Joint optimization of metro travel reservation and compartment capacity allocation for an overcrowded metro line

In some mega cities, metro lines often experience severe congestion during peak hours, posing serious operational risks. To alleviate passenger delay and address overcrowded conditions, this study proposes a novel model for metro travel reservation and carriage reserved capacity. The model comprises three components: off-station queuing restrictions, dynamic loading constraints, and carriage reserved capacity constraints. A particle swarm optimization algorithm is applied to allocate reservation quota by considering time-variant and location-dependent passenger demand and train supply. The paper applies the model to Nanjing Metro Line 3, using historical data to estimate passenger demand and compartment capacity, and evaluates its performance in four scenarios. The results demonstrate proposed approach efficiently obtains high-quality joint reservation plans, resulting in a notable reduction of approximately 20% in platform delay time and 50% in off-platform queuing time in suitable scenarios. The paper also discusses the implementation challenges and limitations, and provides recommendations for effective application.