Evaluation of Cellular Automata for Traffic Flow Simulation on Freeway and Urban Streets

Brilon, Werner; Wu, Ning

doi:10.1007/978-3-642-60236-8_11

Cited by 37 publications

(27 citation statements)

References 2 publications

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“…In order to show the power of the basic model (1), (3) [24], the remaining model specifications (free and safe speeds, fluctuations) will be the same as introduced in different Nagel-Schreckenberg CA-models in the fundamental diagram approach [36,38,39,22,23,49,50] (with a slightly more general modeling of fluctuations). Nevertheless, it will be shown that all features of congested patterns which spontaneously occur upstream of the on-ramp as well as of their evolution (when the flow rate to the on-ramp is changing) are different in our CA-models.…”

Section: Fluctuations Of Acceleration and Decelerationmentioning

confidence: 99%

“…p a + p b ≤ 1 must be fulfilled. In a different way and for a different purpose a random acceleration was also introduced in CA-models by Brilon and Wu [50]. As in a NaSch CA-model in the fundamental diagram approach [39], the probability p b in (13) is taken as a decreasing function of the vehicle speed v n :…”

Section: Fluctuations Of Acceleration and Decelerationmentioning

confidence: 99%

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Cellular automata approach to three-phase traffic theory

Kerner

Klenov

Wolf³

2002

J. Phys. A: Math. Gen.

410

214

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Abstract. The cellular automata (CA) approach to traffic modeling is extended to allow for spatially homogeneous steady state solutions that cover a two dimensional region in the flow-density plane. Hence these models fulfill a basic postulate of a three-phase traffic theory proposed by Kerner. This is achieved by a synchronization distance, within which a vehicle always tries to adjust its speed to the one of the vehicle in front. In the CA models presented, the modelling of the free and safe speeds, the slow-to-start rules as well as some contributions to noise are based on the ideas of the Nagel-Schreckenberg type modelling. It is shown that the proposed CA models can be very transparent and still reproduce the two main types of congested patterns (the general pattern and the synchronized flow pattern) as well as their dependence on the flows near an on-ramp, in qualitative agreement with the recently developed continuum version of the three-phase traffic theory [B. S. Kerner and S. L. Klenov. 2002. J. Phys. A: Math. Gen. 35, L31]. These features are qualitatively different than in previously considered CA traffic models. The probability of the breakdown phenomenon (i.e., of the phase transition from free flow to synchronized flow) as function of the flow rate to the on-ramp and of the flow rate on the road upstream of the on-ramp is investigated. The capacity drops at the on-ramp which occur due to the formation of different congested patterns are calculated. Cellular automata2

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Section: Fluctuations Of Acceleration and Decelerationmentioning

confidence: 99%

Section: Fluctuations Of Acceleration and Decelerationmentioning

confidence: 99%

Cellular automata approach to three-phase traffic theory

Kerner

Klenov

Wolf³

2002

J. Phys. A: Math. Gen.

410

214

View full text Add to dashboard Cite

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“…Time-Oriented CA (TOCA). A modification to make the STCA more realistic is the so-called time-oriented CA (TOCA) (Brilon and Wu 1999). The motivation is to introduce a higher amount of elasticity in the car following, that is, vehicles should accelerate and decelerate at larger distances to the vehicle ahead than in the STCA, and resort to emergency braking only if they get too close.…”

Section: Slow-to-startmentioning

confidence: 99%

Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling

Nagel¹,

Wagner

Woesler

2003

Operations Research

286

165

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Certain aspects of traffic flow measurements imply the existence of a phase transition. Models known from chaos and fractals, such as nonlinear analysis of coupled differential equations, cellular automata, or coupled maps, can generate behavior which indeed resembles a phase transition in the flow behavior. Other measurements point out that the same behavior could be generated by geometrical constraints of the scenario. This paper looks at some of the empirical evidence, but mostly focuses on different modeling approaches. The theory of traffic jam dynamics is reviewed in some detail, starting from the well-established theory of kinematic waves and then veering into the area of phase transitions. One aspect of the theory of phase transitions is that, by changing one single parameter, a system can be moved from displaying a phase transition to not displaying a phase transition. This implies that models for traffic can be tuned so that they display a phase transition or not.This paper focuses on microscopic modeling, i.e., coupled differential equations, cellular automata, and coupled maps. The phase transition behavior of these models, as far as it is known, is discussed. Similarly, fluid-dynamical models for the same questions are considered. A large portion of this paper is given to the discussion of extensions and open questions, which makes clear that the question of traffic jam dynamics is, albeit important, only a small part of an interesting and vibrant field. As our outlook shows, the whole field is moving away from a rather static view of traffic toward a dynamic view, which uses simulation as an important tool.

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“…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). …”

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confidence: 99%

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

Schönhof

Helbing

2007

Transportation Science

233

186

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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...

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Evaluation of Cellular Automata for Traffic Flow Simulation on Freeway and Urban Streets

Cited by 37 publications

References 2 publications

Cellular automata approach to three-phase traffic theory

Cellular automata approach to three-phase traffic theory

Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling

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

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