Managing Peak-Hour Congestion in Urban Rail Transit with the Sub-Train Price Adjustment Strategy

In urban rail transit, adjusting fares to satisfy passenger flow requirements is a new method to relieve urban congestion. A bilevel model is proposed herein to solve the congestion problem for an urban rail line. The upper level of the model determines the discount factor to minimize the total number of passengers exceeding the full-load rate, and the lower level of the model determines the distribution of passengers on the line, in which the cost-minimizing behavior of each passenger is considered using the allocation method based on the probability of selection. To achieve a more realistic model, the range of acceptable train numbers for each passenger is considered. A simulated annealing algorithm is introduced to solve the bilevel model. Based on an example, we obtain the specific fare and passenger flow distribution of each train after fare adjustment. The results show that the objective function is reduced by 17.5%, the congested section is reduced by 9.1% when the full-load rate is 90% of the train loading capacity, and the passenger flow shifts to both ends of the peak period. Finally, relevant parameters are discussed.