In rapidly sprawling urban areas and booming intercity express rail networks, efficiently designed feeder bus systems are more essential than ever to transport passengers to and from trunk-line rail terminals. When the feeder service region is sufficiently large, the spatial heterogeneity in demand distribution must be considered. This paper develops continuous approximation models for optimizing a heterogeneous fixed-route feeder network in a rectangular service region next to a rail terminal. Our work enhances previous studies by: (i) optimizing heterogeneous stop spacings along with line spacings and headways; (ii) accounting for passenger boarding and alighting numbers on bus dwell times and patron transfer delays at the rail terminal; and (iii) examining the advantages of asymmetric coordination between trunk and feeder schedules in both service directions. To tackle the increased modeling complexity, we introduce a semi-analytical method that combines analytically derived properties of the optimal solution with an iterative search algorithm. Local transit agencies can readily utilize this approach to design a real fixed-route feeder system. This paper reveals many findings and insights not previously reported. For instance, integrating the heterogeneous stop spacing optimization further reduces the system cost (by 4% under specific operating conditions). The cost savings increase with demand heterogeneity but decrease with the demand rate and service region size. Choosing the layout of feeder lines where buses pick up and drop off passengers along the service region's shorter side also significantly lowers the system cost (by 6% when the service region's aspect ratio is 1 to 2). Furthermore, coordinating trunk and feeder schedules in both service directions yields an additional cost saving of up to 20%.

30 pages, 9 Figures, 8 Tables