Efficient models for timetable information in public transportation systems

Abstract

We consider two approaches that model timetable information in public transportation systems as shortest-path problems in weighted graphs. In the time-expanded approach, every event at a station, e.g., the departure of a train, is modeled as a node in the graph, while in the timedependent approach the graph contains only one node per station. Both approaches have been recently considered for (a simplified version of) the earliest arrival problem, but little is known about their relative performance. Thus far, there are only theoretical arguments in favor of the time-dependent approach. In this paper, we provide the first extensive experimental comparison of the two approaches. Using several real-world data sets, we evaluate the performance of the basic models and of several new extensions towards realistic modeling. Furthermore, new insights on solving bicriteria optimization problems in both models are presented. The time-expanded approach turns out to be more robust for modeling more complex scenarios, whereas the time-dependent approach shows a clearly better performance.

Fast Routing in Very Large Public Transportation Networks Using Transfer Patterns

“…), including the times of day at which they depart and arrive. For routing, it is represented as a graph, see [10] for a comparison of various graph models. We use a time-expanded graph with three kinds of nodes, each carries a time and belongs to a station.…”

“…. such that all trips on a line share the same sequence of stations, do not overtake each other (FIFO property, like the train routes in [10]), and have the same penalty score between any two stations.…”

Accessibility measures for robustness of the transport system

“…If the PT system is expressed in terms of a network, the calculation of the PT travel options is more or less the same as for PV options. As suggested by Pyrga et al (2008), timetable-based PT schedules can be represented as time-expanded networks, detailing the full link information of in-vehicle, waiting and transfer between different PT routes. Figure 2 presents an example of an s-t (O-D) trip via a PT network, including access and egress and PT travel (taken from Liao et al 2011), in which transfer and waiting occurs at the same PT stops between different PT routes.…”

Engineering Route Planning Algorithms

“…For example, users traveling by train may be willing to accept longer travel times if the number of required transfers is lower or the cost of a journey with longer duration is cheaper. We end up in a multi-criteria scenario [53,57,21] in which none of the high-performance approaches developed in the last years can be applied easily. The adaption of a fast method to this scenario is one of the main challenges in the near future.…”