A closed form railway line delay propagation model

Document Type

Journal Article

Publication Date


Subject Area

mode - rail, operations - scheduling, planning - service quality


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


Railway service quality can be measured by the aggregate delay over a time horizon due to an event that delays a given train. Timetables for railway services may dampen delay propagations to subsequent trains by adding either supplement time or buffer time to the timetable. The evaluation of these variables is often performed by time consuming analysis with simulation software, or other complex, time-consuming calculations. This paper proposes instead an analytical closed form formulation of aggregate delay, which offers theoretical insights into railway delays and managerial insight into the properties of timetables at an aggregate level, and which may function as a fast sub-algorithm for timetable evaluations in larger optimization and transport models. Analysis of the function recommends a restraint in the utilization of timetable supplement and buffer, as their delay-damping effect decreases with their magnitude. Further, the effect of different threshold values in delay measurement is demonstrated, giving information valuable to the design of service contracts. Numerical analysis of a common suburban railway line shows that the polynomial function provides guidance and insight even when theoretical assumptions are violated.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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