A Stochastic Macroscopic Traffic Model Devoid of Diffusion

Khoshyaran, Megan M.; Lebacque, Jean-Patrick

doi:10.1007/978-3-540-77074-9_12

Cited by 8 publications

(8 citation statements)

References 7 publications

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“…A classic example is the seminal cellular automata of Nagel & Schreckenberg (1992). It produces oscillations owing to a braking probability that can be constant or a function of the speed (Barlovic et al 1998(Barlovic et al , 2002, as do the second-order macroscopic models proposed by Khoshyaran & Lebacque (2007). Gas-kinetic models are inherently stochastic (Helbing & Treiber 1998;Shvetsov & Helbing 1999;Helbing et al 2001;Ngoduy et al 2006;Ngoduy 2008), but have decreased in popularity, probably because of the large number of non-physical parameters needed, and the complexity of their implementation.…”

Section: Introductionmentioning

confidence: 99%

A mechanism to describe the formation and propagation of stop-and-go waves in congested freeway traffic

Laval

Leclercq

2010

Phil. Trans. R. Soc. A.

234

102

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This paper introduces a parsimonious theory for congested freeway traffic that describes the spontaneous appearance of oscillations and their ensuing transformation into stopand-go waves. Based upon the analysis of detailed vehicle-trajectory data, we conclude that timid and aggressive driver behaviours are the cause for this transformation. We find that stop-and-go waves arise independently of the details of these behaviours. Analytical and simulation results are presented.

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Section: Introductionmentioning

confidence: 99%

A mechanism to describe the formation and propagation of stop-and-go waves in congested freeway traffic

Laval

Leclercq

2010

Phil. Trans. R. Soc. A.

234

102

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“…• The stochastic GSOM model of Khoshyaran and Lebacque [28]. The driver attribute I is a random variable depending on the vehicle index N and on the random event ω such that I = I(N, t, ω).…”

Section: Examplesmentioning

confidence: 99%

A variational formulation for higher order macroscopic traffic flow models: Numerical investigation

Costeseque

Lebacque²

2014

Transportation Research Part B: Methodological

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This paper deals with numerical methods providing semi-analytic solutions to a wide class of macroscopic traffic flow models for piecewise affine initial and boundary conditions. In a very recent paper, a variational principle has been proved for models of the Generic Second Order Modeling (GSOM) family, yielding an adequate framework for effective numerical methods. Any model of the GSOM family can be recast into its Lagrangian form as a Hamilton-Jacobi equation (HJ) for which the solution is interpreted as the position of vehicles. This solution can be computed thanks to Lax-Hopf like formulas and a generalization of the inf-morphism property. The efficiency of this computational method is illustrated through a numerical example and finally a discussion about future developments is provided.Keywords: Traffic flow, Hamilton-Jacobi equation, Lax-Hopf algorithm, Lagrangian. Introduction General backgroundMacroscopic traffic flow modeling. In order to get a realistic estimation of the real-time traffic states on networks, traffic operators and managers need macroscopic traffic flow models. These models must be simple, robust, allowing to get solutions at a low computational cost. The main macroscopic models are based on conservation laws or hyperbolic systems (see [30,19] for a review). The seminal LWR model (for Lighthill-Whitham and Richards) was proposed in [42,51] as a single conservation law with unknown the vehicles density. This model based on a first order Partial Differential Equation (PDE) is very simple and robust but it fails to recapture some empirical features of traffic. In particular, it does not allow to take into account non-equilibrium traffic states mainly in congested situation. More sophisticated models referred to as higher order models were developed to encompass kinematic constraints of real vehicles or also the wide variety of driver behaviors, even at the macroscopic level. In this paper we deal with models of the Generic Second Order Modeling (GSOM) family. Even if these models are more complicated to deal with, they permit to reproduce traffic instabilities (such as the so-called stop-and-go waves, the hysteresis phenomenon or capacity drop) which move at the traffic speed and differ from kinematic waves [53] Traffic flow monitoring. Before the wide propagation of internet handsets, traffic monitoring has mainly been built on dedicated infrastructure which imply quite important installation and maintenance costs. Traffic flow monitoring and management has been deeply modified with the development of new technologies in mobile sensing aiming to provide a quite important quantity of floating car data. Traffic flow models are needed to be well suited such that managers could use both Eulerian and Lagrangian data for improving traffic state estimation. The term Eulerian refers to "classical" fixed equipment giving records of occupancy or flow of vehicles on a freeway section. This kind of measurements come from e.g. fixed inductive loop detectors, Radio Frequency Identification (R...

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“…The proposed intersection model is based on the EARZ (Extended Aw-Rascle Zhang) second order model recently introduced by Lebacque (Lebacque et al, 2007), now extended as the GSOM model class (Khoshyaran Lebacque 2007). The GSOM exhibits the particularity that it permits an adequate adaptation of the simulation model to field data measurements.…”

Section: The Gsom Modelling Approachmentioning

confidence: 99%

“…where p is the relative traffic pressure. (Mammar et al, 2006), (Lebacque et al, 2007) have shown that an adequate choice of invariant I, makes it possible to derive several traffic models already developed in the literature. For instance, with…”

Section: The Gsom Modelling Approachmentioning

confidence: 99%