Accelerating Scientific Discovery by Formulating Grand Scientific Challenges

One important question for science and society is how to best promote scientific progress. Inspired by the great success of Hilbert's famous set of problems, the FuturICT project tries to stimulate and focus the efforts of many scientists by formulating Grand Challenges, i.e. a set of fundamental, relevant and hardly solvable scientific questions.Comment: To appear in EPJ Special Topics. For related work see http://www.futurict.eu and http://www.soms.ethz.c

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

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

Derivation, Properties, and Simulation of a Gas-Kinetic-Based, Non-Local Traffic Model

We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average velocity contain a non-local interaction term which is very favorable for a fast and robust numerical integration, so that several thousand freeway kilometers can be simulated in real-time. The model parameters can be easily calibrated by means of empirical data. They are directly related to the quantities characterizing individual driver-vehicle behavior, and their optimal values have the expected order of magnitude. Therefore, they allow to investigate the influences of varying street and weather conditions or freeway control measures. Simulation results for realistic model parameters are in good agreement with the diverse non-linear dynamical phenomena observed in freeway traffic.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html and http://www.theo2.physik.uni-stuttgart.de/treiber.htm

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

Memory effects in microscopic traffic models and wide scattering in flow-density data

By means of microscopic simulations we show that non-instantaneous adaptation of the driving behaviour to the traffic situation together with the conventional measurement method of flow-density data can explain the observed inverse-$\lambda$ shape and the wide scattering of flow-density data in ``synchronized'' congested traffic. We model a memory effect in the response of drivers to the traffic situation for a wide class of car-following models by introducing a new dynamical variable describing the adaptation of drivers to the surrounding traffic situation during the past few minutes (``subjective level of service'') and couple this internal state to parameters of the underlying model that are related to the driving style. % For illustration, we use the intelligent-driver model (IDM) as underlying model, characterize the level of service solely by the velocity and couple the internal variable to the IDM parameter ``netto time gap'', modelling an increase of the time gap in congested traffic (``frustration effect''), that is supported by single-vehicle data. % We simulate open systems with a bottleneck and obtain flow-density data by implementing ``virtual detectors''. Both the shape, relative size and apparent ``stochasticity'' of the region of the scattered data points agree nearly quantitatively with empirical data. Wide scattering is even observed for identical vehicles, although the proposed model is a time-continuous, deterministic, single-lane car-following model with a unique fundamental diagram.Comment: 8 pages, submitted to Physical Review

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

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

Pedestrian, Crowd, and Evacuation Dynamics

This contribution describes efforts to model the behavior of individual pedestrians and their interactions in crowds, which generate certain kinds of self-organized patterns of motion. Moreover, this article focusses on the dynamics of crowds in panic or evacuation situations, methods to optimize building designs for egress, and factors potentially causing the breakdown of orderly motion.Comment: This is a review paper. For related work see http://www.soms.ethz.c

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