VEHICLE TRAVEL TIME DISTRIBUTION ESTIMATION AND

We introduce two statistical methods for estimating vehicle travel time distribu-tions on a road network, using Global Positioning System (GPS) data recorded during historical vehicle trips. In the first method, we use a model of the path taken by each vehicle in the data, the travel time on each road segment in the network, and the location and speed errors for each GPS observation. In the sec-ond method, we use a model of the entire travel time of each trip, and include covariates such as the types of roads traveled and time of day. We estimate the parameters of both models by Markov chain Monte Carlo methods. We compare the performance of these methods with two simpler methods, a recently published method, and commercially available travel time estimates, using data from ambulance trips in Toronto and simulated data. Our methods outperform the alternative methods in point and distribution estimation of out-of-sample trip travel times. Our methods also provide more realistic estimates than the recently published method of the probability that an ambulance is able to respond to each intersection in Toronto within a time threshold