A Modification of the Social Force Model by Foresight

The motion of pedestrian crowds (e.g. for simulation of an evacuation situation) can be modeled as a multi-body system of self driven particles with repulsive interaction. We use a few simple situations to determine the simplest allowed functional form of the force function. More complexity may be necessary to model more complex situations. There are many unknown parameters to such models, which have to be adjusted correctly. The parameters can be related to quantities that can be measured independently, like step length and frequency. The microscopic behavior is, however, only poorly reproduced in many situations, a person approaching a standing or slow obstacle will e.g. show oscillations in position, and the trajectories of two persons meeting in a corridor in opposite direction will be far from realistic and somewhat erratic. This is inpart due to the assumption of instantaneous reaction on the momentary situation. Obviously, persons react with a small time lag, while on the other hand they will anticipate changing situations for at least a short time. Thus basing the repulsive interaction on a (linear) extrapolation over a short time (e.g. 1 s) eliminates the oscillations at slowing down and smoothes the patterns of giving way to others to a more realistic behavior. A second problem is the additive combination of binary interactions. It is shown that combining only a few relevant interactions gives better model performance.Comment: 6 pages, 5 figures, Preprint from PED 2008 (Wuppertal

Fundamentals of Traffic Flow

From single vehicle data a number of new empirical results concerning the density-dependence of the velocity distribution and its moments as well as the characteristics of their temporal fluctuations have been determined. These are utilized for the specification of some fundamental relations of traffic flow and compared with existing traffic theories.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Generalized Force Model of Traffic Dynamics

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 have been obtained with the proposed generalized force model.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Macroscopic Dynamics of Multi-Lane Traffic

We present a macroscopic model of mixed multi-lane freeway traffic that can be easily calibrated to empirical traffic data, as is shown for Dutch highway data. The model is derived from a gas-kinetic level of description, including effects of vehicular space requirements and velocity correlations between successive vehicles. We also give a derivation of the lane-changing rates. The resulting dynamic velocity equations contain non-local and anisotropic interaction terms which allow a robust and efficient numerical simulation of multi-lane traffic. As demonstrated by various examples, this facilitates the investigation of synchronization patterns among lanes and effects of on-ramps, off-ramps, lane closures, or accidents.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Gas-Kinetic-Based Traffic Model Explaining Observed Hysteretic Phase Transition

Recently, hysteretic transitions to `synchronized traffic' with high values of both density and traffic flow were observed on German freeways [B. S. Kerner and H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997)]. We propose a macroscopic traffic model based on a gas-kinetic approach that can explain this phase transition. The results suggest a general mechanism for the formation of probably the most common form of congested traffic.Comment: With corrected formula (3). For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

The Inflection Point of the Speed-Density Relation and the Social Force Model

It has been argued that the speed-density digram of pedestrian movement has an inflection point. This inflection point was found empirically in investigations of closed-loop single-file pedestrian movement. The reduced complexity of single-file movement does not only allow a higher precision for the evaluation of empirical data, but it occasionally also allows analytical considerations for micosimulation models. In this way it will be shown that certain (common) variants of the Social Force Model (SFM) do not produce an inflection point in the speed-density diagram if infinitely many pedestrians contribute to the force computed for one pedestrian. We propose a modified Social Force Model that produces the inflection point.Comment: accepted for presentation at conference Traffic and Granular Flow 201

Modeling the desired direction in a force-based model for pedestrian dynamics

We introduce an enhanced model based on the generalized centrifugal force model. Furthermore, the desired direction of pedestrians is investigated. A new approach leaning on the well-known concept of static and dynamic floor-fields in cellular automata is presented. Numerical results of the model are presented and compared with empirical data.Comment: 14 pages 11 figures, submitted to TGF'1

Structure and Instability of High-Density Equations for Traffic Flow

Similar to the treatment of dense gases, fluid-dynamic equations for the dynamics of congested vehicular traffic are derived from Enskog-like kinetic equations. These contain additional terms due to the anisotropic vehicle interactions. The calculations are carried out up to Navier-Stokes order. A linear instability analysis indicates an additional kind of instability compared to previous macroscopic traffic models. The relevance for describing granular flows is outlined.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Drift- or Fluctuation-Induced Ordering and Self-Organization in Driven Many-Particle Systems

According to empirical observations, some pattern formation phenomena in driven many-particle systems are more pronounced in the presence of a certain noise level. We investigate this phenomenon of fluctuation-driven ordering with a cellular automaton model of interactive motion in space and find an optimal noise strength, while order breaks down at high(er) fluctuation levels. Additionally, we discuss the phenomenon of noise- and drift-induced self-organization in systems that would show disorder in the absence of fluctuations. In the future, related studies may have applications to the control of many-particle systems such as the efficient separation of particles. The rather general formulation of our model in the spirit of game theory may allow to shed some light on several different kinds of noise-induced ordering phenomena observed in physical, chemical, biological, and socio-economic systems (e.g., attractive and repulsive agglomeration, or segregation).Comment: For related work see http://www.helbing.or