Modelling the number and location of sidings on a single line railway

This article puts forward a model to determine the required number and position of sidings on a single track rail corridor. The sidings are positioned to minimise both the risk of delays and the delays caused by train conflicts, for a given cyclic train schedule. The key feature of the model is the allowance of variable train velocities and non-uniform departure times. A decomposition procedure, used to partition the mixed integer nonlinear program into easily solvable sub-models was found to converge quickly. Numerical results, using actual train schedules, indicate considerable savings in terms of both conflict delay and risk of delay when track sidings are positioned using the model. Simulations are used to demonstrate how the model can be used determine the required number of sidings given a pre-defined level of service.