Modelling Widely Scattered States in `Synchronized' Traffic Flow and Possible Relevance for Stock Market Dynamics

Traffic flow at low densities (free traffic) is characterized by a quasi-one-dimensional relation between traffic flow and vehicle density, while no such fundamental diagram exists for `synchronized' congested traffic flow. Instead, a two-dimensional area of widely scattered flow-density data is observed as a consequence of a complex traffic dynamics. For an explanation of this phenomenon and transitions between the different traffic phases, we propose a new class of molecular-dynamics-like, microscopic traffic models based on times to collisions and discuss the properties by means of analytical arguments. Similar models may help to understand the laminar and turbulent phases in the dynamics of stock markets as well as the transitions among them.Comment: Comments are welcome. For related work see http://www.helbing.or

Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts

Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner's three-phase traffic theory with the phase diagram approach for traffic models with a fundamental diagram. We discuss the inconsistent use of the term "traffic phase" and show that patterns demanded by three-phase traffic theory can be reproduced with simple two-phase models, if the model parameters are suitably specified and factors characteristic for real traffic flows are considered, such as effects of noise or heterogeneity or the actual freeway design (e.g. combinations of off- and on-ramps). Conversely, we demonstrate that models created to reproduce three-phase traffic theory create similar spatiotemporal traffic states and associated phase diagrams, no matter whether the parameters imply a fundamental diagram in equilibrium or non-unique flow- density relationships. In conclusion, there are different ways of reproducing the empirical stylized facts of spatiotemporal congestion patterns summarized in this contribution, and it appears possible to overcome the controversy by a more precise definition of the scientific terms and a more careful comparison of models and data, considering effects of the measurement process and the right level of detail in the traffic model used.Comment: 18 pages in the published article, 13 figures, 2 table

Interpreting the Wide Scattering of Synchronized Traffic Data by Time Gap Statistics

Based on the statistical evaluation of experimental single-vehicle data, we propose a quantitative interpretation of the erratic scattering of flow-density data in synchronized traffic flows. A correlation analysis suggests that the dynamical flow-density data are well compatible with the so-called jam line characterizing fully developed traffic jams, if one takes into account the variation of their propagation speed due to the large variation of the netto time gaps (the inhomogeneity of traffic flow). The form of the time gap distribution depends not only on the density, but also on the measurement cross section: The most probable netto time gap in congested traffic flow upstream of a bottleneck is significantly increased compared to uncongested freeway sections. Moreover, we identify different power-law scaling laws for the relative variance of netto time gaps as a function of the sampling size. While the exponent is -1 in free traffic corresponding to statistically independent time gaps, the exponent is about -2/3 in congested traffic flow because of correlations between queued vehicles.Comment: For related publications see http://www.helbing.or

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

Online-Marketing im WWW in der deutschen Wirtschaft: Eine vergleichende Untersuchung in vier verschiedenen Branchen

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Online-Marketing im WWW in der Versicherungswirtschaft: Eine empirische Untersuchung

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Akzeptanzorientierte Gestaltung von WWW-Informationsangeboten

Das World Wide Web ist nahezu omnipräsent. In fast jeder Anzeige findet sich ein Hinweis auf das WWW-Informationsangebot von Unternehmen. Selbst im Abspann des abendlichen Nachrichtenprogramms steht die Zeile www.tagesschau.de. Exponentiell wachsende Nutzerzahlen und Prophezeiungen eines gigantischen Marktes, ja sogar einer neuen Weltordnung, bringen immer mehr Unternehmen dazu, schnellstmöglich im WWW präsent zu sein, egal wie. Dabei wird übersehen, daß die Akzeptanz eines WWW-Angebotes von einer Vielzahl von Faktoren beeinflußt wird und bei der Gestaltung des Auftritts völlig andere Wege gegangen werden müssen. In den klassischen Medien erfolgreiche Kommunikationsstrategien werden oft mit nur geringen Anpassungen übernommen. Sie treffen auf ein hoch involviertes und sehr sensibles Publikum. Ein unüberlegter Auftritt hat schwerwiegende Folgen. Sie reichen von der Ablehnung des Informationsangebotes bis hin zu Imageschäden für das Unternehmen. Da sich das WWW erst auf dem Weg vom Insider- zum Massenmedium befindet, sind die derzeitigen Nutzer der Gruppe der early adopters zuzurechnen. Diese Multiplikatoren strahlen auf große Gruppen aus. Die Wirkung eines WWW-Angebotes wird dadurch noch verstärkt. Bisher gibt es jedoch kaum Aussagen, wie ein breit akzeptierter Unternehmensauftritt im World Wide Web gestaltet werden sollte. Dieser Bericht soll zur Verringerung dieses Defizits beitragen. Am Anfang steht eine Einführung in den Akzeptanzprozeß bei WWW-Informationsangeboten. Anschließend wird ein Methodenpaket für eine umfassende und effiziente Akzeptanzanalyse vorgestellt, das zur Untersuchung des WWW-Angebotes der Siemens Nixdorf Informationssysteme AG (SNI) entwickelt wurde. Die Erkenntnisse dieser Untersuchung fließen in die Gestaltungsempfehlungen für einen Unternehmens auftritt im WWW ein, die im letzten Teil gegeben werden. --

Geodesic Deviation in Kaluza-Klein Theories

We study in detail the equations of the geodesic deviation in multidimensional theories of Kaluza-Klein type. We show that their 4-dimensional space-time projections are identical with the equations obtained by direct variation of the usual geodesic equation in the presence of the Lorentz force, provided that the fifth component of the deviation vector satisfies an extra constraint derived here.Comment: 5 pages, Revtex, 1 figure. To appear in Phys. Rev. D (Brief Report

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