To summarize, despite the extensive history of literature on fixed-route feeder service design, the
following research gaps have not yet been adequately addressed:
(i) The optimization of heterogeneous stop spacings has been largely neglected in the literature.
Most studies assume that the stop spacing is a constant or do not explicitly model stop locations
and bus dwell times. Kuah and Perl (1988) is the only work that optimized heterogeneous stop
spacings under heterogeneous demand, but their model also has its drawbacks, as discussed
earlier in this paper. Note that real-world stop spacings vary significantly; for example, Texas
Transportation Institute (1996) states that real-world stop spacings range from 200 m to 800 m.
And they substantially affect passengers’ access distances and in-vehicle travel times (Daganzo
and Ouyang, 2019). Therefore, stop spacings should be jointly optimized with line spacings
and headways in a heterogeneous manner.
(ii) Most studies assume constant dwell times and transfer times for feeder bus services,
oversimplifying the impact of passenger boarding and alighting on dwell times. Su and Fan
(2019) is the only exception, but it assumes uniform demand. Unlike rail transit, bus dwell time
mainly depends on the number of passengers getting on and off at a stop (Daganzo and Ouyang,
2019). Ignoring this relationship can render errors in estimating bus roundtrip times and in-
vehicle travel times for passengers. Particularly, when bus size is jointly optimized, employing
a fleet of smaller vehicles can result in lower operating costs, increased service frequencies,
and reduced travel times and roundtrip durations due to the fewer passengers each vehicle
carries. This trade-off and its impact on the overall system cost cannot be accurately
represented if the relationship between the number of boarding and alighting passengers and
the dwell times is not taken into account.
(iii) While previous studies (e.g., Sivakumaran et al., 2012; Kim and Schonfeld, 2014; Yang et al.,
2020) have investigated the advantages of coordinating schedules between trunk and feeder
services, their conclusions are hindered by modeling limitations. These works, for instance,
overlooked stop spacing and variable dwell times, assumed uniform line spacing and headway,
or generated suboptimal solutions. In addition, these studies only focused on coordination in
one direction (the patron collection direction), while the coordination effects in the patron
distribution direction were ignored. As we will see soon, schedule coordination in the patron
distribution direction provides a smaller yet noteworthy benefit. The overall benefit of schedule
coordination is significantly greater than previously predicted in the literature.
Besides, a simple but important question seems to be neglected in literature. Specifically, for a
rectangular or approximately rectangular feeder service region (which is often found in grid trunk-line
networks; see Chien and Schonfeld, 1997), which feeder line layout is more cost-effective: each line
making stops along the shorter side of the rectangle and traveling nonstop along the longer side, or vice
versa? In this paper, we will demonstrate that the difference between the two layout options is sizeable.
In summary, existing models lack the comprehensive nature required for accurately designing a
fixed-route feeder system and evaluating its cost-effectiveness. More inclusive models are essential for
assisting decision-makers to select the most suitable feeder network design for a trunk-line rail system.
Firstly, the models should reveal the full cost and benefit of fixed-route feeders, providing a sound basis
for comparing against alternative feeder modes, such as flex-route feeder, ride-hailing, and shared bikes.
Secondly, they need to offer detailed guidance on the optimal design of a fixed-route feeder network,
including line layout, stop locations, and service headways. To this end, we formulate more
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