component associated with fleet size, 𝐶 , is proportional to the value of time 𝜃; see the formula for
𝑣ℎ
𝜋 in Table 2 and its derivation in Appendix D. When 𝐶 is converted to hours by dividing by 𝜃
𝑚 𝑣ℎ
(see Eq. (11)), the impact of 𝜃 is mostly neutralized. In essence, since the relationship between the
value of time and agency cost rates is factored into the model, the generalized cost, as well as the optimal
system design, are only marginally influenced by city’s wealth level.
Figs. 7c and d display the optimal stop spacings under the two scenarios. As expected, the stop
spacing also decreases as the demand density increases and appears to be insensitive to the value of
time. In both scenarios, the optimal stop spacing varies in a rather wide range, highlighting the need
for heterogeneous stop spacing planning under the spatially heterogeneous demand.
(a) A low-wage city with 𝜃=5 $/h (b) A high-wage city with 𝜃=20 $/h
Fig. 6 Generalized cost versus bus capacity
(a) Feeder line spacings (b) Feeder headways (collection direction)
(c) Feeder stop spacings (km) in a low-wage city (d) Feeder stop spacings (km) in a high-wage city
Fig. 7 Optimal design variables under the terminal-centered demand
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