Previous descriptions of traffic flow under changing conditions are shown to be untenable. Deterministic relationships between traffic speed and density do not allow for observed scatter and imply that traffic can lock up spontaneously. Equilibrium relationships between speed and density allow impossibly high traffic densities and provide unrealistically slow responses to changes in roadway and traffic conditions. A qualitatively superior representation of traffic flow is developed. Traffic is described as a fluid that cannot be compressed beyond a certain density, kjam. The equations of state are: (1) Volume=speed×density. (2) Continuity of vehicles. (3) Traffic speed ‘relaxes’ to the free-flow speed of the roadway, independent of density except that volume cannot exceed roadway capacity and flow is incompressible when traffic density is equal to the jam density. The representation is innovative in two respects: (1) Traffic flowing with density=kjam is explicitly recognized as being incompressible. (2) No speed-density relationship is contained in or implied by the traffic formulation. The new traffic formulation models both interrupted and uninterrupted traffic flow. It has been tested by simulating several traffic flow situations. The reproductions of light to moderate flows are equal to those of the best previous traffic formulation, and the representations of congested and bottleneck flow are superior. The new traffic formulation also reproduces the general qualities of observed speed/volume curves and provides interpretation of those curves in terms of upstream and downstream bottlenecks.
