Network periodic train timetabling with integrated stop planning and passenger routing: A periodic time–space network construct and ADMM algorithm

Document Type

Journal Article

Publication Date


Subject Area

place - asia, place - urban, mode - rail, mode, operations - scheduling, operations - capacity, planning - integration, planning - methods, planning - service quality, economics - pricing


ADMM, Passenger routing, Periodic train timetabling, Train stop planning


Designing a passenger-centric railway service is of great importance for railway companies to attract more passengers and increase their revenue. Focusing on the passenger-centric operational plans, this paper considers the problem of integrated periodic train timetabling and train stop planning in high speed railway networks. In view of the immediate dependency of passengers’ routes on the train timetable and stop plan, simultaneous passenger routing is included to directly shape the train stops and timetable in a passenger-friendly way. Besides travel time, ticket price is also considered in passenger utility to better depict passengers’ route choices in the railway network. A railway network-based time–space network with train stop-skip technique, periodic properties and detailed consideration of different train headways is designed, based on which a multi-commodity network flow model is developed. With a novel linearization technique of train capacity penalty term, the alternating direction method of multipliers (ADMM) is used to relax and decompose the track and train capacity constraints. Further, time deviation of regular train services is achieved by a new shortest path algorithm to design more flexible timetables, however its application is still limited to small instances due to computational efforts required. The algorithm is finally tested on the Shandong high-speed railway network in China, and demonstrates its capability of providing tighter lower bounds than Lagrangian relaxation method and generating good feasible solutions. Besides, the impacts of different cycle times on service quality and train cost are evaluated.


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


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