Geoscience Reference
In-Depth Information
Subscripts which in the mathematical model represent objects
i,
i
,
j
train
k, k
platform track
Input parameters (constants)
t Pa
i
planned arrival time of train i at the platform
t Pd
i
planned departure time of train i
t Cn
standard amount of time passengers take to change trains (depends
on particular railway station)
I i
arrival line track (in-line) for train i
O i
departure line track (out-line) for train i
c i
category of train i; ci i = 1 for regional stopping trains and increases
with the speed and distance travelled by the train. We have to divide
train into categories, because international fast express trains have
obviously higher importance than the regional ones. Delays of
international trains can commit more traf
c problems and extra costs
than delays of regional trains
min
t
minimum dwell time of a train at the platform
max
t
maximum time interval, in which two train movements are tested for
acon
fl
ict
p ik
preference coef
cient; it re
fl
ects the desirability of the assignment of
platform track k to train i
s ik
number of switches on the route of train i from the arrival line track
to platform track k and from platform track k to the departure line
track
s min
i
number of switches on the shortest train route in the station
s max
i
number of switches on the longest train route in the station
a(l, k,
l
, k
)
coef
cient, which has value true, if the route connecting line l
to
icts with the route connecting line l
platform track k con
fl
to platform
track k
; if there exists any route connecting line l
to track k and any
route connecting line l
such that these two routes do not
conflict, then a(l, k, l , k ) = false. If both trains use the same station
or line tracks (i.e. k = k
to track k
or
l = l
), then a(l, k,
l
, k
) = true. The
existence of route con
fl
icts can be identi
ed in advance from a
detailed map of the track layout.
We adopted the concept of con
fl
icting routes and con
fl
ict solving from Carey and
Carville [ 4 ]. If two trains are on con
icting routes we must ensure that there is at least
a required minimum headway (time interval) between them, for safety and signalling
reasons. For example, let h(i, k,
fl
) da be the minimum headway required between
train i departing from track k and the next train i
i
, k
. The superscripts
d and a denote departure and arrival, and the order of the superscripts indicates the
order of the trains, i.e., train i is followed by i
arriving at track k
) aa , h(i,
. Similarly we have h(i, k, i
, k
) ad and h(i, k,
) dd for combinations arrival
k,
i
, k
i
, k
arrival, arrival
departure,
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