Hybrid Scheduling Model Based on Fare Incentives for Peak Time Interval of the Metro: The Harbin Metro System

Abstract

Considering the operation efficiency of the metro system, the boarding queuing problem is a complex and intractable dilemma caused by the security and ticket checking process in urban metro stations, especially for the mass-transit metro system in China. In this study, a novel scheme of fare differentials based on demand control and congestion management for reducing congestion in the metro boarding process was proposed. In addition, we extended Vickrey’s point-queue model into a boarding congestion model incorporating the bidesired departure time considering the security and ticket checking process in stations as a continuum bottleneck. The train-run and departure time choosing behaviors of passengers under different schedule gaps of the adjacent train runs are explored when the boarding system achieves user equilibrium in the proposed model. Then, we examined the demand regulatory mechanisms of fare incentives (fare differentials) in reducing the queuing boarding time in metro stations when the optimization of the schedule gaps is ineffective in the pattern of mass-scale travel demand. The analytical solutions of these two optimal methods (schedule gaps and fare differentials) for boarding congestion management are presented. After comparing the two congestion-reduced methods, the fare incentive rule has a better regulation effect on the smoothing of travel demand. The results of the sensitivity analysis using numerical simulations reveal the regulatory mechanism of fare differentials in reducing the queuing time and increasing the incremental revenue. (1) The demand threshold is only related to the boarding capacity and schedule gaps (i.e., the greater the boarding capacity and schedule gaps, the greater the passenger capacity of the metro station). (2) The effect of fare incentives in reducing the boarding congestion is better if the lower fare is implemented in the later train runs. (3) A lower fare differential between two adjacent metro runs can be used to regulate the proportion of staggered passengers in the queuing line to reduce the crowd gathering in the metro station hall when travel demand is high, meanwhile, a higher fare differential between two adjacent metro shuttles can increase incremental revenue effectively. (4) The measure of fare differentials causes worse results in both the reduction of the queuing time and the increase of the incremental revenue when the metro travel demand is lower than the demand threshold. This conclusion is consistent with the pattern of reality and experience. Therefore, the definition and judgment conditions of demand thresholds, introduced in this study, can provide theoretical guidance when implementing fare incentive policies in aviation and metro networks.