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An Analytical Theory of Traffic Flow

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Dirk Helbing at ETH Zurich
Dirk Helbing
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A selection of articles by Dirk Helbing reprinted from The European Physical Journal B
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An Analytical Theory of Traffic Flow
Data
May 2015
Dirk Helbing
ResearchGate has not been able to resolve any citations for this publication.
FireFly: A Synchronization Strategy for Urban Traffic Control
Article
Full-text available
  • Sep 1992
The researchers presented a synchronization strategy for urban traffic based on triggering events initiated by traffic lights that improves over existing algorithms. Simulations of urban traffic on a massively parallel machine provide a quantitative measure of the effectiveness of this strategy and allow for comparisons with existing ones. They also showed that augmenting general control procedures with vehicle sensors that provide a measure of queue length in the streets does not lead to improved performance over existing strategies.
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Convective Instability and Structure Formation in Traffic Flow
Article
Full-text available
  • Dec 2000
The effects of a localized perturbation in an initially uniform traffic flow are investigated with the optimal velocity model under an open boundary condition. The parameter region where the uniform solution is convectively unstable is determined by linear analysis. It is shown that the oscillatory flow, which is linearly unstable but convectively stabilized, is triggered out of a linearly unstable uniform flow by a localized perturbation, and in the upper stream it eventually breaks up into an alternating sequence of jams and free flows. This observation suggests that the real traffic flow pattern observed near an on-ramp [B. S. Kerner: Phys. Rev. Lett. 81 (1998) 3797] is a noise-sustained structure in an open flow system. We also find that, in a certain parameter region, the convectively stabilized uniform flow is destabilized by the non-linearly induced free flow.
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Derivation of a Fundamental Diagram for Urban Traffic Flow
Article
Full-text available
  • Jul 2008
Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and the travel time. In the past, empirical measurements have primarily been described by fit curves. Here, we derive expected fundamental relationships from a model of traffic flows at intersections, which suggest that the recently measured fundamental diagrams for urban flows can be systematically understood. In particular, this allows one to derive the average travel time and the average vehicle speed as a function of the utilization and/or the average number of delayed vehicles. Comment: For related work, see http://www.helbing.org
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The Physics of Traffic
Article
  • Aug 1999
Traffic jams are a fact of life for many car drivers. Every morning millions of drivers around the world sit motionless in their vehicles for long periods of time as they try to get to work, and then repeat the experience on their journeys home in the evening. The same thing often happens when they are driving to the coast for the weekend or to the airport to go on their holidays. They blame other drivers, increasing volumes of traffic and, inevitably, roadworks. So what has any of this got to do with physics?
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Fokker-Planck Equation
Chapter
  • Jan 1996
As shown in Sects. 3.1, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (3.1, 31). For nonlinear Langevin equations (3.67, 110) expectation values are much more difficult to obtain, so here we first try to derive an equation for the distribution function. As mentioned already in the introduction, a differential equation for the distribution function describing Brownian motion was first derived by Fokker [1.1] and Planck [1.2]: many review articles and books on the Fokker-Planck equation now exist [1.5 – 15].
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A kinetic model for traffic flow with continuum implications
Article
  • Jan 1979
A statistical model for the flow of traffic on an n lane highway is presented. The model is based on the hypothesis that each driver will maintain a minimum space, between himself and the next car, which is proportional to his speed. Both the first and second order continuum formulations, which are derived from the basic statistical formulations, are also presented.
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The 1/f Fluctuation of a Traffic Current on an Expressway
Article
  • Jun 1976
It is observed that the fluctuation of a traffic current on an expressway obeys the 1/f law for low spectral frequencies. Under proper assumptions the variation of the car concentration is expressed by the Burgers nonlinear differential equation. The observed power spectrum is accounted for as a characteristic feature of the Burgers turbulence.
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Self‐organization Principles in Supply Networks and Production Systems
Chapter
  • Dec 2006
IntroductionComplex Dynamics and ChaosThe Slower-is-faster Effect Observations in Traffic Systems Panicking PedestriansFreeway TrafficIntersecting Vehicle and Pedestrian StreamsRelevance to Production and Logistics Semi-conductor Chip ManufacturingContainer TerminalsPackaging and Other IndustriesAdaptive Control Traffic Equations for Production SystemsRe-routing Strategies and Machine UtilizationSelf-organized SchedulingSummary and OutlookReferences Observations in Traffic Systems Panicking PedestriansFreeway TrafficIntersecting Vehicle and Pedestrian StreamsRelevance to Production and Logistics Semi-conductor Chip ManufacturingContainer TerminalsPackaging and Other Industries Panicking PedestriansFreeway TrafficIntersecting Vehicle and Pedestrian Streams Semi-conductor Chip ManufacturingContainer TerminalsPackaging and Other Industries Traffic Equations for Production SystemsRe-routing Strategies and Machine UtilizationSelf-organized Scheduling
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