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School of Engineering

Evaluation of timetables and schedules from the perspective of operators and customers

Due to increasing automation and rising capacity utilisation in public transport as well as in air transport, the optimal design of timetables and flight schedules is becoming more and more important.

The design of timetables/flight plans plays an important role for both public and air transport. The creation of a timetable / a flight plan is embedded in a comprehensive planning process. For public transport, this includes, among other things, line planning and the planning of the rolling stock required.

But when is a timetable considered "good"? A timetable must meet certain requirements from the point of view of both customers and operators. For example, customers want short travel times, few transfers, high punctuality, and high frequencies. For operators, a timetable must, among other things, have a high degree of stability so that in case of disruptions, the subsequent delays are as short as possible and the effects on the overall operation are minimal. Furthermore, a high utilisation of the infrastructure capacities should be made possible, while at the same time keeping the costs for handling the transport services low.

As part of several projects with SBB AG (see, for example, here and here) and Swiss International Air Lines, methods were developed to evaluate timetables and flight schedules from both the operator's and the customer's point of view and, if necessary, to propose concrete measures for their optimisation. In the following, we concentrate on the topic of timetable stability. Detailed explanations can be found in the publications listed at the end.

Figure 1: Example of a so-called recovery matrix for a simple system with 76 timetable events (departure or arrival). If a timetable is to be stable, one of the requirements must be that between all incoming events (on the y-axis) to all outgoing events (on the x-axis) the buffer is greater than or equal to zero. Each cell in the matrix shown represents the buffer between two events. In this example, the above requirement (≥ 0) is fulfilled for all combinations. The colour code represents the buffer between the events in minutes.

The stability of a timetable is reflected in its robustness to disruptions. A distinction is made between planned (e.g., construction sites) and unplanned disruptions. Unplanned disruptions include, for example, a delayed departure at a station or a reduced travel speed on the route due to poor weather conditions.

A timetable must therefore be able to deal with disruptions of the system as good as possible, i.e., it needs to have appropriate buffers. The larger a potential disruption, the more buffers would have to be available. However, since larger buffers reduce the capacities of the infrastructure and hence are not desirable, it is important to find the best possible compromise during planning. If, for example, it is recognised that a timetable has too little buffers, measures such as the cancellation of planned connections at interchange stations or the adjustment of the preceding line concept may become necessary.

From the customer's point of view, a robust timetable means that even in case of disruptions (up to a certain extent), the connections can be maintained and thus the journey can take place as planned.

Figure 2: For the same system as in figure 1, for each event, its influence on all other timetable events was determined in case of a disruption (here this case: three minutes). The colour code is defined as follows: light: a disruption of this event has only a minor influence on the system, i.e., it is not critical; dark: a disruption of the event has a very large influence on the system and appropriate measures must be examined to reduce this influence.

To evaluate timetables and flight plans regarding stability and other criteria, the so-called Max-Plus-Algebra forms the central methodological framework in our projects. The application of the mathematical procedures available through this allows for an efficient evaluation of plans and provides several useful figures and concrete optimisation options.

In contrast, a timetable can be evaluated from the customer's point of view, for example by calculating the travel times between all relevant origins and destinations, aggregating them, and comparing them for different scenarios.

Within the framework of the above-mentioned projects, these methods were implemented prototypically as software tools and successfully applied and tested in real-world case studies.

Publications