Distribution function properties and the fundamental diagram in kinetic traffic flow theory

Lehmann, Heiko

doi:10.1103/physreve.54.6058

Cited by 32 publications

(17 citation statements)

References 10 publications

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“…Analoguous factorizations hold for an arbitrary number of sites on the lefthand-side of (68), (70) and (72).…”

Section: Site-oriented Cluster-theoretic Approach To the Nasch Modelmentioning

confidence: 99%

“…More recently, Lehmann [72] has attempted to revive the Prigogine approach by reformulating it as a semi-phenomenological theory where the distribution f (x, v; t) is assumed to follow the simpler form…”

Section: Prigogine Modelmentioning

confidence: 99%

“…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%

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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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“…Analoguous factorizations hold for an arbitrary number of sites on the lefthand-side of (68), (70) and (72).…”

Section: Site-oriented Cluster-theoretic Approach To the Nasch Modelmentioning

confidence: 99%

Section: Prigogine Modelmentioning

confidence: 99%

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Statistical physics of vehicular traffic and some related systems

2000

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“…A lot of theories have been proposed such as car-following theory [5], kinetic theory [6][7][8][9][10] and particle-hopping theory [11][12][13]. These theories have the advantages of alleviating the traffic congestion and enhancing the capacity of existing infrastructure.…”

Section: Introductionmentioning

confidence: 99%

Advanced information feedback strategy in intelligent two-route traffic flow systems

Dong

Wang

2010

Sci. China Inf. Sci.

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The optimal information feedback has a significant effect on many socioeconomic systems like stock market and traffic systems aiming to make full use of resources. In this paper, we study dynamics of traffic flow with real-time information. The influence of a feedback strategy named vehicle number feedback strategy (VNFS) is introduced, in which we only calculate the vehicle number of first 500 route sites from the entrance. Moreover, the two-route traffic system has only one entrance and one exit, which is different from those in the previous work. Our model incorporates the effects of adaptability into the cellular automaton models of traffic flow, and simulation results by adopting this optimal information feedback strategy have demonstrated higher efficiency in controlling spatial distribution of traffic patterns than the other three information feedback strategies, i.e., TTFS, MVFS and CCFS. Keywordsvehicle number feedback strategy, two-route selecting traffic flow, intelligent vehicle, cellular automaton model CitationDong C F, Ma X, Wang B H. Advanced information feedback strategy in intelligent two-route traffic flow systems.

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“…A lot of theories have been proposed such as car-following theory [4], kinetic theory [5][6][7][8][9][10][11] and particle-hopping theory [12,13]. These theories have the advantages of alleviating the traffic congestion and enhancing the capacity of existing infrastructure.…”

Section: Introductionmentioning

confidence: 99%

Effects of prediction feedback in multi-route intelligent traffic systems

Dong

Wang

et al. 2010

Physica A: Statistical Mechanics and its Applications

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We first study the influence of an efficient feedback strategy named prediction feedback strategy (PFS) based on a multi-route scenario in which dynamic information can be generated and displayed on the board to guide road users to make a choice. In this scenario, our model incorporates the effects of adaptability into the cellular automaton models of traffic flow. Simulation results adopting this optimal information feedback strategy have demonstrated high efficiency in controlling spatial distribution of traffic patterns compared with the other three information feedback strategies, i.e., vehicle number and flux. At the end of this paper, we also discuss in what situation PFS will become invalid in multi-route systems.

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Distribution function properties and the fundamental diagram in kinetic traffic flow theory

Cited by 32 publications

References 10 publications

Statistical physics of vehicular traffic and some related systems

Statistical physics of vehicular traffic and some related systems

Advanced information feedback strategy in intelligent two-route traffic flow systems

Effects of prediction feedback in multi-route intelligent traffic systems

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