Nonlinear Follow-the-Leader Models of Traffic Flow

Gazis, Denos C.; Herman, Robert K; Rothery, Richard

doi:10.1287/opre.9.4.545

Cited by 1,251 publications

(638 citation statements)

References 10 publications

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“…Apparently the empirical fundamental diagram was the reason that already the first traffic flow models [28,29,30,31,32] were based upon the postulate that hypothetical spatially homogeneous and time-independent solutions, where all vehicles have the same distances to their neighbours and move with the same constant speed, (steady state solutions for short) exist that are related to a fundamental diagram, i.e. a curve in the flow-density plane.…”

Section: The Fundamental Diagram Approach and Cellular Automata Modelmentioning

confidence: 99%

Cellular automata approach to three-phase traffic theory

Kerner

Klenov

Wolf³

2002

J. Phys. A: Math. Gen.

409

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: The Fundamental Diagram Approach and Cellular Automata Modelmentioning

confidence: 99%

Cellular automata approach to three-phase traffic theory

Kerner

Klenov

Wolf³

2002

J. Phys. A: Math. Gen.

409

214

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“…The stability analysis performed in Gazis et al (1961) states that for v l 0 /g m 0 > /2, the solution v = 0 becomes unstable. When looking at more than two cars ("asymptotic stability", or better platoon stability), the model becomes unstable earlier, that is, for a smaller value of v l 0 /g m 0 > 1/2 (Gazis et al 1961, Zhang andJarrett 1997).…”

Section: Continuous Space and Timementioning

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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“…One is developed from the viewpoint of traffic engineering and the other is based on statistical physics. From the perspective of traffic engineers (Brackstone and McDonald, 1999), car-following models can be classified as stimulus-response models (Gazis et al, 1961;Newell, 1961), safety distance models (Gipps, 1981), psychophysical models (Wiedemann, 1974), and artificial intelligence models (Kikuchi and Chakroborty, 1992;Wu et al, 2000).…”

Section: Basic Theoretical Backgroundmentioning

confidence: 99%

Methods for the Assessment of Performance Indication Measures at Amakom Intersection and Their Application in Micro Simulation Modeling

Nyantakyi

Owusu²,

Borkloe³

2014

IJTTE

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Signalized intersections are vital nodal points in a transportation network and their efficiency of operation greatly influences the entire network's performance. Traffic simulation models have been widely used in both transportation operations and traffic analyses because simulation is safer, less expensive, and faster than field implementation and testing. This study assessed performance indication measures at Amakom intersection using micro simulation models in Synchro/SimTraffic. Traffic, geometric and signal control data including key parameters with greatest impact on the calibration process were collected on the field. At 5% significant level, the Chi square test and t-test analyses revealed that headway had a strong correlation with saturation flow compared to speed for both field and simulated conditions. It was concluded that changes in phasing plan with geometric improvement would improve upon the intersection's level of service.

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Nonlinear Follow-the-Leader Models of Traffic Flow

Cited by 1,251 publications

References 10 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

Methods for the Assessment of Performance Indication Measures at Amakom Intersection and Their Application in Micro Simulation Modeling

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