Modeling of freeway breakdown process with log-periodic oscillations
Urban and suburban freeways are designed to allow smooth traffic flow at high speed. However, when traffic demand is high or during irregular events, significant congestion may develop. Traffic breakdown occurs during the phase transition from dense congested stable (DCS) flow to breakdown flow. In this study, the process of freeway flow breakdown was investigated by calibrating models in the density–time plane using morning peak data from Interstate 66, a US highway connecting Washington, D.C., and Virginia. It was shown that the models, which describe the collective behavior of drivers using the mathematical property of the log-periodic oscillations (LPO) process, reflect suitably the phase transition in freeway traffic flow. The LPO process has been used in the past to model stock market crashes and the occurrences of large earthquakes. The cyclic properties of the LPO models developd in this study were found to identify the “critical transition period,” which triggers the traffic breakdown process. This period starts when the density rate of change reaches its maximum during the first cycle that follows the DCS flow regime. This triggers a breakdown of flow conditions, which occur 5–8 min after the density rate of change has achieved its maximum.