Fig. 5 The specific feeder system layout
Table 3. Percentage errors in cost terms
Cost terms CA Specific plan Percentage error
𝐴𝐶, h 98.58 97.85 0.75%
𝐶 , h 85.96 85.38 0.68%
𝐴
𝐶 , h 254.80 254.05 0.30%
𝑊
𝐶 , h 125.33 123.29 1.65%
𝑇
𝑈𝐶, h 466.10 462.73 0.73%
𝐺𝐶, h 564.68 560.58 0.73%
4.3 Optimal feeder system designs without schedule coordination
We use the same terminal-centered demand pattern as described in Section 4.2 and analyze two
scenarios with distinct time values: 𝜃 = 5 $/h for a low-wage city and 𝜃 = 20 $/h for a high-wage
city.
First, we examine how the optimal generalized cost varies with bus capacity 𝐾 in the two
scenarios, as depicted in Figs. 6a–b. These figures reveal that the generalized cost is sensitive to 𝐾
when 𝐾 is small, but becomes less sensitive for larger 𝐾 values. The high-wage city exhibits lower
sensitivity since the agency cost is associated with a smaller weight. For the same reason, the high-wage
city favors a slightly smaller vehicle.9
Throughout the remainder of Section 4, we will focus on the optimal feeder designs using the
optimal 𝐾 obtained through exhaustive search.
Figs. 7a and b plot the optimal line spacings and collection-direction headways against the location
of lines (𝑥 ) under the two scenarios, respectively. In each scenario, the distributions of spatially-
heterogeneous line spacings and headways match the demand distribution (see Fig. 4); that is, greater
transit service frequencies and line densities are observed in areas with higher demand densities near
the terminal. The high-wage city features higher line densities and service frequencies, as patron costs
carry a larger weight. Nonetheless, the discrepancy between low- and high-wage cities remains
relatively small. This can be attributed to the fact that 90% of the agency cost, specifically the cost
Appendix C.
9 Actual values of 𝐾 depend on the available bus models on the market. In addition, the costs of different vehicles might
deviate from the unified cost functions derived in Appendix D. Thus, the optimal bus capacity discussed in this study should
be viewed as a guideline rather than a definitive solution. Transit agencies are advised to consider vehicles with a size
approximate to, but not necessarily equal to, the optimal 𝐾.
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