Speed-Flow-Density Relationship

Speed, flow, and density are all related to each other. The relationships between speed and density are not difficult to observe in the real world, while the effects of speed and density on flow are not quite as apparent.

Under uninterrupted flow conditions, speed, density, and flow are all related by the following equation:

q = k*v

Where
q = Flow (vehicles/hour)
v = Speed (miles/hour, kilometers/hour)
k = Density (vehicles/mile, vehicles/kilometer)

Because flow is the product of speed and density, the flow is equal to zero when one or both of these terms is zero. It is also possible to deduce that the flow is maximized at some critical combination of speed and density.

Two common traffic conditions illustrate these points. The first is the modern traffic jam, where traffic densities are very high and speeds are very low. This combination produces a very low flow. The second condition occurs when traffic densities are very low and drivers can obtain free flow speed without any undue stress caused by other vehicles on the roadway. The extremely low density compensates for the high speeds, and the resulting flow is very low.