A Closed Form Railway Line Delay Propagation Model

Steven Harrod*, Fabrizio Cerreto, Otto Anker Nielsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Delays of railway services can be measured by the aggregate delay over a time horizon due to an event that delay a given train. Timetables for railway service may dampen aggregate delay by adding either supplement time or buffer time to the minimum driving time. The evaluation of these variables is often performed by time consuming numerical analysis with simulation tools and hence with some degree of stochasticity of the outcome. This paper proposes instead an analytical closed form formulation of aggregate delay with a polynomial form. The function returns the aggregate delay of a railway line resulting from an initial, primary, delay. This can be used to get theoretical insights into railway delays and as part of larger railway scheduling systems, where simulation models would require too much calculation time. Analysis of the function recommend a balance between the two remedial measures, supplement and buffer. Further, the effect of different threshold values in delay measurement is depicted, giving information valuable in the design of service contract. Numerical analysis of an example railway line shows that the polynomial function provides guidance and insight even when
theoretical assumptions are violated.
Original languageEnglish
JournalTransportation Research. Part C: Emerging Technologies
Pages (from-to)189-209
Publication statusPublished - 2019


  • Rail transportation
  • Train delays
  • Timetable robustness
  • Timetable design
  • Delay propagation

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