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
View on Royal Society
courses.physics.ucsd.edu
4,465 Citations
Highly Influential Citations
218
Background Citations
896
Methods Citations
910
Results Citations
16

4,465 Citations

Citation Type

Citation Type

Multi-class kinematic wave theory of traffic flow
TLDR
A framework for the different existing multi-class extensions of the kinematic wave theory of traffic flow is proposed and a new model is proposed where classes interact on a non-cooperative way.
Wave theories of traffic flow
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…
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…
Average Velocity of Waves Propagating through Congested Freeway Traffic
This paper employed cross correlation in order to estimate wave velocities between several successive detector stations during congested periods over a large data set. Given homogeneous vehicles and…
An instantaneous kinematic wave theory of diverging traffic
Diverging junctions are an important type of bottlenecks, which can reduce capacities and initiate and propagate traffic congestion in a road network. In this paper, we propose a kinematic wave…
A kinematic wave theory of lane-changing vehicular traffic
TLDR
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 multi-commodity network traffic flow
A systematic understanding of traffic dynamics on road networks is crucial for many transportation studies and can help to develop more efficient ramp metering, evacuation, signal control, and other…
A kinematic wave theory of lane-changing traffic flow
  • W. Jin
  • Mathematics, Engineering
  • 2005
Frequent lane-changes in highway merging, diverging, and weaving areas could disrupt traffic flow and, even worse, lead to accidents. In this paper, we propose a simple model for studying bottleneck…
An application of shock wave theory to urban traffic control via dynamic speed advisory
In this work, shock wave theory is used to model traffic evolution within urban road segments between signalized intersections. The shock wave evolution depends algebraically on the boundary…
...
1
2
3
4
5
...

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…
The flow pattern of a supersonic projectile
On kinem atic waves . I . Flood m ovement in long rivers
  • Proc . Roy . Soc . A
  • 1955
A METHOD OF ESTIMATING SPEED AND FLOW OF TRAFFIC FROM A MOVING VEHICLE.
Road research and its bearing on road transport
  • J . Inst . Transp .
  • 1953
ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH.
Some Theoretical Aspects of Road Traffic Research
...
1
2
3
...