# Finding Robust Periodic Timetables by Integrating Delay Management

## TL;DR

This paper introduces a new mathematical model for creating robust periodic timetables that incorporate delay management, improving delay resistance in large-scale transit scheduling.

## Contribution

It extends the Periodic Event Scheduling Problem by integrating delay management, defining the Robust Periodic Timetabling problem, and proposing solution algorithms for its simplified versions.

## Key findings

- Algorithms produce timetables with better delay resistance
- Timetables are effective on large-scale datasets
- Low computational effort required

## Abstract

This paper defines and solves a mathematical model for finding robust periodic timetables by proposing an extension of the Periodic Event Scheduling Problem (PESP). In order to model delayed and not nominal travel times already in the timetabling step, we integrate delay management into the periodic timetabling problem. After revisiting both (PESP) and delay management individually, we introduce a periodic delay management model capable of evaluating periodic timetables with respect to delay resistance. Having introduced periodic delay management, we define the Robust Periodic Timetabling problem (RPT). Due to the high complexity of (RPT) we propose two different simplifications of the problem and introduce solution algorithms for both of them. These solution algorithms are tested against timetables found by standard procedures for periodic timetabling with respect to their delay-resistance. The computational results show that our algorithms yield timetables which can cope better with occurring delays, even on large-scale datasets and with low computational effort.