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

doi:10.1137/090746677

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

Journal Article•DOI•

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

Nicola Bellomo¹, Christian Dogbe²•Institutions (2)

Polytechnic University of Turin¹, University of Caen Lower Normandy²

01 Aug 2011-Siam Review (Society for Industrial and Applied Mathematics)-Vol. 53, Iss: 3, pp 409-463

TL;DR: A review and critical analysis of the mathematical literature concerning the modeling of vehicular traffic and crowd phenomena and a critical analysis focused on research perspectives that consider the development of a unified modeling strategy are presented.

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Abstract: 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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Journal Article•DOI•

Traffic experiment reveals the nature of car-following.

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Rui Jiang¹, Mao-Bin Hu¹, Hongyong Zhang², Ziyou Gao³, Bin Jia³, Qing-Song Wu¹, Bing Wang⁴, Ming Yang⁴ - Show less +4 more•Institutions (4)

University of Science and Technology of China¹, University of California, Davis², Beijing Jiaotong University³, Shanghai Jiao Tong University⁴

16 Apr 2014-PLOS ONE

TL;DR: Simulations show that by removing the fundamental notion in the traditional car-following models and allowing the traffic state to span a two-dimensional region in velocity-spacing plane, the growth pattern of disturbances has changed qualitatively and becomes qualitatively or even quantitatively in consistent with that observed in the experiment.

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Abstract: As a typical self-driven many-particle system far from equilibrium, traffic flow exhibits diverse fascinating non-equilibrium phenomena, most of which are closely related to traffic flow stability and specifically the growth/dissipation pattern of disturbances. However, the traffic theories have been controversial due to a lack of precise traffic data. We have studied traffic flow from a new perspective by carrying out large-scale car-following experiment on an open road section, which overcomes the intrinsic deficiency of empirical observations. The experiment has shown clearly the nature of car-following, which runs against the traditional traffic flow theory. Simulations show that by removing the fundamental notion in the traditional car-following models and allowing the traffic state to span a two-dimensional region in velocity-spacing plane, the growth pattern of disturbances has changed qualitatively and becomes qualitatively or even quantitatively in consistent with that observed in the experiment.

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332 citations

Cites background from "On the Modeling of Traffic and Crow..."

...In the last few decades, traffic flow studies have attracted wide interests of scientists from various disciplines [1-6]....
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Journal Article•DOI•

Survey on traffic prediction in smart cities

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Attila Matyas Nagy¹, Vilmos Simon¹•Institutions (1)

Budapest University of Technology and Economics¹

01 Oct 2018-Pervasive and Mobile Computing

TL;DR: This paper provides a detailed presentation of the traffic prediction methods for intelligent cities, also giving an overview of the existing data sources and prediction models.

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215 citations

Journal Article•DOI•

Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives

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Giacomo Albi¹, Nicola Bellomo², Luisa Fermo³, Ha S. Y.⁴, Ha S. Y.⁵, Jeongho Kim⁵, Lorenzo Pareschi⁶, David Poyato⁷, Juan Soler⁷ - Show less +5 more•Institutions (7)

University of Verona¹, Collegio Carlo Alberto², University of Cagliari³, Korea Institute for Advanced Study⁴, Seoul National University⁵, University of Ferrara⁶, University of Granada⁷

02 Oct 2019-Mathematical Models and Methods in Applied Sciences

TL;DR: This paper presents a review and critical analysis on the modeling of the dynamics of vehicular traffic, human crowds and swarms seen as living and, hence, complex systems.

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Abstract: This paper presents a review and critical analysis on the modeling of the dynamics of vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It contains a survey of ...

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203 citations

Journal Article•DOI•

Genealogy of traffic flow models

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Femke van Wageningen-Kessels¹, Hans van Lint¹, Kees Vuik¹, Serge P. Hoogendoorn¹•Institutions (1)

Delft University of Technology¹

01 Dec 2015-EURO Journal on Transportation and Logistics

TL;DR: An historical overview of the development of traffic flow models is proposed in the form of a model tree that shows the genealogy of four families: the fundamental relation, microscopic, mesoscopic and macroscopic models.

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177 citations

Cites background from "On the Modeling of Traffic and Crow..."

...It has been found that multiclass models are able to reproduce phenomena related to scatter in the fundamental diagram better than mixed-class models (Treiber and Helbing 1999; Daganzo 2002; Wong and Wong 2002; Ngoduy 2011; Bellomo and Dogbe 2011) and references therein....
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...For example, Darbha et al. (2008), Tyagi et al. (2008), and Bellomo and Dogbe (2011) argue that there are very few vehicles in the area of interest (at most a few 100/km), unlike in for example many applications in thermodynamics with around 1023 particles/cm3....
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...…current state-of-the-art and review the models on their current value (Papageorgiou 1998; Brackstone and McDonald 1999; Zhang 2001; Hoogendoorn and Bovy 2001b; Helbing 2001; Kerner 2009; Treiber and Kesting 2010; Treiber et al. 2010; Orosz et al. 2010; Wilson and Ward 2011; Bellomo and Dogbe 2011)....
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...This especially holds for microscopic models (Brackstone and McDonald 1999; Bellomo and Dogbe 2011)....
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Journal Article•DOI•

Modeling crowd dynamics from a complex system viewpoint

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Nicola Bellomo¹, Benedetto Piccoli², Andrea Tosin•Institutions (2)

Polytechnic University of Turin¹, Rutgers University²

25 Jul 2012-Mathematical Models and Methods in Applied Sciences

TL;DR: This paper aims at indicating research perspectives on the mathematical modeling of crowd dynamics, pointing on the one hand to insights into the complexity features of pedestrian flows and on the other hand to a critical overview of the most popular modeling approaches currently adopted in the specialized literature.

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Abstract: This paper aims at indicating research perspectives on the mathematical modeling of crowd dynamics, pointing on the one hand to insights into the complexity features of pedestrian flows and on the other hand to a critical overview of the most popular modeling approaches currently adopted in the specialized literature. Particularly, the focus is on scaling problems, namely representation and modeling at microscopic, macroscopic, and mesoscopic scales, which, entangled with the complexity issues of living systems, generate multiscale dynamical effects, such as e.g. self-organization. Mathematical structures suitable to approach such multiscale aspects are proposed, along with a forward look at research developments.

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173 citations

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References

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Book•

Linear and Nonlinear Waves

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G. B. Whitham

01 Jan 1974

TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.

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Abstract: Introduction and General Outline. HYPERBOLIC WAVES. Waves and First Order Equations. Specific Problems. Burger's Equation. Hyperbolic Systems. Gas Dynamics. The Wave Equation. Shock Dynamics. The Propagation of Weak Shocks. Wave Hierarchies. DISPERSIVE WAVES. Linear Dispersive Waves. Wave Patterns. Water Waves. Nonlinear Dispersion and the Variational Method. Group Velocities, Instability, and Higher Order Dispersion. Applications of the Nonlinear Theory. Exact Solutions: Interacting Solitary Waves. References. Index.

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8,808 citations

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Swarm intelligence: from natural to artificial systems

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Eric Bonabeau¹, Marco Dorigo, Guy Theraulaz²•Institutions (2)

Santa Fe Institute¹, Centre national de la recherche scientifique²

01 Jan 1999

TL;DR: This chapter discusses Ant Foraging Behavior, Combinatorial Optimization, and Routing in Communications Networks, and its application to Data Analysis and Graph Partitioning.

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Abstract: 1. Introduction 2. Ant Foraging Behavior, Combinatorial Optimization, and Routing in Communications Networks 3. Division of Labor and Task Allocation 4. Cemetery Organization, Brood Sorting, Data Analysis, and Graph Partitioning 5. Self-Organization and Templates: Application to Data Analysis and Graph Partitioning 6. Nest Building and Self-Assembling 7. Cooperative Transport by Insects and Robots 8. Epilogue

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5,822 citations

"On the Modeling of Traffic and Crow..." refers background in this paper

...A specific characteristic is that the swarm has the ability to express a collective intelligence related to the environmental conditions [29], [73], which can evolve by learning processes....
[...]
...In general, a swarm has the ability to express a collective intelligence that is generated by a cooperative strategy [29], [159], [192]....
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Journal Article•DOI•

Social Force Model for Pedestrian Dynamics

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Dirk Helbing¹, Péter Molnár¹•Institutions (1)

University of Stuttgart¹

01 May 1995-Physical Review E

TL;DR: Computer simulations of crowds of interacting pedestrians show that the social force model is capable of describing the self-organization of several observed collective effects of pedestrian behavior very realistically.

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Abstract: It is suggested that the motion of pedestrians can be described as if they would be subject to ``social forces.'' These ``forces'' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal motivations of the individuals to perform certain actions (movements). The corresponding force concept is discussed in more detail and can also be applied to the description of other behaviors. In the presented model of pedestrian behavior several force terms are essential: first, a term describing the acceleration towards the desired velocity of motion; second, terms reflecting that a pedestrian keeps a certain distance from other pedestrians and borders; and third, a term modeling attractive effects. The resulting equations of motion of nonlinearly coupled Langevin equations. Computer simulations of crowds of interacting pedestrians show that the social force model is capable of describing the self-organization of several observed collective effects of pedestrian behavior very realistically.

...read moreread less

5,716 citations

"On the Modeling of Traffic and Crow..." refers background in this paper

...Important examples of social force models can be found in [92], [102], [107], [161], and references therein....
[...]
...Social force models, introduced in [102], are based on the assumption that interactions among pedestrians are implemented by using the concept of a social force or social field [150]....
[...]
...In general, pedestrian dynamics has not been studied as extensively as vehicular traffic, although the literature in the field is rapidly developing, as documented in the papers by Helbing and Molnár [102], Hoogendoorn et al....
[...]

Journal Article•DOI•

Linear and Nonlinear Waves

[...]

G. B. Whitham, T. C. T. Ting¹•Institutions (1)

University of Illinois at Chicago¹

01 Mar 1976-Journal of Applied Mechanics

TL;DR: In this paper, a reference record was created on 2005-11-18, modified on 2016-08-08 and used for the purpose of ondes ; chocs ; onde de : choc reference record.

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Abstract: Keywords: ondes ; chocs ; onde de : choc Reference Record created on 2005-11-18, modified on 2016-08-08

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4,774 citations

"On the Modeling of Traffic and Crow..." refers background in this paper

...The first second-order model was proposed and well argued by Payne [179] and Whitham [213], where the basic assumption refers to the similarity between the traffic flow on roads and an incompressible fluid....
[...]
...Specifically, Whitham [213] proposed taking P(ρ) to be simply proportional to ρ, while Payne [179] suggested...
[...]

Journal Article•DOI•

Simulating dynamical features of escape panic

[...]

Dirk Helbing¹, Illés J. Farkas², Tamás Vicsek²•Institutions (2)

Dresden University of Technology¹, Eötvös Loránd University²

28 Sep 2000-Nature

TL;DR: A model of pedestrian behaviour is used to investigate the mechanisms of panic and jamming by uncoordinated motion in crowds, and an optimal strategy for escape from a smoke-filled room is found, involving a mixture of individualistic behaviour and collective ‘herding’ instinct.

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Abstract: One of the most disastrous forms of collective human behaviour is the kind of crowd stampede induced by panic, often leading to fatalities as people are crushed or trampled. Sometimes this behaviour is triggered in life-threatening situations such as fires in crowded buildings; at other times, stampedes can arise during the rush for seats or seemingly without cause. Although engineers are finding ways to alleviate the scale of such disasters, their frequency seems to be increasing with the number and size of mass events. But systematic studies of panic behaviour and quantitative theories capable of predicting such crowd dynamics are rare. Here we use a model of pedestrian behaviour to investigate the mechanisms of (and preconditions for) panic and jamming by uncoordinated motion in crowds. Our simulations suggest practical ways to prevent dangerous crowd pressures. Moreover, we find an optimal strategy for escape from a smoke-filled room, involving a mixture of individualistic behaviour and collective 'herding' instinct.

...read moreread less

4,334 citations