Primitive cooperative particle flow models

Abstract

Traffic examples from vehicular systems to socio- and micro-biological systems are used to illustrate features relevant for modelling. After some comments on linear flow the emphasis turns to collective traffic flow, as it is captured by driven lattice-based excluding-particle models. An approximate treatment is then given of the most fundamental of these (the one-dimensional “ASEP”), covering its “jamming” steady-state phase transition and its kink dynamics, in both discrete and continuum versions. Necessary generalisations of the process, and of the geometry (to multi-lanes and to higher dimensions), as well as multi-species generalisations, are then briefly discussed, followed by an introduction to exact analytic approaches and recent developments.