Hazard-Based Model for Estimation of Congestion Duration in Urban Rail Transit Considering Loss Minimization

Because there is a conflict between promoting the level of service and saving operation resources in passenger flow congestion management for urban rail transit (URT), the congestion duration forecast has become an important decision-support element for management optimization. This paper presents a hazard-based duration model for the purpose of accurate duration forecasting considering loss minimization for decision making. The congestion duration was modeled with a hazard-based approach and revised by a strategy imitating the Bayesian minimum risk rule. Six hundred twenty-seven congestion instances during 470 days from Metro Line 2 of Nanjing, China, were divided into a training data set and a testing data set and were used for model implementation and performance evaluation. The model estimation results indicate that the log-logistic distribution produces the best fit for congestion during weekdays according to the Akaike information criterion, and the accuracy of the duration model is high according to the mean absolute percentage error. The model was also confirmed to be stable over time in the two data sets. In addition, the contrast of losses for the median forecast and the revisionary forecast based on numerical examples in the data set shows that the forecast revising strategy realizes a considerable relative decrease in the loss caused by the randomness of duration. The results of this study are useful for URT congestion management and provide a demonstration of a revising method to reduce economic loss resulting from forecast deviation.