Fairness-oriented train service design for urban rail transit cross-line operation

With the network operation in urban rail transit (URT), accessibility to the URT network increases markedly, leading to a growing transfer demand. As the URT system resource is equivalent to a bottleneck resource, it needs to be fairly allocated to transfer passengers (TP) and direct passengers (DP). Most existing studies focus on single line operation optimization but ignore the transfer demands of TPs. Cross-line operation (CO) has been verified as an efficient way to improve TP travel efficiency. This study focuses on the issue of passenger travel fairness with CO in the URT system. The concept of passenger effective travel time (ET) and ineffective travel time (IET) are proposed first. Based on the concept of α-fairness, the fairness of different classes of passengers was calculated through IET and ET. A mathematical model with decision variables of the turn-back station for CO and train frequency was constructed by analyzing the travel characteristics of passengers in two types of intersecting URT lines (“Y/T”-type and “X”-type) to minimize the passenger IET cost, fairness, and operation cost. Finally, the Changping Line and Line 8 in the Beijing URT system were considered as examples to verify the effectiveness of the proposed approach. The results indicate that from an overall perspective, CO can improve passenger travel fairness without increasing the IET cost for all passengers. Furthermore, considering the fairness of passenger travel may increase the operation costs. Study results contribute to a more fair URT system.