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Physica D 211 (2005) 277293 Bifurcations and multiple traffic jams in a car-following

Summary: Physica D 211 (2005) 277­293
Bifurcations and multiple traffic jams in a car-following
model with reaction-time delay
G´abor Orosz, Bernd Krauskopf, R. Eddie Wilson
Bristol Centre for Applied Nonlinear Mathematics, Department of Engineering Mathematics,
University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK
Received 20 December 2004; accepted 1 September 2005
Communicated by Y. Kuramoto
Available online 5 October 2005
We investigate an optimal velocity car-following model for n cars on a circular single-lane road, where reaction-time delay
of drivers is taken into account. The stability of the uniform flow equilibrium is studied analytically, while bifurcating periodic
solutions for different wave numbers are investigated with numerical continuation techniques. This reveals that the periodic
solution with the smallest wave number may be stable, and all other periodic solutions are unstable.
As n is increased, periodic solutions develop stop- and go-fronts that correspond to rapid deceleration and acceleration between
regions of uniformly flowing and stagnant traffic. In terms of the positions of all cars on the ring these fronts are associated with
traffic jams. All traffic jams form a traffic pattern that evolves under time, due to slow motion of the fronts. The traffic pattern
corresponding to the stable periodic motion of cars is the only stable one. However, we find that other periodic orbits may be
unstable only so weakly that they give rise to transient traffic jams that may persist for long times. Eventually, such traffic jams
either merge with one another or disperse, until the stable traffic pattern is reached.


Source: Awtar, Shorya - Department of Mechanical Engineering, University of Michigan


Collections: Engineering