In Traffic Flow, Cellular Automata = Kinematic Waves

This paper proves that the vehicle trajectories predicted by a simple linear carfollowing model, CF(L), the kinematic wave model with a triangular fundamental diagram, KW(T), and two cellular automata models CA(L) and CA(M) match everywhere to within a tolerance comparable with a single "jam spacing" Thus, CF(L) = KW(T) = CA(L,M).

[1]  Robert Herman,et al.  Traffic Dynamics: Analysis of Stability in Car Following , 1959 .

[2]  G. F. Newell.  A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks , 1993 .

[3]  Henryk Fuk,et al.  Critical behaviour of number-conserving cellular automata with nonlinear fundamental diagrams , 2004 .

[4]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[5]  Gordon F. Newell,et al.  A simplified car-following theory: a lower order model , 2002 .

[6]  M. Lighthill,et al.  On kinematic waves I. Flood movement in long rivers , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[7]  Carlos F. Daganzo,et al.  A Variational Formulation for a Class of First Order PDE's , 2003 .

[8]  Gordon F. Newell,et al.  A SIMPLIFIED THEORY OF KINEMATIC WAVES , 1991 .

[9]  Carlos F. Daganzo,et al.  Multi-lane hybrid traffic flow model: quantifying the impacts of lane-changing maneuvers on traffic flow , 2004 .

[10]  C. Daganzo.  A variational formulation of kinematic waves: basic theory and complex boundary conditions , 2005 .

[11]  G. F. Newell.  A simplified theory of kinematic waves in highway traffic, part I: General theory , 1993 .

[12]  Nagel.  Particle hopping models and traffic flow theory. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Monica Menendez,et al.  A Variational Formulation of Kinematic Waves , 2005 .

[14]  Michael Schreckenberg,et al.  A cellular automaton model for freeway traffic , 1992 .