Traffic congestion and the fundamental relationships of traffic flow

Abstract

The fundamental relationships of traffic flow describe traffic behaviour in terms of three variables: flow, density and speed. Among other things, they are useful for predicting the effect of changing demand conditions on the level of service. Their basic form was postulated in the 1930s, and many experiments have been carried out since then to determine their precise shape. But they have not yielded consistent results, partly because of confusion about the causal links among the variables, which operate differently depending on whether the speeds and flows are sampled over short periods of time, or over long periods of time. The mechanism of cause and effect is different and the roles of the explanatory and response variables (flow and speed respectively) are reversed. In this paper, the authors use simple models to show that the shape of the relationship between speed and flow varies according to the unit of observation, and that in the steady-state case, the form differs from the one that is conventionally pictured. The paper concludes by suggesting a modified representation, and briefly discusses the practical consequences.