Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ``phantom traffic jams'' even though drivers 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 in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ``freeze by heating''? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include 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, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

Traffic and related self-driven many-particle systems

Statistical physics of vehicular traffic and some related systems

There has been increasing interest in the exploitation of advances in information technology in surface transportation systems. One trend is to exploit on-board sensing, computing and communication capabilities in vehicles, e.g., to augment and enhance existing intelligent transportation systems. A natural approach is to use vehicle-to-vehicle communications to disseminate information. In this paper, we propose MDDV, a mobility-centric approach for data dissemination in vehicular networks designed to operate efficiently and reliably despite the highly mobile, partitioned nature of these networks. MDDV is designed to exploit vehicle mobility for data dissemination, and combines the idea of opportunistic forwarding, trajectory based forwarding and geographical forwarding. We develop a generic mobile computing approach for designing localized algorithms in vehicular networks. Vehicles perform local operations based on their own knowledge while they collectively achieve a global behavior. We evaluate the performance of the MDDV algorithm using realistic simulation of the vehicle traffic in Atlanta area.

/pdf/mddv-a-mobility-centric-data-dissemination-algorithm-for-3er5bufwfg.pdf

MDDV: a mobility-centric data dissemination algorithm for vehicular networks

We examine a simple two-lane cellular automaton based upon the single-lane CA introduced by Nagel and Schreckenberg. We point out important parameters defining the shape of the fundamental diagram. Moreover we investigate the importance of stochastic elements with respect to real life traffic.

Two lane traffic simulations using cellular automata

This paper shows how particle hopping models fit into the context of traffic flow theory, that is, it shows connections between fluid-dynamical traffic flow models, which derive from the Navier-Stokes equations, and particle hopping models. In some cases, these connections are exact and have long been established, but have never been viewed in the context of traffic theory. In other cases, critical behavior of traffic jam clusters can be compared to instabilities in the partial differential equations. Finally, it is shown how all this leads to a consistent picture of traffic jam dynamics. In consequence, this paper starts building a foundation of a comprehensive dynamic traffic theory, where strengths and weaknesses of different models (fluid-dynamical, car-following, particle hopping) can be compared, and thus allowing to systematically chose the appropriate model for a given question.

/pdf/particle-hopping-models-and-traffic-flow-theory-47uzppgci8.pdf

Particle hopping models and traffic flow theory

This monograph which is primairly addressed to graduate students in traffic engineering, is also intended to be a reference book and an introduction to traffic flow theory in general The 10 chapters of this book cover aspects of measurement, statistical distributions, models, information processing, noise and simulations The various methods of measurement currently available to the traffic engineer are considered, and the definitions of characteristics are related to these methods of measurement Methods of averaging are also considered The quantities to statistical distributions of various traffic characteristics are considered, as well as the uses of distributions Models that relate pairs of the basic traffic flow characteristics (speed/flow, speed/ concentration etc) are examined, as are models that consider travel time as one of the variables Insight is provided into the way drivers use the information they receive It is shown that although a driver is continuously making decisions, his control actions are limited to control of heading and control of acceleration Car following and acceleration noise is considered, and acceleration noise is developed as a measure of the quality of traffic flow Models that have been developed for fluids are applied to traffic continuity equations for fluids are developed Studies are described which have been used to improve flow through tunnels and explain traffic behavior at bottlenecks, and the continuum and car-following theories are unified A Boltzman-like theory of traffic is briefly discussed The chapter on queueing models, presents some of the results of studies of served, delays at intersections and unsignalized intersections Simulation of traffic flow by digital computers is detailed

Daniel L. Gerlough

Papers

Traffic Flow Theory

Traffic flow theory : a monograph