Efficient Computation of Multi-Modal Public Transit Traffic Assignments using ULTRA

Abstract

We study the problem of computing public transit traffic assignments in a multi-modal setting: Given a public transit timetable, an additional unrestricted transfer mode (in our case walking), and a set of origin-destination pairs, we aim to compute the utilization of every vehicle in the network. While it has been shown that considering unrestricted transfers can significantly improve journeys, computing such journeys efficiently remains algorithmically challenging. Since traffic assignments require the computation of millions of shortest paths, using a multi-modal network has previously not been feasible. A recently proposed approach (ULTRA) enables efficient algorithms with UnLimited TRAnsfers at the cost of a short preprocessing phase. In this work we combine the ULTRA approach with a state-of-the-art assignment algorithm, making multi-modal assignments practical. Careful algorithm engineering results in a new public transit traffic assignment algorithm that even outperforms the algorithm it builds upon, while enabling unlimited walking which has not been considered previously. We conclude our work with an extensive evaluation of the algorithm, showing its versatility and efficiency. On our real world instance, the algorithm computes over 15 million unique journeys in less than 17 seconds.Figure 1: Utilization of public transit vehicles between 8:30 a.m. and 9:00 a.m. in the Stuttgart area (Germany), as computed by our assignment algorithm. Vehicles used by only a few passengers are depicted using thin, green lines. As vehicles are used by more passengers, their line is gradually drawn thicker and their color changes to red. The transfer graph is depicted in gray.