Estimating Probability Distributions of Travel Times by Fitting a Markovian Velocity Model

To improve the routing decisions of individual drivers and the management policies designed by traffic operators, one needs reliable estimates of travel time distributions. Since congestion caused by both recurrent patterns (e.g., rush hours) and non-recurrent events (e.g., traffic incidents) leads to potentially substantial delays in highway travel times, we focus on a framework capable of incorporating both effects. To this end, we propose to work with the Markovian velocity model, based on an environmental background process that tracks both random and (semi-)predictable events affecting the vehicle speeds in a highway network. We show how to operationalize this flexible data-driven model in order to obtain the travel time distribution for a vehicle departing at a known day and time to traverse a given path. Specifically, we detail how to structure the background process and set the speed levels corresponding to the different states of this process. First, for the inclusion of non-recurrent events, we study incident data to describe the random durations of the incident and inter-incident times for different periods of day. Second, for an estimation of the speed patterns in both incident and inter-incident regime, loop detector data for each of these periods is studied. In numerical examples that use road network detector data of the Dutch highway network, we obtain the travel time distribution estimates that arise under different traffic regimes, and illustrate the advantages compared to deterministic travel time prediction methods, or methods that only take recurrent patterns into account.