Three-Dimensional Representation of Traffic Flow

Yasuji Makigami, G. F. Newell and Richard Rothery
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Yasuji Makigami: University of California, Berkeley
G. F. Newell: University of California, Berkeley
Richard Rothery: General Motors Research Laboratories, Warren, Michigan

Transportation Science, 1971, vol. 5, issue 3, 302-313

Abstract: If one numbers vehicles consecutively along a roadway and draws the space-time trajectory of each vehicle on the same x - t graph, then this family of curves can be interpreted as the contours of a three-dimensional surface for which the third dimension is vehicle number n . The intersection of the surface with planes of constant x are the cumulative arrival curves, n vs. t , at the location x . If the surface is smoothed, the orientation of the tangent plane at any point determines the flow q , density k , and car velocity v . All commonly observed properties of traffic flow have simple geometric interpretations in this three-dimensional model.

Date: 1971
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