Feeder bus service design under spatially heterogeneous demand
Li Zhen a, Weihua Gu a
c Department of Electrical Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China
Abstract
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%.
Keywords: feeder bus, bus network, heterogeneous demand, continuous approximation, schedule
coordination
1. Introduction
The global trend of urbanization has accelerated in recent decades (Mor et al., 2020), leading to the
growing urban sprawl and the emergence of new mega-cities (Yu et al., 2019). In response, fast and
efficient mass transit systems have been developed to accommodate the growing long-distance
commuting demands between suburbs and central urban areas, as well as between neighboring cities.
These transit lines often feature stations spaced several kilometers apart. One example is the Bay Area
Rapid Transit (BART) system, which connects dozens of small cities in the East Bay and San Francisco
Peninsula to the downtown areas of San Francisco and Oakland, with station spacings up to 8 km
(https://www.bart.gov/; https://www.google.com/maps). Other examples include the rising number of
satellite cities supported by China’s booming high-speed rail network (e.g., the city of Langfang,
situated 60 km from Beijing and only a 20-minute ride by high-speed train). A station on these commuter
rail lines serves a vast catchment area where most patrons live beyond walking distance from the rail
station, and the demand is unevenly distributed. Consequently, designing efficient feeder service
 Corresponding author. Email: weihua.gu@polyu.edu.hk
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