Kinetic Theory of Vehicular Traffic

Prigogine, Ilya; Herman, Robert K; Schechter, R.S.

doi:10.1109/tsmc.1972.4309114

Cited by 329 publications

(289 citation statements)

References 0 publications

Supporting

Mentioning

278

Contrasting

Unclassified

Order By: Relevance

“…Gas-kinetic models agglomerate over many vehicles and formulate a partial differential equation for the spatio-temporal evolution of the vehicle density and the velocity distribution. While Boltzmann-like approaches (Prigogine and Andrews, 1960;Prigogine and Herman, 1971;Paveri-Fontana, 1975;Phillips, 1977Phillips, , 1979aNelson, 1995;Helbing, 1995c) are mainly suitable for small densities, Enskog-like approaches (Helbing, 1995d(Helbing, , 1996b(Helbing, , 2001aWagner, 1997a; Wegener, 1997, 1999a, b; Helbing and Treiber, 1998a; Shvetsov and Helbing, 1999) take into account corrections due to finite space requirements of vehicles. The main application of gas-kinetic models is the theoretical derivation of macroscopic traffic equations for the vehicle density and average velocity.…”

Section: Modeling Approachesmentioning

confidence: 99%

Empirical Features of Congested Traffic States and Their Implications for Traffic Modeling

Schönhof

Helbing

2007

Transportation Science

237

186

View full text Add to dashboard Cite

We investigate characteristic properties of the congested traffic states on a 30 km long stretch of the German freeway A5 north of Frankfurt/Main. Among the approximately 245 breakdowns of traffic flow in 165 days, we have identified five different kinds of spatio-temporal congestion patterns and their combinations. Based on an "adaptive smoothing method" for the visualization of detector data, we also discuss particular features of breakdowns such as the "boomerang effect" which is a sign of linearly unstable traffic flow. Controversial issues such as "synchronized flow" or stop-and-go waves are addressed as well. Finally, our empirical results are compared with different theoretical concepts and interpretations of congestion patterns, in particular first-and second-order macroscopic traffic models. Summary of Previous Models and Empirical ResultsUnderstanding traffic dynamics can not only help to identify reasons for bottlenecks. It also contributes to the development of modern driver and traffic assistance systems aiming at the improvement of safety, comfort, and capacity. Progress has been made by empirical studies and theoretical modelling approaches. Apart from traffic scientists, mathematicians and physicists have also recently contributed to these fields. Because 1 of the numerous publications, our introductory overview can only be selective, so that we refer the reader to some comprehensive reviews (e.g., Gerlough and Huber, 1975;Vumbaco, 1981;Leutzbach, 1988;May, 1990;Brilon et al., 1993; Transportation Research Board, 1996; Gartner et al., 1997; Helbing, 1997a; Daganzo, 1997a;Bovy, 1998;Hall, 1999;Brilon et al., 1999; Chowdhury et al., 2000b, with a focus on cellular automata; Helbing, 2001a, containing 800 references; Nagatani, 2002). Modeling ApproachesThe main modeling approaches can be classified as follows: Car-following models focus on the non-linear interaction and dynamics of single vehicles. They specify their acceleration mostly as a function of the distance to the vehicle ahead, the own and relative velocity (e.g., Reuschel, 1950a, b;Gazis et al., 1959Gazis et al., , 1961May and Keller, 1967;Gipps, 1981;Gibson, 1981;Bando et al., 1994Bando et al., , 1995a Krauß, 1998;Treiber et al., 2000;Brackstone and McDonald, 2000). Submicroscopic models take into account even details such as perception thresholds, changing of gears, acceleration characteristics of specific car types, reactions to brake lights and winkers (Wiedemann, 1974;Fellendorf, 1996;Ludmann et al., 1997). In favour of numerical efficiency, cellular automata describe the dynamics of vehicles in a coarse-grained way by discretizing space and time (Cremer and Ludwig, 1986;Biham et al., 1992;Nagel and Schreckenberg, 1992; Chowdhury et al., 2000b). Gas-kinetic models agglomerate over many vehicles and formulate a partial differential equation for the spatio-temporal evolution of the vehicle density and the velocity distribution. While Boltzmann-like approaches (Prigogine and Andrews, 1960;Prigogine and Herman, 1971;Paveri-Fontana, 197...

show abstract

Section: Modeling Approachesmentioning

confidence: 99%

Empirical Features of Congested Traffic States and Their Implications for Traffic Modeling

Schönhof

Helbing

2007

Transportation Science

237

186

View full text Add to dashboard Cite

show abstract

“…The first kinetic model for traffic flow was suggested by Prigogine and Herman [1], followed several years later by a model proposed by Paveri-Fontana [2]. More recently, Klar and Wegener [3,4,5,6] have introduced kinetic equations of Enskog type for multilane traffic.…”

Section: Introductionmentioning

confidence: 99%

On Vlasov-Fokker-Planck Type Kinetic Models for Multilane Traffic Flow

Illner¹,

Klar²,

Materne³

2003

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. We discuss rationales for kinetic descriptions of traffic dynamics and present a class of new models of VlasovFokker-Planck type. These models incorporate (nonlocal and time-delayed) braking and acceleration terms which are consistent with realistic time scales. Correlation assumptions are made such that braking and acceleration terms depend only on macroscopic densities and the relative speeds with respect to the average speed; the braking term includes lane change probabilities, and reasonable assumptions on the dependencies of these probabilities on the traffic situation lead to multivalued fundamental diagrams, consistent with traffic observations.

show abstract

“…The first Boltzmann-like (gas-kinetic) model was proposed by Prigogine and co-workers [39][40][41]. However, Paveri-Fontana [42] has pointed out that this model has some peculiar properties.…”

Section: Boltzmann-like Multi-lane Theorymentioning

confidence: 99%

Modeling and simulation of multilane traffic flow

Helbing¹,

Greiner²

1997

Phys. Rev. E

View full text Add to dashboard Cite

A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multilane model for uni-directional freeways including acceleration, deceleration, velocity fluctuations, overtaking and lane-changing maneuvers is systematically deduced from a gas-kinetic (Boltzmann-like) approach. The resulting equations contain corrections with respect to previous models. For efficient computer simulations, a reduced model delineating the coarse-grained temporal behavior is derived and applied to bottleneck situations.

show abstract

Kinetic Theory of Vehicular Traffic

Cited by 329 publications

References 0 publications

Empirical Features of Congested Traffic States and Their Implications for Traffic Modeling

Empirical Features of Congested Traffic States and Their Implications for Traffic Modeling

On Vlasov-Fokker-Planck Type Kinetic Models for Multilane Traffic Flow

Modeling and simulation of multilane traffic flow

Contact Info

Product

Resources

About