Periodic Timetabling with Cyclic Order Constraints

Authors Enrico Bortoletto , Niels Lindner , Berenike Masing

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Author Details

Enrico Bortoletto
  • Zuse Institute Berlin, Germany
Niels Lindner
  • Freie Universität Berlin, Germany
Berenike Masing
  • Zuse Institute Berlin, Germany


We thank DB Netz AG for providing real-world data and timetabling parameters for the S-Bahn Berlin network.

Cite AsGet BibTex

Enrico Bortoletto, Niels Lindner, and Berenike Masing. Periodic Timetabling with Cyclic Order Constraints. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Periodic timetabling for highly utilized railway networks is a demanding challenge. We formulate an infrastructure-aware extension of the Periodic Event Scheduling Problem (PESP) by requiring that not only events, but also activities using the same infrastructure must be separated by a minimum headway time. This extended problem can be modeled as a mixed-integer program by adding constraints on the sum of periodic tensions along certain cycles, so that it shares some structural properties with standard PESP. We further refine this problem by fixing cyclic orders at each infrastructure element. Although the computational complexity remains unchanged, the mixed-integer programming model then becomes much smaller. Furthermore, we also discuss how to find a minimal subset of infrastructure elements whose cyclic order already prescribes the order for the remaining parts of the network, and how cyclic order information can be modeled in a mixed-integer programming context. In practice, we evaluate the impact of cyclic orders on a real-world instance on the S-Bahn Berlin network, which turns out to be computationally fruitful.

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Mathematics of computing → Permutations and combinations
  • Mathematics of computing → Combinatorial optimization
  • Periodic Timetabling
  • Railway Timetabling
  • Periodic Event Scheduling Problem
  • Cyclic Orders
  • Mixed-Integer Programming


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