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

Bellomo, Nicola; Dogbe, Christian

doi:10.1137/090746677

Cited by 383 publications

(290 citation statements)

References 191 publications

(257 reference statements)

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“…It is of great interest, both theoretically and practically, to understand via simple models the emergent behaviours of the complex systems containing a large number of interacting components. Examples like crowd dynamics [1,2], highway traffic systems [3,4], and the more recent urban traffic flows [5] have attracted physicists for decades. Despite the observed complex patterns from these systems, some of the essential characteristics are universally well-defined [6,7].…”

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confidence: 99%

“…We can thus expand the master model around a chosen ground state:ã n = p,q κ p,q h n ṽ n − V op h n p ∆ṽ q n (2) κ p,q h n = 1 p!q! ∂ p+qf ∂ pṽ n ∂ q ∆ṽ n ṽn=Ṽop(hn) ∆ṽn=0 (3) where V op (h) satisfiesf (h, V op (h) , 0) = 0. Clearly any existing two-phase models can be expanded this way, and they can be quantitatively compared by the set of coefficients κ p,q .…”

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confidence: 99%

“…h max/min ∈ h max/min λ h min , h max/min λ h max (9) If λ h min < 2sech(h min ) or λ h max < 2sech(h max ), the vehicles in the clusters (or anti-clusters) are also linearly unstable and their bumper-to-bumper distances will fluctuate (see λ (3) in Fig. (4a) and the inset), in contrast to the original OV model.…”

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confidence: 99%

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Classification and unification of the microscopic deterministic traffic models

Yang

Monterola

2015

Phys. Rev. E

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We identify a universal mathematical structure in microscopic deterministic traffic models (with identical drivers), and thus show that all such existing models in the literature, including both the two-phase and three-phase models, can be understood as special cases of a master model by expansion around a set of well-defined ground states. This allows any two traffic models to be properly compared and identified. The three-phase models are characterised by the vanishing of leading orders of expansion within a certain density range, and as an example the popular intelligent driver models (IDM) is shown to be equivalent to a generalized optimal velocity (OV) model. We also explore the diverse solutions of the generalized OV model that can be important both for understanding human driving behaviours and algorithms for autonomous driverless vehicles. It is of great interest, both theoretically and practically, to understand via simple models the emergent behaviours of the complex systems containing a large number of interacting components. Examples like crowd dynamics [1,2], highway traffic systems [3,4], and the more recent urban traffic flows [5] have attracted physicists for decades. Despite the observed complex patterns from these systems, some of the essential characteristics are universally well-defined [6,7]. In contrast to the traditional many-body physical systems (e.g. involving identical particles like electrons), the crowd or traffic systems lack almost any symmetry at the microscopic level: even individual components are different from one another, with intrinsic stochasticity. This poses great challenges in finding the simplest model with enough predictive power to adequately characterise these complex systems.The lack of symmetries at the microscopic level leads to a certain arbitrariness in the model construction. The modelling of the highway traffic system has led to a plethora of traffic models [3,4,6,7]. Analysis of the empirical data has led to profound understanding of the traffic dynamics [8,9]; however due to non-linear interactions between drivers, simple interactions can lead to complex spatiotemporal patterns. It is thus difficult to decide which detailed driving behaviours or specific functional forms should be used in the model. This is the primary concern behind the controversy between the two-phase and three-phase traffic theories [10,12], which leads to two classes of traffic models. While both the two-phase and the three-phase traffic models can simulate the scattering of the data points on the flow-density plane when the traffic is congested, the two classes are distinguished by the presence or absence of a continuous fundamental diagram in the flow-density plot [7]. Moreover, the lack of a fundamental principle in understanding various different traffic models makes it difficult to decide if, in addition to the non-linear interactions between the vehicles, factors like stochasticity or diversity of driving behaviours are also essential to certain observed empirical features.To tack...

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Classification and unification of the microscopic deterministic traffic models

Yang

Monterola

2015

Phys. Rev. E

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“…The functions β are chosen to fit with the so-called fundamental diagram which represents the experimental flux of cars as a function of their density as explained in [15] or [4]. Our previous study on the microscopic system (see § 1.3) leads us to consider a function of Greenshields type,…”

Section: Conservation Laws For Congestionmentioning

confidence: 99%

“…There are mainly three approaches to model traffic motion, each corresponding to a specific scale: microscopic scale (each entity is individually followed), macroscopic scale (the collection of entities is described by a local density), and mesoscopic scale (kinetic description). In this paper we will focus on the first two descriptions, the interested reader is referred to [4] for a review of the kinetic models.…”

Section: Introductionmentioning

confidence: 99%

Non classical solution of a conservation law arising in vehicular traffic modelling

et al. 2016

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Abstract. We are interested in this paper in the modelling and numerical simulation of some phenomena that are observed in the context of car dynamics, in particular the appearance of persistent jams upstream critical points with no real cause of flux limitation. We shall consider the case of a stable jam on a freeway upstream an accident that took place on the opposite lane. This situation is not properly handled by most models, either micro-or macroscopic ones, since it corresponds to a phenomenon that does not have a counterpart in gas dynamics, for which only entropy solution are usually considered as physically feasible. The approach we propose consists in accounting for the very behaviour of agents in the neighbourhood of the discontinuity, and makes it possible to numerically recover in a robust way steady traffic jams.Résumé. Nous nous intéressons dans cet article à la modélisation et à la simulation numérique de phénomènes particuliers observés dans le contexte du trafic routier, plus particulièrement le phénomène d'apparition et de persistance de bouchons en amont de points critiques sans cause objective de ralentissement. Nous considérerons notamment le cas d'un bouchon persistant sur une autoroute en amont d'un accident qui s'est produit sur la voie d'en face. Cette situation n'est pas reproduite par la plupart des modèles, qu'ils soient microscopiques ou macroscopiques, car elle correspond à un phénomène qui n'a pas d'équivalent en dynamique des gaz, pour lesquels seules les solutions dites entropiques sont en général considérées comme correspondant à un comportement observable dans la réalité. L'approche que nous proposons, aux niveaux microscopique et macroscopique, consiste à prendre en compte le comportement particulier des agents humains au voisinage de la discontinuité, et permet de retrouver numériquement de façon robuste des bouchons stables.

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Data‐driven models for traffic flow at junctions

Herty,

Kolbe

2024

Math Methods in App Sciences

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The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws, there exist nowadays many ad‐hoc models describing this behavior. Based on real‐world car trajectory data we propose a new class of data‐driven models with the requirements of being consistent to networked hyperbolic traffic flow models. To this end, the new models combine artificial neural networks with a parametrization of the solution space to the half‐Riemann problem at the junction. A method for deriving density and flux corresponding to the traffic close to the junction for data‐driven models is presented. The model parameters are fitted to obtain suitable boundary conditions for macroscopic first‐ and second‐order traffic flow models. The prediction of various models are compared considering also existing coupling rules at the junction. Numerical results imposing the data‐fitted coupling models on a traffic network are presented exhibiting accurate predictions of the new models.

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

Cited by 383 publications

References 191 publications

Classification and unification of the microscopic deterministic traffic models

Classification and unification of the microscopic deterministic traffic models

Non classical solution of a conservation law arising in vehicular traffic modelling

Data‐driven models for traffic flow at junctions

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