Second-order continuum traffic flow model

Wagner, Christoph; Hoffmann, Clemens; Sollacher, Rudolf; Wagenhuber, J.; Schürmann, Bernd

doi:10.1103/physreve.54.5073

Cited by 79 publications

(68 citation statements)

References 18 publications

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“…Moreover, he assumed that the distribution of desired velocitiesP 0 (v) depends on the density ρ and the average velocity V . Finally, he made several proposals for the velocity variance θ. Prigogine's model has been also improved by Andrews (1970aAndrews ( , b, 1973a, Phillips (1977Phillips ( , 1979a, PaveriFontana (1975), Nelson (1995) and others (Helbing, 1995c(Helbing, , d, 1996a(Helbing, , b, 1997a(Helbing, , d, 1998aWagner et al, 1996;Wagner, 1997aWagner, , b, c, 1998bNagatani, 1996aNagatani, , b, c, 1997aWegener and Klar, 1996;Klar et al, 1996;Wegener, 1997, 1999a, b;Shvetsov and Helbing, 1999). They modified the acceleration term, introduced velocity correlations among successive vehicles, investigated interactions among neighboring lanes, and/or considered space requirements.…”

Section: Prigogine's Boltzmann-like Modelmentioning

confidence: 99%

Traffic and related self-driven many-particle systems

2001

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46 1. Gas-kinetic and macroscopic models 46 2. Microscopic models and cellular automata 47 E. Bi-directional and city traffic 47 F. Effects beyond physics 48 G. Traffic control and optimization 48 V. Pedestrian traffic 49 A. Observations 49 B. Behavioral force model of pedestrian dynamics 50 C. Self-organization phenomena and noise-induced ordering 51 1. Segregation 51 2. Oscillations 52 3. Rotation 52 D. Collective phenomena in panic situations 53 1. "Freezing by heating" 53 2. "Faster-is-slower effect" 53 3. "Phantom panics" 54 4. Herding behavior 54 VI. Flocking and spin systems 54 A.

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Section: Prigogine's Boltzmann-like Modelmentioning

confidence: 99%

Traffic and related self-driven many-particle systems

2001

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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%

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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“…In theoretical investigations, the velocity distribution P (v; x, t) has mostly been assumed to have the Gaussian form [5][6][7] …”

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Fundamentals of traffic flow

Helbing

1997

Phys. Rev. E

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From single vehicle data a number of new empirical results concerning the density-dependence of the velocity distribution and its moments as well as the characteristics of their temporal fluctuations have been determined. These are utilized for the specification of some fundamental relations of traffic flow and compared with existing traffic theories. 89.40.+k,47.20.-k,47.50.+d,47.55.-t Typeset using REVT E X 1 D. Helbing: Fundamentals of traffic flow, PRE2 For the prosperity in industrialized countries, efficient traffic systems are indispensable.However, due to an overall increase of mobility and transportation during the last years, the capacity of the road infrastructure has been reached. Some cities like Los Angeles and San Francisco already suffer from daily traffic collapses and their environmental consequences.About 20 percent more fuel consumption and air pollution is caused by impeded traffic and stop-and-go traffic.For the above mentioned reasons, several models for freeway traffic have been proposed, microscopic and macroscopic ones (for an overview cf. Ref.[1]). These are used for developing traffic optimization measures like on-ramp control, variable speed limits or re-routing systems [1]. For such purposes, the best models must be selected and calibrated to empirical traffic relations. However, some relations are difficult to obtain, and the lack of available empirical data has caused some stagnation in traffic modeling.Further advances will require a close interplay between theoretical and empirical investigations [2]. On the one hand, empirical findings are necessary to test and calibrate the various traffic models. On the other hand, some hardly measurable quantities and relations can be reconstructed by means of theoretical relations.Therefore, a number of fundamental traffic relations will be presented in the following.Until now, little is known about the velocity distribution of vehicles, its variance or skewness.A similar thing holds for the functional form of the velocity-density relation or the variancedensity relation at high densities. Empirical results have also been missing for the fluctuation characteristics of the density or average velocity. These gaps will be closed in the following.Although the data are varying in detail from one freeway stretch to another, the essential conclusions are expected to be universal.In a recent paper [3] it has been shown that the traffic dynamics on neighboring lanes is strongly correlated. Therefore, it is possible to treat the total freeway cross section in an overall way. Consequently, we will only discuss the properties of the lane averages of [3]). These data were detected by induction loops at discrete places x of the roadway and include the passage times t α (x), velocities v α (x), and lengths l α (x) of the single vehicles α. Consequently, it was possible to calculate the number N(x, t) of vehicles which passed the cross section at place x during a time interval [t − T /2, t + T /2], the traffic flowand the macroscopic velocity mo...

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Second-order continuum traffic flow model

Cited by 79 publications

References 18 publications

Traffic and related self-driven many-particle systems

Traffic and related self-driven many-particle systems

Statistical physics of vehicular traffic and some related systems

Fundamentals of traffic flow

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