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leads to a larger number of trains running in the sys-
tem, in order to eliminate completely the propagation
of the disturbance. There is a tradeoff between the
size of the time horizon of traffic prediction (bigger
time horizon meaning better quality) and the compu-
tational time. In fact, in a small time horizon the real-
time dispatching does not take into account conflict-
ing trains outside the time horizon. On the other hand,
a conflict arising far in the future may not be as rele-
vant as a closer conflict, since other unforeseen events
could still affect the further conflict, see (D’Ariano,
2008). In a small time horizon, the computational
time is smaller because datas are limited.
Usually the train dispatcher reschedules the in-
volved trains, depending on the known duration of
the disturbance. He bases his decisions on his own
knowledge, resolving a conflict at a time when it oc-
curs, and then manually rebuilds the timetable, with
a considerable waste of time and no certainty that its
decisions will lead to an optimal solution.
Building on the formalism given in (Dotoli et al.,
2013), we present a model that solves the reschedul-
ing problemforregionalpassenger transport networks
with stations of equal importance, where the CTC sys-
tem is installed. We formulate the problem as a Mixed
Integer Linear Programming Problem (MILP).
In the original model the new timetable after the
disturbance is obtained by minimizing train delays
in all the stations programmed in their path, while
considering constraints regarding travel times, stop
times at stations, safety standards and network capac-
ity. The model is applied to a limited time horizon
that is choosen by the analyst. In order to solve con-
flicts that may occur in the rescheduled timetable af-
ter the time horizon, an iterative heuristic algorithm is
applied. The heuristic algorithm solves a conflict at
the time when it occurs; priority is given to the train
with the highest traveling time, namely the longest
presence on the line. The computational time for
limited time horizons is of the order of seconds, but
the heuristic algorithm requires an elevated computa-
tional time that depends on the number of trains and
the complexity of the raiway line. The methodology
provides a decision support system to the train dis-
patcher that has to take decisions in order to restore
traffic and limit inefficiencies for passengers.
We adapt the previous methodology to regional
networks mainly made of single tracks and take into
account the constraints imposed by the railway infras-
tructure and the time constraints imposed by the ini-
tial schedule.
The revised model solves all conflicts that arise
along the railway line after the occurrence of the
disturbance; the heuristic algorithm is therefore no
longer applied. The rescheduled timetable is estab-
lished in a shorter time, then discomfort for passen-
gers is restricted and the quality of the transport ser-
vice is increased.
To show its effectiveness, we study the problem
in a particular section of a railway network located in
Southern Italy, see (FSE - Ferroviedel Sud Est, 2013).
The FSE network is constituted by single tracks with
few double track segments and in some stations only
one train can stop or pass through.
The paper is organized as follows. In Section 2 we
present the problem formalization. In Section 3 the
mathematical model for the resolution of the problem
is proposed. In section 4 we present the application
of the model to the case study of the FSE railway net-
work. Finally, Section 5 contains some concluding
remarks and suggestions for further research.
2 PROBLEM FORMALIZATION
2.1 Initial Scheduling
Definition 1 (Railway Network). A railway network
is defined by a set of segments on which trains runs.
Segment (b
i
): A segment b is a railway section
between two points. We define by B =
{b
1
, b
2
, . . . , b
B
} = {b
i
}
i∈[[1,B]]
the set of segments.
B denote the cardinality of the set B. The set of
segments is partitioned into the subset B
s
corre-
sponding to segments into a station, and B
c
corre-
sponding to the subset of rail connections outside
stations.
Track (v
j
): Let b be a segment ∈ B. We define by
V
b
= {v
b
1
, v
b
2
, . . . v
b
V
b
} = {v
b
j
}
j∈[[1,V
b
]]
the set of par-
allel tracks in b. The set of all tracks in the railway
network is denoted by V. V and V
b
denote respec-
tively the cardinality of V and V
b
for a given seg-
ment b. Given a track v ∈ V, we denote by b
v
its
corresponding segment.
Circulations in a railway network are defined by a
set of trains. Train’s path is made of an ordered set of
movements.
Definition 2 (Trains and Movements). We assume
that the train’s length is compatible with the length
of all tracks that compose the railway line. Trains are
thus defined as follows.
Train (t
k
): The set of trains using the railway
network is denoted as T = {t
1
,t
2
, . . . , t
T
} =
{t
k
}
k∈[[1,T]]
. T denotes the cardinality of T.
Train Direction (d
t
): Each train is defined by a di-
rection parameter expressing the position of its
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