  This study examines the route design of a semi-on-demand hybrid route
directional service in the public transit network, offering on-demand flexible
route service in low-density areas and fixed route service in higher-density
areas with Shared Autonomous Mobility Service (SAMS). The study develops
analytically tractable cost expressions that capture access, waiting, and
riding costs for users, and distance-based operating and time-based vehicle
costs for operators. Two formulations are presented for strategic and tactical
decisions in flexible route portion, fleet size, headway, and vehicle size
optimization, enabling the determination of route types between fixed, hybrid,
and flexible routes based on demand, cost, and operational parameters. The
practical applications and benefits of semi-on-demand feeders are demonstrated
with numerical examples and a large-scale case study in the Chicago
metropolitan area. Findings reveal scenarios in which flexible route portions
serving passengers located further away reduce total costs, particularly user
costs. Lower operating costs in lower-demand areas favor more flexible routes,
whereas higher demand densities favor more traditional line-based operations.
On two studied lines, a current cost forecast favors smaller vehicles with
flexible routes, but operating constraints and higher operating costs would
favor bigger vehicles with hybrid routes. The study provides an analytical tool
to design SAMS as directional services and transit feeders, and tractable
continuous approximation formulations for future research in transit network
design.
