Analysis of the single-regime speed-density fundamental relationships for varying spatiotemporal resolution using Zen Traffic Data

This study analyzed the single-regime speed-density (v v-k ) relationships for urban expressways using high resolution Zen Traffic Data (ZTD) containing all vehicles' trajectory data obtained using image sensing technology. The steady-state traffic data were extracted for varying spatiotemporal resolutions, followed by estimation of traffic flow parameters, namely, jam density, kinematic-wave-speed, and proportionality factor, a behavioral parameter, using empirical data. Functional and shape parameters were estimated using the Levenberg-Marquardt algorithm. Statistical metrics were used to assess the performance and model fitness in all categories of linear, exponential and logarithmic, and complex forms of v-k relationships for different resolutions. The theoretical analysis revealed that certain relationships satisfy all the static properties and that only one satisfies both the dynamic properties of traffic behavior. Highly parameterized forms had the lowest errors. However, the linear form of model developed by May and Keller has high application potential.