On kinematic waves II. A theory of traffic flow on long crowded roads

@article{Lighthill1955OnKW,
  title={On kinematic waves II. A theory of traffic flow on long crowded roads},
  author={Michael James Lighthill and Gerald Beresford Whitham},
  journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences},
  year={1955},
  volume={229},
  pages={317 - 345}
}
  • M. LighthillG. Whitham
  • Published 10 May 1955
  • Engineering
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
This paper uses the method of kinematic waves, developed in part I, but may be read independently. [] Key Method The hump gradually spreads out along the road, and the time scale of this process is estimated. The behaviour of such a hump on entering a bottleneck, which is too narrow to admit the increased flow, is studied (§5), and methods are obtained for estimating the extent and duration of the resulting hold-up. The theory is applicable principally to traffic behaviour over a long stretch of road, but…

Kinematic wave theory of bottlenecks of varying capacity

  • S. C. DeM. Lighthill
  • Engineering
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1956
ABSTRACT This paper discusses a problem in traffic flow by the method of kinematic waves developed by Lighthill and Whitham(1,2). The theory of kinematic waves introduced by Lighthill and Whitham has

On kinematic waves I. Flood movement in long rivers

In this paper and in part II, we give the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point

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A simple kinematic wave theory of lane-changing dynamics is developed, from whose Riemann solutions the authors present new definitions of local traffic supply and demand and incorporate additional effective density from lane- changing traffic into the fundamental diagram.

A kinematic wave theory of lane-changing traffic flow

Analyses of shock waves and jams in traffic flow

In this paper, we study the certain qualitative properties of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic
...

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In this paper and in part II, we give the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point

A PROBLEM OF INTERFERENCE BETWEEN TWO QUEUES

It is shown that increasing the acceleration capability even at the expense of reducing the maximum speed, (e.G., by lowering the top gear ratio), would result in increased journey speeds for most modern cars under typical traffic conditions, and that reducing the safety margins in passing would not normally provide any worthwhile increase in mean journey speed.

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On kinematic waves I. Flood movement in long rivers

  • M. LighthillG. Whitham
  • Engineering
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1955
In this paper and in part II, we give the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point

Methods of making traffic surveys especially 'before and after

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