Dynamics of traffic jams: order and chaos

By means of a novel variational approach, we study the ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations of particles (roughly speaking satisfying the Law of Large Numbers) the complete description of their limit behaviour (in time) is obtained, as well as estimates of the transient period. In this period the main object of interest is the dynamics of ‘traffic jams’, which is rigorously defined and studied. It is shown that the dynamical system under consideration is chaotic in the sense that its topological entropy (calculated explicitly) is positive. Statistical quantities describing limit configurations are obtained as well.