Modelling decisions of control transitions and target speed regulations in full-range Adaptive Cruise Control based on Risk Allostasis Theory

Abstract

Adaptive Cruise Control (ACC) and automated vehicles can contribute to reduce traffic congestion and accidents. Recently, an on-road study has shown that drivers may prefer to deactivate full-range ACC when closing in on a slower leader and to overrule it by pressing the gas pedal a few seconds after the activation of the system. Notwithstanding the influence of these control transitions on driver behaviour, a theoretical framework explaining driver decisions to transfer control and to regulate the target speed in full-range ACC is currently missing.
This research develops a modelling framework describing the underlying decision-making process of drivers with full-range ACC at an operational level, grounded on Risk Allostasis Theory (RAT). Based on this theory, a driver will choose to resume manual control or to regulate the ACC target speed if its perceived level of risk feeling and task difficulty falls outside the range considered acceptable to maintain the system active. The feeling of risk and task difficulty evaluation is formulated as a generalized ordered probit model with random thresholds, which vary between drivers and within drivers over time. The ACC system state choices are formulated as logit models and the ACC target speed regulations as regression models, in which correlations between system state choices and target speed regulations are captured explicitly. This continuous-discrete choice model framework is able to address interdependencies across drivers’ decisions in terms of causality, unobserved driver characteristics, and state dependency, and to capture inconsistencies in drivers’ decision making that might be caused by human factors.
The model was estimated using a dataset collected in an on-road experiment with full-range ACC. The results reveal that driver decisions to resume manual control and to regulate the target speed in full-range ACC can be interpreted based on the RAT. The model can be used to forecast driver response to a driving assistance system that adapts its settings to prevent control transitions while guaranteeing safety and comfort. The model can also be implemented into a microscopic traffic flow simulation to evaluate the impact of ACC on traffic flow efficiency and safety accounting for control transitions and target speed regulations.

Full text

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Modelling decisions of control transitions and target speed regulations in
full-range Adaptive Cruise Control based on Risk Allostasis Theory
Silvia F. Varottoa*, Haneen Faraha, Tomer Toledob, Bart van Arema, Serge P. Hoogendoorna
aDepartment of Transport and Planning, Faculty of Civil Engineering and Geosciences, Delft University of
Technology, Stevinweg 1, P.O. Box 5048, 2600 GA Delft, The Netherlands
bTransportation Research Institute, Faculty of Civil and Environmental Engineering, Technion - Israel
Institute of Technology, 711 Rabin Building, 32000 Haifa, Israel
*Corresponding author. Tel: +31 (0)15 2789575, Fax: +31 (0)15 2783179.
Email addresses: s.f.varotto@tudelft.nl (S. F. Varotto), h.farah@tudelft.nl (H. Farah),
toledo@technion.ac.il (T. Toledo), b.vanarem@tudelft.nl (B. van Arem), s.p.hoogendoorn@tudelft.nl (S. P.
Hoogendoorn)
This manuscript version is a preprint of the following journal article:
Varotto, S.F., Farah, H., Toledo, T., van Arem, B., Hoogendoorn, S.P., 2018. Modelling decisions of control
transitions and target speed regulations in full-range Adaptive Cruise Control based on Risk Allostasis
Theory. Transportation Research Part B: Methodological 117, 318-341.
https://doi.org/10.1016/j.trb.2018.09.007
The journal article is available open access until November, 9th 2018 using the following link:
https://authors.elsevier.com/a/1XljChVEAsvAi
©2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
https://creativecommons.org/licenses/by-nc-nd/4.0/

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Modelling decisions of control transitions and target speed regulations in
full-range Adaptive Cruise Control based on Risk Allostasis Theory
Abstract
Adaptive Cruise Control (ACC) and automated vehicles can contribute to reduce traffic congestion and
accidents. Recently, an on-road study has shown that drivers may prefer to deactivate full-range ACC when
closing in on a slower leader and to overrule it by pressing the gas pedal a few seconds after the activation of
the system. Notwithstanding the influence of these control transitions on driver behaviour, a theoretical
framework explaining driver decisions to transfer control and to regulate the target speed in full-range ACC
is currently missing.
This research develops a modelling framework describing the underlying decision-making
process of drivers with full-range ACC at an operational level, grounded on Risk Allostasis Theory (RAT).
Based on this theory, a driver will choose to resume manual control or to regulate the ACC target speed if its
perceived level of risk feeling and task difficulty falls outside the range considered acceptable to maintain
the system active. The feeling of risk and task difficulty evaluation is formulated as a generalized ordered
probit model with random thresholds, which vary between drivers and within drivers over time. The ACC
system state choices are formulated as logit models and the ACC target speed regulations as regression
models, in which correlations between system state choices and target speed regulations are captured
explicitly. This continuous-discrete choice model framework is able to address interdependencies across
drivers’ decisions in terms of causality, unobserved driver characteristics, and state dependency, and to
capture inconsistencies in drivers’ decision-making that might be caused by human factors.
The model was estimated using a dataset collected in an on-road experiment with full-range ACC.
The results reveal that driver decisions to resume manual control and to regulate the target speed in
full-range ACC can be interpreted based on the RAT. The model can be used to forecast driver response to a
driving assistance system that adapts its settings to prevent control transitions while guaranteeing safety and
comfort. The model can also be implemented into a microscopic traffic flow simulation to evaluate the
impact of ACC on traffic flow efficiency and safety accounting for control transitions and target speed
regulations.
Keywords: Control transitions, Adaptive Cruise Control, on-road experiment, driver behaviour,
continuous-discrete choice model.

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1. Introduction
Automated vehicles are expected to mitigate traffic congestion and accidents (European Commission,
2017). Automated vehicles may have a beneficial impact on road capacity, traffic flow stability, and queue
discharge rates (Hoogendoorn et al., 2014). The first step towards predicting these impacts is to investigate
currently available systems such as Adaptive Cruise Control (ACC). ACC assists drivers in maintaining a
target speed and time headway and therefore has a direct adaptation effect on the longitudinal control task
(Martens and Jenssen, 2012). The influence of ACC systems on driver behaviour has been investigated,
mainly via driving simulator studies, since the 1990s. On-road experiments (Alkim et al., 2007; Malta et al.,
2012; NHTSA, 2005; Schakel et al., 2017) have shown that ACC systems influence substantially driver
behaviour. When the ACC is active, drivers keep larger time headways (Alkim et al., 2007; Malta et al.,
2012; NHTSA, 2005; Schakel et al., 2017), and change lane in advance to anticipate possible interactions
with slower vehicles (Alkim et al., 2007). These results, however, might be influenced by the conditions in
which the ACC system is activated, such as light-medium traffic, medium-high speeds, and non-critical
traffic situations.
In certain traffic conditions, drivers might prefer to disengage the system and resume manual
control, or the system disengages because of its operational limitations. These control transitions (Lu et al.,
2016) between automated and manual driving may influence traffic flow efficiency (Varotto et al., 2015)
and safety (Vlakveld et al., 2015). Lu et al. (2016) classified control transitions based on who (automation
or driver) initiates the transition and who is in control afterwards: ‘Driver Initiates transition, and Driver
Controls after’ (DIDC), ‘Driver Initiates transition, and Automation Controls after’ (DIAC), and
‘Automation Initiates transition, and Driver Controls after’ (AIDC). The situations in which these
transitions happen are influenced by the characteristics of the driving assistance system, the drivers
themselves, the road, and the traffic flow (Varotto et al., 2014). Field Operational Tests (FOTs) have
suggested that drivers initiate DIDC transitions with ACC systems that do not operate at speeds lower than
30 km/h to avoid potentially safety-critical situations (Xiong and Boyle, 2012), to keep a stable speed in
medium–dense traffic conditions (Viti et al., 2008), to adapt the speed before changing lane, to create or
reduce a gap when other vehicles merge into the lane, and to avoid passing illegally a slower vehicle on the
left lane (Pauwelussen and Feenstra, 2010). Recently, ACC systems operating also at low speeds in
stop-and-go traffic conditions (full-range ACC), therefore overcoming the functional limitations of earlier
versions, have been introduced into the market. These ACC systems might be activated and deactivated in
different situations, and are more likely to be active in dense traffic conditions. A controlled on-road
experiment showed that drivers using full-range ACC initiate DIDC transitions when exiting the freeway,
when approaching a moving vehicle, when changing lane, and when a vehicle cuts in or the leader changes
lane (Pereira et al., 2015).
ACC might have a positive impact on traffic flow efficiency when it is active in dense traffic (Van
Driel and Van Arem, 2010). To evaluate this impact, mathematical models of automated and manually
driven vehicles can be implemented into microscopic traffic simulation models. However, most
car-following and lane-changing models currently used to evaluate the impact of ACC do not describe
control transitions. A few microscopic traffic simulation models (Klunder et al., 2009; Van Arem et al.,
1997; Xiao et al., 2017) have proposed deterministic decision rules for transferring control, disregarding
inconsistencies in the decision-making process, heterogeneity between and within drivers, and
dependencies between different levels of decision making (for a review, see Varotto et al. (2017)). Thus, the
traffic flow predictions based on these models could be unreliable.
To improve the realism of current traffic flow models, insights from driver psychology and human
factors should be incorporated (Hamdar et al., 2015; Saifuzzaman and Zheng, 2014). To date, few studies
have proposed a conceptual model framework explaining control transitions based on theories of driver
behaviour and have estimated the probability that drivers transfer control based on empirical data. Using a
mixed logit model, Xiong and Boyle (2012) predicted the likelihood that drivers would brake resuming
manual control while they were closing in on a leader. Recently, we identified the main factors influencing
drivers’ choice to initiate a DIDC transitions with full-range ACC in a wider range of situations which did
not involve lane changes (Varotto et al., 2017). Drivers have higher probabilities to deactivate the ACC

4
when closing in on a slower leader, when supposing vehicles cutting in, and before exiting the freeway.
Drivers have higher probabilities to overrule the ACC system by pressing the gas pedal when the vehicle
decelerates and a few seconds after the activation of the system. Interestingly, some drivers have higher
probabilities to resume manual control than others. However, this study did not capture explicitly the
unobservable constructs that inform driver decisions and ignored the possibility of adapting the ACC
system settings (speed and time headway) to regulate the longitudinal control task.
This study develops such a mathematical framework to model driver decisions to resume manual
control and to regulate the target speed in full-range ACC. The model is based on the Risk Allostasis Theory
(RAT) (Fuller, 2011), captures explicitly interdependencies between the two decisions, and can be fully
estimated based on driver behaviour data. The paper is organised as follows. Section 2 reviews driver
control theories and driver behaviour models that are suitable to explain driver interaction with ACC. This
section concludes with the identified research gaps. Section 3 proposes the conceptual model framework for
driver decisions to resume manual control and to regulate the target speed in full-range ACC. Section 4
describes the mathematical formulation of the modelling framework and Section 5 the maximum likelihood
estimation method. Section 6 presents the case study, including a description of the on-road experiment, the
data analysis, the estimation results, and validation analyses of the model. Section 7 summarizes the main
contributions of the proposed modelling framework and directions for future research.
2. Literature review
The literature review focuses on studies proposing conceptual and mathematical models of driver behaviour
that are suitable to explain control transitions and target speed regulations in ACC. Section 2.1 introduces
driver control theories and Section 2.2 conceptual models explaining adaptations in driver behaviour.
Section 2.3 discusses a model framework which has the potential to capture interdependencies between
different driver behaviours. Section 2.4 summarizes the research gaps and formulates the research
objectives.
2.1. Driver control theories
The driving task can be divided into three levels: strategical (planning), tactical (manoeuvring), and
operational (control) (Michon, 1985). The strategical level represents the planning phase of the trip, for
instance in terms of mode and route choice. The tactical level includes decisions on manoeuvres such as
overtaking and gap acceptance. The operational level defines the direct longitudinal and lateral control of
the vehicle. This level has been studied in driver control theories (for a review, refer to Ranney (1994),
Rothengatter (2002) and Fuller (2011)). Several theories have been developed to explain the underlying
motivational and cognitive aspects of driver control, such as the Risk Homeostasis Theory (Wilde, 1982),
the Zero-risk Theory (Näätänen and Summala, 1974; Summala, 1988), the Task-Capability-Interface (TCI)
model (Fuller, 2000, 2005), the Monitor Model (Vaa, 2007), and the Safety Margin Model (Summala,
2007). These models differ in terms of the reference criteria in the control system (e.g., risk of collision,
task difficulty, emotions, driving comfort). However, these different reference criteria may reflect a hidden
consensus (Fuller, 2011): the most important motives influencing drivers’ decisions may be classified
under task demand elements, while motives such as driving comfort can be considered secondary to those
relating to safety.
Fuller (2011) proposed the Risk Allostasis Theory (RAT), which assimilated the most recent
competing theories (Summala, 2007; Vaa, 2007) into the TCI model (Fuller, 2000, 2005). The RAT argues
that driver control actions are primarily informed by the desire to maintain the feeling of risk and task
difficulty within an acceptable range, which varies over time. Drivers perceive risk feelings in the same way
as they experience task difficulty (Fuller et al., 2008). The maximum value of task difficulty acceptable is
associated with fear of losing control and the minimum value of task difficulty acceptable is associated with
frustration determined by low driving performances (Fuller, 2011). The perceived task difficulty is related
to the difference between perceived task demand and perceived driver capability (Fuller, 2000, 2005).
The perceived task demand is influenced by the presence and behaviour (both actual and
anticipated) of other road users, by the road environment (e.g., road surface and visibility), and by the

5
characteristics of the vehicle (e.g., interface and vehicle performance) (Fuller, 2002; Fuller and Santos,
2002). The perceived driver capability is determined by driver characteristics such as driving experience
and age and by human factors such distraction, emotions, stress and fatigue (Fuller, 2002; Fuller and
Santos, 2002). The perceived driver capability is ultimately expressed in driver behaviour characteristics
such as the chosen speed and distance headway (Fuller, 2011). When the perceived capability is stable,
variations in the perceived task demand directly influence the feeling of risk and task difficulty. Empirical
findings have shown that the feeling of risk and task difficulty increase when the speed increases (Fuller et
al., 2008; Lewis-Evans and Rothengatter, 2009) and when the time headway decreases (Lewis-Evans et al.,
2010). At speeds higher than the most comfortable speed for the driver, the perceived feeling of risk and
task difficulty are correlated to estimates of statistical risk (Fuller et al., 2008). The latter can be expressed
by measurable variables such as time to collision or time to line crossing. At lower speeds, however, the
perceived feeling of risk is not correlated to estimates of statistical risk (Fuller et al., 2008). This is one of
the key differences from previous driver control theories based on estimates of statistical risk (Wilde,
1982). It is still subject of debate in the field of driver psychology whether drivers can perceive changes in
risk feelings in low risk situations and are informed by these changes in their behaviours (Fuller, 2011;
Lewis-Evans et al., 2010; Lewis-Evans and Rothengatter, 2009).
The acceptable level of risk feeling and task difficulty can be influenced by driver characteristics
(gender, experience, age and personality) and factors that vary over time for each individual driver (e.g.,
journey goals and emotional state) (Fuller, 2011). This variation of the risk thresholds over time is one of
the key features that distinguish the Risk Allostasis Theory from previous theories based on risk
homeostasis. Drivers decrease their speed when the risk feeling and task difficulty are higher than the
maximum value acceptable and increase the speed when they are lower than the minimum value acceptable.
However, they might be constrained in their decisions by performance limitations of the vehicle, congested
traffic, and compliance to speed limits. These findings from driver psychology should be included into a
conceptual model framework to explain driver behaviour with driving assistance systems such as the ACC.
2.2. Conceptual models of adaptations in driver behaviour
In driver psychology, adaptations are defined as the behavioural aspects that can be observed after a change
in road traffic (Martens and Jenssen, 2012). Few studies have proposed conceptual models of adaptations in
driver behaviour based on the control theories described in the previous section. The usage of ACC, which
maintains a target speed and time headway, has a direct impact on the longitudinal control task of drivers.
Xiong and Boyle (2012) proposed a conceptual model of drivers’ adaptation to ACC which includes
initiating factors (actual risk) and mediating factors (perceived risk). In this model, the actual risk is
determined by the distance headway, environmental conditions (weather, road type, lighting conditions,
traffic density) and the response of the system, while the perceived risk is influenced by the ACC system
settings (speed and time headway), the driver characteristics, experience with and attitudes towards the
system. This model is applied to predict driver decision-making (i.e., manually brake or not) when
approaching a slower leader.
Similarly, driver control theories have been used to explain adaptation effects in longitudinal
driving behaviour. Hoogendoorn et al. (2013) and Saifuzzaman et al. (2015) incorporated the
Task-Capability-Interface (TCI) model proposed by Fuller (2005) into car-following models to capture
compensation effects due to driver distraction. Hoogendoorn et al. (2013) assumed that the maximum
acceleration, the maximum deceleration, the free speed and the desired time headway are dependent on the
task difficulty, expressed as difference between task demand and driver capability. However, the task
difficulty was not explicitly linked to measurable driver behaviour characteristics and driver characteristics.
Saifuzzaman et al. (2015) defined the task difficulty as the ratio of task demand and driver capability. The
task demand increases when the speed of the subject vehicle increases and when the distance headway
decreases. The driver capability is inversely proportional to the desired time headway (unobservable) and
the sensitivity towards the task difficulty level is captured by a specific parameter. Human factors are
captured by a component of the reaction time and a parameter representing the perceived risk. The task
difficulty function was used to modify the desired acceleration in existing car-following models. These
advanced car-following models were applied to predict driver behaviour in regular driving conditions and

6
under distraction due to phone usage.
These studies show that driver control theories can be incorporated into existing models of driver
behaviour to capture adaptations. The feeling of risk and task difficulty can be expressed as a function of
driver behaviour characteristics such as speed and distance headway. A conceptual model framework
similar to that one proposed by Xiong and Boyle (2012) can be developed to explain different driver
behaviours with ACC (control transitions and target speed regulations) in a wide range of traffic situations.
2.3. Integrated driver behaviour models
Few driver behaviour models (e.g., car-following and lane changing models) have captured the
interdependencies between different driving behaviours and explained these behaviours based on
underlying constructs that motivate drivers’ decisions. For these purposes, previous studies have proposed
modelling frameworks based on discrete choice models, which are flexible from a behavioural perspective,
provide statistical techniques to capture complex error structures and facilitate a rigorous estimation of the
model parameters (Choudhury, 2007; Danaf et al., 2015; Farah and Toledo, 2010; Koutsopoulos and Farah,
2012; Toledo, 2003). In addition, these models are suitable for implementation into a microscopic traffic
flow simulation because each individual is modelled independently. Toledo (2003) developed an integrated
driving behaviour model predicting both acceleration (regression models) and lane changes (discrete choice
models) based on drivers’ unobservable short-term goals and plans. This model structure accommodates
changes in both discrete and continuous variables, capturing interdependencies across driving decisions in
terms of causality, unobserved driver and vehicle characteristics, and state dependency (Toledo et al., 2007;
Toledo et al., 2009). The parameters of all model components were estimated simultaneously using
maximum likelihood methods (Toledo et al., 2009). We conclude that an integrated driver behaviour model
can be developed to model mathematically driver decisions to transfer control and regulate the target speed
in full-range ACC capturing unobservable constructs such as feeling of risk and task difficulty.
2.4. Research gaps and objectives
Few studies have proposed conceptual model frameworks based on insights from driver psychology to
explain drivers’ choices to resume manual control in ACC. The model framework proposed by Xiong and
Boyle (2012) is limited to situations in which the subject vehicle approaches a slower leader. A
comprehensive conceptual framework for driver behaviour at an operational level with ACC and a flexible
mathematical formulation for this modelling framework are currently missing. Previous studies ignored the
possibility of adapting the ACC system settings (time headway and speed) to regulate the longitudinal
control task. Drivers can decrease their actual speed by braking or by decreasing the ACC target speed and
can increase their actual speed by pressing the gas pedal or by increasing the target speed. To model
decisions that are naturally linked such as control transitions and target speed regulations and to explain
these decisions based on current theories of driver behaviour, we need a flexible modelling framework
capturing unobservable constructs and interdependencies between discrete and continuous variables. The
main objectives of the current study are as follows:
(1) to develop a conceptual model framework that explains driver decisions to resume manual control
and to regulate the target speed grounded on the Risk Allostasis Theory (Fuller, 2011);
(2) to develop a mathematical formulation for this modelling framework based on the integrated driver
behaviour models (Toledo, 2003), which describes underlying constructs, captures
interdependencies between different decisions, and can be fully estimated using driver behaviour
data.

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3. Modelling framework for driver decisions to resume manual control and to regulate the target
speed in full-range ACC
The conceptual modelling framework assumes that feeling of risk and task difficulty (Fuller, 2011) are the
main factors that inform drivers’ decisions with full-range ACC at an operational level. This hypothesis is
supported by empirical findings in Varotto et al. (2017). Drivers will choose to decrease (or increase) their
actual speed if the perceived level of risk feeling and task difficulty (RFTD) is higher (or lower) than the
maximum (or minimum) value which is considered acceptable to maintain the ACC active and the current
ACC target speed. The actual speed can be regulated by adapting the ACC target speed or by resuming
manual control.
Figure 1 presents the model framework. We propose two levels of decision making describing
both transitions to manual control (discrete choice) and target speed regulations (continuous choice) with
ACC: risk feeling and task difficulty evaluation, and ACC system state and ACC target speed regulation
choice. The decision-making process is latent (unobservable). Driver actions to resume manual control and
to regulate the target speed are observed, while the perceived level of RFTD is latent. At the highest level,
the driver evaluates whether the perceived level of RFTD falls within the range which is considered
acceptable to maintain the ACC active and the current ACC target speed. The perceived RFTD is
influenced by the driver behaviour characteristics of the subject vehicle and of the leader. The acceptable
range with the ACC active varies between drivers and within drivers over time, being influenced by driver
characteristics, by the functioning of the system, and by the environment. If the perceived RFTD level is
higher than the maximum value acceptable, the driver will choose to deactivate the system or to decrease
the ACC target speed maintaining the system active. If the perceived RFTD level is lower than the
minimum value acceptable, the driver will choose to overrule the ACC by pressing the gas pedal, to
increase the ACC target speed maintaining the system active, or not to intervene. The latter is introduced to
capture drivers’ difficulties to perceive changes in feeling of risk and task difficulty in low risk situations,
which might be influenced by human factors (unobservable) such as errors, shifts in attention and
distraction (Fuller and Santos, 2002). These decisions are influenced by the driver behaviour
characteristics, by the functioning of the system, by environmental conditions, and by driver characteristics.
The model framework allows interdependencies among decisions to transfer control and to
regulate the target speed to be directly captured through appropriate model specifications at the different
levels of decision-making. This is further explained in Section 4, which presents the mathematical
formulation of the model based on this conceptual structure.
Figure 1 Conceptual model for driver decisions to resume manual control and to regulate the target speed in
full-range ACC.

8
4. Mathematical formulation of the model for driver decisions to resume manual control and to
regulate the target speed in full-range ACC
To implement the conceptual model presented in Section 3, we need a flexible mathematical framework
which is able to capture unobservable constructs and interdependencies between different decisions made
by the same driver. Modelling frameworks based on choice models satisfy these requirements. In this study,
choice models are preferred to alternative methods (e.g., artificial intelligence) because the model structure
can be selected based on insights from driver control theories and the estimation results are directly
interpretable.
In this mathematical framework, the magnitude of the ACC target speed regulation is chosen
simultaneously to the system state and correlations between these two choices are captured explicitly. In
addition, interdependencies across decisions are addressed in terms of causality, unobserved driver
characteristics, and state dependency (Toledo, 2003). Causality is addressed by modelling the decisions
taken at the lower levels as conditional on the decisions taken at the higher levels. Unobserved driver
characteristics are captured by introducing driver-specific error terms in each level of decision making.
State dependency is addressed by including the driver behaviour characteristics of the subject vehicle and
of its direct leader as explanatory variables in the different levels. The model formulation is presented in
Sections 4.1-4.3.
4.1. Level 1: risk feeling and task difficulty evaluation (discrete choice)
The risk feeling and task difficulty evaluation (RFTDE) model is formulated as a generalized ordered probit
model with random thresholds (Castro et al., 2013; Eluru et al., 2008; Greene and Hensher, 2009, 2010).
This model formulation represents the ordinal and discrete nature of the risk feeling and task difficulty
evaluation (risk lower than acceptable, acceptable risk, and risk higher than acceptable), capturing both
observed and unobserved heterogeneity in the minimum and in the maximum risk acceptable. This ordinal
response structure is based on the assumption that an unobservable risk feeling and task difficulty (RFTD)
determines the observable decisions of drivers. The RFTD is modelled as a latent variable that follows a
normal distribution. Driver n chooses at time t whether the perceived RFTD is lower than the minimum risk
acceptable (L), falls within the acceptable risk range (Ac) or is higher than the maximum risk acceptable
(H) as presented in eq. (1):
󰇛󰇜󰇱󰇛󰇜󰇛󰇜
󰇛󰇜󰇛󰇜󰇛󰇜
󰇛󰇜󰇛󰇜 (1)
where RFTDE is the choice indicator, and 󰇛󰇜 and 󰇛󰇜 are the variables that represent the
minimum and the maximum acceptable risk for each driver at time t. The non-linear formulation of the
minimum and of the maximum risk acceptable allows to distinguish mathematically the thresholds from the
latent regression, guarantees that both thresholds are positive, and preserves the ordering of the thresholds
(󰇛󰇜󰇛󰇜) (Greene and Hensher, 2009, 2010). The lowest and the highest
acceptable risk are functions of explanatory variables as shown in eqs. (2-3):
󰇛󰇜
󰇛󰇜 (2)
󰇛󰇜󰇛󰇜
󰇛󰇜 (3)
where  and  are the constants, and are vectors of parameters associated with the explanatory
variables 
󰇛󰇜 and 
󰇛󰇜,  and  are the parameters associated with the individual specific error term
󰇛󰇜. The thresholds vary within individuals over time due to observed variables and between
individuals due to observed variables and unobserved heterogeneity. Relevant explanatory variables that
can be included into the threshold equations are driver characteristics, variables related to the functioning of

9
the ACC system, and characteristics of the freeway segment. The driver-specific error term captures
unobserved preferences that influence all choices taken by the individual over time. The mean risk feeling
and task difficulty perceived by drivers is a function of explanatory variables as described in eq. (4):
󰇛󰇜󰇛󰇜󰇛󰇜

󰇛󰇜
Where  is the constant,  is a vector of parameters associated with the explanatory variables 󰇛󰇜, and
is the parameter associated with the observation specific error term 󰇛󰇜󰇛󰇜. Relevant explanatory
variables are the driver behaviour characteristics of the subject vehicle and of the leader, such as speed,
relative speed, and distance headway (Fuller, 2011). The risk feeling and task difficulty evaluation
conditional on the value of  is calculated as follows in eqs. (5-7):
󰇛󰇛󰇜󰇜󰇧󰇛󰇜󰇛󰇜
󰇨󰇛󰇜
󰇛󰇛󰇜󰇜󰇧󰇛󰇜󰇛󰇜
󰇨󰇧󰇛󰇜󰇛󰇜
󰇨󰇛󰇜
󰇛󰇛󰇜󰇜󰇧󰇛󰇜󰇛󰇜
󰇨󰇛󰇜
where 󰇛󰇜 is the cumulative distribution function of the standardized normal distribution. The parameters
, τ  are estimated while  is fixed to one and  is fixed to zero for identification purposes. In
this framework, the driver-specific error terms are estimated in both threshold equations to capture the
impact of unobserved heterogeneity on both the minimum and maximum risk acceptable.
4.2. Level 2: choice of ACC system state (discrete choice)
Drivers who consider the RFTD lower than the minimum value acceptable choose to overrule the ACC by
pressing the gas pedal (AAc), to maintain the system active and increase the target speed (󰇜, or not to
intervene (AL). This decision is formulated as a logit model, in which the utility functions U for driver n at
time t are given by eqs. (8-10):
󰇛󰇜
󰇛󰇜
󰇛󰇜 (8)
󰇛󰇜
󰇛󰇜
󰇛󰇜 (9)
󰇛󰇜
󰇛󰇜 (10)
where  and  are alternative specific constants, and  are vectors of parameters associated
with the explanatory variables 
󰇛󰇜 and 
󰇛󰇜, and  are the parameters associated with the
individual specific error term 󰇛󰇜, and 
󰇛󰇜, 
󰇛󰇜, and 
󰇛󰇜 are i.i.d. Gumbel –
distributed error terms. In the utility of not intervening in low risk conditions, the constant and the
driver-specific error term are estimated while the explanatory variables are assumed to have an impact
equal to zero for identification purposes (Choudhury, 2007; Choudhury et al., 2007). Relevant explanatory
variables can include the driver behaviour characteristics of the subject vehicle and of its leader, variables
related to the functioning of the system, characteristics of the freeway segment, and driver characteristics.
The probability of choosing the ACC system state  with 󰇝󰇞 in low risk situations
is presented in eq. (11):
󰇛󰇛󰇜󰇛󰇜󰇜
󰇛󰇜

󰇛󰇜
󰇛󰇜

10
Drivers who consider the RFTD higher than the maximum value acceptable choose to deactivate the ACC
(I) or to maintain the system active and decrease the target speed (). This decision is formulated as a
logit model, in which the utility functions U for driver n at time t are given by eqs. (12-13):

󰇛󰇜
󰇛󰇜
󰇛󰇜 (12)
󰇛󰇜
󰇛󰇜 (13)
where  is an alternative specific constant, is the vector of parameters associated with the explanatory
variables 
󰇛󰇜, is the parameters associated with the individual specific error term 󰇛󰇜, and

󰇛󰇜, and 
󰇛󰇜 are i.i.d. Gumbel – distributed error terms. Relevant explanatory variables are similar
to those listed above for low risk conditions. The probability of choosing the ACC system state  with
󰇝󰇞 in high risk situations is presented in eq. (14):
󰇛󰇛󰇜󰇛󰇜󰇜
󰇛󰇜

󰇛󰇜
󰇛󰇜
The parametersare estimated and can be assumed to have a different value in each level of feeling of
risk and in each utility function.
4.3. Level 2: choice of ACC target speed regulation (continuous choice)
ACC target speed regulations are observed only when drivers choose to regulate the ACC target speed. The
magnitude of the regulation depends on the choice of increasing or decreasing the ACC target speed. In this
framework, decisions to increase or decrease the ACC target speed are captured explicitly (i.e., if a driver
chooses to increase the ACC target speed, the increase will be always positive). To represent this process,
the error term is assumed to be a positive random variable. In this case study, the absolute values of the
observed ACC target speed increase (ACCTarSpeed+) and decrease (ACCTarSpeed-) are log-transformed.
The regression equations of the ACC target speed increase () and decrease (󰇜 conditional upon
choosing to increase or decrease the ACC target speed are given in eqs. (15-16):
󰇛󰇜
󰇛󰇜


󰇛󰇜 󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜 󰇛󰇜
Where 󰇛󰇜 is the constant, 󰇛󰇜is the vector of parameters associated with the explanatory
variables 
󰇛󰇜󰇛󰇜,  with 󰇝󰇞 and  are the parameters associated with the selectivity
correction terms and  respectively, 󰇛󰇜 is the parameter associated with the individual
specific error term 󰇛󰇜, 󰇛󰇜 is the parameter associated with the observation specific error
term 
󰇛󰇜󰇛󰇜󰇛󰇜. The selectivity correction terms  and are given in eqs. (17-18):
󰇩󰇡󰇢
󰇡󰇢󰇪 (17)
󰇩󰇡󰇢
󰇡󰇢󰇪 (18)
Where   and  are the choice probabilities to overrule the ACC system, not to intervene, and
to increase the target speed in the low-risk logit model (eq. 11), and  and  are the choice
probabilities to deactivate and decrease the target speed in the high-risk logit model (eq. 14). The inclusion
of the selectivity correction terms into the regression equations corrects for the system state selectivity bias
under the assumption that the choice probabilities are logit and the error terms are normally distributed
(Dubin and McFadden, 1984; Train, 1986). Relevant explanatory variables can include the driver behaviour
characteristics of the subject vehicle and of its leader, variables related to the functioning of the system,

11
characteristics of the freeway segment, and driver characteristics. The probability density functions of the
target speed increase and decrease conditional on the choices to decrease or increase the ACC target speed
are given by eqs. (19-20):
󰇝󰇛󰇜󰇛
󰇛󰇜󰇜󰇛󰇜󰇛󰇜󰇞

󰇛
󰇛󰇜󰇜󰇛󰇜


󰇛󰇜
󰇝󰇛󰇜󰇛
󰇛󰇜󰇜󰇛󰇜󰇛󰇜󰇞
 
󰇧󰇛
󰇛󰇜󰇜󰇛󰇜
󰇨󰇛󰇜
The parameters  are estimated and can assume a different value in each regression equation.
5. Maximum likelihood estimation of the integrated continuous-discrete choice model
The parameters of both the choice probabilities and the equations for the ACC target speed regulation are
estimated simultaneously with full information maximum likelihood methods. Given 󰇛󰇜 the indicator
associated with the system state choice, 󰇛󰇜 the indicator associated with the observed values of the
ACC target speed regulations, and 󰇛󰇜the indicator associated with the unobservable risk feeling
and task difficulty evaluation, the unconditional probability of deactivating (or overruling) the system (eq.
21), of increasing (or decreasing) the ACC target speed (eq. 22), and of not intervening (eq. 23) in a single
observation are given as follows:
󰇛󰇛󰇜󰇜󰇛󰇛󰇜󰇛󰇜󰇜󰇛󰇛󰇜󰇜󰇛󰇜
󰇛󰇛󰇜󰇛󰇜󰇜
󰇛󰇛󰇜󰇛󰇜󰇛󰇜󰇜󰇛󰇛󰇜󰇛󰇜󰇜󰇛󰇛󰇜󰇜󰇛󰇜
󰇛󰇛󰇜󰇜󰇛󰇛󰇜󰇜
󰇛󰇛󰇜󰇛󰇜󰇜󰇛󰇛󰇜󰇜󰇛󰇜
Where 󰇛󰇛󰇜󰇜 is presented in eqs. (19-20), 󰇛󰇛󰇜󰇜 in eqs. (11, 14), and 󰇛󰇛󰇜󰇜 in eqs.
(5-7). Notably, the unconditional probability of not intervening is the sum of the probabilities of perceiving
the feeling of risk as to be acceptable and of not intervening when the feeling of risk is lower than the
minimum risk acceptable. This formulation allows decisions of not intervening to arise from two different
levels of perceived risk (acceptable and low) and captures explicitly drivers’ propensity to not intervene
when the system is active (Greene et al., 2013). The joint probability of the T observations over time for the
same driver is given by eq. (24):
󰇛󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇜󰇛󰇛󰇜󰇛󰇜󰇜

 󰇛󰇜
The unconditional joint probability of the observations for each driver is obtained by integrating over the
distribution of , which is assumed to be standard normal, as presented in eq. (25):
󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜  󰇛󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜󰇜󰇛󰇜󰇛󰇜

 

12
The integral is calculated using Monte-Carlo integration. The random draws are generated using the
‘Modified Latin Hypercube Sampling’ method (Hess et al., 2006). The log-likelihood function for all
drivers 1, …, N is given by eq. (26):
󰇛󰇜󰇛󰇜󰇛󰇜󰇛󰇜

 󰇛󰇜
6. Case study
The model can be estimated using driving behaviour data with ACC and information on individual drivers.
Section 6.1 briefly describes the on-road experiment, the characteristics of the ACC system, and the
participants (for a detailed description, see Varotto et al. (2017)). Section 6.2 presents the analysis of the
data to explore the conditions in which drivers resumed manual control and regulated the target speed.
Section 6.3 discusses the estimation results of the model and the impact of the explanatory variables on the
choice probabilities. Section 6.4 proposes in-sample-out-of-time and out-of-sample-in-time validation
analyses of the model estimated.
6.1. Data collection
The on-road experiment consisted of a single drive (46-km long) on a pre-set test route on the A99 in
Munich. The test route comprised four freeway segments mostly composed of three lanes per direction. In
the first freeway segment, participants tested the system and found their preferred gap setting. During the
experiment on the remaining three freeway segments (35.5 km), participants were instructed to drive as
they normally would, regulating the target speed settings and resuming manual control at any time.
The research vehicle used was a BMW 5 Series equipped with a regular version of full-range
ACC, which maintains a target speed at speeds between 0 and 210 km/h and a target time headway at speeds
higher than 30 km/h. The range of the radar is 120 m. The target time headways that can be set are 1.0, 1.4,
1.8, and 2.2 s. The maximum acceleration and deceleration supported by the system are 3 m/s2 and –3 m/s2.
When the system is active, it is possible to set a target speed and time headway by using the switches.
Drivers can resume manual control temporarily by pressing the gas pedal (transition to Active and
accelerate) and can deactivate the system by pressing the on/off button or the brake (transition to Inactive).
Twenty-three participants recruited among BMW employees in Munich completed the
experiment. Fifteen participants were male, and eight were female. Participants had between 3 and 33 years
of driving experience. Six participants had never used ADAS (Advanced Driving Assistance Systems)
before the experiment (no experience), nine had driven with ADAS less often than once a month during the
previous year (medium experience), and eight once a month or more often (high experience). None of them
had been directly working on the development of the ACC system. Before the experiment, participants were
instructed on the specifications of the system, signed an informed consent form, and filled a questionnaire
reporting demographic characteristics (Kyriakidis et al., 2014), driving experience (Kyriakidis et al., 2014),
experience with ADAS, and driving styles (Taubman-Ben-Ari et al., 2004). The experiment was carried out
during the peak hours of the morning (7-9 am) and of the evening (4-6 pm, 6-8 pm) from June 29th to July
9th 2015. Participants drove between 45 and 90 minutes, based on the traffic flow conditions. Speed,
acceleration, distance headway (from radar), speed of the leader (from radar), ACC system settings and
state, and GPS position were measured and registered in the Controller Area Network (CAN) of the
instrumented vehicle. After the experiment, participants filled a questionnaire about the usage of the ACC
system, workload experienced (Byers et al., 1989; Kyriakidis et al., 2014), and the usefulness and
satisfaction of the system (Kyriakidis et al., 2014; Van der Laan et al., 1997).
6.2. Data analysis
The data collected in the experiment (23 drives of 35.5 km) were analysed to investigate the situations in
which drivers resumed manual control (presented in Varotto et al. (2017)) and regulated the ACC target
speed. We did not analyse control transitions initiated by the system, and transitions or target speed
regulations that occurred between 10 s before and 10 s after a lane change. We reduced the data to 1 Hz
resolution, obtaining 31,165 observations. In this paper, we analyse 23,568 observations of 1 s in which a

13
leader is detected by the radar (120 m) and the ACC system is active. 106 observations (0.45%) were
immediately followed by a DIDC transition to Active and accelerate (overruling), 210 (0.89%) by an
increase in the ACC target speed, 55 (0.23%) by a DIDC transition to Inactive (deactivations), 125 (0.53%)
by a decrease in the ACC target speed, and 23,072 (97.9%) by neither transitions nor speed regulations.
Drivers transferred to Active and accelerate from 0 to 26 times (M=4.61, SD=5.88), increased the ACC
target speed from 1 to 24 times (M=9.13, SD=5.34), transferred to Inactive from 0 to 7 times (M=2.39,
SD=1.83), and decreased the ACC target speed from 1 to 11 times (M=5.43, SD=2.86).
To gain insight into the conditions in which control transitions and speed regulations were
initiated, we analysed the empirical distribution functions of the driver behaviour characteristics when
neither transitions nor speed regulations happened, when the ACC was deactivated or overruled, and when
the ACC target speed was reduced or increased (Appendix A, Figure 1A). The mean and the standard
deviation of these variables are presented in Table 1. The similarity of the distributions between the different
groups was tested using two-sample Kolmogorov-Smirnov tests (Appendix A, Table 1A). Most transitions
to Active and accelerate were initiated a few seconds after the activation. At high speeds, deactivations and
target speed reductions occurred more often than overruling actions and target speed increments. When the
vehicle decelerated, transitions to Active and accelerate happened more often than target speed increments.
Deactivations happened more often than target speed reductions when the target speed was lower than the
actual speed. Overruling actions occurred more often than target speed increments when the target speed was
higher than the actual speed. On average, deactivations and target speed reductions were associated with
larger distance headways. Deactivations and target speed reductions happened most often when the subject
vehicle was faster than the leader, while target speed increments happened most often when the subject
vehicle was slower. Most deactivations occurred when the subject vehicle accelerated more than the leader.
Most target speed regulations ranged between -20 and +20 km/h. In addition, cut-in manoeuvres were
detected as described in Varotto et al. (2017). These findings suggest that the driver behaviour characteristics
of the subject vehicle and of the leader may impact significantly drivers’ decisions to regulate the target
speed and to resume manual control.
Control transitions and target speed regulations occurred more often in freeway sections where
vehicles change lanes more frequently, potentially disturbing traffic flow. Drivers deactivated the system
more often in proximity to an on-ramp and before exiting the freeway (Varotto et al., 2017). Drivers
overruled the system or increased the ACC target speed more often between ramps that are closer than 600
m (FGSV, 2008) and in proximity to an on-ramp. Drivers showed significant differences in resuming
manual control and regulating the ACC target speed based on their individual characteristics. Correlation
analysis was conducted to explore the relations between the driver characteristics, the number of transitions
executed, and the magnitude of the target speed regulation selected for each driver. Drivers who deactivated
the ACC more often also overruled the system more often. Drivers inexperienced with ADAS chose smaller
target speed increments. Individual characteristics such as gender and age were correlated significantly with
driving styles, workload experienced during the drive, and usefulness and satisfaction of the ACC. Further
analysis is needed to investigate moderate correlation results.

14
Table 1 Mean and standard deviation of the driver behaviour characteristics when drivers transfer the ACC to
Inactive (I), decrease the ACC target speed (AS-), maintain the ACC Active (A), increase the ACC target speed
(AS+), and transfer to Active and accelerate (AAc); a reduced version of this table focusing on transitions to
manual control was presented in Varotto et al. (2017);
Variables
Description
I
AS-
A
AS+
AAc
Time after last
activation
Time after the ACC has been
activated in s
76.0
(83.2)
102
(117)
153
(156)
115
(130)
50.3
(128)
Speed
Speed of the subject vehicle in
km/h
94.8
(40.9)
93.1
(34.5)
72.6
(38.0)
82.1
(28.9)
86.5
(36.9)
Acceleration
Acceleration of the subject vehicle
in m/s2
-0.0491
(0.549)
-0.0935
(0.480)
-0.00294
(0.390)
0.0956
(0.332)
-0.272
(0.462)
Target time
headway – time
headway
Difference between the ACC target
time headway and the time
headway (front bumper to rear
bumper) in s
-0.574
(0.758)
-0.546
(0.682)
-0.361
(0.558)
-0.585
(0.710)
-0.160
(0.780)
Target speed –
speed
Difference between the ACC target
speed and the subject vehicle speed
in km/h
16.2
(22.2)
18.5
(21.0)
25.8
(25.0)
8.97
(12.1)
20.2
(24.9)
Distance
headway
Distance headway (front bumper to
rear bumper) in m
49.8
(27.5)
49.8
(24.2)
36.5
(22.9)
44.7
(22.0)
39.1
(23.1)
Relative speed
Speed difference between leader
speed and subject vehicle in km/h
-7.84
(11.8)
-3.16
(8.51)
-0.829
(5.69)
2.62
(6.36)
-1.04
(6.33)
Relative
acceleration
Acceleration difference between
the leader and the subject vehicle
in m/s2
-0.287
(0.609)
-0.0234
(0.517)
0.0140
(0.375)
0.0618
(0.377)
0.225
(0.479)

15
6.3. Estimation results
In this case study, we assumed that only one decision happens within a 1-s interval. This interval of time is
similar to the mean reaction time between the recognition of a stimulus and the execution of the response in
literature (Toledo, 2003). The decisions are related to the driver behaviour characteristics recorded at the
beginning of the interval. Multiple 1-s observations, repeated over time, are available for each driver (panel
data). Notably, the model specification presented in this section is the result of an intensive modelling
process in which several specifications and model structures were compared based on statistical tests. We
estimated the model using the software PythonBiogeme (Bierlaire, 2016). All model components were
estimated simultaneously using full-information maximum likelihood methods as described in Section 5.
The log likelihood and the goodness of fit indicators are presented in Table 2 and the estimation results in
Table 3. Most parameters are statistically significant at the 95% confidence level. Sections 6.3.1-6.3.3
discuss the estimation results of each model component and Section 6.3.4 presents the impact of the
explanatory variables on the unconditional choice probabilities.
Table 2 Statistics of the continuous-discrete choice model
Statistics
Number of drivers
23
Number of observations
23,568
Number of constants
8
Number of parameters associated with explanatory variables (K)
28
Constant log likelihood 󰇛󰇜
-3496
Final log likelihood 󰆹
-3078
Adjusted likelihood ratio index (rho-bar-squared) 

󰇛󰇜
0.112
Table 3 Estimation results of the continuous-discrete choice model (1 variable centred on the mean value
between drivers; ** p-value>0.10, * 0.05<p-value<0.10; the table continues in the next page)
Variable
Description
Parameters
Estimate
T-test
Risk feeling and task difficulty evaluation
-
Constant risk feeling and task difficulty with ACC active

1.76
8.55
Speed/DHW
Speed of the subject vehicle in km/h divided by distance
headway (front bumper to rear bumper) in m

0.0426
1.52
*
RelSpeed
Relative speed (leader speed – subject vehicle speed) in
km/h

-0.0381
-9.64
RelAcc
Relative acceleration (leader acceleration – subject vehicle
acceleration) in m/s2

-0.249
-3.87
AntCutIn3
Number of cut-ins in the following three seconds

0.528
7.12
-
Constant highest acceptable risk with ACC active

1.05
18.74
TimeAct
Logarithm of time after the activation of ACC in s


-0.125
-3.98
TimeAct
Logarithm of time after the activation of ACC in s


0.0646
13.54
PatCar
Score on the driving-style factor ‘Patient and careful’1
(MDSI (Taubman-Ben-Ari and Yehiel, 2012))


0.337
1.32
*
PatCar
Score on the driving-style factor ‘Patient and careful’1
(MDSI (Taubman-Ben-Ari and Yehiel, 2012))


-0.119
-2.03

Individual specific error term

0.383
3.31

Individual specific error term

-0.0705
-5.15

16
Table 3 Estimation results of the continuous-discrete choice model (** p-value>0.10, * 0.05<p-value<0.10)
Variable
Description
Parameters
Estimate
T-test
ACC system state choice
-
Alternative specific constant

0.195
0.30
**
-
Alternative specific constant

1.41
3.57
-
Alternative specific constant

-1.51
-3.53
TimeAct
Logarithm of time after the activation of ACC in s


-0.72
-6.68
DiffTarSpeed
Difference between the ACC target speed and the speed of
the subject vehicle in km/h


-0.0156
-1.80
*
DiffTarSpeed
Difference between the ACC target speed and the speed of
the subject vehicle in km/h


-0.0622
-7.50
Acc
Acceleration of the subject vehicle in m/s2


-2.04
-7.18
RelAcc
Relative acceleration (leader acceleration – subject vehicle
acceleration) in m/s2


-1.11
-2.65
AntCutIn3
Number of cut-ins in the following three seconds


1.45
2.42
OnRamp
Binary variable equal to 1 when the drivers are in the
mainline close to an on-ramp, or between two ramps closer
than 600 m (FGSV, 2008)


1.30
3.70
Exit
Binary variable equal to 1 when the drivers are in the
mainline closer than 1600 m to the exit (first exit sign)


3.08
5.21

Individual specific error term

1.00
2.99

Individual specific error term

0.470
1.77
*
ACC target speed regulation choice
-
Mean ACC target speed increase

1.97
4.70
-
Mean ACC target speed decrease

1.86
6.63
DiffTarSpeed
Difference between the ACC target speed and the speed of
the subject vehicle in km/h


0.0240
3.49
RelSpeed
Relative speed (leader speed – subject vehicle speed) in
km/h


-0.0299
-2.41
NoviceADAS
Binary variable equal to 1 when the driver is inexperienced
with ADAS


-0.518
-3.30


Selectivity correction term in low risk situations


1.44
2.45


Selectivity correction term in low risk situations


-1.24
-2.24

Selectivity correction term in high risk situations

0.0301
0.19
**

Individual specific error term

0.355
2.20

󰇛󰇜
Observation specific error term

0.682
14.04

󰇛󰇜
Observation specific error term

1.10
6.15

17
6.3.1. Risk feeling and task difficulty evaluation
In the ordered probit model, the risk feeling and task difficulty RFTD are influenced by the driver behaviour
characteristics of the subject vehicle and of its leader as shown in eq. (27):
󰇛󰇜
󰇛󰇜
󰇛󰇜󰇛󰇜
󰇛󰇜󰇛󰇜󰇛󰇜
(27)
Where  is the constant, 
, , ,  are the parameters associated with the
explanatory variables listed in Table 3, and 󰇛󰇜󰇛󰇜 is the observation specific error term. Speed is
divided by distance headway because drivers are assumed to be more sensitive to changes in risk feelings at
short distance headways and at high speeds. In addition, speed and distance headway are highly correlated.
The lowest and the highest acceptable risk are functions of the functioning of the ACC system and driver
characteristics as presented in eqs. (28-29):
󰇛󰇜
󰇛󰇜
 (28)
󰇛󰇜󰇛󰇜
󰇛󰇜
(29)
where  is the constant, 
, 
, 
, and 
 are the parameters associated with the
explanatory variables listed in Table 3,  and  are the parameters associated with the individual specific
error term 󰇛󰇜. The logarithmic transformation of the time after last activation is consistent with the
empirical findings and showed a significant better fit than a linear specification. The road location, the other
driving styles (reckless and careless, angry and hostile, and anxious), gender, age, experience with ADAS,
workload, and usefulness and satisfaction with ACC did not influence significantly the acceptable range.
The estimation results in Table 3 show that drivers perceive higher risk at higher speeds and at
shorter distance headways. In addition, they perceive higher risks when they are faster (negative relative
speed) and accelerate more (negative relative acceleration) than the leader, and when they suppose that a
vehicle will cut in during the next three seconds. To analyse the impact of variations in the explanatory
variables in the threshold equations, we calculated the lowest and highest risk acceptable with ACC active
and the mean feeling of risk in observations in which only one explanatory variable was altered while
maintaining all the other variables fixed. We assumed that, in the baseline observation, the driver had
experience with ADAS and a score on the patient and careful driving style equal to the mean in this sample.
The speed was equal to 87.2 km/h, the ACC target speed 102 km/h, the acceleration -0.0467 m/s2, the
distance headway 45.3 m, the relative speed -0.781 km/h, and the relative acceleration 0.0365 m/s2. The
ACC system had been activated for 94 s and cut-in manoeuvres, ramps, and exits did not influence the
driver. We selected these values based on the average conditions of the control transitions and target speed
regulations observed. The results are presented in Figure 2. Few seconds after the system has been activated
(Figure 2a), drivers showed a higher minimum risk acceptable and a lower maximum risk acceptable (i.e.,
drivers’ acceptable range with the ACC active is smaller). This means that, immediately after activation,
drivers press the gas pedal or increase the target speed when the risk feeling is higher in low risk situations
and deactivate or decrease the speed when the risk is lower in high risk situations. Interestingly, drivers who
reported a high score on the patient and careful driving style (Figure 2b) showed a higher minimum risk
acceptable and a lower maximum risk acceptable (their acceptable range with the ACC active is smaller).
This result means that patient and careful drivers resume manual control or regulate the target speed when
the risk feeling is higher in low risk situations and when it is lower in high risk situations. The driver
specific error term has a different effect on the minimum and on the maximum acceptable risk (Figure 2c):
certain drivers showed a higher risk acceptable in high risk situations and a lower risk acceptable in low risk
situations (larger acceptable range with the ACC active), while others showed a higher risk acceptable in
high risk situations and a higher risk acceptable in low risk situations (smaller acceptable range with the

18
ACC active). This means that drivers, who deactivate or decrease the speed when the risk feeling is higher
in high risk situations, can press the gas pedal or increase the target speed in low risk situations when the
risk feeling is lower or when it is higher.
Figure 2 Impact of the explanatory variables and of the driver specific error term on the minimum (light blue
dashed line) and on the maximum (purple dashed line) risk acceptable with ACC active, compared to the mean
feeling of risk and task difficulty (black dotted line). The variables are listed as follows: (a) time after last
activation, (b) patient and careful driving style (centred on the mean value between drivers), and (c) driver
specific error term.
6.3.2. ACC system state choice
In low risk situations, the utility functions to overrule the ACC by pressing the gas pedal (AAc), to maintain
the system active and increase the target speed (󰇜, and not to intervene (AL) are influenced by the
driver behaviour characteristics of the subject vehicle and of its leader, and by the functioning of the ACC
system as shown in eqs. (30-32):
󰇛󰇜
 󰇛󰇜
󰇛󰇜

 󰇛󰇜
󰇛󰇜 (30)
󰇛󰇜
󰇛󰇜
󰇛󰇜 (31)
󰇛󰇜
󰇛󰇜 (32)
where  and  are alternative specific constants, 
 , 
, 
 , 
 are the
parameters associated with the explanatory variables in Table 3, and  are the parameters
associated with the individual specific error term 󰇛󰇜, and 
󰇛󰇜, 
󰇛󰇜, and 
󰇛󰇜 are i.i.d.
Gumbel – distributed error terms. The specification proposed, which includes the alternative not to
intervene in low risk situations, resulted in a considerable improvement in goodness of fit compared to a
similar specification in which drivers could choose only to overrule the ACC system or to increase the
target speed in low risk situations. This means that drivers showed a propensity to maintain the ACC active
and do not regulate the target speed in low risk situations. Time after activation, acceleration, and expected
cut-ins had a non-significant impact on target speed increments. The other explanatory variables described
in Section 6.2 did not impact significantly the choice to increase the target speed or to overrule the ACC.
In high risk situations, the utility functions to deactivate the ACC (I) or to decrease the target speed
() are influenced by the driver behaviour characteristics of the subject vehicle and of its leader, by the
functioning of the ACC system, and by characteristics of the freeway segment as shown in eqs. (33-34):

󰇛󰇜
󰇛󰇜
󰇛󰇜

19

󰇛󰇜
󰇛󰇜
󰇛󰇜 (33)
󰇛󰇜
󰇛󰇜 (34)
where  is an alternative specific constant, 
, 
, 
, 
 are the parameters
associated with the explanatory variables in Table 3, is the parameter associated with the individual
specific error term 󰇛󰇜, and 
󰇛󰇜, and 
󰇛󰇜 are i.i.d. Gumbel – distributed error terms. A
similar specification including the alternative not to intervene in high risk situations did not result in a
significant improvement in the goodness of fit. This means that drivers showed a more consistent behaviour
in high risk situations than in low risk situations. The other explanatory variables in Section 6.2 did not
influence significantly the choice to deactivate the ACC.
The estimation results in Table 3 show that, in low risk situations, the alternative specific constant
of overruling the ACC system by pressing the gas pedal is non-significant while the alternative specific
constant of not intervening is significant and positive. This result means that drivers are more likely not to
intervene than to overrule the ACC or to increase the target speed everything else being equal. In high risk
situations, the alternative specific constant of deactivating the system is negative. This suggests that drivers
are more likely to decrease the target speed than to deactivate the system everything else being equal. In low
risk situations, drivers are more likely to increase the ACC target speed when the ACC target speed is lower
than the actual speed and to overrule the ACC few seconds after the system has been activated. Drivers are
more likely to overrule the system by pressing the gas pedal when the ACC acceleration is low and when
they expect cut-ins during the next three seconds. In high risk situations, drivers are more likely to
deactivate the ACC when the target speed is lower than the actual speed and when they accelerate more than
the leader (negative relative acceleration). In addition, drivers are influenced by the road location and are
more likely to deactivate the ACC in proximity to an on-ramps, between two ramps, and before exiting the
freeway (similar to findings in Pereira et al. (2015)). The driver-specific error term has a significant effect
on the system state choices in high and low risk situations, meaning that certain drivers are more likely to
resume manual control or not to intervene in low risk situations than others. The effect of this term on
overruling the ACC was larger than the effect on deactivations and of not intervening in low risk situations,
which did not differ significantly. This means that drivers showed a larger variability in overruling the
system by pressing the gas pedal.
6.3.3. ACC target speed regulation choice
The regression equations of the ACC target speed increase () and decrease (󰇜 are influenced
significantly by the target speed set in the system, by the relative speed and by driver characteristics as
shown in eqs. (35-36):
󰇛󰇜






󰇛󰇜

󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜
 
󰇛󰇜 󰇛󰇜
Where  and  are constants, 
, 
, 
 are the parameters associated
with the explanatory variables listed in Table 3, 
, 
 and  are the parameters associated with the
selectivity correction terms 
, 
, and ,  is the parameter associated with the individual
specific error term 󰇛󰇜, and and  are the parameters associated with the observation
specific error terms 
󰇛󰇜󰇛󰇜 and 
󰇛󰇜󰇛󰇜. The logarithmic transformation of the ACC
target speed regulation is consistent with the empirical findings and showed a significant improvement in
goodness of fit compared to a linear specification. The relative speed and the difference between the target
speed and the actual speed did not impact significantly the ACC target speed increments. Experience with
ADAS did not influence significantly the target speed decrements. Gender, age, driving styles, workload,

20
and usefulness and satisfaction with ACC did not influence significantly the magnitude of the ACC target
speed regulations.
The estimation results in Table 3 show that drivers select a larger ACC target speed decrement
when the ACC target speed is higher than the current speed and when they are faster than the leader
(negative relative speed). Drivers inexperienced with ADAS prefer smaller ACC target speed increments.
The selectivity correction terms have a significant impact on the ACC target speed increments. Drivers
choose larger ACC target speed increments in situations in which they are more likely to overrule the
system by pressing the gas pedal and less likely not to intervene. This means that, everything else being
equal, the magnitude of the increment is positively correlated with the choice probability of overruling the
ACC and negatively correlated with the probability of not intervening. The selectivity correction term had a
non-significant impact on the target speed decrement. The driver-specific error term has a significant effect
on the magnitude of the target speed regulations, meaning that certain drivers choose larger ACC target
speed regulations than others. The effect of this term did not differ significantly between target speed
increments and decrements, meaning that drivers show a similar variability in increasing and decreasing the
speed. Comparing the impact of the driver-specific error terms on the two levels of decision making, we
conclude that drivers who have a smaller acceptable range with ACC active are more likely to resume
manual control and to choose larger target speed regulations.
6.3.4. Impact of explanatory variables on the unconditional choice probabilities
To analyse the effect of variations in the explanatory variables on the unconditional ACC system state
choice probabilities and on the magnitude of the ACC target speed regulations, we calculated the choice
probability ratio and the target speed regulation ratio between a baseline observation and observations in
which only one explanatory variable was altered while maintaining all the others fixed. In the baseline
observation (choice probability ratio and target speed regulation ratio equal to 1), the driver had experience
with ADAS and a score on the patient and careful driving style equal to the mean in this sample. The speed
was equal to 87.2 km/h, the ACC target speed 102 km/h, the acceleration -0.0467 m/s2, the distance
headway 45.3 m, the relative speed -0.781 km/h, and the relative acceleration 0.0365 m/s2. The ACC
system had been activated for 94 s and the driver was not affected by cut-in manoeuvres, ramps, and exits.
These values were selected based on the average situations in which control transitions and target speed
regulations occurred. The unconditional ACC system state choice probabilities are influenced by the
explanatory variables impacting the risk feeling and task difficulty evaluation and the ACC system state
choices. The magnitude of the ACC target speed regulations is related to the variables influencing the ACC
system state choices and the ACC target speed regulation.
The results for ratio variables are presented in Figure 3 and Figure 4, and for ordinal and nominal
variables in Table 4. All findings support the previous interpretations. Comparing the results in Figure 3, we
note that the time after activation, the acceleration (negative), and the driver specific error term are the
variables that have a largest impact on the choice of overruling the system. The difference between the ACC
target speed and the actual speed (negative) has the largest impact on the choice of increasing the ACC
target speed. The relative speed (negative) and the relative acceleration (negative) have the strongest effect
on the choice of deactivating the system. The relative speed (negative) has also the largest impact on the
choice of decreasing the ACC target speed. In Table 4, the number of expected cut-ins during the next three
seconds has the strongest effect on the probability of deactivations and target speed decrements. In Figure 4,
the difference between the ACC target speed and the actual speed and the relative speed have the largest
impact on the magnitude of the target speed decrement.

21
Figure 3 Impact of the explanatory variables and of the driver specific error terms on the choice probability
ratio (probability predicted divided by probability baseline observation) of transferring to Inactive (red),
decreasing the ACC target speed (orange), maintaining the ACC active (blue), increasing the ACC target speed
(dark green), and transferring to Active and accelerate (light green). The variables are listed as follows: (a)
time after last activation, (b) speed, (c) acceleration, (d) target speed – speed, (e) distance headway, (f) relative
speed, (g) relative acceleration, (h) patient and careful driving style (centred on the mean value between
drivers), and (i) driver specific error term.

22
Table 4 Impact of the ordinal and nominal explanatory variables on the choice probability ratio (probability
predicted divided by probability baseline observation) of transferring to Inactive (I), decreasing the ACC
target speed (AS-), maintaining the ACC Active (A), increasing the ACC target speed (AS+), and transferring
to Active and accelerate (AAc), and on the target speed regulation ratio (ACC target speed regulation
predicted divided by ACC target speed regulation baseline observation) of decreasing (TS-) and increasing
(TS+) the ACC target speed;
Variables
I
AS-
A
AS+
AAc
TS-
TS+
AntCutIn3 = 1
3.981
3.981
0.9884
0.3373
1.438
1.000
0.8444
AntCutIn3 = 2
12.38
12.38
0.9427
0.0804
1.461
1.000
0.5557
AntCutIn3 = 3
30.41
30.41
0.8413
0.0110
0.8522
1.000
0.2613
OnRamp
2.648
0.7216
1.000
1.000
1.000
0.9822
1.0000
Exit
5.438
0.2499
1.000
1.000
1.000
0.9432
1.0000
Novice ADAS
1.000
1.000
1.000
1.000
1.000
1.000
0.5957
Figure 4 Impact of the explanatory variables and of the driver specific error term on the target speed
regulation ratio (ACC target speed regulation predicted divided by ACC target speed regulation baseline
observation) of decreasing (orange) and increasing (dark green) the ACC target speed. The variables are listed
as follows: (a) time after last activation, (b) acceleration, (c) target speed – speed, (d) relative speed, (e) relative
acceleration, and (f) driver specific error term.

23
6.4. Validation analysis
In this section, we analyse the validity of the continuous-discrete choice model presented in Table 3
compared to a choice model that has the same structure and includes only the constants. The aim is to
understand the ability of the model to predict the choices of individual drivers on a different road segment
and the choices of drivers not included in the estimation sample. The model should be applied to an
independent dataset to understand its prediction capability. Since no similar independent datasets are
available, two different approaches are proposed: the model is estimated on the observations of all drivers in
two freeway segments and validated on the observations in the freeway segment excluded in the estimation
phase (in-sample-out-of-time); the model is estimated on the observations of 80% of the drivers in the three
freeway segments and validated on the observations of the drivers excluded in the estimation phase
(out-of-sample-in-time).
To test out-of-time performances, the model was estimated on two freeway segments and
validated on the freeway segment excluded in the estimation phase. The procedure was repeated for each
freeway segment. To test out-of-sample performances, a five-fold cross validation approach was used due
to the limited number of drivers available (Hastie et al., 2009). Drivers were assigned randomly to five
groups, the model was estimated on four groups and validated on the group excluded in the estimation
phase. The procedure was repeated five times. These approaches aimed to investigate differences between
freeway segments and between drivers which were not captured in the model.
Table 5 presents the final log likelihood values of the model with constant only and of the model
estimated in Table 3 on the validation samples. Notably, the model proposed has higher forecasting
accuracy than the model with constants only both in-sample-out-of-time and out-of-sample-in-time.
Comparing the three freeway segments, we note that the smallest accuracy improvement occurs when the
model is validated on the third freeway segment. This result might be explained by different geometric
characteristics of the third freeway segment which were not captured by the explanatory variables.
Comparing the five groups of drivers, we note that the smallest accuracy improvements occur when the
model is validated on groups 2, 4 and 5. This means that certain drivers in these groups showed a different
behaviour than the others. Although further analysis is needed to investigate the origin of these differences,
we conclude that the model developed is useful to predict the decision-making process of individual drivers
on a different freeway segment and of drivers not included in the estimation sample.
Table 5 Validation analysis of the continuous-discrete choice model
Drivers
Obs.
Constant log
likelihood 󰇛󰇜
Final log
likelihood 󰆹
󰇛󰇜󰆹
󰇛󰇜
Two freeway segments vs one freeway segment (in-sample-out-of-time)
2nd, 3rd seg. vs. 1st seg.
23
7598
-1371
-1235
0.0995
1st, 3rd seg. vs. 2nd seg.
23
7344
-1176
-1063
0.0963
1st, 2nd seg. vs. 3rd seg.
23
8626
-1038
-975
0.0606
M
23
7856
-1195
-1091
0.0855
SD
0
678.83
167.46
132.15
0.0216
80% of drivers vs 20% of drivers (out-of-sample-in-time)
Groups 2-5 vs. group 1
5
4742
-818
-734
0.1027
Groups 1, 3-5 vs. group 2
4
4687
-622
-564
0.0939
Groups 1-2, 4-5 vs. group 3
5
4658
-679
-589
0.1333
Groups 1-3, 5 vs. group 4
4
4758
-651
-590
0.0924
Groups 1-4 vs. group 5
5
4723
-749
-681
0.0910
M
4.60
4714
-704
-632
0.1027
SD
0.55
40.82
79.45
72.64
0.0177

24
7. Conclusions and future research
This paper has proposed a comprehensive model framework explaining the underlying decision-making
process of drivers at an operational level based on Risk Allostasis Theory (RAT) (Fuller, 2011). This
framework represents one of the first attempts to develop a conceptual model explaining driver interaction
with driver assistance systems based on theories developed in the field of driver psychology. We proposed
two levels of decision-making describing both control transitions and target speed regulations with
full-range ACC: risk feeling and task difficulty evaluation, and ACC system state and ACC target speed
regulation choice. If the perceived risk feeling and task difficulty level is higher than the maximum value
acceptable, the driver will choose to deactivate the system or to decrease the ACC target speed maintaining
the system active. If the perceived risk feeling level is lower than the minimum value acceptable, the driver
will choose to overrule the ACC by pressing the gas pedal, to increase the ACC target speed maintaining the
system active, or not to intervene. Notably, this conceptual framework supports the specification and the
estimation of mathematical models that capture interdependencies between decisions of control transitions
and target speed regulations in full-range ACC.
The mathematical formulation proposed accommodates decisions on both discrete and continuous
variables, modelling unobservable constructs and interdependencies between decisions in terms of
causality, unobserved driver characteristics, and state dependency. The model explicitly recognizes the
ordinal and discrete nature of the underlying risk feeling and task difficulty evaluation, capturing both
observed and unobserved heterogeneity in the minimum and in the maximum risk acceptable. The
magnitude of the ACC target speed regulation is chosen simultaneously to the system state and correlations
between these two choices are captured explicitly. Causality is addressed by modelling the observable
decisions (control transitions and target speed regulations) as conditional on the unobservable constructs
(feeling of risk and task difficulty evaluation). This formulation allows choices to maintain the system
active to arise from different levels of perceived risk (acceptable and low), capturing explicitly drivers’
propensity not to intervene. Correlations among decisions made by an individual driver are captured by
introducing driver-specific error terms in each level of decision-making. State dependency is addressed by
including the driver behaviour characteristics of the subject vehicle and of its direct leader as explanatory
variables in the different levels. The model allows to investigate the impact of different explanatory
variables on each level of decision making and to quantify the impact of changes in these variables on
drivers’ decisions to transfer control and to regulate the target speed. The model parameters can be
rigorously estimated based on empirical data using maximum likelihood methods.
The findings in the case study support the hypothesis that feeling of risk and task difficulty are the
main factors informing drivers’ decisions to transfer control and to regulate the target speed in full-range
ACC. The model was estimated using driver behaviour data collected in an on-road experiment. Transitions
to Inactive (deactivations) and ACC target speed reductions occurred most often in high risk feeling and
task difficulty situations (high speeds, short distance headways, slower leader, and cut-ins expected), while
transitions to Active and accelerate (overruling actions by pressing the gas pedal) and target speed
increments in low risk feeling and task difficulty situations (low speeds, large distance headways and faster
leader). Control transitions and ACC target speed regulations can be interpreted as an attempt to decrease or
increase the complexity of a traffic situation. Individual characteristics and the functioning of the system
influenced drivers’ decisions significantly. These factors should be accounted for when analysing the
acceptability of a full-range ACC. Interestingly, sometimes drivers do not intervene in low risk feeling and
task difficulty situations. This result might be explained by difficulties in perceiving changes in low risk
feelings, which might be influenced by human factors such as errors, shifts in attention and distraction.
The principal implication of this study is that, to describe driver interaction with ACC, we need a
conceptual model framework that connects driver behaviour characteristics, driver characteristics, ACC
system settings, and environmental factors. This conceptual framework can be formulated mathematically
using discrete choice models, which are able to capture unobservable constructs and interdependencies
between different decisions made by the same driver. Other advantages of discrete choice models are that
the model structure can be selected based on insights from driver control theories, the parameters can be
formally estimated, and the estimation results are directly interpretable.

25
The estimation results presented in the case study need to be interpreted with caution. The sample of
participants was limited (23) and was not representative of the driver population in terms of gender, age,
experience with ADAS, and employment status. It is advised that future studies are carried out with a larger
sample of participants that is representative of the driver population. Moreover, further analysis is needed to
generalize the results, which are influenced by the characteristics of the ACC system, to other types of
driving assistance systems.
Nonetheless, the results have important implications for developing new driving assistance
systems that can adapt their settings based on different traffic situations and driver characteristics to prevent
control transitions while guaranteeing safety and comfort. The model proposed can be implemented into
these new systems to identify the situations in which drivers are likely to resume manual control.
Accounting for a certain variability in drivers’ decision-making, the model can also be used to forecast the
probability that drivers resume manual control based on the programmed response of the system. These
findings contribute to the development of new driving assistance systems that are acceptable for drivers in a
wider range of traffic situations (Bifulco et al., 2013; Goodrich and Boer, 2003).
The model proposed can be directly implemented into a microscopic traffic flow simulation to
analyse the impact of ACC on traffic safety and traffic flow efficiency at different penetration rates
accounting for drivers’ interventions. Previous microscopic traffic simulation models have proposed
deterministic decision rules for resuming manual control in ACC, which were not supported by current
theories of driver behaviour and were not estimated based on empirical data. The possibility of regulating
the longitudinal control task by adjusting the ACC target speed was ignored. These methodological
limitations were addressed in the current study. The data collection method proposed (controlled on-road
experiment) allows analysing driving behaviour with full-range ACC in real traffic, controlling for
potentially confounding factors such as road design and traffic conditions. In addition, the driver
characteristics collected using the questionnaires contributed to explain the observed behaviour. These
findings can increase the realism and accuracy of current driver behaviour models.
Further research is recommended to focus on increasing the behavioural realism of the model
framework proposed. The framework is generic and can be extended to accommodate other explanatory
variables and unobservable constructs. Driver decisions can be influenced by factors such as congestion
levels, time pressure, presence of vehicles in the nearby lanes, number of heavy vehicles, number of lanes
available, and lane width. Physiological measurements capturing the workload and the stress level
experienced by drivers can be integrated into the framework as indicators of the feeling of risk and task
difficulty perceived. Driver state monitor systems (e.g., eye-tracking) can be used to investigate the origin
of drivers’ choices to maintain the ACC active and the current target speed in low risk situations. These
measurements could be integrated into the choice model using, for instance, latent variable models (Vij and
Walker, 2016; Walker, 2001). Similar model frameworks can be developed to investigate driver adaptations
at an operational level to other driving assistance systems and to higher levels of vehicle automation. When
the driver monitors the environment permanently (SAE Level 1 and 2), risk feeling is expected to be the
main construct informing the decision-making process. When the driver is requested to monitor the
environment only in specific traffic situations (SAE Level 3 and 4), new constructs such as driving comfort
and engagement in non-driving tasks can be explored.
Acknowledgments
Silvia Varotto, Haneen Farah, Bart van Arem and Serge Hoogendoorn were funded by the project HFAuto
– Human Factors of Automated Driving, while Tomer Toledo was supported by the Israeli Ministry of
National Infrastructure, Energy and Water Resources. The authors are grateful to Klaus Bogenberger at
Universität der Bundeswehr in Munich for his valuable contribution in designing the experiment, and
Werner Huber, Pei-Shih (Dennis) Huang and Martin Friedl at BMW group in Munich for their appreciated
technical support in collecting the data. Special thanks to Michel Bierlaire at Ecole Polytechnique Fédérale
de Lausanne, Cinzia Cirillo at University of Maryland, Moshe Ben-Akiva at Massachusetts Institute of
Technology, and Kenneth Train at University of California Berkeley for insightful comments which
contributed to improve the model specification and the validation.

26
Appendix A. Data analysis
Figure A 1 Empirical cumulative distribution functions of the driver behaviour characteristics of transferring
to Inactive (red), decreasing the ACC target speed (orange), maintaining the ACC active (blue), increasing the
ACC target speed (dark green), and transferring to Active and accelerate (light green). The variables are listed
as follows: (a) time after last activation, (b) speed, (c) acceleration, (d) target time headway – time headway, (e)
target speed – speed, (f) distance headway, (g) relative speed, (h) relative acceleration, and (i) ACC target speed
regulation. A reduced version of the figure focusing on transitions to manual control was presented in Varotto
et al. (2017).

27
Table A 1 Two sample Kolmogorov-Smirnov test (p-value) of the driver behaviour characteristics when drivers
transfer the ACC to Inactive (I), decrease the ACC target speed (AS-), maintain the ACC Active (A), increase
the ACC target speed (AS+), and transfer to Active and accelerate (AAc); (**) p-value>0.05; (*)
0.01<p-value<0.05; a reduced version of the table focusing on transitions to manual control was presented in
Varotto et al. (2017);
Variables
I vs.
AS-
I vs.
A
I vs.
AAc
AS- vs.
A
AS- vs.
AS+
AS+ vs.
A
AS+ vs.
AAc
AAc vs.
A
Time after
last activ.
0.254(**)
4.10·10-5
8.64·10-5
0.000354
0.301(**)
4.10·10-6
3.04·10-10
5.78·10-27
Speed
0.320(**)
0.00107
0.0486(*)
1.16·10-5
0.000212
3.02·10-7
0.0182(*)
4.27·10-5
Acceleration
0.438(**)
0.428(**)
0.00320
0.000546
2.43·10-5
0.00189
5.70·10-13
2.19·10-10
Target time
headway –
time head.
0.900(**)
0.185(**)
0.000110
0.00149
0.424(**)
2.01·10-8
0.0905(**)
1.74·10-11
Target speed
– speed
0.613(**)
0.228(**)
0.464(**)
0.00214
3.36·10-5
8.66·10-29
5.99·10-9
0.00496
Distance
headway
0.781(**)
0.00837
0.0335(*)
1.69·10-8
0.121(**)
3.69·10-8
1.17·10-6
0.128(**)
Relative
speed
0.0680(**)
2.83·10-8
0.000230
3.26·10-5
1.94·10-10
1.34·10-17
1.30·10-8
0.0952(**)
Relative
acceleration
0.000485
1.17·10-8
7.67·10-9
0.0694(**)
0.0296(*)
0.000271
0.0626(**)
0.00108
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