Estimation of speeds from single-loop freeway flow and occupancy data using cusp catastrophe theory model

Many freeway management systems rely on single-loop detectors, which can measure only flow and occupancy, for information on freeway operating conditions. Although it is possible to estimate average speeds from those data by assuming a constant vehicle length, such estimates are not particularly good. The catastrophe theory model for these variables provides an alternative procedure for estimating average speeds. To apply it, different procedures are needed to calibrate the model. Such procedures are developed and their generally is tested, by applying them first across different days at the same (double-loop) station, then to other double-loop stations, and finally to single-loop stations. The first two tests allow for direct comparisons with measured average speeds; the final comparison can be made only with other estimated speeds, which is done on the basis of speed-flow diagrams. The results suggest that the catastrophe theory estimates are better than those made assuming a constant vehicle length. Estimates based on concurrent nearby measured vehicle lengths are similar to the catastrophe theory estimates on average, but the former overestimate the scatter and the latter underestimate it.