with optimized uniform stop spacing, and the savings could be over 10% when contrasted with previous
studies that only optimized line spacings and headways. Additionally, our model that integrates schedule
coordination reveals greater benefits (cost savings up to 20%) when trunk and feeder services are
coordinated in both feeder travel directions, potentially surpassing the combined savings of
coordination in each individual direction. This suggests that trunk and feeder schedules should be
coordinated in both service directions whenever feasible.
Other important findings and their practical implications are summarized as follows:
(i) The benefit of the heterogeneous design largely depends on the demand’s spatial pattern.
Greater benefits were observed for more heterogeneous demand and when the spatial
concentration of demand shifted away from the rail terminal. Higher demand rates and larger
service region sizes tend to reduce the benefit.
(ii) Compared to homogeneous or partially-homogeneous feeder network designs, an optimal
heterogeneous feeder network uses smaller buses. This is because the heterogeneous design
better accommodates heterogeneous demand, resulting in more evenly distributed passenger
loading across lines and vehicles.
(iii) Feeder lines should be designed to enable buses to travel along the shorter side of the service
region for pick-up and drop-off, while traveling nonstop along the longer side to the rail station.
Selecting the appropriate layout can further reduce system costs by 6% or more, depending on
the service region’s shape.
(iv) Our models and algorithms (including the algorithm for generating a specific feeder system
design) can be readily used by local transit agencies to design a fixed-route feeder network
within a rectangular service region. The generated plan can be fine-tuned to align with the local
street network.
Our models can be moderately adapted to include currently overlooked minor cost items, such as
those related to bus deadheading trips, layover times, and environmental impacts (Cheng et al., 2016).
Additionally, we are currently exploring the comparison between the optimal fixed-route feeder system
and alternative trunk-line access modes, including shared bikes, modular vehicles, ride-hailing, and
flex-route feeders. Built upon our models, we aim to further optimize a heterogeneous trunk-and-feeder
transit network that serves a city-wide demand. This research direction is also under investigation.
Acknowledgments:
This study is supported by a General Research Fund (Project No. 15224818) provided by the Research
Grants Council of Hong Kong.
Appendix A. Table of notations
Table A1. List of notations
Notation Description Unit
Decision variables
𝐵(𝑥,𝑦) Stop spacing at location (𝑥,𝑦) km
𝑆(𝑥) Line spacing at location 𝑥 km
𝐼
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