Guaranteed Bounds on Highway Travel Times Using Probe and Fixed Data

This article investigates the problem of incorporating mobile probe data collected from GPS equipped cell phones into estimation algorithms for travel time. We use kinematic wave theory to create a modeling framework capable of incorporating trajectory data into the model. The problem of including loop detector data in this model is performed using a standard approach available in the literature. The problem of fusing this data with probe data is formulated using the Moskowitz function, which results from kinematic wave theory. Using this formulation, two linear programs are posed to compute upper and lower bounds travel time through the corresponding section of highway. The method thus provides a guaranteed range for the average travel time experienced by vehicles on the highway. The method is illustrated with data collected during the Mobile Century experiment on February 8th, 2008, using 100 Nokia N95 phones traveling onboard cars driving loops on I880 in California. A sampling and penetration rate study shows that the method provides accurate travel time estimates for penetration rates as low as 0.1% and spatial sampling strategies on the order of 0.2 miles. The performance of the method is illustrated with several case studies, in which measurements gathered by a few vehicles are sufficient to significantly improve results obtained from sparse loop detectors.