A Two-Stage Stochastic Optimization Model for Integrated Tram Timetable and Speed Control with Uncertain Dwell Times

Modern trams usually own passive transit signal priority (TSP) to avoid interruption from traffic signals along the route. The key to TSP depends on the strictly stick to the recommend travel time between intersections. However, the effectiveness of the TSP can be weakened by dwell time fluctuation due to uncertain passenger demand at the stations. This paper proposes a two-stage stochastic optimization model for timetable and tram control to improve the TSP reliability considering uncertain dwell times. The first stage of the study focuses on designing timetable alternatives, and the second stage evaluates the timetables through expected travel time and energy consumption under different dwell time disturbance scenarios. The Brute force algorithm is developed to attain the optimal tram control, while the non-dominated sorting genetic algorithm II (NSGA-II) and GUROBI solver are both adopted to optimize the timetables. A case study of Nanjing Tram Line 1 in China is performed to demonstrate the effectiveness of the proposed approach. The results show that compared to the existing method, the proposed method reduces energy consumption by 9.6% and the number of stops at intersections decreases by 26.3% with the same travel time