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A Contribution to Theory of Traffic Flow
SAE Technical Paper Series, 1968<div class="htmlview paragraph">This paper presents an analysis of a car following model of general form: ẍ<sub>n + 1</sub> = A (ẋ<sub>n</sub> -ẋ<sub>n + 1</sub>)/(x<sub>n</sub> - x<sub>n + 1</sub>)<sup>m</sup>, where A and m are constants, x<sub>n + 1</sub> is ...
L. A. Pipes, C. K. Wojcik
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On the Statistical Distribution Function Theory of Traffic Flow [PDF]
Operations Research, 1962 The homogeneous time-independent solution for a one-car speed distribution function is derived for a Boltzmann-like approach to the statistical theory of traffic flow. Numerical results are discussed for a number of different desired speed-distribution functions.
Anderson, Robert +2 more
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A Queueing Theory Model of Nonstationary Traffic Flow
Transportation Science, 2001The queueing-theoretical model for stationary traffic flow developed in a former paper is extended and modified for nonstationary flow. In particular it is shown how speed-flow-density relationships under nonstationary conditions may deviate from those obtained for stationary conditions.
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Journal of the Franklin Institute, 1965
Abstract Two types of mathematical models are presented to explain the empirical observation that a form of “wave phenomenon” occurs when a long line of vehicles on a crowded highway is stopped or started by a signal. The interruption of the steady flow of vehicles initiates “waves of stopping” or “waves of starting.” The first model considered is a
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Abstract Two types of mathematical models are presented to explain the empirical observation that a form of “wave phenomenon” occurs when a long line of vehicles on a crowded highway is stopped or started by a signal. The interruption of the steady flow of vehicles initiates “waves of stopping” or “waves of starting.” The first model considered is a
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1983
Let us derive the basic conservation equation for traffic flow. We consider the flow of vehicles on a long road where the features of the flow we wish to calculate, such as bottlenecks, etc., are long compared with the average distances between vehicles.
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Let us derive the basic conservation equation for traffic flow. We consider the flow of vehicles on a long road where the features of the flow we wish to calculate, such as bottlenecks, etc., are long compared with the average distances between vehicles.
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Selected mathematical problems of traffic flow theory
International Journal of Computer Mathematics, 2012In spite of the long history of traffic flow theory development, a lot of its aspects are still unsettled, initiate debates and criticism and require further research. The main reasons for such a situation are the high level of complexity of the study object and difficulties in formalizing its behaviour as a complex social technical system.
Alexander P. Buslaev +2 more
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A Similitude Theory for Modeling Traffic Flow Dynamics
IEEE Transactions on Intelligent Transportation Systems, 2019Similitude theory, particularly dimension analysis, is a common tool for testing scaled-down engineering models and is widely used in vehicle dynamics and other engineering fields. However, it is barely employed in scaling traffic flow dynamics. In this paper, dimension analysis is adopted to scale car-following dynamics.
Xuan Di +3 more
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Journal of the Operational Research Society, 1963
W. R. Buckland, Robert Herman
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W. R. Buckland, Robert Herman
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An Introduction to Traffic Flow Theory.
Journal of the Royal Statistical Society. Series A (General), 1965M. S. Bartlett +2 more
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