Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model

Helbing, Dirk; Moussaïd, Mehdi

doi:10.1140/epjb/e2009-00042-6

Cited by 31 publications

(26 citation statements)

References 26 publications

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“…This results goes beyond [12] and suggests not only that the total number of conflict-related news and its change over time can be used as early warning signals for war, but also that timevariability in the number of news could significantly improve upon existing forecasting efforts. This finding is also in line with [110], since increased levels of variability can be used as early warning signals for critical transitions in a large number of physical, biological and socio-economic systems characterized by complexity and non-linearity (see also [111]).…”

Section: Interstate Wars and How To Predict Themsupporting

confidence: 74%

Saving Human Lives: What Complexity Science and Information Systems can Contribute

et al. 2014

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We discuss models and data of crowd disasters, crime, terrorism, war and disease spreading to show that conventional recipes, such as deterrence strategies, are often not effective and sufficient to contain them. Many common approaches do not provide a good picture of the actual system behavior, because they neglect feedback loops, instabilities and cascade effects. The complex and often counter-intuitive behavior of social systems and their macro-level collective dynamics can be better understood by means of complexity science. We highlight that a suitable system design and management can help to stop undesirable cascade effects and to enable favorable kinds of self-organization in the system. In such a way, complexity science can help to save human lives.

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Section: Interstate Wars and How To Predict Themsupporting

confidence: 74%

Saving Human Lives: What Complexity Science and Information Systems can Contribute

et al. 2014

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“…A systematic analysis using simulations and qualitative analysis of the solutions was developed by Goatin et al [38], [47], [84] to show the existence of phase transitions. Phase transitions can be related to instability problems [99], [104].…”

Section: Critical Analysismentioning

confidence: 99%

On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives

Bellomo¹,

Dogbe²

2011

SIAM Rev.

389

284

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This paper presents a review and critical analysis of the mathematical literature concerning the modeling of vehicular traffic and crowd phenomena. The survey of models deals with the representation scales and the mathematical frameworks that are used for the modeling approach. The paper also considers the challenging objective of modeling complex systems consisting of large systems of individuals interacting in a nonlinear manner, where one of the modeling difficulties is the fact that these systems are difficult to model at a global level when based only on the description of the dynamics of individual elements. The review is concluded with a critical analysis focused on research perspectives that consider the development of a unified modeling strategy.

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“…For more details about the techniques used and results presented, one may consult Gasser et al (2004), Orosz & Stépán (2006) and Orosz et al (2009). Some claims about multi-stability are also given in Krauss et al (1997), Lee et al (1998), Igarashi et al (2001), Safonov et al (2002) and Helbing & Moussaid (2009) by using different tools.…”

Section: Nonlinear Traffic Dynamicsmentioning

confidence: 99%

Traffic jams: dynamics and control

Orosz

Wilson

Stépàn

2010

Phil. Trans. R. Soc. A.

350

215

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This introductory paper reviews the current state-of-the-art scientific methods used for modelling, analysing and controlling the dynamics of vehicular traffic. Possible mechanisms underlying traffic jam formation and propagation are presented from a dynamical viewpoint. Stable and unstable motions are described that may give the skeleton of traffic dynamics, and the effects of driver behaviour are emphasized in determining the emergent state in a vehicular system. At appropriate points, references are provided to the papers published in the corresponding Theme Issue.Keywords: vehicular traffic; congestion; stop-and-go waves; Hopf bifurcation; driver reaction time; unstable waves I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, 'How many arbitrary parameters did you use for your calculations?' I thought for a moment about our cut-off procedures and said, 'Four'. He said, 'I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk '. (Dyson 2004, p. 297) Background and challengesThe introduction of the assembly line in the automotive industry about a century ago allowed the mass production of automobiles, which, in turn, revolutionized land transportation. At the same time, a problem was also generated that has not yet been resolved: traffic congestion. Since then, researchers from many different disciplines (mathematics, physics and engineering) have targeted this problem, *Author for correspondence (gabor@engineering.ucsb.edu).One contribution of 10 to a Theme Issue 'Traffic jams: dynamics and control'.This journal is © 2010 The Royal Society 4455 on May 10, 2018 http://rsta.royalsocietypublishing.org/ Downloaded from 4456 G. Orosz et al. often using sophisticated mathematical tools brought from their own area of expertise. Also, analogies between traffic flow and other flows (fluid flow, gas flow and granular flow) were established. Although such analogies may help scientists to gain understanding of vehicular systems, it is becoming more and more obvious that traffic flows like no other flow in the Newtonian universe.To date, a vast number of different models have been constructed, but still no first principles have been established to guide the modelling procedure (if such principles exist at all). In many cases, authors claimed that the developed model described traffic better than models prior to that point, and such claims were often justified by fitting the models to empirical data. The quote at the beginning of this paper tries to illustrate, without questioning the importance of any specific model, that the above approach may easily lead to research capturing, but also missing, some essential characteristics. We believe that another way to conduct research in traffic can be by studying general classes of models and classifying their qualitative dynamical features (including 'hidden' unstable motions) when varying model parameters. To...

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Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model

Cited by 31 publications

References 26 publications

Saving Human Lives: What Complexity Science and Information Systems can Contribute

Saving Human Lives: What Complexity Science and Information Systems can Contribute

On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives

Traffic jams: dynamics and control

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