Integrated Models in Public Transport

Lately, integrated models for public transport planning have become increasingly popular, with plenty of new publications as a fruit of renewed research effort.

The idea is really quite intuitive: To arrive at a public transport system, several successive planning steps need to be considered. Where do we locate stops? How do we design lines, and with what frequency should they be used? What is a good timetable? How many vehicles will we need? And many more variations of such questions.

Usually, each planning problem is studied on its own. There are good reasons for doing so. Problems are already very hard to solve in this form, and will be tackled by different planning departments, each with different objectives.

But: Designing a line plan, for example, will have big impact on the quality of a subsequent timetable. To integrate several planning steps into an even more complex single step might therefore result in a much better overall solution than an iterative approach.

There are two papers I was involved with that went into this direction.

In “Evaluating line concepts using travel times and robustness“, we looked at the impact of line plans on later planning steps. To do so, we generated a large set of possible line plans (using LinTim), and went through the planning process with each of them. In the end, you can see which parameters of the line plan influence the later planning steps more, and which are less important. Such an analysis can be seen as a much easier alternative to solving an integrated problem, as you can condense the relevant parameters into the line planning step.

This is the abstract:

Line planning is an early step in the planning process in public transportation, usually followed by designing the timetable. The problems related to both steps are known to be NP-hard, and an integrated model finding a line plan and a timetable simultaneously seems out of scope from a computational point of view. However, the line plan influences also the quality of the timetable to be computed in the next planning step.

In this paper we analyze the impact of different line planning models by comparing not only typical characteristics of the line plans, but also their impact on timetables and their robustness against delays. To this end, we set up a simulation platform LinTim which enables us to compute a timetable for each line concept and to experimentally evaluate its performance under delays. Using the German railway intercity network, we evaluate the quality of different line plans from a line planning, a timetabling, and a delay management perspective.

In the second paper, “An experimental comparison of periodic timetabling models“, we looked at the problem of integrating a timetable with passenger routing. There is a kind of chicken-egg problem here, as passenger routes depend on the timetable, but to find a good timetable, we need to know passenger routes. Our approach was to use an iteration between both problems to find timetables that allowed much better travel times than with the usual method.

This is the abstract:

In the Periodic Timetabling Problem, vehicle arrivals and departures need to be scheduled over a periodically repeating time horizon. Its relevance and applicability have been demonstrated by several real-world implementations, including the Netherlands railways and the Berlin subway.

In this work, we consider the practical impact of two possible problem variations: firstly, how passenger paths are handled, and secondly, how line frequencies are included. In computational experiments on real-world and close-to real-world networks, we can show that passenger travel times can significantly benefit from extended models.