A subjective capacity evaluation model for single-track railway system with δ-balanced traffic and λ-tolerance level

•The concepts of a δ-balance degree and a λ-tolerance level are introduced to reflect the subjective measure of the railway administrator for capacity evaluation.•A train balance scheduling problem with initial departure time choice of trains is embedded into the measure of railway capacity.•A highly efficient heuristic procedure based on the concept of compaction distribution is developed to solve the train balance scheduling problem.•The two-way traffic loading capacity of a single-track railway corridor is analyzed in detail under different tolerance levels and balance degrees.•The transition regions of traffic loading capacity are identified.

In this paper, we propose a method to measure the capacity of single-track railway corridors subject to a given degree of balance between the two directional traffic loads and a permitted overall delay level. We introduce the concepts of δ-balance degree and λ-tolerance level to reflect the subjective measures of the railway administrator for capacity evaluation. A train balance scheduling problem with initial departure time choice of trains is embedded into the measure of railway capacity. The combined scheduling and capacity evaluation method is formulated as a 0-1 mixed integer programming model, and solved using a simple dichotomization-based heuristic method. A highly efficient heuristic procedure based on the concept of compaction pattern is developed to solve the train balance scheduling problem, and the numerical results demonstrate that the method yields high-quality solutions close to the optimal ones using the CPLEX solver. The two-way traffic loading capacity of a single-track railway corridor is analyzed in detail under different tolerance levels and balance degrees. The transition regions of traffic loading capacity are identified, and provide a useful decision support tool for the railway administrators in dealing with train rescheduling requests under disturbance or disruption scenarios.