Route Reconstruction from Traffic Flow via Representative Trajectories

Abstract

Understanding human mobility patterns is an important aspect of traffic analysis and urban planning. Trajectory data provide detailed views on specific routes, but typically do not capture all traffic. On the other hand, loop detectors built into the road network capture all traffic flow at specific locations, but provide no information on the individual routes. Given a set of loop-detector measurements as well as a (small) set of representative trajectories, our goal is to investigate how one can effectively combine these two partial data sources to create a more complete picture of the underlying mobility patterns. Specifically, we want to reconstruct a realistic set of routes from the loop-detector data, using the given trajectories as representatives of typical behavior.We model the loop-detector data as a network flow that needs to be covered by the reconstructed routes and we capture the realism of the routes via the strong Fréchet distance to the representative trajectories. We prove that several forms of the resulting algorithmic problem are NP-hard. Hence we explore heuristic approaches which decompose the flow well while following the representative trajectories to varying degrees. First of all, we propose an iterative Fréchet Routes (FR) heuristic which generates candidates routes which have bounded Fréchet distance to the representative trajectories. Second we describe a variant of multi-commodity min-cost flow (MCMCF) which is only loosely coupled to the trajectories. Lastly we also consider global min-cost flow (GMCF) which is essentially agnostic to the representative trajectories.We perform an extensive experimental evaluation of our two proposed approaches in comparison to the min-cost flow baseline, both on synthetic and on real-world trajectory data. To create a ground truth for our experiments, we extract the flow information from map-matched trajectories. We find that GMCF explains the flow best, but produces a large number of routes (significantly more than the ground truth); these routes are often nonsensical. Also MCMCF produces a large number of routes which explain the flow reasonably well, however, the routes are mostly realistic. In contrast, FR produces significantly (orders of magnitude) smaller sets of realistic routes which still explain the flow well, albeit at the cost of a higher running time.