𝐻 (𝑥) Feeder bus headway in the patron-collection direction at location 𝑥 h
𝐼𝑝
𝐻 (𝑥) Feeder bus headway in the patron-distribution direction at location 𝑥 h
𝐼𝑑
𝐾 The patron-carrying capacity of a feeder bus patrons/vehicle
Cost terms and parameters (all cost terms are per hour of operations)
𝐴𝐶 Total agency cost h
𝑈𝐶 Total user cost h
𝐺𝐶 Generalized cost h
𝐶 Total access and egress time h
𝐴
𝐶 Total wait and transfer time h
𝑊
𝐶 Wait and transfer time in the collection direction h
𝑊𝑝
𝐶 Wait and transfer time in the distribution direction h
𝑊𝑑
𝐶 Total in-vehicle travel time h
𝑇
𝐶 In-vehicle travel time to overcome the distance h
𝑇1
𝐶 Patrons’ time loss due to bus deceleration, acceleration, door opening and h
𝑇2
closing
𝐶 Patrons’ time loss due to boarding and alighting behavior h
𝑇3
𝐶 Stop infrastructure cost h
𝑠
𝐶 Operating cost associated with bus-km traveled h
𝑣𝑘
𝐶 Operating cost related to bus fleet size h
𝑣ℎ
𝑉 Bus fleet size
ℎ
𝑉 Number of buses that are actively travelling between stops
ℎ1
𝑉 Number of buses needed due to deceleration, acceleration, door opening
ℎ2
and closing at stops
𝑉 Number of buses required for passenger boarding and alighting
ℎ3
𝜋 The amortized unit cost of feeder stop infrastructure per operation hour $/stop/h
𝑠
𝜋 The unit cost per bus-km traveled $/vehicle⋅km
𝑣
𝜋 The unit cost per bus hour $/vehicle⋅h
𝑚
Other parameters and variables
𝜆 (𝑥,𝑦) Demand density in the patron-collection direction at location (𝑥,𝑦) patrons/km2/h
𝑝
𝜆 (𝑥,𝑦) Demand density in the patron-distribution direction at location (𝑥,𝑦) patrons/km2/h
𝑑
Λ Total demand in the patron-collection direction patrons/h
𝑝
Λ Total demand in the patron-distribution direction patrons/h
𝑑
Λ ′ Total demand in the collection direction after removing walking patrons patrons/h
𝑝
Λ ′ Total demand in the distribution direction after removing walking patrons patrons/h
𝑑
𝜃 Value of time $/h
𝑊 Width of the service region km
𝐿 Length of the service region km
𝑣 Walking speed km/h
𝑊
𝑣 Feeder bus cruise speed km/h
𝐼
𝜏 Time loss per stop due to bus deceleration, acceleration, door opening and h/stop
0
closing
𝜏 Alighting time per patron h/patron
𝑎
25