Table 1 Parameters of this paper...

Table 1

Parameters of this paper

Notations	Definition
$L$	total number of trains
$S$	total number of stations
$X$	total number of positions
$l$	train index, $l \in {1,2, \dots, L}$
$s$	station index, $s \in {1,2, \dots, S}$
$x$	position index, $x \in {1,2, \dots, X}$
$Γ$	current time instant
$x_{l + 1, Γ}^{E O A}$	position of end of Authority (EOA) for train $l + 1$ at time instant $Γ$
$v_{l + 1, Γ}^{E O A}$	speed of EOA for train $l + 1$ at time instant $Γ$
$x_{l, Γ}$	current position for train $l$ at time instant $Γ$
$x_{l + 1, Γ}$	current position for train $l + 1$ at time instant $Γ$
$v_{l, x}$	current speed for train $l$ at position $x$
$L_{s a f e}$	protection distance
$F (v)$	maximum traction force
$B (v)$	maximum braking force
$W_{0}$	basic resistance
$W_{1}$	additional resistance
$C_{l, x} (v)$	resultant force train $l$ at position $x$
$Δ x$	distance step
$a_{l, x}$	acceleration for train $l$ at position $x$
$a_{\max}$	maximum acceleration
$m$	train mass
$δ_{\max}$	maximum impact rate
$Δ Γ_{l, x - 1, x}$	time interval of train $l$ between distance step $(x - 1, x)$
${\tilde{v}}_{l, x}^{k}$	speed restriction value of train $l$ running to position point $x$ due to the influence of the kth TSR section
$Γ_{l, x}$	passing time for train $l$ at position $x$
$Γ_{s t a r t}$	start time of TTR-MTTO’s calculation
$Γ_{e n d}$	end time of TTR-MTTO’s calculation
$Γ_{l e f t}^{k}$	start time of the kth TSR section
$Γ_{r i g h t}^{k}$	end time of the kth TSR section
$x_{l e f t}^{k}$	start position of the kth TSR section
$x_{r i g h t}^{k}$	end position of the kth TSR section
$L_{t r a i n}$	train length
$L_{b l o c k}$	distance between the backward train and its nearest block section

Notations	Definition
$L$	total number of trains
$S$	total number of stations
$X$	total number of positions
$l$	train index, $l \in {1,2, \dots, L}$
$s$	station index, $s \in {1,2, \dots, S}$
$x$	position index, $x \in {1,2, \dots, X}$
$Γ$	current time instant
$x_{l + 1, Γ}^{E O A}$	position of end of Authority (EOA) for train $l + 1$ at time instant $Γ$
$v_{l + 1, Γ}^{E O A}$	speed of EOA for train $l + 1$ at time instant $Γ$
$x_{l, Γ}$	current position for train $l$ at time instant $Γ$
$x_{l + 1, Γ}$	current position for train $l + 1$ at time instant $Γ$
$v_{l, x}$	current speed for train $l$ at position $x$
$L_{s a f e}$	protection distance
$F (v)$	maximum traction force
$B (v)$	maximum braking force
$W_{0}$	basic resistance
$W_{1}$	additional resistance
$C_{l, x} (v)$	resultant force train $l$ at position $x$
$Δ x$	distance step
$a_{l, x}$	acceleration for train $l$ at position $x$
$a_{\max}$	maximum acceleration
$m$	train mass
$δ_{\max}$	maximum impact rate
$Δ Γ_{l, x - 1, x}$	time interval of train $l$ between distance step $(x - 1, x)$
${\tilde{v}}_{l, x}^{k}$	speed restriction value of train $l$ running to position point $x$ due to the influence of the kth TSR section
$Γ_{l, x}$	passing time for train $l$ at position $x$
$Γ_{s t a r t}$	start time of TTR-MTTO’s calculation
$Γ_{e n d}$	end time of TTR-MTTO’s calculation
$Γ_{l e f t}^{k}$	start time of the kth TSR section
$Γ_{r i g h t}^{k}$	end time of the kth TSR section
$x_{l e f t}^{k}$	start position of the kth TSR section
$x_{r i g h t}^{k}$	end position of the kth TSR section
$L_{t r a i n}$	train length
$L_{b l o c k}$	distance between the backward train and its nearest block section

Source(s): Authors own work

[ViewLarge]