Assessment of the RSS Model Suitability using Graph Neural Network

based on a Naturalistic Driving Dataset

Sungmoon Ahn

and Shiho Kim

School of Integrated Technology, Yonsei University, Incheon, 21983, Republic of Korea

Keywords:

Neural Nets and Fuzzy Systems, Data Analytics and Simulation, Intelligent Transportation.

Abstract:

We propose a method to evaluate the RSS model using data obtained from real roads. Recently, the

Responsibility-Sensitive Safety (RSS) model representing the minimum safety distance has been proposed.

After that, there were studies to evaluate the RSS model using simulators. Most virtual simulation studies

showed that the RSS model guarantees safety but adversely affects trafﬁc ﬂow by estimating the distance too

long than necessary. We evaluated the RSS model using data obtained in natural situational environments, un-

like previous studies. First, we found correlations representing distances between vehicles from the data using

Graph Neural Networks. Using the obtained correlations, we expressed it as a mathematical model through

symbolic regression. As a result of comparing the model we found with the RSS model, we veriﬁed that the

RSS model has a signiﬁcant trade-off between safety and trafﬁc ﬂow.

1 INTRODUCTION

Although many research efforts on autonomous driv-

ing have not yet been perfect for fully autonomous

driving, advanced driving assistant systems (ADAS),

which require lower technologies than fully au-

tonomous driving, have already been commercialized

(Chai et al., 2020; Mishra et al., 2021; Mishra et al.,

2022). Among ADAS, adaptive cruise control (ACC)

is a typical longitudinal control system and is a tech-

nology that maintains a safe distance between the sub-

ject vehicle and the leading vehicle. The ACC system

might not work correctly if the front vehicle suddenly

decelerates or another vehicle abruptly cuts in front of

the subject vehicle (Magdici and Althoff, 2017; Bae

et al., 2020).

There have been many studies to set the safety dis-

tance standard between a leading vehicle and a subject

vehicle to improve the safety of ACC against these

worst conditions. Intel Mobileye proposed the Re-

sponsibility Sensitive Safety (RSS) model associated

with NHTSA and IEEE SA (Shashua et al., 2018).

RSS model suggests a safety distance model through

mathematical methodologies using the subject vehi-

cle’s response time, velocity, and acceleration and the

velocity and deceleration of the leading vehicle.

https://orcid.org/0000-0002-6209-7309

https://orcid.org/0000-0001-9935-1721

In particular, since it is a safe distance calculated

based on the worst-case, it is a model that emphasizes

that a collision does not occur if this distance is main-

tained within the RSS model (Shalev-Shwartz et al.,

2017).

A simple mathematical model can express the cor-

relation between the leading vehicle and the subject

vehicle. Most safety-distance studies have proposed

slightly modiﬁed models of the RSS model based on

theoretical analysis or evaluated the suitability of the

RSS model through simulations.

In this work, we propose a new method to evaluate

the safety distance margin of the RSS model through

artiﬁcial intelligence (AI) approach based on actual

road data. First, we identiﬁed the correlations be-

tween vehicles with Neural Networks using accident-

free vehicle data obtained from the natural road en-

vironments. Second, the correlations found through

Neural Networks were expressed in a formula us-

ing symbolic regression. We propose a new model

representing the safety distance between the leading

vehicle and the subject vehicle through this process.

This study aims to demonstrate that the proposed

model could reduce the trade-off between safety dis-

tance and improving trafﬁc ﬂow compared to the RSS

model. We also veriﬁed that the RSS model could af-

fect the trafﬁc ﬂow by estimating more space than the

required minimum distance for safety.

210

Ahn, S. and Kim, S.

Assessment of the RSS Model Suitability using Graph Neural Network based on a Naturalistic Driving Dataset.

DOI: 10.5220/0011139800003274

In Proceedings of the 12th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2022), pages 210-217

ISBN: 978-989-758-578-4; ISSN: 2184-2841

2 RELATED WORK

2.1 Car-Following Model

The Car-Following Model refers to an analysis tech-

nique developed to deﬁne the correlation through

changes in acceleration, velocity, and headway dis-

tance between two consecutively driving vehicles.

The purpose is to predict the response of the sub-

ject vehicle according to the movement of the leading

vehicle. We can divide the car-following model into

three main domains: Gazis-Herman-Rothery (GHR),

safety distance or collision avoidance (CA), and psy-

chophysical or behavioral points (AP) (Brackstone

and McDonald, 1999). This paper utilizes the CA

ﬁeld approach. There have been many studies in the

ﬁeld of CA. Lefevre et al. proposed a model that cre-

ates a model from the driver’s actual driving trajec-

tory and mixes a controller that restricts driving for

safety (Lefevre et al., 2015). Wen-Xing and Li-Dong

proposed a safety distance model using the expected

average velocity (Wen-Xing and Li-Dong, 2018). It

is similar to our methodology because it uses the pre-

dicted velocity. Still, the difference is that we propose

the formula through correlations predicted through

GNNs based on data obtained from the actual envi-

ronments rather than using mathematical approaches.

And there is the RSS model that has been evaluated

and used a lot recently. The RSS model is divided

into ﬁve cases as follows;

• Safe longitudinal distance — same directions

• Safe longitudinal distance — opposite directions

• Safe Lateral Distance

• Longitudinal Safe Distance for Two Routes of

Different Geometry

• Lateral Safe Distance for Two Routes of Different

Geometry

Since our purpose is to evaluate using data obtained

from the natural environment, only the safety distance

model for the same direction can be obtained from the

referred database. Equation (1) shows the Safe longi-

tudinal distance formula of the RSS model (Shashua

et al., 2018).

min

ρ +

max,accel

+ ρa

max,accel

)

min,brake

−

max,brake

]

(1)

where [x]

= max{x,0}.

indicates the subject vehicle and v

indicates

the leading vehicle. This is a formula considering

the worst-case scenario in which the subject vehicle

accelerates to α

max,accel

for ρ time when the leading

vehicle rapidly decelerates to α

max,brake

. It may not

always be proper to consider the worst-case scenario.

For this reason, numerous studies evaluating the ad-

equacy of RSS have been conducted. Among them,

there were studies that RSS improves the safety per-

formance of ACC, but it can reduce trafﬁc ﬂow efﬁ-

ciency in terms of the trafﬁc ﬂow by maintaining a

distance longer than necessary (Mattas et al., 2019).

There were several studies to solve this problem. Li

et al. proposed a modiﬁed model that can reduce the

safety gap and make trafﬁc ﬂow more efﬁcient at the

same time based on the RSS through a theoretical

analysis method (Li et al., 2018). Chai et al. pro-

posed an efﬁcient model that can reduce the trade-off

between safety and trafﬁc ﬂow by dividing the inter-

val between the leading vehicle and the subject vehi-

cle into three sections and slightly modifying the RSS

depending on the situation (Chai et al., 2020). Nau-

mann et al. proposed a methodology to ﬁnd reason-

able parameters of RSS based on physical limitations

(Naumann et al., 2021). Kim et al. extracted and ver-

iﬁed the safety distance for each velocity by applying

the actual vehicle spec to the RSS model (Kim et al.,

2021).

Previous papers have proposed methodologies

that verify the RSS through simulation or slightly

modify the existing model through mathematical

analysis. The RSS model was created by combin-

ing widely known physical and mathematical theo-

ries. Cranmer et al. showed that the formula derived

through artiﬁcial intelligence (AI) expresses the ac-

tual motion of atoms better than the formula used in

the existing atomic motion theories (Cranmer et al.,

2020). Based on the results of Cranmer et al., the

purpose of this paper is not to slightly modify the ex-

isting model or verify it through simulations but to

ﬁnd a new formula using the results of extracting cor-

relations between vehicles through AI based on data

obtained from natural road environments (Cranmer

et al., 2020).

2.2 Graph Neural Networks

First, we need to ﬁgure out the correlations repre-

senting the distance between vehicles. The vehi-

cle data obtained from the natural road environments

we want to use is not structured data such as im-

ages. Graph Neural Networks (GNN) are Neural Net-

works structures suitable for analyzing unstructured

data. The advantage of GNN is that GNN can work

with unstructured data such as images without pre-

processing. Therefore, compared to other types of

Neural Networks, GNNs are relatively more robust

Assessment of the RSS Model Suitability using Graph Neural Network based on a Naturalistic Driving Dataset

211

to inductive bias compared with Convolution Neu-

ral Networks (CNNs) and Recurrent Neural Networks

(RNNs) (Battaglia et al., 2018). An additional advan-

tage of GNN is that the correlations between nodes

can be found via the edges between each node. For

these reasons, we used GNNs to ﬁnd the safety dis-

tance between vehicles in this work. In this paper, the

nodes of GNNs will be each vehicle, and the edges

represent the distance between the vehicles, which are

the correlations between the nodes we want to ﬁnd.

GNNs started by applying Neural Networks to

acyclic graphs proposed in Sperdui and Starita, and

many studies were conducted until the late 2000s

(Sperduti and Starita, 1997). They aimed to learn the

target node’s representation by iteratively propagat-

ing neighbor information. However, these method-

ologies required too much computation. Since then,

ConvGNNs studies have applied many CNN’s meth-

ods that can compute in parallel to solve various prob-

lems (Wu et al., 2020).

We can classify ConvGNNs into two spectral-

based and spatial-based architectures. Spectral-based

ConvGNNs are trained to learn ﬁlter parameters using

the concept of Graph Fourier Transform throughout

the graph signal processing.

However, in spectral-based, the eigenbasis prob-

lem changes when graph perturbation occurs. The is-

sue is that the learned ﬁlters are domain-dependent

and cannot apply to other structures, and the eigen-

decomposition O(n

) computational complexity (Wu

et al., 2020). In particular, to solve the compu-

tational complexity problem, ChebNet (Defferrard

et al., 2016) and GCN (Kipf and Welling, 2016) re-

duced the amount of computation through several ap-

proximations and simpliﬁcations. Nevertheless, there

are still issues such as per- forming eigendecomposi-

tion on a spectral basis or processing the entire graph

at once (Wu et al., 2020). Many other studies have

been done to solve hard problems based on GCN

(Chen et al., 2018; Chen et al., 2017; Chiang et al.,

2019).

There are also spatial-based ConvGNNs studies

to solve the aforementioned spectral-based problems.

Spatial-based ConvGNNs are derived from the con-

cept of existing CNNs that set the representation of a

speciﬁc node and the representation of adjacent nodes

as one patch and update it through convolution. It is

the same concept as the initial GNNs but differs in

performing a convolution operation.

Compared to spectral-based ConvGNNs, it does

not require expensive operations such as eigendecom-

position and is easy to generalize to new graphs be-

cause it does not rely on Fourier-based. And it has

the advantage of solving the problem that can only

be computed on the undirected graph, which is a

disadvantage of spectral-based. Many studies have

used performance development using these advan-

tages (Micheli, 2009; Li et al., 2017; Masci et al.,

2015).

In particular, the performance of inductive data

has been greatly improved due to Graph Attention

Networks (GAT) (Veli

ckovi

c et al., 2017). They

applied a self-attentional layer that applies attention

mechanisms to learning the relative weights of two

connected nodes, allowing us to generalize the unseen

graph. In general, the adjacency matrix, which means

Graph Structure, is used as an input for GNNs. The

adjacency matrix refers to a matrix indicating the cor-

relations between each node. In particular, GCN is

ﬁxed with the given Adjacency Matrix values as the

features of edges, which mean the connections be-

tween nodes. However, GAT does not ﬁx these val-

ues but applies attention mechanisms to learn the cor-

relation between nodes. Therefore, it can adapt to

a new graph more efﬁciently with a bit of training.

Since the data used in this paper is realtime vehicle

data at a ﬁxed location, it is necessary to repeatedly

train the unseen graph in which vehicle information

changes continuously. Therefore, attention mecha-

nisms, which are the core of GAT, are essential for

ﬁnding the correlations between two vehicles, which

is the most important part of this paper. More details

on data are described in the Method.

In addition to ﬁnding correlations between the cur-

rent data of each vehicle, we can ﬁnd more sophis-

ticated correlations if historical data can be used to-

gether.

We used Spatio-Temporal Graph Neural Networks

(STGNNs) to get more accurate correlations, which

added the concept of time to the spatial-based Con-

vGNNs. Based on STGNNs, many studies have im-

proved the performance in various ﬁelds such as rec-

ommendation system and trafﬁc prediction (Li et al.,

2017; Guo et al., 2019; Wu et al., 2019; Roy et al.,

2021; Tian and Chan, 2021).

We found that the structure of STAWNet (Tian and

Chan, 2021) is most suitable for our purposes. The

ﬁrst reason is that most GNNs required an Adjacency

Matrix, which is graph structure information, as input.

However, it is difﬁcult to understand the connection

structures between all vehicles with the data obtained

from the real environments we want to use.

To solve this problem, STAWNet did not use an

adjacency matrix but applied the self-attentional layer

used in GAT to obtain the adjacency edge weights.

As a result, we can ﬁnd that the self-learned relation-

ship showed a similar relationship found in the actual

data. At the same time, it was possible to ﬁnd a hid-

SIMULTECH 2022 - 12th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

212

den relationship between the remaining nodes that did

not appear. We thought it was appropriate for the part

where we wanted to see the correlations between the

leading vehicle and the subject vehicle. And since it

is the architecture that includes the concept of tempo-

ral, a more sophisticated correlation can be inferred

by using past data simultaneously as the present.

We utilized STAWNet, which uses a Spatio-

Temporal architecture without requiring an adjacency

matrix as input, to ﬁnd the correlations between the

two vehicles by training it after modifying it for our

data set and purpose.

2.3 Symbolic Regression

Symbolic regression is an analysis method that di-

rectly creates a function that can explain the re-

relationship between dependent and independent vari-

ables for given data. A lot of studies have been

done based on (Sampson, 1976), which is one of the

techniques to solve the optimization problem. Sym-

bolic regression has been generally studied based

on genetic algorithms (GA), genetic programming

(GP), and Neural Networks (NN) (Mundhenk et al.,

2021). We used GA based Eureq (Schmidt and Lip-

son, 2009). Eureqa stochastically combines algebraic

expressions to create an optimized closed-form equa-

tion. The criteria for optimization are computational

complexity and accuracy. In the problem of ﬁnd-

ing the safety distance in realtime, if the realtime

is not guaranteed through complex calculations, it

may cause a collision, so we used only simple +,-,/,*

among many operators. For example, suppose a com-

plex operation such as power appears in an expression

obtained through symbolic regression. In that case,

realtime performance may not be guaranteed as the

time complexity is O(n) or more.

3 METHOD

Our process can be summarized as follows.

• First, the Graph Neural Network is trained using

vehicle data obtained from the real road environ-

ments to ﬁnd the edge embedding features and

correlations between each vehicle.

• Second, we apply symbolic regression using the

found correlations (edge embedding features) to

ﬁnd the optimal formula to describe the relation-

ships.

• Finally, the optimal formula found is applied to

the dataset to calculate the error from the real val-

ues and validate the formula.

Figure 1: Proposed process for extracting the safety dis-

tance model using Graph Neural Network based on the nat-

uralistic driving dataset.

Our overall process is shown in Figure 1.

3.1 Dataset

We used the highD dataset as data obtained from nat-

ural real road environments. The highD dataset is

the data captured using a drone on German Highways

(Krajewski et al., 2018). Other naturalistic datasets

(Geiger et al., 2013; Yu et al., 2020; Caesar et al.,

2020; Lee et al., 2014; Houston et al., 2020) are those

typically obtained via vehicles. We needed data that

could get information about multiple vehicles simul-

taneously. Using a drone’s data observed with a bird-

eye view was suitable for our purpose. The highD

dataset has data on the current velocity and accelera-

tion of the subject vehicle, the ID of the sur- rounding

vehicle, the velocity and acceleration of the leading

vehicle, the distance to the vehicle in front, headway

distance, time-to-collision.

We can see that this dataset contains information

that can be utilized to compare the RSS model. This

allowed us to select only the data from the highD

dataset and use it to input the GNNs. The informa-

tion we used is as below.

• Subject vehicle Velocity & Acceleration

• Leading vehicle Velocity & Acceleration

• The initial distance between two vehicles

Since our purpose is to compare the natural driving

pattern with the RSS, only the information used in the

RSS was extracted from the dataset and used. Next,

we trained the GNN using the data.

3.2 Graph Neural Network Training

We used a modiﬁed structure of STAWNet. First, we

deﬁned each input feature as a temporal data frame.

Second, the ﬁnal input features were characterized by

Assessment of the RSS Model Suitability using Graph Neural Network based on a Naturalistic Driving Dataset

213

concatenating all input information. While the train-

ing phase, the output is trained to predict the velocity

of each vehicle. GNNs have the advantage of being

able to derive the results of all nodes at once. This set-

ting of GNN helps ﬁnd the correlations between ve-

hicles by predicting the velocity, which is the move-

ment of all vehicles. The feature maps of the self-

attentional layers indicating the correlations of each

node were extracted by the training. Based on the

feature maps, the embedding space with signiﬁcant

variance mentioned in Cranmer et al. can general-

ize well and have high performance (Cranmer et al.,

2020). Only the feature map with the largest vari-

ance was extracted among many self-attention feature

maps. The results are shown in Figure 2. Figure 2.(a)

shows the 2-hops adjacency matrix from the highD

dataset. It is the result of normalization with the fol-

lowing equation in order to represent it on the same

scale as Figure 2.(b).

i j

= exp(−

dist(v

) i f dist(v

) ≤ κ

(2)

i j

represents the correlation between each node

calculated by dist(v

), which denotes the euclidean

distance between node v

and v

, σ is the standard de-

viation of the distances and κ

means distance thresh-

old (Li et al., 2017).

Next, Figure 2.(b) shows the test result with the

largest variance among self-attentional feature maps.

The result of the corresponding feature map was ex-

tracted through the equation shown below.

i j



i f W

i j

≥ κ

(3)

i j

can determine the correlation between node

embeddings based on cosine similarity. That is, it is

possible to know the edge weights between each node

(Tian and Chan, 2021).

Looking at the thick red line, we can see the cor-

relation similarity between the real adjacency matrix

and the edge weights of the prediction results is sim-

ilarly well expressed. Therefore, we can extract the

self-learned adjacency matrix, which is the distance

between vehicles obtained through training, In addi-

tion, the relationship between vehicles with unknown

correlations in the dataset was able to ﬁnd hidden re-

lationships through self-learned to some extent. So,

we used the correlations extracted through GNNs as

the y value of symbolic regression.

3.3 Symbolic Expression

The extracted edge correlations were set to y, and the

information used as input to the GNN was set to x,

Figure 2: The comparison between (a) the real adjacency

relationship from dataset and (b) the self-learned relation-

ship on the training.

and applied to Eureqa, a symbolic regression pack-

age. The advantage of Eureqa is that it provides vari-

ous information, such as accuracy and computational

complexity, and at the same time ﬁnds the optimal

formula through ranking. Since our goal is to ﬁnd the

required safety distance formula for vehicles in real-

time, we chose an equation that exhibits relatively low

computational complexity and high accuracy.

4 RESULTS & DISCUSSION

Using the learned results, the optimal formula was

derived through symbolic regression. We obtained

safety distance from the naturalistic driving dataset,

which shows that the safety distance was relatively

small compared to the RSS model. And as a result

of applying the formula to accident-free data used for

learning and checking the error with the real value, it

was conﬁrmed that there was almost no error.

It can be a formula that can reduce the trade-off

between the safety distance and the trafﬁc ﬂow. The

best matching formula found through symbolic re-

gression is as follows;

min

+ v

+ a

+ v

α × v

(4)

where v

indicates the subject vehicle, v

indicates the

leading vehicle and a

means acceleration of the sub-

ject vehicle. α is hyper-parameter.

Correlations extracted from GNN appear as values

between 0 and 1 due to soft-max knowing the impor-

tance of each other. So, after performing symbolic re-

gression, we additionally proceeded to ﬁnd α that can

reduce the error with the data. As a result, α becomes

approximately 2.0.

Comparing the number of parameters required for

the RSS model with the number of necessary param-

eters for our model, we can see that few are required.

Table 1 shows the parameter comparison. In Table 1,

SV means the subject vehicle and LV means the lead-

ing vehicle.

SIMULTECH 2022 - 12th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

214

Table 1: Comparison of the number of parameters in our

model and RSS model.

Our Model RSS Model

SV Velocity Yes Yes

SV Accel Yes Yes

LV Accel No Yes

LV Velocity Yes Yes

Response Time No Yes

Using parameters such as the RSS model can

be more conservative due to unnecessary parameter

combinations. The model with more considerable

margins for the necessary distance may impede the

trafﬁc ﬂow while autonomous vehicles drive in the

actual road environment (Chai et al., 2019). So we

can see that our model with fewer parameters is more

efﬁcient. Finally, we compared the number of vari-

ous cases according to the velocity change between

the leading vehicle and the subject vehicle. The re-

sults are shown in Table 2. At this time, the RSS

model needs a response time of ρ. Since we trained

the GNNs assuming the data period is 1 second, we

set ρ to compare it to the same environments. In ad-

dition, For the maximum acceleration/deceleration of

the vehicle, we put a value of 4m/s

for maximum

acceleration and of -4.9m/s

for maximum decelera-

tion, respectively, as deﬁned by the FSRA (Full Speed

Range Adaptive Cruise Control) system of the inter-

national standard ISO-22179 (Park et al., 2018). The

results can be divided into three cases. First, assuming

that the subject vehicle is driving faster than the lead-

ing vehicle by more than 20km/h, the RSS model re-

sults show that the distance should maintain a distance

from 1.2 to 1.4 times greater than our model. Sec-

ond, assuming that the subject vehicle and the lead-

ing vehicle drive at the same velocity, our model esti-

mates the safety distance to be about 9m smaller than

the RSS model. Finally, when the leading vehicle is

driving faster than the subject vehicle by more than

40km/h, the RSS model showed that the safety dis-

tance was 0, indicating no need to keep the safety dis-

tance.

In contrast, our model showed that a smaller dis-

tance than the required distance of the RSS had to

be maintained. And to validate the safety of our

model, we compared using the highD dataset, which

is accident-free data. As a result of substituting the ac-

tual values of the dataset, the RSS model estimated a

distance 10 to 30m larger than the actual inter-vehicle

distance, and our model estimated a distance of 0

to 10m larger than the real inter-vehicle distance. It

shows that both the RSS and our models are safe mod-

els that prevent crashes. Therefore, although the RSS

model has a low accident probability, we could afﬁrm

that the trade-off between trafﬁc ﬂow and safety is

Table 2: Comparison of our model and RSS model for var-

ious situations.

Subject Vehicle(km/h)RSS

Model 120 110 100 90 80 70 60

120 70.9 47.7 26.1 6.1 - - -

110 89.0 65.8 44.3 24.2 5.8 - -

100 105.5 82.4 60.8 40.8 22.4 5.5 -

90 120.5 97.3 75.7 55.7 37.3 20.5 5.2

80 133.9 110.7 89.1 69.1 50.7 33.8 18.6

70 145.7 122.5 100.9 80.9 62.5 45.7 30.4

Leading

Vehicle

(km/h)

60 155.9 132.8 111.2 91.2 72.7 55.9 40.6

Subject Vehicle(km/h)Our

Model 120 110 100 90 80 70 60

120 61.0 51.4 42.6 34.6 27.5 21.2 15.8

110 66.5 56.0 46.4 37.7 30.0 23.1 17.2

100 73.1 61.6 51.0 41.5 32.9 25.4 18.8

90 81.2 68.4 56.6 46.0 36.5 28.1 20.9

80 91.3 76.8 63.7 51.7 41.0 31.6 23.4

70 104.2 87.7 72.7 59.0 46.8 36.0 26.7

Leading

Vehicle

(km/h)

60 121.5 102.3 84.7 68.8 54.5 41.9 31.0

signiﬁcant by estimating a relatively large safety dis-

tance.

5 CONCLUSIONS & FUTURE

WORK

This paper evaluated the RSS model by comparing

the RSS model with the safety distance model found

through Graph Neural Networks (GNNs) based on a

real road dataset. In the previous safety distance mod-

els, there is a representative RSS model. However,

it is inefﬁcient for trafﬁc ﬂow to estimate the safety

distance longer than necessary. Most studies have

evaluated the RSS model through simulations or pro-

posed a model with a slight modiﬁcation of the RSS

model to solve the problem. Unlike previous stud-

ies, we proposed a new model through machine learn-

ing rather than a mathematical car-following model.

First, we trained GNNs using data obtained from real

road environments. After that, edge weights, which

are the correlations of nodes representing each vehi-

cle obtained through GNNs learning, were extracted.

Finally, the optimized formula was derived through

symbolic regression using the extracted edge weights.

The formula we found estimates a relatively short

safety distance compared to the RSS model when the

velocity of the leading vehicle is comparable to or

slower than the velocity of the subject vehicle. Con-

versely, the results showed that the minimum safety

distance should be maintained even when the speed

of the leading vehicle is signiﬁcantly faster than that

of the subject vehicle. In addition, compared with

accident-free data to verify safety, there was little er-

Assessment of the RSS Model Suitability using Graph Neural Network based on a Naturalistic Driving Dataset

215

ror between our safety distance and the actual dis-

tance. As a result, our model can reduce the safety

margin between safety and trafﬁc ﬂow compared to

the RSS model. Therefore, we conclude that the RSS

model needs improvement.

Like the follow-up studies on the RSS model, we

will verify our model through various additional sim-

ulations (Chai et al., 2020; Xu et al., 2021).

ACKNOWLEDGEMENTS

This work was supported by Institute for Infor-

mation & communications Technology Planning &

Evaluation(IITP) grant funded by the Korea gov-

ernment(MSIT) (No.2021-0-01352, Development of

technology for validating the autonomous driving ser-

vices in perspective of laws and regulations)

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