Long-Range Dependence of Traffic Flow and Speed of a Motorway: Dynamics and Correlation with Historical Incidents

Abstract

Speed and flow of vehicles tend to have several effects on the dynamics of a transport system. Fluctuations of these variables can implicate congestion, can lower predictability, and may even catalyze crashes. A concept of fractal theory called the Hurst exponent—a measure of the long-range dependence (LRD) of a time series—was used to understand the fluctuations in flow and speed of a motorway in Sydney, Australia. The spatial and temporal variation of the LRD for flow (H_flow) and speed (H_speed) at several monitor sites is discussed. Furthermore, the effects of number of lanes on flow and speed predictability are explored. It was observed that the flow predictability of two-lane sections was significantly lower when compared with three-lane and four-lane sections. Conversely, the speed predictability of four-lane sections was considerably higher than that of two-lane and three-lane sections. Finally, traffic congestion was defined with regard to the LRD of speed, and its correlation with historical incident rates was measured. It was ascertained that monitor sites with a historically high proportion of large H_speed were correlated with unsafe locations. This study could lead to many applications of fractal analysis on highways and urban traffic.

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