Minimum time-dependent travel times with contraction hierarchies

Abstract

Time-dependent road networks are represented as weighted graphs, where the weight of an edge depends on the time one passes through that edge. This way, we can model periodic congestions during rush hour and similar effects. In this work we deal with the special case where edge weights are time-dependent travel times. Namely, we consider two problems in this setting: Earliest arrival queries ask for a minimum travel time route for a start and a destination depending on a given departure time. Travel time profile queries ask for the travel time profile for a start, a destination, and an interval of possible departure times. For an instance representing the German road network, for example, we can answer earliest arrival queries in less than 1.5ms. For travel time profile queries, which are much harder to answer, we need less than 40ms if the interval of possible departure times has a width of 24 hours. For inexact travel time profiles with an allowed error of about 1% this even reduces to 3.2ms. The underlying hierarchical representations of the road network, which are variants of a time-dependent contraction hierarchy (TCH), need less than 1GiB of space and can be generated in about 30 minutes. As far as we know, TCHs are currently the only method being able to answer travel time profile queries efficiently. Altogether, with TCHs, web servers with massive request traffic are able to provide fast time-dependent earliest arrival route planning and computation of travel time profiles.