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. Lighthill, G. Whitham
  • Published 10 May 1955
  • Engineering, Computer Science
  • 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…Expand
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  • Mathematics
    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
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References

SHOWING 1-10 OF 29 REFERENCES
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
On kinematic waves I. Flood movement in long rivers
  • M. Lighthill, G. Whitham
  • Mathematics
    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
A PROBLEM OF INTERFERENCE BETWEEN TWO QUEUES
A two-lane road is assumed to be occupied mainly by platoons of cars travelling along the two opposite directions at constant speeds. A single car is assumed to try to move at a speed higher than
A study of traffic capacity
The results of a traffic capacity study started in june 1934 by the traffic bureau of the ohio state highway department are presented. The data were collected by the photographic method described in
On kinem atic waves . I . Flood m ovement in long rivers
  • Proc . Roy . Soc . A
  • 1955
Road research and its bearing on road transport
  • J . Inst . Transp .
  • 1953
Some Theoretical Aspects of Road Traffic Research
...
1
2
3
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