Reducing passengers’ travel time by optimising stopping patterns in a large-scale network: A case-study in the Copenhagen Region

Document Type

Journal Article

Publication Date


Subject Area

economics - benefits, economics - operating costs, mode - rail, operations - scheduling, place - europe, place - urban, ridership - demand


Public transport passengers’ behaviour, Stopping patterns, Public transport optimisation, Railway timetabling, Large-scale networks


Optimising stopping patterns in railway schedules is a cost-effective way to reduce passengers’ generalised travel costs without increasing train operators’ costs. The challenge consists in striking a balance between an increase in waiting time for passengers at skipped stations and a decrease in travel time for through-going passengers, with possible consequent changes in the passenger demand and route choices. This study presents the formulation of the skip-stop problem as a bi-level optimisation problem where the lower level is a schedule-based transit assignment model that delivers passengers’ route choices to the skip-stop optimisation model at the upper level, and where the upper level in return provides an improved timetable to the lower level. A heuristic method for large-scale urban networks is presented to solve this extremely complex bi-level problem, where the skip-stop optimisation is a mixed-integer problem, whereas the route choice model is a non-linear non-continuous mapping of the timetable. The method was tested on the suburban railway network in the Greater Copenhagen Region (Denmark): the reduction in railway passengers’ in-vehicle travel time was 5.5%, the reduction in passengers’ generalised travel cost was 3.2% and, at the system level, the yearly consumer surplus amounted at 76.7 million DKK (about 10.3 million EUR or 12.7 million USD) when compared to the existing stopping patterns.


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


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