Geoscience Reference
In-Depth Information
departure
departure. We need not introduce subscripts to denote the in-lines or out-
lines used by trains since for an arriving train i
—
the in-line is already speci
ed by I
i
,
and for a departing train i
the out-line is speci
ed by O
i
.
The preference coef
cient p
ik
may re
fl
ect:
operator
'
s preferences of platforms,
the distance of the track k to the connecting trains,
the length of the route used by train i arriving to or departing from platform
track k. The smoother and shorter the route is, the less the possibility of a
con
fl
ict with other
trains is, hence the probability of delay propagation
decreases.
In our model, coef
cient p
ik
is set according to the following formula:
8
<
:
1
if track k is the planned
ð
or desired) track for train i
0
9
if track k is located at the same platform as the planned track
:
p
ik
¼
otherwise
8
s
ma
i
s
ik
s
ma
i
s
min
i
0
:
Sets of objects
K
set of all platform tracks
K
ð
i
Þ
set of feasible platform tracks for train
i
U
set of all arriving, departing, and transit trains
W
ð
j
Þ
set of all connecting trains, which has to wait for train
j
V
aa
fði;
i
;
j
Þ
:
i
;
j
2
U
;
i
\
j
;
j
t
P
i
t
P
j
j
t
max
g
set of ordered pairs of those trains that may
arrive concurrently
V
ad
fði;
i
;
j
Þ
:
i
;
j
2
U
;
i
\
j
;
j
t
P
i
t
P
j
j
t
max
g
set of ordered pairs of those trains that arriving
train i and departing train j may travel concurrently
V
da
fði;
i
;
j
Þ
:
i
;
j
2
U
;
i
\
j
;
j
t
P
i
t
P
j
j
t
max
g
set of ordered pairs of those trains that departing
train i and arriving train j may travel concurrently
V
dd
fði;
i
;
j
Þ
:
i
;
j
2
U
;
i
\
j
;
j
t
P
i
t
P
j
j
t
max
g
set of ordered pairs of those trains that may
depart concurrently
Decision and Auxiliary Variables of the Model
1
if track k is assinged to train i
for i
;
j
2
U
;
k
2
K
ð
i
Þ
:
x
ik
¼
0
otherwise
u
i
difference between the planned and real arrival time of train i at a platform,
i
∈
U
v
i
difference between the planned and real departure time of train
i
from a
platform,
i
∈
U.
The following auxiliary variables
y
are introduced for the couple of those trains
i and j that may travel concurrently. They enable to express safety headways
between conflicting trains.
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