Integrated Planning Model of Fixed-Route and Demand-Responsive Transit Services under Rail Feeder Perspective

To address the mismatch between supply and demand in conventional fixed-route bus services caused by significant peak and off-peak variations in rail feeder demand in residential areas, an integrated service planning model combining fixed-route and demand-responsive transit is developed. Taking the number of operating vehicles and service frequency as decision variables, a two-stage integrated service planning model is formulated to account for the differences in peak and off-peak passenger demand. During peak periods, the existing fixed-route bus service is maintained, with the generalized travel cost of bus relative to cycling introduced as a passenger satisfaction constraint, and vehicle allocation and service frequency optimized to minimize operating costs. During off-peak periods, demand-responsive transit is introduced without increasing the system fleet size, and surplus capacity is reallo cated between fixed-route and demand-responsive services. A demand allocation coefficient is introduced to represent the passenger demand split between the two service modes, and a bi-objective optimization model is formulated to minimize operating service costs and passengers' generalized travel time costs by jointly optimizing the capacity allocation and service frequency of the two service modes. A single-objective genetic algorithm (GA) and a bi-objec tive non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) are employed to solve the peak- and off-peak planning stages, respectively. An empirical study is conducted for the residential area surrounding Longchi Station of the Nanjing rail transit system. The results show that, during off-peak periods, compared with the pure fixed-route service mode, the benefit-optimal scheme of the integrated fixed-route and demand-responsive service mode increases vehicle utilization by 9.7%, while increasing per-capita operating cost by 2.13 CNY and reducing per-capita travel cost by 2.73 CNY. When the off-peak-to-peak passenger demand ratio α is no greater than 0.11 and the proportion β of passengers choosing fixed-route feeder services is less than 0.7, the integrated service mode achieves better overall benefits, demonstrating the effectiveness of the proposed model in improving resource utilization efficiency and service level of rail transit feeder bus systems.