A Navier-Stokes-like traffic model

Wagner, Christoph

doi:10.1016/s0378-4371(97)00182-9

Cited by 15 publications

(7 citation statements)

References 20 publications

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“…The various different versions of the kinetic theory of vehicular traffic [12,[70][71][72][73][74][75][76] have been developed by modifying the kinetic theory of gases.…”

Section: Kinetic Theories Of Vehicular Trafficmentioning

confidence: 99%

“…For example, the finite sizes of the vehicles must be taken into account at high densities. Besides, the assumption (iv) of instantaneous relaxation has also been relaxed in a more recent extension [74].…”

Section: Paveri-fontana Modelmentioning

confidence: 99%

“…In the kinetic theory, traffic is treated as a gas of interacting particles where each particle represents a vehicle. The various different versions of the kinetic theory of vehicular traffic [12,[70][71][72][73][74][75][76] have been developed by modifying the kinetic theory of gases.…”

Section: Kinetic Theories Of Vehicular Trafficmentioning

confidence: 99%

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Statistical physics of vehicular traffic and some related systems

2000

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In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the way the vehicles influence each others' movement. Therefore, vehicular traffic, modeled as a system of interacting "particles" driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called "particle-hopping" models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.

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“…The various different versions of the kinetic theory of vehicular traffic [12,[70][71][72][73][74][75][76] have been developed by modifying the kinetic theory of gases.…”

Section: Kinetic Theories Of Vehicular Trafficmentioning

confidence: 99%

Section: Paveri-fontana Modelmentioning

confidence: 99%

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Statistical physics of vehicular traffic and some related systems

2000

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“…The kinetic theory treats vehicles as a gas of interacting particles. Various versions have been developed to extend and modify the gas-kinetic theory for traffic flow (Prigogine and Herman 1971, Paveri-Fontana 1975, Ben-Naim et al 1994, Helbing 1996a, Nagatani 1996, 1997a, b, Wagner et al 1996, Ben-Naim and Krapivsky 1997, Wagner 1997, Helbing and Treiber 1998a. Prigogine and Herman have proposed the Boltzmann equation for the traffic ∂f (x, v, t) ∂t…”

Section: Gas-kinetic Modelsmentioning

confidence: 99%

“…The macroscopic traffic models have been derived from the gas kinetic models (Helbing 1996b,1998c, Wagner 1997, Treiber et al 1999, Klar and Wegener 1999a. Very recently, Lee et al (2001) have addressed the relationship between microscopic car-following models and macroscopic traffic models.…”

Section: Micro-macro Linkmentioning

confidence: 99%

The physics of traffic jams

2002

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Traffic flow is a kind of many-body system of strongly interacting vehicles. Traffic jams are a typical signature of the complex behaviour of vehicular traffic. Various models are presented to understand the rich variety of physical phenomena exhibited by traffic. Analytical and numerical techniques are applied to study these models. Particularly, we present detailed results obtained mainly from the microscopic car-following models. A typical phenomenon is the dynamical jamming transition from the free traffic (FT) at low density to the congested traffic at high density. The jamming transition exhibits the phase diagram similar to a conventional gas-liquid phase transition: the FT and congested traffic correspond to the gas and liquid phases, respectively. The dynamical transition is described by the time-dependent Ginzburg-Landau equation for the phase transition. The jamming transition curve is given by the spinodal line. The metastability exists in the region between the spinodal and phase separation lines. The jams in the congested traffic reveal various density waves. Some of these density waves show typical nonlinear waves such as soliton, triangular shock and kink. The density waves are described by the nonlinear wave equations: the Korteweg-de-Vries (KdV) equation, the Burgers equation and the Modified KdV equation. Subjects like the traffic flow such as bus-route system and pedestrian flow are touched as well. The bus-route system with many buses exhibits the bunching transition where buses bunch together with proceeding ahead. Such dynamic models as the car-following model are proposed to investigate the bunching transition and bus delay. A recurrent bus exhibits the dynamical transition between the delay and schedule-time phases. The delay transition is described in terms of the nonlinear map.

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Introduction—The Reason for Paradigm Shift in Transportation Science

Kerner

2017

Breakdown in Traffic Networks

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A Navier-Stokes-like traffic model

Cited by 15 publications

References 20 publications

Statistical physics of vehicular traffic and some related systems

Statistical physics of vehicular traffic and some related systems

The physics of traffic jams

Introduction—The Reason for Paradigm Shift in Transportation Science

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