Travel Time Estimation

Abstract

For most persons, the individual travel time is the most relevant criterion when planning a route from a given origin to a given destination. Road managers and national economists are interested in the total travel time in a certain region over a certain time interval. Of particular interest is the total delay caused by conges-tion. The methods to estimate these quantities can be applied directly to stationary detector and probe-vehicle data, or to microscopic and macroscopic models. While microscopic models give the travel time directly in terms of the duration of trajecto-ries, macroscopic models require additional evaluations, either integrating the flow at fixed positions (" virtual detectors "), or generating virtual trajectories from the local speed field V (x, t). Generally, the macroscopic estimation is more robust. We define the travel time τ 12 in the obvious way as the time a vehicle needs to pass a road section [x 1 , x 2 ]. Generally, τ 12 depends on x 1 , x 2 , and on time t itself. Since τ 12 is neither a local quantity (as the flow Q) nor an instantaneous quantity (as the density ρ), the above definition is incomplete. Denoting the times when a vehicle enters and leaves the considered section by t 1 and t 2 , respectively, we disambiguate the definition in two ways: The realized travel time τ 12 (t) is the time a vehicle needs to travel from x 1 to x 2 when it leaves the considered road section at time t: τ 12 (t 2) = t 2 − t 1 . (19.1)