# 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} }

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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## References

SHOWING 1-10 OF 29 REFERENCES

On kinematic waves I. Flood movement in long rivers

- 1954

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

- MathematicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1955

A PROBLEM OF INTERFERENCE BETWEEN TWO QUEUES

- Mathematics
- 1953

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

- Engineering
- 1935

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