An Integrated Model of Train Timetable and Speed Profile for Single Bi-directional Track

Abstract

In this paper, we consider the integrated model of train timetable and speed profile for a single bi-directional track. This problem aims to schedule train passes along single track from opposite directions to avoid conflicts. It is assumed that there are different types of stations along the track, and trains can only pass each other simultaneously at stations that have sidings. Focusing on the operation scenario, we propose an integrated model of train timetable and speed profile optimization. To address the nonlinear constraints generated by the meeting conflicts in the single bi-directional operation, the Big-M method is used to transform the constraints into linear constraints incorporating binary integer variables such as meeting and train priority. Thus, a mixed integer linear programming (MILP) model is constructed, which can be solved using the Gurobi solver. The model is formulated with two objective functions: one aims to minimize the time deviation of trains running in pairs considering passenger satisfaction, and the other is to minimize the total train travel time. The proposed model is applied to solve the problem based on a single-line urban railway and the feasibility of the model is verified. The results show that the total train travel time is effectively reduced by 29.8%.