An interpretation of speed-flow-concentration relationships using catastrophe theory

Abstract

The occurence of gaps in freeway operations data, for example in flow-concentration plots, and the accompanying jumps in the behavior of some of the variables, have been observed in many data sets. Conventional representations of speed-flow-concentration relationships do not address those jumps, much less explain why the jumps occur at different values of the variables in different data sets. Catastrophe theory provides a way to understand that behavior. In particular, the cusp catastrophe replicates quite well the functions derived from data collected on the Queen Elizabeth Way in Ontario. Simple linear transformations between traffic operations variables and catastrophe theory variables are shown to provide a feasible explanation for the occurrence of these jumps. Although the theory does not lead to a single unique solution, it provides fresh insight into the operation of freeways, and suggests several avenues for further research.