Estimation of the generalised average traffic speed based on microscopic measurements

The average speed of vehicles plays an important role in traffic engineering. In almost any model-based traffic monitoring, analysis, or control application the average speed is required as a measure of performance or as an input for traffic models used to simulate fuel consumption, vehicle emissions, or traffic noise. The average speed is also used in algorithms that estimate the travel time. It also appears in the fundamental equation of traffic where density is calculated based on the average speed and flow. This article presents a new methodology for estimating the time–space–mean speed (TSMS), which is an equivalent for the generalised speed introduced by Edie [1963. “Discussion of Traffic Stream Measurements and Definitions”. Proceedings of the 2nd international symposium on the theory of traffic flow. Paris, France, 139–154]. To this aim, first tight upper and lower bounds are developed for the TSMS using individual vehicle speeds that are obtained via point measurements. To estimate the TSMS from these bounds, and to deal with the cases where the trajectories of the vehicles might not be straight lines, a convex combination of the upper and lower bounds is introduced. In order to assess the convex combination and to compare its performance with other formulas in the literature, two real-life data sets corresponding to the NGSIM data for the I-880 highway in the San Francisco Bay Area, and the A13 data near Rotterdam–Delft are used. At the end, MATLAB simulations are presented to cover scenarios that are not included in the available real-life data sets. The results produced by the new formula, both for the real-life data sets and for MATLAB simulations, are found to be more accurate compared with other available formulas in the literature.