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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

Helbing1,3

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.

1 Introduction

Traﬃc congestion is a severe problem on European freeways. According to a

study of the European Commission [1], 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 [2],

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

behavior

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 [9], 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

behavior.

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 [13]. Moreover, single-vehicle data for German freeways

[10] 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) [14] 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 [14]. 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) [15], 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.

˙vα=a"1−vα

v04

−s∗(vα, ∆vα)

sα2#.(1)

The deceleration term depends on the ratio between the eﬀective ’desired mini-

mum gap’

s∗(v, ∆v) = s0+vT +v∆v

2√ab (2)

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 [15].

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

traﬃc stability.

(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

Qtheo

max =1

T1−leﬀ

v0T+leﬀ .(3)

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

6

8

10

12

14

16

18

20

1 1.5 2 2.5 3 3.5 4 4.5 5

Actual travel time (min)

Simulation time (h)

(a)

0% ACC

10% ACC

20% ACC

30% ACC

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5

Cumulated travel time (h)

Simulation time (h)

(b)

0% ACC

10% ACC

20% ACC

30% ACC

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

styles. Qfree

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

max. Remarkably,

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.

Qtheo

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%.

1600

1700

1800

1900

2000

2100

2200

2300

2400

2500

2600

0 0.2 0.4 0.6 0.8 1

Maximum flow before breakdown (1/h)

Proportion of ACC vehicles

(a)

λa=2.0, λb=0.5

λa=2.0, λb=1.0

λa=1.0, λb=1.0

single run

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

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)

(b)

λa=2.0, λb=0.5

λa=2.0, λb=1.0

λa=1.0, λb=1.0

Theoretical Qmax

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 [16]. 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

regression.

’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

free-ﬂow capacity!

1400

1500

1600

1700

1800

1900

2000

2100

2200

2300

2400

2500

0 0.2 0.4 0.6 0.8 1

Dynamic capacity Qout (1/h)

Proportion of ACC vehicles

(a)

λa=2.0, λb=0.5

λa=2.0, λb=1.0

λa=1.0, λb=1.0

Static road

0

500

1000

1500

2000

2500

0 20 40 60 80 100

Flow Q (1/h)

Density (1/km)

1-min data (8km)

Equilibrium flow

Maximum

Dynamic

drop

Capacity

capacity

free flow

capacity

(b)

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.

5 Discussion

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

fundamentally diﬀerent.

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

even more.

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 [18].

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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