K-means clustering is employed to identify recurrent delay patterns on a high traffic railway line north of Copenhagen, Denmark. The clusters identify behavioral patterns in the very large ("big data") datasets generated automatically and continuously by the railway signal system. The results reveal the conditions where corrective actions are necessary, showing the cases where recurrent delay patterns take place. Delay profiles and delay change profiles are generated from timestamps to compare different train runs and to partition the set of observations into groups of similar elements. K-means clustering can identify and discriminate different patterns affecting the same stations, which is otherwise difficult in previous approaches based on visual inspection. Classical methods of univariate analysis do not reveal these patterns. The demonstrated methodology is scalable and can be applied to any system of transport.

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.

This data article offers two reference simulation models for the evaluation of performance and delays of a suburban railway line. Further, a sample output dataset is provided for validation of the model, and the sample output dataset could be used independently if the reader desires. The simulation is programmed in the OpenTrack railway simulation software Nash et al., 2004 ([2]). The models are provided as a reference and tool for other researchers to validate and extend their studies in railway operations. These models were originally created for the research article “A Closed Form Railway Line Delay Propagation Model” Harrod et al., 2019 [1]. That article proposes an analytical estimation of railway delay, and these models were used to validate the findings.

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Realtidsforudsigelser af passagerefterspørgsel på jernbanen kan bidrage til smartere trafikstyring og på sigt til at udvikle et offentligt transportsystem som på forskellig vis imødekommer ekstraordinær efterspørgsel. Dette kræver adgang til detaljeret information om efterspørgselsmønstre i form af løbende indsamling af passagertal for hvert par af oprindelses- og destinationsstationer i korte tidsintervaller. I dette studie udvikles en machine learning model til forudsigelser af afvigelser fra det periodiske efterspørgselsmønster på Københavns S-bane i 15 minutters intervaller ved hjælp af realtidsdata fra Rejsekortet på efterspørgselssiden og Banedanmarks driftsstatistikker på udbudssiden. Studiet belyser dels betydningen af udbud for forudsigelse af efterspørgsel og dels udforskes måden hvorpå spatiotemporal data indlejres i modeller fra dyb læring for at opnå nøjagtige forudsigelser for mange-dimensionale og sparsomme data som disse.