Method for Comparison of Surrogate Safety
Measures in Multi-Vehicle Scenarios
Enrico Del Re
Chair Sustainable Transport Logistics 4.0
Johannes Kepler University Linz
Linz, Austria
enrico.del [email protected]
Cristina Olaverri-Monreal
Chair Sustainable Transport Logistics 4.0
Johannes Kepler University Linz
Linz, Austria
cristina.olav[email protected]
Abstract—With the race towards higher levels of automation
in vehicles, it is imperative to guarantee the safety of all involved
traffic participants. Yet, while high-risk traffic situations between
two vehicles are well understood, traffic situations involving
more vehicles lack the tools to be properly analyzed. This
paper proposes a method to compare Surrogate Safety Measures
values in highway multi-vehicle traffic situations such as lane-
changes that involve three vehicles. This method allows for a
comprehensive statistical analysis and highlights how the safety
distance between vehicles is shifted in favor of the traffic conflict
between the leading vehicle and the lane-changing vehicle.
Index Terms—Surrogate safety measures, lane-change, traffic
safety, multi-vehicle
I. INTRODUCTION
In the quest to improve traffic safety, a significant chal-
lenge is the ability to differentiate between safe and unsafe
situations. Initially, unsafe situations could only be identified
by analyzing recorded accidents, but the frequency of these
accidents in recorded datasets was too low to provide a
comprehensive understanding. As a result, Traffic Control
Techniques (TCTs) such as the Swedish TCT [1] have been
developed to evaluate safety in non-accident scenarios.
These TCTs rely on a combination of the in-person ob-
servation by experts and measurement of parameters, such
as Surrogate Safety Measures (SSMs) [2], to detect unsafe
situations. These measures have been linked to accident rates
and have been used to increase vehicle safety in conjunction
with Advanced Driver Assist Systems (ADAS) [3]. Vehicles
equipped with such systems are considered Level 1 Au-
tonomous Vehicles (AVs), and it is likely that they will also
play an important role in higher-level AVs.
However, the relationship between SSMs, accident rates and
human driving behavior is more complex. For example, the
authors in [4] have shown that several SSMs do not fully
match human driving acceleration and deceleration rates in
car-following scenarios, and in [5] also the limitations and
challenges of SSMs with connected and automated vehicles
and mixed traffic situations have been highlighted. Addition-
ally, human estimation and adherence to SSMs are not always
accurate, further emphasizing the need for modifications.
Therefore, since autonomous vehicles should rely on and
take into account human-like behavior [6], modifications or
alternatives to currently used SSMs are necessary and research
regarding their development is being performed [7]. Most
microscopic traffic safety research is focused on the interaction
between only two vehicles, the ego vehicle and one vehicle it is
in conflict with. As a result, SSMs are also typically defined
regarding only one other traffic participant (or obstacle). In
order to use SSMs in vehicles with high levels of automation,
it is necessary to understand their role in traffic situations
involving more vehicles and how human driving behavior
differs from the optimal safe trajectory predictions that result
from estimations using SSMs.
Research on lane-change scenarios [8] revealed that there
is a statistically significant difference in SSM values in lane-
changing maneuvers, depending on whether the ego vehicle is
changing lanes in front of or behind another vehicle. Intuitively
this result can be expected, though a quantitative analysis
is necessary to take that behavior into account for AVs. In
the past work however, these SSMs were mainly calculated
between two vehicles only. Extending the observations to
multi-vehicle scenarios lead to the research presented here.
The focus of this paper is to propose a method to compare
the SSM values of different traffic participants and apply it to
lane-changes involving three vehicles on a highway. We thus
formulate the following hypothesis: When performing a lane-
change between two vehicles, the safety distance measured by
SSMs is identical between the lane-changing (ego vehicle) and
leading vehicle, and the lane-changing and the following ve-
hicle. After all, for an AV this could be the optimal trajectory.
In section IV we propose a methodology that tests the defined
hypothesis.
The next section presents a review of related literature,
section III the lane-change situation and dataset, and section
IV a description of the applied methodology. The results of
applying the method are shown in section V and section VI
presents the conclusion and future research directions.
II. RELATED LITERATURE
The groundwork for this paper comprises various research
on SSMs, which can be found summarized in [9]. Especially
various modifications of SSMs such as extending them to
consider more dynamic traffic situations [7] or combining
them to new ones [10]. However, to the authors’ knowledge
arXiv:2304.08998v1 [cs.RO] 18 Apr 2023
Fig. 1: Lane-change to the adjacent lane by the vehicle E in
between two vehicles, the leading vehicle (LV) and following
vehicle (FV) of the final traffic situation. Visualized here for
a lane-change to the right adjacent lane, though lane-changes
to the left were also taken into consideration.
SSMs have remained focused on traffic situations involving
only two vehicles.
One approach which does consider multi-vehicle conflicts
has been presented in [11]. Instead of calculating SSM values
between two vehicles, it defines a safety field for the ego
vehicle where each position is influenced by the surrounding
environment and vehicles. Still, attributing a safety value at
each position requires the use of SSMs.
The factors affecting lane-change crashes specifically have
also been analyzed in past research, though from a subjective
approach [12]. Current regulations for the use of higher level
AVs however are based on SSMs for safety assessment and
decision making [13]. An amendment to [13] would allow an
AV to perform a lane-change if it fulfills SSM-based safety
thresholds with regards to the leading and following vehicle
separately, splitting the lane-change into two separate traffic
situations.
Thus, although there are existing works in the field of re-
search, there is a research gap regarding the number of vehicles
involved. Therefore we contribute in this paper to the body of
knowledge and present a method to compare SSM values in
highway lane-changes scenarios that involve three vehicles.
This method allows for a comprehensive statistical analysis
and highlights how the safety distance between vehicles is
shifted in favor of the traffic conflict between the leading
vehicle and the lane-changing vehicle.
III. STUDIED ROAD SCENARIO AND DATASET DESCRIPTION
A. Lane-change scenario
The scenario chosen for comparing SSM values between
multiple vehicles is a lane-change that is performed by an ego
vehicle (E) in between a leading vehicle (LV) and a following
vehicle(FV), as shown in Figure 1.
B. Dataset
The dataset used is part of the datasets recorded within
the Next Generation SIMulation (NGSIM) program [14],
specifically the dataset recorded on the Interstate 80 high-
way in California. The recorded area is approximately 500
meters long and consists of six freeway lanes, with one high-
occupancy vehicle (HOV) lane and an additional lane on which
vehicles drive onto the highway (on-ramp). In total 45 minutes
of highway traffic between 4.00 p.m. and 5.30 p.m. were
recorded.
This dataset was chosen since in (parts of) the US overtaking
is allowed on both sides and could thus yield an equal number
of lane-changes for both directions.
IV. PROPOSED METHODOLOGY
A. Surrogate Safety Measures
This paper only uses a limited number of SSMs to assess
traffic safety. However, the methodology for comparison in-
troduced in Section IV-B is suitable for a far larger number
of SSMs and can be adapted if needed.
In general, SSMs can be grouped into proximity-based
and deceleration-based categories, and they are most suitable
for specific traffic situations. We limited ourselves to three
distance-based (Time Headway, Inverse Time-to-Collision,
Potential Index for Collision with Urgent Deceleration) and
one deceleration-based SSM (minimum Deceleration Required
to Avoid Crash). They are all well suited for car-following
situations. Their parameters, which are defined for interactions
between two vehicles only are depicted in Table I. In order
to apply them to this work they will be calculated separately
between the ego and the leading vehicle, as well as between
the following and ego vehicle.
TABLE I: Parameters used to calculate SSMs
Parameter Definition
distance between the front of the following
D vehicle and the rear part of the leading vehicle
v
F
velocity of the following vehicle
v
L
velocity of the leading vehicle
a deceleration rate of both vehicles FV and LV for PICUD
reaction time of the following vehicle
t
R
to a deceleration of the leading vehicle
1) Time Headway (TH): Time Headway is defined as the
time required for the following vehicle to reach the current
position of the leading vehicle:
T H =
D
v
F
. (1)
A higher value indicates a safer traffic situation, with values
above 2[s] rarely seen in congested traffic [15]. This threshold
is thus used to filter out free-flowing traffic as we are only
interested in situations where interactions with other drivers
have to be taken into account.
2) Potential Index for Collision with Urgent Deceleration
(PICUD): PICUD is defined as the distance between two
vehicles if they come to a full stop after decelerating with the
same force and the following vehicle is delayed by a reaction
time. The deceleration rate and the reaction time are predefined
parameters, in this case set to a = 3.3[m/s
2
] and t = 1[s] [9].
P ICU D =
v
2
L
− v
2
F
2a
+ D − v
F
t
R
(2)
Again, a higher value indicates a safer traffic situation,
though any value above 0 can be considered safe. Notably,
negative values are possible in contrast with TH or the DRAC
explained in the next paragraph.
3) Minimum Deceleration Required to Avoid Crash
(DRAC): DRAC indicates the deceleration rate required to
avoid a collision, thus a lower value indicates a safer situation.
If the two vehicles are not on a collision course the value is
set to 0.
DRAC =
(
(v
F
−v
L
)
2
D
, v
F
> v
L
0, else
(3)
4) Inverse Time-To-Collision (ITTC): While the standard
Time-To-Collision (TTC) is more frequently used, it is un-
defined for non-collision trajectories. Though this is not an
issue when calculating it between two vehicles, it becomes
one when trying to compare TTC values with respect to both
a leading and a following vehicle. Comparisons with two, or
even one (as happens more frequently), undefined values are
not possible.
Thus we are using in this work instead the inverse as defined
in [16]:
IT T C =
v
F
− v
L
D
(4)
A lower value indicates a safer situation, with only values
above 0 indicating a collision in 1/IT T C[s]. Negative values
instead increase with the acceleration and/or deceleration
required to reach a collision course.
B. Comparing SSMs
Since SSMs are used to evaluate the safety of any traffic
situation, comparing two SSM values appears to be trivial,
with their ratio being defined as:
SSM
R
=
SSM
A
SSM
B
, (5)
where SSM
A
and SSM
B
are the measured values of a single
SSM.
For strictly positive- or negative-definite SSMs this is suf-
ficient. However, PICUD, ITTC and DRAC amongst others
do not fulfill this criterion. The information about the sign of
SSM
A
and SSM
B
would be lost or it would be undefined for
SSM
B
= 0. Looking at the ratio from equation 5 in a 2-D
plane (Figure2), we notice that it also corresponds to tan α
for the point (x, y) = (SSM
B
, SSM
A
). As arctan(y/x) is
defined for any real value of y and x, we can thus extend
equation 5. For convenience we further choose to rescale the
angle to [−1, 1], with the following conditions:
f(SSM
A
, SSM
B
) : R
+
× R
+
→ [−1, 1] (6)
f(x, x) = 0 (7)
f(0, x) = 1 (8)
f(x, 0) = −1, (9)
which are fulfilled by
Fig. 2: Visualization of the ratio transformation from equation
5 with the angle α = arctan(y/x) with x the value of SSM
B
and y the value of SSM
A
. The dotted line marks the angle
where the new ratio should take the value 0, at π/4.
Fig. 3: Visualization of the boundary conditions for an ex-
tension of the domain of the ratio between two SSMs to R,
defined in equations 11-15. The dotted lines mark the angle
where the ratio has to take the values 0,1 and −1.
f
P
(x, y) = −1 + 2 sin (arctan(y/x)). (10)
Extending the domain of definition to include negative
numbers we get the following conditions:
f(SSM
A
, SSM
B
) : R × R → [−1, 1] (11)
f(x, x) = 0 (12)
f(x, y) = −f(−x, −y) (13)
f(−x, x) = 1, x > 0 (14)
f(x, −x) = −1, x > 0, (15)
which are fulfilled by
f
R
(x, y) = sin
arctan(
y
x
) −
π
4
. (16)
Again, a negative f
R
(x, y) indicates that x had a higher value
than y, with the highest relative value achieved at f
R
(x, y) =
−1, and vice-versa for f
R
(x, y) positive or f
R
(x, y) = 1.
For both f
P
and f
R
it is assumed that a higher value of an
SSM indicates a safer situation. In case this is inverted (e.g.
DRAC), using the negative of the function instead is sufficient
to keep the previous definition of −1 and 1.
Within this paper SSM
A
(y) is the SSM value calculated
between the ego and the leading vehicle and SSM
B
(x)
between the ego and the following vehicle. Thus a ratio of
−1 indicates that the ego vehicle has kept a higher safety
distance to the following vehicle than to the leading one. A
0 indicates an even split in the safety distance between the
leading and following vehicles. The function f
P
(x, y) is used
to compare TH and DRAC (image domain R
+
), whereas f
R
is used for ITTC and PICUD (image domain R).
C. Statistical Methods
The method to compare SSMs introduced above allows us
to perform statistical tests on the null hypothesis mentioned in
the introduction, that the distribution of the ratio is symmetric
around 0. As the distributions of the ratio of SSMs differ from
a normal distribution we have to rely on non-parametric tests.
A Wilcoxon signed-rank test is used to analyze the median
of the distributions and thus the null hypothesis. The alterna-
tive hypothesis is that the ratio is centered around a higher
value. The statistical value of the test corresponds to the sum
of ranks where the ratio is above 0, the corresponding p-value
indicates the likelihood to obtain a statistical value as large or
larger with an underlying distribution centered around 0.
To analyze differences between lanes and direction a
Kruskal-Wallis H-test is used. The null hypothesis for this test
is a lack of differences between the various groups (especially
the median). It calculates the test statistic H with the sum of
the average rank of each group. The corresponding p-value is
obtained with H having a hypothetical χ
2
distribution. It is the
survival function of the χ
2
distribution evaluated at H. Should
the null hypothesis be rejected, a Dunn’s Multiple Comparison
Test is used as post hoc test to analyze which groups are
different.
A Spearman R test is used to analyze the correlation
between SSM
R
s and traffic situations, in order to understand
whether differences observed with the above tests are intrinsic
properties of a lane-changes or consequences of external
circumstances such as the velocities of the leading, following
and ego vehicle.
The tests are all performed with a 5% confidence level.
V. RESULTS
A. Data
Extracting all lane-changes from the dataset, limiting the
time headway between the leading vehicle and ego, as well as
between the following vehicle and ego to less than 2[s] resulted
in 320 lane-changes. The only type of vehicles considered here
were cars.
Further, eliminating lane-changes involving the HOV and
on-ramp reduced the number of lane-changes to 199, which
were further distributed as follows in Table II. Lane 2 only
includes left lane-changes, i.e. lane-changes from lane 3 to
lane 2, since lane 1 is the HOV lane. Similarly, lane 6 only
includes right lane-changes as lane 7 is the on-ramp.
B. Ratio of SSMs
For TH, PICUD and ITTC their ratios T H
R
, P ICUD
R
and IT T C
R
show a distribution between [−1, 1], as can be
TABLE II: Lane-change scenarios from the NGSIM I-80
dataset used for the analysis
Lane Direction
Right Left Total
2 0 38 40
3 4 27 31
4 7 44 51
5 6 59 65
6 14 0 14
Total 31 168 199
Fig. 4: Histogram of the T H
R
visualized for different lane-
change directions.
seen in Figure 4, Figure 5 and Figure 7. For DRAC however,
in most lane-change situations (188) the ego vehicle is on a
collision course with only one of the vehicles, resulting in the
DRAC
R
= −1 or DRAC
R
= 1 values, as shown in Figure
6.
The results from the Wilcoxon signed-rank test with regards
to the defined null and alternative hypothesis of a higher
median are shown in Table III. The null hypothesis is rejected
in all cases in favor of the alternative.
TABLE III: Wilcoxon signed rank test for overall SSM ratios.
W is the Wilcoxon test statistic with its corresponding p-value.
SSM W p-value
T H
R
14918 5.06e-10
P IC U D
R
12945 1.15e-4
DRAC
R
16470 9.97e-20
IT T C
R
15948 8.29e-14
All SSM ratios indicate that a higher safety distance has
been kept with the leading vehicle than with the following one.
In particular, DRAC
R
shows that collision courses with only
the following vehicle are by far the more prevalent situation,
156 cases versus 32.
The results of the Spearman R test are shown in Table IV
and indicate either statistically insignificant or no correlations.
For lane and direction, the results of the Kruskal-Wallis H-
Fig. 5: Histogram of the P ICUD
R
visualized for different
lane-change directions.
Fig. 6: Histogram of the DRAC
R
visualized for different lane-
change directions.
Fig. 7: Histogram of the IT T C
R
visualized for different lane-
change directions.
TABLE IV: Spearman R test to test the influence of velocities
on SSM ratios. Correlation and statistical significance values
are shown for the velocity of each vehicle.
v
ego
v
LV
v
F V
SSM corr. p-value corr. p-value corr. p-value
T H
R
0.059 0.411 0.028 0.697 0.047 0.511
P IC U D
R
0.335 0.000 0.123 0.084 0.047 0.511
DRAC
R
0.415 0.000 0.117 0.099 0.047 0.511
IT T C
R
0.527 0.000 0.002 0.977 0.114 0.110
test are shown in Table V and show a difference for T H
R
and
DRAC
R
when separated into lanes.
TABLE V: Kruskal-Wallis H-test for different lanes, with H
the test statistic and p-value the survival function of the chi
2
distribution at H.
SSM H p-value
T H
R
8.526 0.074
P IC U D
R
14.005 0.007
DRAC
R
6.066 0.194
IT T C
R
12.462 0.014
Using Dunn’s Multiple Comparison Test as post hoc test
yields a significant difference between all lanes for DRAC
R
and for nearly all for T H
R
, with the exception of the third
and fifth lane.
For the direction of the lane-change the Kruskal-Wallis H-
test resulted in a significant difference of the median only for
IT T C
R
, as depicted in Table VI.
TABLE VI: Kruskal-Wallis H-test for different lane-change
direction, with H the test statistic and p-value the survival
function of the chi
2
distribution at H
SSM H p-value
T H
R
0.076 0.783
P IC U D
R
0.803 0.370
DRAC
R
1.469 0.226
IT T C
R
13.563 0.000
The combination of different lanes and lane-change direc-
tion was only possible for vehicles changing towards the left,
due to a low number of right-changing cases. The results are
shown in Table VII and indicate a difference in the median for
P ICU D
R
only. The Dunn’s Multiple Comparison Test post
hoc test showed a difference for all lanes.
TABLE VII: Kruskal-Wallis H-test for left changing vehicles
split into different lanes, with H the test statistic and p-value
the survival function of the chi
2
distribution at H
SSM H p-value
T H
R
7.465 0.058
P IC U D
R
13.693 0.003
DRAC
R
3.724 0.293
IT T C
R
6.603 0.086
Therefore, it is necessary to analyze the mean for individual
lanes and directions as well. The Wilcoxon test results are
shown in Table VIII. Only for the 5
th
lane was the hypothesis
of a median at 0 accepted. Everywhere else this null hypothesis
was rejected in favor of the alternative of being a median
higher than 0.
TABLE VIII: Wilcoxon rank test for left changing vehicles
split into different lanes for each SSM
R
with the test statistic
W
T H
R
Lane W p-value
2 582 0.000
3 330 0.000
4 797 0.000
5 1070 0.081
P IC U D
R
Lane W p-value
2 586 0.001
3 308 0.002
4 651 0.034
5 842 0.627
DRAC
R
Lane W p-value
2 658 1.477 · 10
−06
3 326.5 0.000
4 893 8.658 · 10
−08
5 1355.5 3.284 · 10
−05
IT T C
R
Lane W p-value
2 677 4.396 · 10
−06
3 326 0.000
4 895 1.520 · 10
−06
5 1263 0.002
VI. CONCLUSION AND OUTLOOK
A new method to compare SSMs in multi-vehicle traffic
situations was presented and applied to lane-change scenarios.
It has allowed a more extensive statistical analysis which
was previously impossible due to the variety of SSMs’ image
domains.
Vehicles changing lanes between two other vehicles have
shown a strong preference towards keeping a higher safety
distance towards the leading vehicle than the following one.
The lane where the lane-change occurs has an impact on the
median for DRAC, TH and ITTC, though it stays above 0
for all SSMs and nearly all lanes. However, the velocity of
the vehicles itself has no significant impact on the ratio of the
SSMs, thus not yielding a conclusive reason for the differences
between lanes. Unfortunately, the limited number of lane-
changes in the dataset also limited the statistical options,
particularly when comparing the directions of the lane-change.
For this reason and to have more controllable surrounding
conditions as well as more accurate data on the vehicles, a
simulation with human participants is necessary. The resulting
model for lane-changes will then be tested with participants
to assess whether it accurately captured their safety concerns
and would be acceptable for an AV.
ACKNOWLEDGEMENT
This work was supported by the Austrian Science Fund
(FWF), project number P 34485-N. It was additionally sup-
ported by the Austrian Ministry for Climate Action, Environ-
ment, Energy, Mobility, Innovation, and Technology (BMK)
Endowed Professorship for Sustainable Transport Logistics
4.0., IAV France S.A.S.U., IAV GmbH, Austrian Post AG and
the UAS Technikum Wien
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