherby, Car following models, in Traffic Flow Theory - A State of the Art Report, Special Report 165, Transportation Research Board, Washington, DC, 1975 Chapter 4; also available online from http://www.tfhrc.gov/its/tft/chap4.html.
9. H.M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior, Transportation Res. B, 36 (2002), pp. 275-290.