Deterministic approach to microscopic three-phase traffic theory

Two different deterministic microscopic traffic flow models, which are in the context of the Kerner's there-phase traffic theory, are introduced. In an acceleration time delay model (ATD-model), different time delays in driver acceleration associated with driver behaviour in various local driving situations are explicitly incorporated into the model. Vehicle acceleration depends on local traffic situation, i.e., whether a driver is within the free flow, or synchronized flow, or else wide moving jam traffic phase. In a speed adaptation model (SA-model), vehicle speed adaptation occurs in synchronized flow depending on driving conditions. It is found that the ATD- and SA-models show spatiotemporal congested traffic patterns that are adequate with empirical results. In the ATD- and SA-models, the onset of congestion in free flow at a freeway bottleneck is associated with a first-order phase transition from free flow to synchronized flow; moving jams emerge spontaneously in synchronized flow only. Differences between the ATD- and SA-models are studied. A comparison of the ATD- and SA-models with stochastic models in the context of three phase traffic theory is made. A critical discussion of earlier traffic flow theories and models based on the fundamental diagram approach is presented.Comment: 40 pages, 14 figure

Traffic and Related Self-Driven Many-Particle Systems

Since the subject of traffic dynamics has captured the interest of physicists, many astonishing effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by so-called ``phantom traffic jams'', although they all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction of the traffic volume cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize in lanes, while similar systems are ``freezing by heating''? Why do self-organizing systems tend to reach an optimal state? Why do panicking pedestrians produce dangerous deadlocks? All these questions have been answered by applying and extending methods from statistical physics and non-linear dynamics to self-driven many-particle systems. This review article on traffic introduces (i) empirically data, facts, and observations, (ii) the main approaches to pedestrian, highway, and city traffic, (iii) microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts like a general modelling framework for self-driven many-particle systems, including spin systems. Subjects such as the optimization of traffic flows and relations to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are discussed as well.Comment: A shortened version of this article will appear in Reviews of Modern Physics, an extended one as a book. The 63 figures were omitted because of storage capacity. For related work see http://www.helbing.org