Highlights•Two relative spatial position designs are analyzed in a hybrid transit system.•The optimal design problems are formulated based on continuous approximation.•Numerical experiments are performed to compare the optimal designs.•A discreet-event simulation model is developed to validate the analysis.

AbstractThis paper analyzes and compares two different relative spatial position (RSP) designs in an integrated e-hailing/fixed-route transit system: a zone-based design that operates e-hailing vehicles within a zone, and a line-based design that operates e-hailing vehicles along a fixed-route transit line and with a stable headway. To conduct a meaningful comparison, the optimal design problems for both systems are formulated using a same analytical framework based on the continuous approximation approach. A comprehensive numerical experiment is performed to compare various cost components corresponding to the optimal designs, and a discrete-event simulation model is developed to validate the analysis. The analytical and simulation results agree with each other well, with a discrepancy in the total system cost less than 5% in most test scenarios. These results also suggest that the line-based system consistently outperforms the zone-based system in terms of both agency and user costs, for all scenarios tested. Compared to the zone-based design, the line-based design features a sparser fixed-route network (resulting in larger stop spacing) but a higher dispatching frequency. It is concluded that the higher efficiency of the line-based design is likely derived from the strategy of operating e-hailing vehicles with a more regular route/headway structure and allowing ride-sharing.