Collaborative train timetabling and passenger flow control in oversaturated metro lines considering state-dependence

Abstract

Congestion downgrades the moving speed of passengers in trains and platforms. This in turn affects congestion. That is, the moving speed of passengers interacts with congestion. It is state-dependent and obeys the fundamental diagram. This interaction makes the system unstable and can result in substantial passenger delays and heightened security risks in oversaturated metro lines. This study aims to rectify this by developing a more realistic collaborative optimization approach. Firstly, we formulate a deterministic fluid queuing network model to accurately capture the dynamic propagation of congestion in oversaturated metro lines. This model incorporates the fundamental diagram, thereby effectively considering the interaction between passenger movement speeds and congestion. A recursive algorithm is devised to solve the fluid queuing network model. The complexity of the algorithm is independent of the capacities of the stations and trains. This provides the possibility of analyzing large-scale metro networks. Based on the queuing network model, a mixed-integer nonlinear programming model aimed at minimizing the total passenger waiting time is built. To solve the model effectively, we employ an alternating direction method of multipliers framework to decompose the model into nonlinear programming and integer nonlinear programming problems, which are respectively solved by improved simultaneous perturbation stochastic approximation and adaptive large neighborhood search algorithms. Finally, a small-scale case and a real-world case with data from Chengdu metro lines are implemented to demonstrate the performance and effectiveness of the proposed approach. The experimental results provide some interesting insights. (1) Without consideration of state-dependence, the queuing model underestimates the passenger waiting time and overestimates the service levels. (2) As demand increases, excluding extreme oversaturation scenarios, the optimized results of the state-independent model progressively deteriorate compared to our state-dependent model, with the largest percentage decline being 50.23%. This is especially noticeable when the train capacity is limited. (3) The contribution ratio of passenger flow control in mitigating congestion gradually surpasses that of train timetabling with increasing demand. In the small-scale case, the former contribution ratio to optimization rises from negligible to 98.19%.