Integrated Model for Timetabling and Circulation Planning on an Urban Rail Transit Line: a Coupled Network-Based Flow Formulation

The recent development of advanced communication and data collection technologies enables a wide range of possibilities for systematic planning, operation, and control of urban rail transit systems in many megacities. While traditional methods consider tactical transit timetabling and operational circulation planning as two independent stages, this study aims to propose an optimization model and solution scheme to fully integrate these two supply-side stages in response to passenger demand dynamics. We first construct a new formulation through two coupled space-time network representations, namely, the transit space-time network and passenger space-time network, with many embedded constraints. In detail, the transit space-time network covers constraints involving train fleet size, deadheading and holding operations, headway requirements, and running and dwell times; meanwhile, the passenger space-time network is used to represent passenger traveling processes and the resulting trajectories. A coupled network-based flow optimization model is accordingly established to minimize passenger total travel time with a fixed train fleet size. To handle large-scale problem instances, we first adopt a constraint splitting technique to form two subsets of Lagrangian multipliers corresponding to individual passenger decision constraints and train capacity constraints. A dual decomposition scheme is then developed to iteratively coordinate the adjustment of Lagrangian multipliers and solve the related two subproblems. Specifically, the passenger subproblem is solved by a passenger loading algorithm, and the train subproblem is decomposed and solved by the alternating direction method of multipliers. The effectiveness of the proposed model and solution approach is evaluated on a real-world case study based on the Batong Line in the Beijing subway network.