Probabilistic estimation of travel times in arterial streets using sparse transit bus data

This paper presents methods for estimating statistics of travel time in arterial roads by utilizing sparse vehicular probe data. We use a public data feed from transit buses in the City of San Francisco as an example data source. Sparsity of time and location updates along with frequent stops, at bus stops and traffic lights, complicates estimation of travel time for each link based on a single bus pass. Unlike most previous papers that focus on estimation of link travel times, we divide each link into shorter segments, and propose two iterative methods for allocating travel time statistics to each segment. Inspired by K-means and Expectation Maximization (EM) algorithms, we iteratively update the mean and variance of travel time for each segment based on historical probe data. Our preliminary results show convergence to reasonable travel time patterns; for instance they clearly reveal the location of bus stops and traffic signals and statistics of delay across them. Applications of this work are in better traveler information systems and in estimation of maximum likelihood trajectory of vehicles in arterial roads.