An iterative procedure for estimating the generalized average speed using microscopic point measurements

Various traffic applications including model-based analysis and control of traffic need the average speed. The average speed is used as a measure of performance, and as an input for traffic models. It is also used to obtain the density from a known flow or vice versa. In this paper, a new iterative procedure is presented that uses point measurements from inductive loop detectors for estimating the time-space-mean speed (TSMS), which is an equivalent for the generalized average speed introduced by Edie (1965). An important subject that is missing in the literature considering estimation of the average speed is how to handle the vehicles that remain on a given road section, i.e., a part of the road that is extended between two consecutive loop detectors, for more than one sampling cycle. The problem occurs for the vehicles that are still in the road section at the end of the cycle. These vehicles are detected by the upstream loop detector once they enter the road section. However, in future cycles the data of these vehicles will not be considered by the loop detector. The iterative approach of the new procedure makes it possible to adequately take into account the vehicles that will stay on the same road section for several sampling cycles when estimating the TSMS. To evaluate the new procedure, the NGSIM data, which provides detailed information of a collection of vehicle trajectories on the I-880 highway in the San Francisco Bay Area is utilized. The simulation results illustrate the excellent performance of the iterative procedure for estimating the TSMS compared with previous approaches.