Investigation of temporal freeway traffic patterns in reconstructed state spaces

The characterization of the dynamics of traffic states remains fundamental to seeking for the solutions of diverse traffic problems. To gain more insights in traffic dynamics in the temporal domain, this paper explored traffic patterns in higher-dimensional state spaces, where we attempted to map the one-dimensional traffic series into appropriate multidimensional spaces by Takens’ algorithm. After such a state space reconstruction, we then made use of the largest Lyapunov exponent to depict the rate of expansion or contraction of traffic state trajectories in the reconstructed spaces. The correlation dimension was further estimated to examine if the traffic state trajectories exhibited chaotic-like or stochastic-like motions. An empirical study using flow, speed, and occupancy time-series data as well as the speed-flow, speed-occupancy, and flow-occupancy paired data collected from dual-loop detectors on a freeway of Taiwan was conducted. The numerical results revealed that different nonlinear traffic patterns could emerge depending on the observed time-scale, history data and time-of-day. In addition, with consideration of sequential order and spatiotemporal features, more information about traffic dynamical evolution was extracted.