Integrating short-turning strategy into timetabling for first train coordination in subway networks

Ensuring connectivity in extended and continuously growing subway networks during the early morning start-up period becomes more and more challenging due to the limited number of trains and increasing infrastructure restrictions. In the present paper, train coordination strategies to maximize the connectivity of all origin-destination (OD) pairs and their effectiveness are investigated. An integrated mixed-integer nonlinear programming model is developed to simultaneously optimize short-turning plans and first train timetables. The model takes into account travel path choices between OD pairs and the impact of short-turning trains on ride plans. As the number of potential short-turning plans grows exponentially, computing an optimal solution incorporating all possible timetable schemes will be nearly impossible. As a result, a hierarchical two-stage optimization framework is developed to improve train short-turning and timetable coordination, which combines a breadth-first branch-and-cut algorithm for generating short-turning plans with a customized column generation algorithm for determining optimal train timetable coordination. To investigate the influence of network structure on coordination, we conducted two case studies with distinct network characteristics: Munich (shared-corridor network) and Beijing (grid network). The experimental results show that the proposed short-turning strategy effectively improves operational efficiency in both networks. Furthermore, comprehensive comparisons of solution accuracy and computational time demonstrate that our algorithm outperforms several commonly-used heuristic algorithms. Moreover, compared to the exhaustive enumeration benchmark, our algorithm sacrifices only 0.22% of solution accuracy while saving 55.26% of CPU time in the tested network. In particular, in Munich, affected passengers are roughly evenly divided between adapting by adjusting their travel paths and switching to alternative shared-corridor services. In contrast, in Beijing’s grid network, passengers can only detour their travel paths due to the lack of substitute services. These findings highlight that while short-turning operations facilitate faster transfers and reduce overall travel time, the impacts of short turnings on travel efficiency strongly depend on the underlying network structure. In conclusion, integration of short-turning and timetabling can effectively improve first train coordination in subway networks.