Asymmetric demand oriented train service design with skip-stop tactics for a metro line

Metro lines usually provide equal service frequency for two running directions. This strategy yet cannot fit the asymmetric demand, where one direction carries far more passengers than the opposite direction. In this study, we propose a novel asymmetric strategy that combines the rolling stock pre-allocation and skip-stop tactics to rationalize the allocation of capacity in two directions, where a skip-stop tactic in the low-demand direction and optimal allocation of rolling stocks in two depots are incorporated to enhance the asymmetric strategy. A mixed integer linear programming (MILP) model is built to determine bidirectional service frequencies, stop patterns, train departure times, and rolling stock circulation, taking into account limited train capacity and passengers' first-come-first-served (FCFS) principle. The objective is to minimize the total passenger travel time and number of used train services. A heuristic algorithm based on iterated local search (ILS) and customized linear programming relaxation (LPR) method is proposed to solve the MILP model more efficiently. Additionally, we design a decomposition strategy to expedite the solution process. Numerical experiments and a large-scale case are performed to verify the effectiveness of the proposed method. Compared to the existing strategy, the asymmetric strategy can reduce the total passenger travel time by 5.24% without increasing the operating costs. Operating express trains reduces their circulation time and saves the usage of rolling stocks. Sensitivity analysis shows that it is more favorable to implement the asymmetric strategy when the directional imbalance coefficient exceeds 1.7 and the duration of peak-demand is less than 2 h.