Closed Form Expressions of Optimal Buffer Times between Scheduled Trains at Railway Bottlenecks

This paper presents an analytical approach for optimally allocating the buffer times between scheduled trains at railway bottlenecks based on a recently developed probabilistic delay propagation model. The design of the buffer times between consecutive trains in a timetable period is improved by minimizing the sum of weighted knock-on delays of the trains. Closed form expressions have been derived for the optimal buffer times by adopting a weighted exponential distribution model for primary delays. An application example reveals that the derived expressions of the optimal buffer times can be used in the design of railway timetables by incorporating the impact of primary delays and priority of trains.