Table 1. Notations and definitions...

Table 1.

Notations and definitions

Notation	Definition
Sets
L	Set of lines indexed by l, with two directions: up (u) and down (d) direction, l ∈ L
S	Set of stations indexed by s
W	Set of OD pairs with \|Ω_o_,_d\| = 1 and no transfer process, indexed by $w$
D_l	Set of line directions of line l, l ∈ L, D_l ∈{l^u, l^d}
H	Set of trains indexed by h
P	Set of passengers indexed by p
P_o_,_d	Set of passengers on the OD pair (o, d ), (o, d ) ∈ W
Parameters
l_o_,_d	The line of feasible route on the OD pair (o, d ), (o, d ) ∈ W
dl_o_,_d	Direction of l_o_,_d, $d l_{o, d} \in D_{l_{o, d}}$
hw_o_,_d	Headway of line l_o_,_d in direction dl_o_,_d
$t_{a c, o}^{z}$	Tap-in timestamp at origin station o of passenger z, z ∈ P_o_,_d
$t_{e g, d}^{z}$	Tap-out timestamp at destination station d of passenger z, z ∈ P_o_,_d
$t t_{o, d}^{z}$	Travel time of passenger z on OD pair (o, d), z ∈ P_o_,_d, (o, d) ∈ W, $t t_{o, d}^{z} = t_{e g, d}^{z} - t_{a c, o}^{z}$
$t t_{o, d}^{\min}$	The minimum travel time on OD pair (o, d), (o, d) ∈ W
$w t_{o, d}^{z}$	Waiting time of passenger z at origin station o in line direction dl_o_,_d, z ∈ P_o_,_d, o ∈ S
WT_o_,_d	The set of $w t_{o, d}^{z}$ ⁠, $W T_{o, d} = \cup (w t_{o, d}^{z} \| z \in P_{o, d})$
Estimation variables
k_o_,_d	The maximum number of trains that passengers need to wait for at origin station o in direction dl_o_,_d, o ∈ S
µ_o_,_d/σ_o_,_d/ω_o_,_d	Estimated mean/standard deviation/weight of waiting time of passengers who boarding ith train at origin station o in direction dl_o_,_d, o ∈ S

Notation	Definition
Sets
L	Set of lines indexed by l, with two directions: up (u) and down (d) direction, l ∈ L
S	Set of stations indexed by s
W	Set of OD pairs with \|Ω_o_,_d\| = 1 and no transfer process, indexed by $w$
D_l	Set of line directions of line l, l ∈ L, D_l ∈{l^u, l^d}
H	Set of trains indexed by h
P	Set of passengers indexed by p
P_o_,_d	Set of passengers on the OD pair (o, d ), (o, d ) ∈ W
Parameters
l_o_,_d	The line of feasible route on the OD pair (o, d ), (o, d ) ∈ W
dl_o_,_d	Direction of l_o_,_d, $d l_{o, d} \in D_{l_{o, d}}$
hw_o_,_d	Headway of line l_o_,_d in direction dl_o_,_d
$t_{a c, o}^{z}$	Tap-in timestamp at origin station o of passenger z, z ∈ P_o_,_d
$t_{e g, d}^{z}$	Tap-out timestamp at destination station d of passenger z, z ∈ P_o_,_d
$t t_{o, d}^{z}$	Travel time of passenger z on OD pair (o, d), z ∈ P_o_,_d, (o, d) ∈ W, $t t_{o, d}^{z} = t_{e g, d}^{z} - t_{a c, o}^{z}$
$t t_{o, d}^{\min}$	The minimum travel time on OD pair (o, d), (o, d) ∈ W
$w t_{o, d}^{z}$	Waiting time of passenger z at origin station o in line direction dl_o_,_d, z ∈ P_o_,_d, o ∈ S
WT_o_,_d	The set of $w t_{o, d}^{z}$ , $W T_{o, d} = \cup (w t_{o, d}^{z} \| z \in P_{o, d})$
Estimation variables
k_o_,_d	The maximum number of trains that passengers need to wait for at origin station o in direction dl_o_,_d, o ∈ S
µ_o_,_d/σ_o_,_d/ω_o_,_d	Estimated mean/standard deviation/weight of waiting time of passengers who boarding ith train at origin station o in direction dl_o_,_d, o ∈ S

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