The dynamics of vehicular traffic with reaction-time delay and stochasticity of drivers

Dr Gabor Orosz, Research Fellow
Dynamical Systems and Control Research Group
Mathematics Research Institute
University of Exeter, Room 319, Harrison Building
North Park Road, Exeter, EX4 4QF

A nonlinear car-following model of highway traffic is considered that includes the reaction-time delay of drivers. Linear stability investigations show that the uniform flow solution may loose its stability via Hopf bifurcations. Studying these bifurcations by normal form calculations reveal the possibility of bistable behaviour. Regions in parameter space are determined by numerical continuation techniques where the stable uniform flow co-exists with single or multiple stop-and-go traffic jams. Detailed stability investigation of the corresponding oscillations explains the low-dimensional dynamics of the merging and the dispersion of traffic jams. Stochastic effects are also studied by numerical simulation when a driver parameter is varied according to a random walk. This is a joint work with Gabor Stepan (Budapest University of Technology and Economics) and with Eddie Wilson and Bernd Krauskopf (University of Bristol).