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

Many observations of the dynamics of pedestrian crowds, including various self-organization phenomena, have been successfully described by simple many-particle models. For ethical reasons, however, there is a serious lack of experimental data regarding crowd panic. Therefore, we have analyzed video recordings of the crowd disaster in Mina/Makkah during the Hajj in 1426H on 12 January 2006. They reveal two subsequent, sudden transitions from laminar to stop-and-go and ``turbulent'' flows, which question many previous simulation models. While the transition from laminar to stop-and-go flows supports a recent model of bottleneck flows [D. Helbing et al., Phys. Rev. Lett. 97, 168001 (2006)], the subsequent transition to turbulent flow is not yet well understood. It is responsible for sudden eruptions of pressure release comparable to earthquakes, which cause sudden displacements and the falling and trampling of people. The insights of this study into the reasons for critical crowd conditions are important for the organization of safer mass events. In particular, they allow one to understand where and when crowd accidents tend to occur. They have also led to organizational changes, which have ensured a safe Hajj in 1427H.

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Dynamics of crowd disasters: an empirical study.

1 Introduction 2 Travel Demand 3 Costs 4 Pricing 5 Investment 6 Industrial Organization of Transportation Providers 7 Conclusion

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The economics of urban transportation

Starting with a short review of the available literature in the field of pedestrian and evacuation research, an overview is given over the observed collective phenomena in pedestrian crowds. This includes lane formation in corridors and oscillations at bottlenecks in normal situations, while different kinds of blocked states are produced in panic situations. By means of molecular-dynamic-like microsimulations based on a generalized force model of interactive pedestrian dynamics, the spatio-temporal patterns in pedestrian crowds are successfully reproduced and interpreted as self-organized phenomena. In contrast to previous socio-psychological approaches, this allows a physical understanding of the observations. Despite the significantly different phenomena occuring in normal and panic situations, the main effects can be described by a unified model containing only well interpretable and plausible terms. The transition between the “rational” normal behavior and the apparently “irrational” panic behavior is controlled by a single parameter, the “nervousness”, which influences fluctuation strengths, desired speeds, and the tendency of herding. Thereby, it causes paradoxial effects like “freezing by heating”, “faster is slower”, and the ignorance of available exits. Nevertheless, there are measures to improve pedestrian flows, both in normal and panic situations. For example, the suitable placement of columns can help, although they reduce the accessible space.

Simulation of pedestrian crowds in normal and evacuation situations

Nowadays traffic flow and congestion is one of the main societal and economical problems related to transportation in industrialized countries. In this respect, managing traffic in congeste...

State-of-the-art of vehicular traffic flow modelling

Extended time-to-collision measures for road traffic safety assessment.

Gaining insights into pedestrian flow operations and assessment tools for pedestrian walking speeds and comfort is important in, for instance, planning and geometric design of infrastructural facilities, as well as for management of pedestrian flows under regular and safety-critical circumstances. Pedestrian flow operations are complex, and vehicular flow simulation modelling approaches are generally not applicable to pedestrian flow modelling. This article focusses on pedestrian walking behaviour theory and modelling. It is assumed that pedestrians are autonomous predictive controllers that minimize the subjective predicted cost of walking. Pedestrians predict the behaviour of other pedestrians based on their observations of the current state as well as predictions of the future state, given the assumed walking strategy of other pedestrians in their direct neighbourhood. As such, walking can be represented by a (non-co-operative or co-operative) differential game, where pedestrians may or may not be aware of the walking strategy of the other pedestrians. Copyright © 2003 John Wiley & Sons, Ltd.

Simulation of Pedestrian Flows by Optimal Control and Differential Games

Capacity is a central concept in roadway design and traffic control. Estimation of empirical capacity values in practical circumstances is not a trivial problem; it is very difficult to define capacity in an unambiguous manner. Empirical capacity estimation for uninterrupted roadway sections has been studied. Headways, traffic volumes, speed, and density are traffic data types used to identify four groups of capacity estimation methods. Aspects such as data requirement, location choice, and observation period were investigated for each method. The principles of the different methods and the mathematical derivation of roadway capacity are studied and discussed. Among the methods studied are the headway distribution approaches, the bimodal distribution method, the selected maxima, and the direct probability method. Of the methods based on traffic volume counts, the product limit method is recommended for practical application because of sound underlying theory. An example of the application of this promisin...

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Assessment of roadway capacity estimation methods

On Modelling Route Choice Sets in Transportation Networks: A Synthesis

Insight into pedestrian flow operations is important in both planning and geometric design of infrastructure facilities such as railway stations as well as in the management of pedestrian flows in such facilities. Lack of empirical knowledge regarding the characteristics of pedestrian flows under varying circumstances and designs motivates using a model-based approach. In this study, a new pedestrian flow model based on the gaskinetic modeling paradigm is established. The mesoscopic equations describe the dynamics of so-called pedestrian phase-space density, which can be considered as a two-dimensional generalization of the phase-space density used in gas-kinetic vehicular traffic flow. Convection, acceleration, and noncontinuum transition terms govern the dynamics. The latter terms reflect the dynamic influence of pedestrians decelerating and the changing angle of movement due to pedestrians interacting. Numerical solutions of the resulting gas-kinetic equations are established by using a novel particle ...

Piet H. L. Bovy

Papers

Extended time-to-collision measures for road traffic safety assessment.

Simulation of Pedestrian Flows by Optimal Control and Differential Games

Assessment of roadway capacity estimation methods

On Modelling Route Choice Sets in Transportation Networks: A Synthesis

Gas-Kinetic Modeling and Simulation of Pedestrian Flows