It is suggested that the motion of pedestrians can be described as if they would be subject to ``social forces.'' These ``forces'' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal motivations of the individuals to perform certain actions (movements). The corresponding force concept is discussed in more detail and can also be applied to the description of other behaviors. In the presented model of pedestrian behavior several force terms are essential: first, a term describing the acceleration towards the desired velocity of motion; second, terms reflecting that a pedestrian keeps a certain distance from other pedestrians and borders; and third, a term modeling attractive effects. The resulting equations of motion of nonlinearly coupled Langevin equations. Computer simulations of crowds of interacting pedestrians show that the social force model is capable of describing the self-organization of several observed collective effects of pedestrian behavior very realistically.

Social Force Model for Pedestrian Dynamics

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

We introduce a new "second order" model of traffic flow. As noted in [C. Daganzo, Requiem for second-order fluid with approximation to traffic flow, Transportation Res. Part B, 29 (1995), pp. 277--286], the previous "second order" models, i.e., models with two equations (mass and "momentum"), lead to nonphysical effects, probably because they try to mimic the gas dynamics equations, with an unrealistic dependence on the acceleration with respect to the space derivative of the "pressure." We simply replace this space derivative with a convective derivative, and we show that this very simple repair completely resolves the inconsistencies of these models. Moreover, our model nicely predicts instabilities near the vacuum, i.e., for very light traffic.

Resurrection of “second order” models of traffic flow

Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been carried out, e.g., of a moving car which approaches a stopped car. It turned out that, in order to manage such kinds of situations without producing accidents, improved traffic models are needed. Good results were obtained with the proposed generalized force model.

Generalized force model of traffic dynamics

THE THEORY OF MULTIPLE-LANE TRAFFIC FLOW IS EXAMINED. A PREDICTION OF THE CHARACTER OF THE TRAFFIC FLOW IS MADE AT ARBITARY DENSITY IN TERMS OF DRIVER BEHAVIOR IN DILUTE, NONINTERACTING TRAFFIC, AND A KINETIC EQUATION IS DERIVED TO DESCRIBE THE SPACE-TIME EVOLUTION OF THE VELOCITY DISTRIBUTION OF CARS. THE ANALOGIES THAT EXIST BETWEEN STATISTICAL PHYSICS AND TRAFFIC HAVE BEEN EMPLOYED IN DEVELOPING A VIABLE THEORY. THE PROBLEM IS FORMULATED AND THE THEORY IS DEVELOPED TO A POINT WHERE THE MEETING OF THEORETICAL CONCEPTS WITH EXPERIMENTAL OBSERVATIONS WILL BE FRUITFUL. /AUTHOR/

Kinetic theory of vehicular traffic

The stability of a two‐component fluid layer subjected to a temperature gradient has been studied, and the associated thermal diffusion separation has been found to exert a large influence even when the separations are small. The most unexpected and perhaps important result is that an instability has been found which can give rise to convection currents even though the density gradient is not adverse. Thus, a system heated from above can become unstable even when the fluid is less dense at the top of the system provided the more dense substance rises to the upper plate. Many measurements of the Soret coefficient could be subject to this instabilitity.

R. S. Schechter

Papers

Kinetic theory of vehicular traffic

Thermal Diffusion and Convective Stability