Variational Principles in the Analysis of Traffic Flows (Why it is Worth to Go Against the Flow)
2000, v.6, №3, 287-304
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their limit (in time) behavior in the space of configurations. Using these results we study the motion of a speedy passive particle (tracer) moving along/against the flow of slow particles and demonstrate that the latter case might be more efficient.
Keywords: traffic flow,dynamical system,variational principle,skew product map