arXiv:physics/0601096v1 [physics.soc-ph] 13 Jan 2006
Jam-avoiding adaptive cruise control (ACC) and
its impact on traﬃc dynamics
Arne Kesting1, Martin Treiber1, Martin Sch¨onhof1, Florian Kranke2, and Dirk
1Technische Universit¨at Dresden, Institute for Transport & Economics,
Andreas-Schubert-Strasse 23, D-01062 Dresden, Germany
2Volkswagen AG, Postfach 011/1895, D-38436 Wolfsburg, Germany
3Collegium Budapest – Institute for Advanced Study,
Szenth´aroms´ag u. 2, H-1014 Budapest, Hungary
Abstract. Adaptive-Cruise Control (ACC) automatically accelerates or decelerates a
vehicle to maintain a selected time gap, to reach a desired velocity, or to prevent a
rear-end collision. To this end, the ACC sensors detect and track the vehicle ahead for
measuring the actual distance and speed diﬀerence. Together with the own velocity,
these input variables are exactly the same as in car-following models. The focus of
this contribution is: What will be the impact of a spreading of ACC systems on the
traﬃc dynamics? Do automated driving strategies have the potential to improve the
capacity and stability of traﬃc ﬂow or will they necessarily increase the heterogeneity
and instability? How does the result depend on the ACC equipment level?
We discuss microscopic modeling aspects for human and automated (ACC) driving.
By means of microscopic traﬃc simulations, we study how a variable percentage of
ACC-equipped vehicles inﬂuences the stability of traﬃc ﬂow, the maximum ﬂow under
free traﬃc conditions until traﬃc breaks down, and the dynamic capacity of congested
traﬃc. Furthermore, we compare diﬀerent percentages of ACC with respect to travel
times in a speciﬁc congestion scenario. Remarkably, we ﬁnd that already a small amount
of ACC equipped cars and, hence, a marginally increased free and dynamic capacity,
leads to a drastic reduction of traﬃc congestion.
Traﬃc congestion is a severe problem on European freeways. According to a
study of the European Commission , its impact amounts to 0.5% of the gross
national product and will increase even up to 1% in the year 2010. Since building
new infrastructure is no longer an appropriate option in most (Western) coun-
tries, there are many approaches towards a more eﬀective road usage and a more
’intelligent’ way of increasing the capacity of the road network. Examples of ad-
vanced traﬃc control systems are, e.g., ’intelligent’ speed limits, adaptive ramp
metering, or dynamic routing. These examples are based on a centralized traﬃc
management, which controls the operation and the response to a given traﬃc
situation. In this contribution, we focus on a local strategy based on autonomous
vehicles, which are equipped with adaptive cruise control (ACC) systems. The
motivation is that a ’jam-avoiding’ driving strategy of these automated vehicles
2 A. Kesting, et al.
might also help to increase the road capacity and thus decrease traﬃc conges-
tion. Moreover, ACC systems become commercially available to an increasing
number of vehicle types.
An ACC system is able to detect and to track the vehicle ahead, measuring
the actual distance and speed diﬀerence. Together with the own speed, these in-
put data allow the system to calculate the required acceleration or deceleration
to maintain a selected time headway, to reach a desired velocity, or to prevent
a rear-end collision. It should be emphasized that ACC systems control the lon-
gitudinal driving task. Merging, lane changing or gap-creation for other vehicles
still needs the intervention of the driver. ACC systems promise a gain in comfort
and safety in applicable driving situations, but they are not yet applied in con-
gested traﬃc conditions. The next generation of ACC will successfully extend
the application range to all speed ranges and most traﬃc situations on freeways
including stop-and-go traﬃc. This leads to the question: In which way does a
growing market penetration of ACC-equipped vehicles inﬂuence the capacity and
stability of traﬃc ﬂow? Although there is considerable research on this topic ,
there is even no clarity up to now about the sign of the eﬀect. Some investigations
predict a positive eﬀect [3,4], while others are more pessimistic [5,6].
The contribution is organized as follows: We start with a discussion of mod-
eling issues concerning the description of human vs. automated driving and pin-
point the diﬀerences between ACC-driven vehicles and human drivers. In Sec. 3,
we will model three ACC driving styles, which are explicitly designed to increase
the dynamic capacity and traﬃc stability by varying the individual driving be-
havior. Since the impact on the traﬃc dynamics could solely be answered by
means of traﬃc simulations, in Sec. 4 we perform a simulation study of mixed
freeway traﬃc with a variable percentage of ACC vehicles. In Sec. 5, we conclude
with a discussion of our results.
2 Modeling human and automated (ACC) driving
Most microscopic traﬃc models describe the acceleration and deceleration of
each individual ’driver-vehicle unit’ as a function of the distance and velocity
diﬀerence to the vehicle in front and on the own velocity [7,8]. Some of these car-
following models have been successful to reproducing the characteristic features
of macroscopic traﬃc phenomena such as traﬃc breakdowns, the scattering in
the fundamental diagram, traﬃc instabilities, and the propagation of stop-and-
go waves or other patterns of congested traﬃc. While these collective phenomena
can be described by macroscopic, ﬂuid-dynamic traﬃc models as well , mi-
croscopic models are more appropriate to cope with the heterogeneity of mixed
traﬃc, e.g., by representing individual driver-vehicle units by diﬀerent parameter
sets or even by diﬀerent models.
Remarkably, the input quantities of car-following models are exactly those of
an ACC system. As in microscopic models, the ACC controller unit calculates
the acceleration with a negligible response time. Therefore, one might state that
’Jam-avoiding’ adaptive cruise control (ACC) 3
car-following models describe ACC systems more accurately than human drivers
despite of their intention to reproduce the traﬃc dynamics of human driving
Thus, the question arises, how to take into account the human aspects of driv-
ing for a realistic description of the traﬃc dynamics. The nature of human driving
is apparently more complex. First of all, the ﬁnite reaction time of humans results
in a delayed response towards the traﬃc situation. Furthermore, human drivers
have to cope with imperfect estimation capabilities resulting in perception er-
rors and limited attention spans. These destabilizing inﬂuences alone would lead
to a more unsafe driving and a high number of accidents if the reaction time
reached the order of the time headway. But in day-to-day situations the con-
trary is observed: In dense (not yet congested) traﬃc, the modal value of the
time headway distribution on German or Dutch freeways (i.e., the value where
it reaches its maximum) is around 0.9 s [10,11,12], which is of the same order
of typical reaction times . Moreover, single-vehicle data for German freeways
 indicate that some drivers even drive at headways as low as 0.3 s, which
is below the reaction time by a factor of at least 2-3 even for a very attentive
driver. For principal reasons, therefore, safe driving is not possible in this case
when considering only one vehicle in front.
This suggests that human drivers achieve additional stability and safety by
scanning the traﬃc situation several vehicles ahead and by anticipating future
traﬃc situations. The question is, how this behavior aﬀects the overall driving
behavior and performance with respect to ACC-like driving mimicked by car-
following models. Do the stabilizing eﬀects (such as anticipation) or the destabi-
lizing eﬀects (such as reaction times and estimation errors) dominate, or do they
eﬀectively cancel out each other? The human driver model (HDM)  extends
the car-following modeling approach by explicitly taking into account reaction
times, perception errors, spatial anticipation (more than one vehicle ahead) and
temporal anticipation (extrapolating the future traﬃc situation). It turns out
that the destabilizing eﬀects of reaction times and estimation errors can be com-
pensated for by spatial and temporal anticipation . One obtains essentially
the same longitudinal dynamics, which explains the good performance of the
simpler, ACC-like car-following models.
Thus, for the sake of simplicity, we model both automated ACC-driving and
human driving with the same microscopic traﬃc model, but diﬀerentiate the
driving strategies by diﬀerent parameter sets.
3 ’Jam-avoiding’ ACC driving strategies
As discussed in the previous section, both human drivers and ACC-controlled
vehicles are eﬀectively described by the car-following model approach. Here, we
will use the intelligent driver model (IDM) , according to which the accelera-
tion of each vehicle αis a continuous function of the velocity vα, the net distance
gap sα, and the velocity diﬀerence (approaching rate) ∆vαto the leading vehicle:
4 A. Kesting, et al.
The deceleration term depends on the ratio between the eﬀective ’desired mini-
s∗(v, ∆v) = s0+vT +v∆v
and the actual gap sα. The minimum distance s0in congested traﬃc is signiﬁcant
for low velocities only. The dominating term in stationary traﬃc is vT , which
corresponds to following the leading vehicle with a constant safe time headway T.
The last term is only active in non-stationary traﬃc and implements an accident-
free, ’intelligent’ driving behavior including a braking strategy that, in nearly all
situations, limits braking decelerations to the ’comfortable deceleration’ b. The
IDM guarantees crash-free driving. The parameters for the simulations are given
in Table 1.
In order to design a jam-avoiding behavior for the ACC vehicles, we modify
the ACC model parameters. The (average) time headway has a direct relation to
the maximum (static) road capacity: Neglecting the length of vehicles leads to
the approximative relationship Q≈1/T between the ﬂow Qand the headway T
(cf. Eq. (3) below). The crucial parameter controlling the capacity is, therefore,
the safe time headway, which is an explicit parameter of the IDM. Moreover, the
system performance is not only determined by the time headway distribution,
but also depends on the stability of traﬃc ﬂow. An ACC driving behavior aiming
at increasing the traﬃc performance should, therefore, additionally consider a
driving strategy which is able to stabilize the traﬃc ﬂow, e.g. by a faster dynamic
adaptation to the new traﬃc situation. The stability is mainly aﬀected by the
IDM parameters ’maximum acceleration’ and ’desired deceleration’, see .
In the following, we will investigate the potentials of three diﬀerent parameter
sets for jam-avoiding driving behavior, varying the IDM parameters T,aand
b. In order to refer to the values given in Table 1, we express the parameter
changes by simple multipliers. For example, λa= 2 represents an increased
ACC parameter a′=λaa, where ais the value listed in Table 1.
(1) The reduction of the time headway Tby a factor λT= 2/3 has a posi-
tive impact on the capacity. The other model parameters of Table 1 remain
unchanged, i.e., in particular, λa= 1, λb= 1.
(2) Besides setting λT= 2/3, we increase the desired acceleration by choosing
λa= 2. The faster acceleration towards the desired velocity increases the
(3) The additional reduction of the desired deceleration by λb= 1/2 corresponds
to a more cautious and more anticipative driving style. This behavior also
increases the stability.
’Jam-avoiding’ adaptive cruise control (ACC) 5
Model Parameter Value
Desired velocity v0120 km/h
Save time headway T1.5 s
Maximum acceleration a1.0 m/s2
Desired deceleration b2.0 m/s2
Jam distance s02 m
Table 1. Model parameters of the intel ligent driver model (IDM) used in our simu-
lations. The vehicle length is 5 m. In order to model ’jam-avoiding’ ACC strategies,
we modify the safe time headway parameter T, the ’maximum acceleration’ aand the
’desired deceleration’ bby multipliers λT,λa, and λb, respectively.
4 Microscopic simulations of mixed traﬃc
Let us now investigate the impact of ACC vehicles which are designed to enhance
the capacity and stability of traﬃc ﬂows. We will simulate mixed traﬃc consisting
of human and automated (ACC) longitudinal control with a variable percentage
of ACC vehicles.
Our simulation is carried out a single-lane road with an on-ramp serving
as bottleneck and with open boundary conditions. To keep matters simple, we
replace an explicit modeling of the merging of ramp vehicles to the main road by
inserting ramp vehicles centrally into the largest gap within a 300 m long ramp
section. In order to generate a suﬃcient velocity perturbation in the merge area,
the speed of the accelerating on-ramp vehicles at the time of insertion is assumed
to be 50% of the velocity of the respective front vehicle.
Moreover, we neglect trucks and multi-lane eﬀects. While these aspects are
relevant in real traﬃc, they do not change the picture qualitatively. Nevertheless,
the induction of a second driver-vehicle type, e.g., ACC vehicles, always has the
potential to reduce the traﬃc performance by an increased level of heterogene-
ity. We have compared the simulation results with Gaussian distributed model
parameters, but found no qualitative diﬀerence for this single-lane scenario.
4.1 Spatiotemporal dynamics and travel time
Let us now demonstrate that already a moderate increase in the dynamic ca-
pacity obtained by a small percentage of ’jam-avoiding’ ACC vehicles may have
a signiﬁcant eﬀect on the system performance.
We have simulated idealized rush-hour conditions by linearly increasing the
inﬂow at the upstream boundary over a period of 2 hours from 1200 vehicles/h
to 1600 vehicles/h. Afterwards, we have linearly decreased the traﬃc volume to
1000 vehicles/h until t= 5 h. Moreover, we have assumed a constant ramp ﬂow
of 280 vehicles/h. Since the maximum overall ﬂow of 1880 vehicles/h exceeds the
road capacity, a traﬃc breakdown is provoked at the bottleneck. We have used
the IDM parameters from Table 1 and parameter set (3) for ACC vehicles, i.e.,
λT= 2/3, λa= 2, λb= 1/2.
6 A. Kesting, et al.
Figure 1 shows the spatiotemporal dynamics of the traﬃc density for 0% and
10% ACC vehicles. The increased capacity obtained by the induced ACC vehicles
leads to a strong reduction of the traﬃc jam already for a small percentage of
ACC vehicles. For 30% ACC vehicles, the traﬃc jam disappears completely.
An increased percentage of ’jam-avoiding’ ACC vehicles has a strong eﬀect
on the travel time: Figure 2 shows the actual and cumulated travel times for
various ACC percentages. At the peak of congestion (t= 3.2 h), the travel time
for individual drivers is nearly triple that of the uncongested situation (t < 1 h).
Already 10% ACC vehicles reduce the maximum travel time delay of individual
drivers by about 30% (Fig. 2(a)), and the cumulated time delay (which can be
associated with the economic cost of this jam) by 50% (Fig. 2(b)). Several fac-
tors contribute to this enhanced system performance. First, an increased ACC
percentage leads to a delay of the traﬃc breakdown. Second, the ACC vehicles
reduce the maximum queue length signiﬁcantly. Third, the jam dissolves earlier.
These eﬀects, which are responsible for the drastic increase in the system per-
formance already for a small proportion of ’jam-avoiding’ ACC vehicles, will be
investigated in the following.
Fig. 1. Spatiotemporal dynamics of the traﬃc density (a) without ACC vehicles and
(b) with 10% ACC vehicles (parameter set (3)). Already a small increase in the road
capacity induced by a small percentage of ’jam-avoiding’ ACC vehicles leads to a
signiﬁcant reduction of traﬃc congestion (light high-density area).
4.2 Maximum capacity in free traﬃc
The static road capacity Qt heo
max , which corresponds to the maximum of the ﬂow-
density diagram, is mainly determined by the average time headway T. However,
the theoretical capacity depends also on the ’eﬀective’ length leﬀ =lveh +s0of
a driver-vehicle unit and is given by
The maximum capacity Qfree
max before traﬃc breaks down (which is a dynamic
quantity), however, is typically lower than Qthe o
max , since it depends on the traf-
’Jam-avoiding’ adaptive cruise control (ACC) 7
1 1.5 2 2.5 3 3.5 4 4.5 5
Actual travel time (min)
Simulation time (h)
0 1 2 3 4 5
Cumulated travel time (h)
Simulation time (h)
Fig. 2. Time series for (a) the actual and (b) the cumulated travel times for simulation
runs with diﬀerent percentages of ACC vehicles. The traﬃc breakdown leads to a sig-
niﬁcant prolongation of travel time. A proportion of 30% ACC vehicles can completely
prevent the traﬃc breakdown.
ﬁc stability as well. Therefore, we have analyzed the ’maximum free capacity’
resulting from the traﬃc dynamics as a function of the average time head-
way Tand the percentage of ACC vehicles. Our related simulation runs start
with a low upstream inﬂow and linearly increase the inﬂow with a rate of
Qin = 800 vehicles/h2. We have checked other progression rates as well, but
found a marginal diﬀerence only.
For determining the traﬃc breakdown, we have used ’virtual detectors’ lo-
cated 1 km upstream and downstream of the on-ramp location. In analogy to
the real-world double-loop detectors, ’virtual detectors’ count the passing vehi-
cles, measure the velocities, and aggregate the data within a time interval of one
minute. For each simulation run, we have recorded the maximum ﬂow before
traﬃc has broken down (single dots in Fig. 3(a)). Due to the complexity of the
simulation and the 1-min data aggregation, Qfree
max varies stochastically. We have,
therefore, averaged the data with a linear regression using a Gaussian weight of
width σ= 0.2, and plotted the expectation value and the standard deviation.
Figure 3(a) shows the maximum free capacity as a function of the ACC per-
centage for the three diﬀerent parameter sets representing diﬀerent ACC driving
max increases approximately linearly with increasing percentage of ACC
vehicles. The parameter amainly increases the traﬃc stability, which leads to
a delayed traﬃc breakdown and, thus, to higher values of Qfree
the values are nearly identical with those for heterogenous traﬃc consisting of
driver-vehicle units with Gaussian distributed parameters.
In Fig. 3(b) the most important parameter, the time headway T, is varied for
a homogeneous ensemble of 100% ACC vehicles. Obviously, Qfree
max decreases with
increasing T. Furthermore, the dynamic quantity Qfree
max remains always lower
than the theoretical capacity Qtheo
max given by Eq. (3), which is only reached for
perfectly stable traﬃc. The three parameter sets show the inﬂuence of the IDM
parameters aand b: The acceleration ahas a strong impact on traﬃc stability,
while the stabilizing inﬂuence of bis smaller. Finally, as the diﬀerence between
8 A. Kesting, et al.
max and the dynamic maximum free capacity Qfree
max increases for lower values
of T, one ﬁnds that a smaller Treduces stability as well.
In order the assess the potentials of various driving styles, we have evaluated
an approximate relationship as a function of the ACC equipment level αACC.
The relative gain γin system performance is given by
γ≈[0.95(1 −λT) + 0.07λa+ 0.08(1 −λb)] αACC.(4)
Thus, λTis the most crucial parameter, while λbhas hardly any inﬂuence. For
example, lowering the time headway by λT= 0.7 with αACC = 1 results in a
maximum gain of γ≈30%.
0 0.2 0.4 0.6 0.8 1
Maximum flow before breakdown (1/h)
Proportion of ACC vehicles
0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
Maximum flow before breakdown (1/h)
Time headway T (s)
Fig. 3. Maximum free capacity as a function of (a) the percentage of ACC vehicles,
and (b) the time headway Tfor 100% ACC vehicles. We have simulated three diﬀerent
parameter sets for ACC vehicles with λT= 2/3 and varying values of λaand λb
(see main text). Dots indicate results of single simulation runs, while the solid lines
correspond to averages over several simulations and the associated bands to plus/minus
one standard deviation.
4.3 Dynamic capacity after a traﬃc breakdown
Let us now investigate the system dynamics after a traﬃc breakdown. The crucial
quantity is the dynamic capacity, i.e., the downstream outﬂow from a traﬃc
congestion Qout . The diﬀerence between the free capacity Qfree
max and Qout is
denoted as capacity drop with typical values between 5% and 30%.
We have used the same simulation setup as in the previous section. After a
traﬃc breakdown was provoked by an increasing inﬂow, we have averaged over
the 1-min ﬂow data of the ’virtual detector’ 1 km downstream of the bottleneck.
We have identiﬁed the congested traﬃc state by ﬁltering out for velocities smaller
than 50 km/h at a cross-section 1 km upstream of the bottleneck. Again, we have
averaged over multiple simulation runs by applying a Gaussian-weighted linear
’Jam-avoiding’ adaptive cruise control (ACC) 9
Figure 4(a) shows the dynamic capacity for a variable percentage of ACC
vehicles for the three diﬀerent parameter sets speciﬁed before. Interestingly, the
capacity increase is not linear as in Fig. 3(a). Above approximately 50% ACC
vehicles, the dynamic capacity increases faster than for lower percentages. We
explain this behavior with an ’obstruction eﬀect’: the faster accelerating ACC
vehicles are hindered by the slower accelerating drivers. In fact, the slowest
vehicle type determines the dynamic capacity, which could be called a ’weakest
link eﬀect’. In conclusion, distributed model parameters have a quantitative
eﬀect on the outﬂow from congested traﬃc (it is lower than for homogeneous
traﬃc with averaged parameters), while such an eﬀect is not observed for the
0 0.2 0.4 0.6 0.8 1
Dynamic capacity Qout (1/h)
Proportion of ACC vehicles
0 20 40 60 80 100
Flow Q (1/h)
1-min data (8km)
Fig. 4. (a) Dynamic capacity as a function of the percentage of ACC vehicles. The
curves represent three diﬀerent parameter sets corresponding to diﬀerent ACC driving
strategies. The results from multiple simulation runs are averaged using a linear re-
gression with a Gaussian weight of width σ= 0.2. (b) Flow-density data for the traﬃc
breakdown determined from a ’virtual’ detector 2 km upstream of the bottleneck with-
out ACC vehicles. The equilibrium ﬂow-density curve of identical vehicles corresponds
to the parameter set given in Table 1.
Adaptive cruise control (ACC) systems are already available on the market. The
next generations of ACC systems will extend their range of applicability to all
speeds, and it is assumed that their spreading will grow in the future. In this
contribution, by means of microscopic traﬃc simulations we have investigated
the impact that an automated longitudinal driving control of ACC systems based
on the intelligent driver model (IDM) is expected to have on the traﬃc dynamics.
ACC systems are closely related to car-following models as their reaction
is restricted to a leading vehicle. Moreover, we have explained why such a car-
following approach also captures the main aspects of longitudinal driver behavior
so well. We, therefore, expect that both ACC systems and human driver behavior
10 A. Kesting, et al.
will mix consistently in future traﬃc ﬂows although the driving operation is
The equipment level of ACC systems provides an interesting option to en-
hance the traﬃc performance by automated driving strategies. In order to an-
alyze the potentials, we have studied ACC driving styles, which are explicitly
designed to increase the capacity and stability of traﬃc ﬂows. We have varied
the percentage of ACC vehicles and found that already a small proportion of
ACC vehicles, which implies a marginally increased free and dynamic capacity,
leads to a drastic reduction of traﬃc congestion. Furthermore, we have shown
that, capacity and stability do have similar importance for the traﬃc dynamics.
We have assumed that the ACC systems have a more ’jam-avoiding’ driving
style than the human drivers. One might additionally take into account ineﬃcient
human behavior when traﬃc gets denser and the time headway increases with
increasing local velocity variance [12,17]. In this case, a constant time headway
policy for automated driving is expected to improve the system performance
Up to now, ACC systems are only optimized for the user’s driving comfort
and safety. In fact, present ACC systems may have a negative inﬂuence on the
system performance when their percentage becomes large. The design of ACC
strategies, which also consider their impact on traﬃc dynamics, will be crucial
for the next ACC generations.
Furthermore, we propose to implement an ’intelligent’ ACC strategy that
adapts the ACC driving style dynamically to the overall traﬃc situation. For
example, in dense, but not yet congested traﬃc, a jam-avoiding parameter set
could help to delay or suppress traﬃc breakdowns as shown in our simulations,
while in free traﬃc a parameter set mimicking natural driver behavior may be
applied instead. The respective ’traﬃc state’ could be autonomously detected
by the vehicles using the history of their sensor data in combination with dig-
ital maps. Moreover, inter-vehicle communication could contribute information
about the traﬃc situation in the neigborhood, e.g., by detecting the downstream
front of a traﬃc jam .
Acknowledgments: The authors would like to thank Hans-J¨urgen Stauss,
and Klaus Rieck for the excellent collaboration and the Volkswagen AG for
partial ﬁnancial support within the BMBF project INVENT.
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