  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%.
