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Fig. 3. Evaluating criticality at test points in a scenario with parameters
v
diff
(speed difference to cars on the right lane, [km/h]) and
dist
(gap size, [m]).
- Further simulation refines the approximation in areas of interest (e.g., in
regions with high function values) by selecting input values accordingly.
Via such a guided simulation, maxima (or minima) of the property function
can be detected with far less simulation runs than by brute force. We have
instantiated this approach for our application scenario, where indeed the main
factors determining the course a simulation run takes are the parameters of
the trac scenario to be explored and the decisions the driver model takes in
reaction to the scenario. We will not describe here the adaptations necessary
to cope with the nondeterminism occurring in practice, which results from,
e.g., race conditions.
Results of an exploration where we applied Monte-Carlo simulation at
each test point are depicted in Fig. 3. The property used is defined by the
formula (4) from Sec. 3. It yields negative values for critical runs, so we
seek minima of this function. We considered variations of the attributes
v
diff
[
,
where
dist
denotes the size of the gap
size on the right lane of the expressway to be used by the ego car, and
v
diff
is the speed difference to the cars on the right lane at the point in time
when the ego car enters the acceleration lane. Each combination of values of
these attributes yields a test point, and
km
/h
]
, dist
[
m
]
∈{
20
,
30
,
40
}
simulation runs were performed
for each point. Entries in the result matrix are the numbers of
unacceptable
and
severely critical
runs, defined by formula values below -10 or in [-10,-2],
respectively. For instance, we get
20
6
unacceptable and
10
severely critical runs
for the test point
v
diff
=40
m.
These rather high critical-
ities have their reason in the fact that, with these parameters, the scenario is
very demanding and that the driver model we used was not yet fully adapted
to the scenario. The right part of Fig. 3 shows how the criticality function is
refined in the vicinity of the point with highest observed criticality.
A better evaluation of the property value at a test point can be achieved
by replacing the Monte-Carlo simulation by a systematic exploration of the
probability space. This is possible in our setup as we can control the proba-
bilistic decisions of the driver model externally. Depending on the history of
the simulation, the driver model reaches points where it uses random num-
bers to chose between different courses of action. Conceptually, this yields a
km
/h
and
dist
=30
