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Probabilistic Safety Analysis of High Speed and Conventional Railway Lines

that the driver does nothing, “alert” means that the driver makes correct decisions, that is,
without error, and, finally, “attentive” implies normally a correct decision but some errors with
a very small probability.

Figure 1 Illustration of the Markovian model used to model the driver’s attention.
Therefore, the changes of driver’s attention state due to the different line incidences; as well
as how erroneous decisions are corrected by the supervisor systems must be modeled.
Since travel times of the different trains circulating along the network or line could be very
different and it is not the same a delay of five minutes in a one hour trip than in a three
hours trip, we use in our model relative travel times. The relative travel time is defined as
the quotient between the actual travel time and the minimum possible travel time, that is,
at maximum speed. This means that a relative travel time 1 means that the train travels at
maximum speed, and a relative travel time of 1.10 menas that the travel time is 10 % above
the minimum travel time. In this way we can combine trains with small and large travel times
and also freight trains. In addition a train priority is considered as a factor to be applied to the
relative travel time of each train.

2.1.4 Bayesian Network

A Bayesian network consists of two elements:

1. A directed acyclic graph, which includes one node per variable and links which determine
from which variables (nodes) each variable directly depends on.
2. Tables of conditional probabilities of each variable given its parents, which quantifies
the dependence relations among the variables.

This allow us to reproduce any joint multidimensional probability distribution without any
restriction, so that we can model any set of multidimensional variables.

To simplify the Bayesian network building process, it can be divided in parts, each part
corresponds to one item or element with its variables and links or to the segment between
consecutive items and its variables and links. Figure 2 illustrates how these different parts are
assembled in order to obtain the whole Bayesian network from the parts. It contains the real

International Congress on High-speed Rail: Technologies and Long Term Impacts - Ciudad Real (Spain) - 25th anniversary Madrid-Sevilla corridor 133