Traffic and related self-driven many-particle systems

This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic, including microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models.

Abstract

Since the subject of traffic dynamics has captured the interest of\nphysicists, many astonishing effects have been revealed and explained. Some of\nthe questions now understood are the following: Why are vehicles sometimes\nstopped by so-called ``phantom traffic jams'', although they all like to drive\nfast? What are the mechanisms behind stop-and-go traffic? Why are there several\ndifferent kinds of congestion, and how are they related? Why do most traffic\njams occur considerably before the road capacity is reached? Can a temporary\nreduction of the traffic volume cause a lasting traffic jam? Under which\nconditions can speed limits speed up traffic? Why do pedestrians moving in\nopposite directions normally organize in lanes, while similar systems are\n``freezing by heating''? Why do self-organizing systems tend to reach an\noptimal state? Why do panicking pedestrians produce dangerous deadlocks? All\nthese questions have been answered by applying and extending methods from\nstatistical physics and non-linear dynamics to self-driven many-particle\nsystems. This review article on traffic introduces (i) empirically data, facts,\nand observations, (ii) the main approaches to pedestrian, highway, and city\ntraffic, (iii) microscopic (particle-based), mesoscopic (gas-kinetic), and\nmacroscopic (fluid-dynamic) models. Attention is also paid to the formulation\nof a micro-macro link, to aspects of universality, and to other unifying\nconcepts like a general modelling framework for self-driven many-particle\nsystems, including spin systems. Subjects such as the optimization of traffic\nflows and relations to biological or socio-economic systems such as bacterial\ncolonies, flocks of birds, panics, and stock market dynamics are discussed as\nwell.\n