Shock waves on the highway. (English) Zbl 1414.90094

Summary: A simple theory of traffic flow is developed by replacing individual vehicles with a continuous “fluid” density and applying an empirical relation between speed and density. Characteristic features of the resulting theory are a simple “graph-shearing” process for following the development of traffic waves in time and the frequent appearance of shock waves. The effect of a traffic signal on traffic streams is studied and found to exhibit a threshold effect wherein the disturbances are minor for light traffic but suddenly build to large values when a critical density is exceeded.


90B20 Traffic problems in operations research
35L67 Shocks and singularities for hyperbolic equations
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