Fig. 5: Video snapshots of the seventh multi-lane Koopman mode.
From: Data-driven analysis and forecasting of highway traffic dynamics
The mode has a period of approximately 6 minutes and the time for each figure is given in minutes:seconds. Mode 7 clearly captures the dynamics of a highway wide traffic jam. It is interesting to note how the moving localized cluster’s (MLC) travel can be out of phase across differing lanes. This results in the apparent top-left to a bottom-right direction of travel and is a feature impossible to recover from a single-lane analysis. Lastly, one can observe that the on-ramp density of vehicles is not merging at the time of peak congestion. Specifically, the on-ramp is most heavily congested during (c and d) at which point the MLC has already propagated by. However, mode 14, a harmonic of this mode, clearly displays the opposite effect. This demonstrates how our multi-lane analysis can be utilized to verify the successful timing of static ramp metering algorithms and identify the correct timescales for dynamic ramp metering algorithms. Mode 14 can be referenced in Supplementary Fig. 22.
