A Boltzmann-Like Approach for Traffic Flow

Prigogine, Ilya; Andrews, Frank C.

doi:10.1287/opre.8.6.789

Cited by 215 publications

(145 citation statements)

References 1 publication

Supporting

Mentioning

138

Contrasting

Unclassified

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

“…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

View full text Add to dashboard Cite

show abstract

“…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

233

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

“…The number of vehicles entering a certain region equals the number leaving the same region. Gas kinetic traffic flow models were first proposed by Prigogine [8] and are based upon the analogy between gas flows and traffic flows. Where in the former case the dynamics are governed by interacting gas particles the latter deals with interacting vehicles.…”

Section: Governing Equationsmentioning

confidence: 99%