Document [original]

IEEE VEHICULAR TECHNOLOGY SOCIETY SECTION

Received January 31, 2022, accepted March 9, 2022, date of publication April 14, 2022, date of current version April 28, 2022.

Digital Object Identifier 10.1109/ACCESS.2022.3167424

A Numerical Study on Constant Spacing

Policies for Starting Platoons at

Oversaturated Intersections

KAY MASSOW 1, ILJA RADUSCH2, AND ROBERT SHORTEN 3, (Senior Member, IEEE)

1Daimler Center for Automotive Information Technology Innovations, Technische Universität Berlin, 10587 Berlin, Germany

2Fraunhofer Institute for Open Communication Systems (FOKUS), 10589 Berlin, Germany

3Dyson School of Design Engineering, Imperial College London, London SW7 2AZ, U.K.

Corresponding author: Kay Massow (kay[email protected])

ABSTRACT Cooperative Adaptive Cruise Control (CACC) is considered as a key potential enabler to

improve driving safety and traffic efficiency. It allows for automated vehicle following using wireless

communication in addition to onboard sensors. To achieve string stability in CACC platoons, constant time

gap (CTG) spacing policies have prevailed in research; namely, vehicle interspacing grows with the speed.

While constant distance gap (CDG) spacing policies provide superior potential to increase traffic capacity

than CTG, their major drawbacks are a smaller safety margin at high velocities and that string stability cannot

be achieved using a one-vehicle look-ahead communication. In this work, we propose to apply CDG only in

a few driving situations, when traffic throughput is of highest importance and safety requirements can be met

due to relatively low velocities. As the most relevant situations where CDG could be applied, we identify

starting platoons at signalized intersections. With this application scenario we show that applying CDG only

in a few specific and crucial situation can have a major impact on traffic efficiency. Specifically, we compare

CTG with CDG regarding its potential to increase the capacity of traffic lights. Starting with the elementary

situation of single traffic lights we expand our scope to whole traffic networks including several thousand

vehicles in simulation. Using real world data to calibrate and validate vehicle dynamics simulation and traffic

simulation, the study discusses the most relevant working parameters of CDG, CTG, and the traffic system

in which both are applied.

INDEX TERMS Cooperative adaptive cruise control, constant spacing, traffic light, signalized intersection,

vehicle simulation, traffic simulation, capacity, throughput.

I. INTRODUCTION

CACC is the extension of Adaptive Cruise Control (ACC),

a driver assistance system which automatically adjusts the

speed of a road vehicle to maintain a safe distance from

vehicles ahead [1]. Today’s ACC systems use radar sen-

sors to measure this distance. CACC extends ACC by addi-

tional communication components to exchange information

with preceding vehicles. This information exchange helps to

increase the density of platoons of vehicles with activated

ACC and to potentially tackle string instabilities occurring in

such platoons. String instability in vehicle platoons is caused

by radar sensor delays and the dynamics of the vehicles

and their power trains. To facilitate string stable spacing

policies, the constant time gap (CTG) has prevailed in

The associate editor coordinating the review of this manuscript and

approving it for publication was Jie Gao .

research; namely, the target distance between vehicles grows

with the speed. However, increasing distances entails effi-

ciency loss. This fact is reflected by the recent decision of

Daimler to cancel their truck platooning program, which

aimed on a 0.68 seconds time gap (15 m at 80 Km/h [40])

and did not achieve the expected efficiency in terms of fuel

saving as stated in [2].

In this work, a constant distance gap (CDG) policy for

CACC is considered. Although CDG can improve traffic

throughput enormously, its applicability in urban environ-

ments has been proven to be very limited, due to its demand

on communication structures to achieve robust string sta-

bility [3]. This demand includes communication with more

vehicles than the direct preceding vehicle. Additionally,

CDG only makes sense in combination with very small gaps,

which implies potential safety issues at increasing velocities.

The hypothesis of this work is to apply CDG only in few

43766 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 10, 2022

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

driving situations, when the following circumstances occur

at the same time:

•Traffic throughput is of crucial importance.

•Platoon sizes are short enough that string instability or

communication topology complexity can be handled,

e.g., employing mini-platoon control strategy [3].

•Velocities are low enough to cover safety requirements,

acceleration is smooth and predictable.

In all other situations, there either is limited benefit in

applying CDG or it entails too much difficulties, so that

CTG should be applied. While there are several use cases in

which such conditions prevail, clearly, traffic-light-controlled

intersections are one of the most relevant. At intersections,

the traffic flow of two crossing streets share one spot in a

time-duplex manner. Thus, exhibiting the highest possible

traffic density on this spot is of high importance. Intersections

controlled by traffic lights in addition provide clearly regu-

lated right-of-way, i.e., during a green light phase, a platoon

can pass this spot as a whole without paying attention to the

cross traffic. Moreover, starting up from a stop line when

the traffic light changes to green results in a smooth and

predictable acceleration maneuver. Thus, as the most relevant

application scenario for the hypothesis of this work presented

above, we will focus on starting platoons at oversaturated,

traffic-light-controlled intersections subsequently. Further

application scenarios will be investigated in future work.

By oversaturated we mean the traffic demand is higher

than the intersection capacity, i.e., its maximum traffic

throughput [26], a situation commonly found in major cities.

Accordingly, we shall assume urban speeds of up to 50 km/h

and stable platoons on intersection either achieved by lim-

ited length or a capable communication topology [3]. The

research questions discussed in the rest of this paper focus

on capacity improvement of CDG over CTG at oversatu-

rated, signalized intersections. Our model for car following

dynamics is based on the controller design presented in [30],

parameterized using real world data.

Remark: Before proceeding, some comments on string sta-

bility are in order. Although string stability is a very important

aspect for realizing CDG in platoons (see related work in the

next section), we do not address string stability nor related

control theory in this work. Instead, we focus on assessing

the traffic performance of CDG over other spacing policies.

While there are many other publications dealing with string

stability, the rationale for this work is the usefulness of pla-

toons, string stability permitting, in the context of specific

use-cases. Our objective here is to study one such situation

in detail, and to illustrate the effectiveness of platoons in an

elementary situation in which string stability is not likely to

be a serious technical issue.

A. MAIN FINDINGS OF THIS WORK AND THE STRUCTURE

OF THIS PAPER

The contribution of this work is to show the benefit of

applying CDG at starting platoons at oversaturated, signal-

ized intersections. Assessing related benefits and potential

drawbacks requires a comprehensive and thorough consid-

eration of the whole traffic system. This includes many

microscopic and macroscopic aspects and aggregating par-

tial results. From the authors’ perspective, these should be

presented as a whole and not be split apart in different

papers. With this in mind, after discussing related work in the

Section II, the remainder of the paper is structured as follows.

•In Section III, we define the scope of our research and

assess the CDG capacity improvement at a single traffic

light on a straight road. For this purpose, we parameter-

ize a CDG policy for vehicle simulation using real world

data. CDG shows a traffic throughput improvement over

the CTG baseline of up to 140%.

•In Section IV, we extend our study to a whole intersec-

tion, in order to cover traffic related aspects which lower

the traffic throughput, such as turning vehicles and right-

of-way. Vehicle simulations, including 160 vehicles,

showed that these aspects can lower the CDG throughput

improvement down to 27% in worst case. We further

found that CDG benefit on throughput grows superlin-

early with the CDG penetration rate among vehicles.

•In Section V, we present a method to calibrate a traffic

simulation model using vehicle dynamics simulation.

This is a prerequisite to include consideration of vehi-

cle dynamics in a traffic simulation with thousands of

vehicles to simulate CDG in a whole traffic system.

•In Section VI we study the impact of CDG on mutually

influencing intersections of a traffic system. A synthetic

arterial scenario of five intersections revealed that CDG

may create backlogs of adjacent intersections, which

block the cross traffic. A synthetic grid scenario of

25 intersections revealed that CDG is vulnerable to cre-

ate gridlocks. We show the impact of these effects on

traffic throughput and how they are related to the traffic

light configurations with respect to green light times and

offset.

•In Section VII, we complement our findings with study-

ing CDG in a real world road network simulation sce-

nario including ten intersections in Berlin, Germany.

CDG gains a throughput improvement of 70%, while

a penetration of 50% CDG reached an improvement

of 25%. To exhibit its full potential in urban traffic,

CDG needs to incorporate cooperative behavior between

vehicles in order to enable cutting in and to prevent

junction blocking.

We conclude this paper in Section VIII. In order to help

the reader to follow the main findings arising throughout the

study, each section concludes with a discussion of its main

findings.

II. RELATED WORK

The most relevant goals for the design of CACC systems are

to create small gaps between vehicles to increase road capac-

ity, guarantee string stability [5], while keeping the commu-

nication topology as simple as possible [1]. The latter is,

in the best case, reduced to each vehicle in a platoon receiving

VOLUME 10, 2022 43767

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

data from its direct preceding vehicle. Further possible com-

munication structures may include receiving data from the

platoon leader, multiple predecessors, the successor, or from

a fully networked platoon [25]. Each of these structures entail

different advantages regarding control quality, string stability

and, thus, on the minimum gap size. Further goals on control

optimization are ride comfort and fuel/energy consumption,

which are both dependent from acceleration profiles.

A. CONSTANT TIME GAP POLICY (CTG)

The constant time gap policy refers to maintaining a time

gap between vehicles in a platoon, which means that the gap

increases linearly with the velocity. This policy has received

most attention in the literature as it is known to improve

string stability even with the simplest communication

structure [5], [6]. The policy alsocontributes to safety, driving

comfort, and imitates human driver behavior. However, the

downside of velocity dependent gaps is the platoon length

growing linearly with the velocity and the associated required

road space. Commonly suggested time gaps of 0.6 s [7]

correspond relates to additional road space of 8 m at 50km/h

compared to stand still.

B. CONSTANT DISTANCE GAP POLICY (CDG)

The constant distance gap policy refers to a fixed gap between

vehicles, independent from the velocity. This policy achieves

the maximum efficiency in terms of road capacity improve-

ment [50]; however string stability cannot be achieved using

the information of the preceding vehicle only. In [8] it was

shown that including additional information from the platoon

leader is required. In order to address string stability, further

communication topologies like mini-platoons [3] or multiple

vehicles look ahead are reviewed in [3] [49]. Cyclic as well

as bidirectional communication architectures are discussed

in [9]. These approaches require a formal platoon architecture

in order to determine a leader and the order of vehicles in a

platoon [1]. This is more difficult to achieve than a simple

communication with the preceding vehicle, which seems to

make it unattractive to employ CDG rather than CTG, even

with the drawback in terms of efficiency. With our hypothesis

in mind, to employ CDG in very specific situations only, for

this work, we can summarize the most relevant information

on the state of the art regarding CDG as follows. After very

early work [8], [50] on CDG showed that overall string stable

platoons cannot be established using a one-vehicle look-

ahead communication, CDG received less subsequent atten-

tion in literature than CTG. Most works on CDG focused on

achieving string stability for the employment of CDG at the

full range of driving conditions [3], [5], [9], [45], [49], [50].

Since this goal is out of scope of this work, we omit a deeper

literature review in this field. However, the interested reader

is referred to the survey article [45] and [1], [49].

C. ADAPTIVE GAP POLICIES

In contrast to CTG, many more parameters than a constant

time factor can be incorporated in the spacing strategy, such

as the spacing strategy proposed in this work. In the follow-

ing, we give an overview of different approaches of such a

kind, summarized under the term adaptive gap policies. The

hypothesis of this work is to apply CDG only in few driving

situations, realized by a context aware switch between CTG

and CDG. This switch is depending on the current importance

of traffic throughput, platoon length, and velocity. To our best

knowledge, switching between CDG and CTG as we propose

in this work, nor solely at a certain velocity threshold, has

not been presented in literature before. In fact, this switching

is not exactly an adaptive gap policy but rather an exchange

of the policy online. In contrary, most works in literature

either aim on designing one variable time gap (VTG) policy

for the full range of driving conditions or switch between

different longitudinal controllers while targeting the same

spacing strategy. Switching between longitudinal controllers,

mostly refers to different controller parameterization, e.g.,

regarding the information flow topology [43], or safety mea-

sures [44], triggered by ambient traffic conditions or com-

munication impairments. The desired inter-vehicle spacing

of VTG policies, in contrast to CTG, is treated as a func-

tion that has more parameters than a constant multiplier of

velocity. There are different approaches that either combine

the benefits of CDG and CTG in one VTG policy in different

ways, or further include different control goals by making

the gap dependent from more parameters than velocity [45],

e.g., to address traffic safety, stability, and efficiency [47].

The latter is mainly addressed by reducing the gap compared

with CTG while keep it smaller in general, but enlarge it

at higher absolute [48] and relative velocities [46]. Further

work has been done to improve the traffic flow stability in

comparison to CTG [10], to integrate safety aspects in the

spacing, such as the constant-safety-factor criterion (CSF)

[1], [47], and vehicle limitations [11], or to adapt it to human

behavior [12]. These adaptive policies gain their positive

effect mostly at shorter distances at lower speeds compared

to CTG. More detailed information about different types of

VTG and other spacing policies can be found in the survey

article [45] and [47].

D. COOPERATIVE MANEUVERS REGARDING

CROSS/PARALLEL TRAFFIC

Another important aspect regarding the spacing of CACC

platoons, is related to cooperative maneuvering [13]. Since

platoons need to allow for cut-in maneuvers of other vehicles,

required gaps have to be provided on demand. For urban

applications, cooperation is especially required at intersec-

tions when platoons need to be crossed by other vehicles.

We do not go into further detail on the wide field of related

applications and the performance of different concepts among

them, since cooperative maneuvering is not the focus of this

work. However, although this work does not deal with such

cooperative coordination strategy explicitly, the subsequent

sections reveal that under certain conditions, CDG should

be complemented by them. Such applications [14] which

extend CACC to accommodate cross traffic and parallel

43768 VOLUME 10, 2022

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

traffic are currently being researched, as an example the

interested reader can refer to the German research project,

IMAGinE [36]. Its applications ‘‘cooperative lane merging’’

and ‘‘cooperative decentralized intersection’’ enable cutting-

in maneuvers and ensure clearing intersections for cross traf-

fic, which is relevant for this paper.

E. COOPERATIVE START-UP AT TRAFFIC LIGHTS

In the field of combining CACC with traffic-light control,

most research is aimed at synchronization of platoons and

green lights phases, so that stop and go can be prevented,

such as [15]. Very few works focus on start-up control coordi-

nating vehicles and traffic lights, so that as many vehicles as

possible can pass an intersection after stand still. [16] studies

platoons of vehicles waiting in front of a traffic-light regu-

lated intersection, using SUMO [34]. A coordinated start-up

initiated by a V2X message SPAT (SAE 2735) of the traffic

light is proposed and the underlying algorithm also addresses

the problem of low market penetrations. [17] considers a

cooperative start-up of real world platoons at traffic lights.

Findings indicate that a constant and preferably small gap is

essential for increasing the throughput at traffic light regu-

lated intersections. [18] presents an automatic start-up control

to start up vehicles with less delay (47.2%) to improve traffic

throughput, while [19] addresses an optimized acceleration

profile to reduce fuel consumption.

F. PLATOONS IN SIGNALIZED NETWORKS

One important aspect of our study is the impact of CDG on

mutually influencing intersections in a traffic system. In order

to assess the impact of CACC on whole traffic systems, it is

not sufficient to consider isolated intersections. In fact, multi-

ple mutually influencing intersections such as signalized arte-

rials need to be considered. This becomes especially relevant

for dense platoons of vehicles, as shown in the subsequent

sections.

Most research in this field focus on the control of traf-

fic lights. In [20] and [51], the authors present algorithms

to optimize signals at arterials, based on real-time platoon

information. Different penetration rates are evaluated on

an eight-intersection arterial using the VISSIM simulator,

achieving a throughput improvement around 10% at 100%

penetration in [20]. A travel time improvement of 70% on an

arterial in a 4 ×4 grid network was achieved in [51] using

SUMO [34].

While this shows the potential of including platoon infor-

mation in the control strategies of traffic lights, in our study

we focus on the benefits of optimizing platoon interspac-

ing, rather than the signal control. Related work like [15]

addresses optimization from the perspective of the vehicles

in a cooperative way. Clusters of vehicles are formed that

approach and depart at intersections on signalized arteri-

als. The approach [15] requires a penetration rate of 100%

and showed an increased traffic throughput of 50%, while

reducing energy consumption. In [24], the authors showed,

by means of a 16-intersection arterial, that without changing

the signal control, throughput can be doubled if vehicles are

organized to cross the intersections in platoons with 0.75 s

headway, i.e., by reducing human delay and time gap only.

Other works, such as [21] and [22] aim to prevent platoon

stops by slowing down until the queue waiting at the inter-

section starts moving in order to safe energy/fuel. Penetration

rates lower than 100% are considered in [21]. In [23] splitting

up platoons and predicting trajectories aim on ideally passing

green light phases. However, this requires a certain space

while approaching the intersection and may hardly work for

arterials with small intersection interspaces.

The trend of studies on platoons in signalized networks

show that the most influencing factor regarding traffic

throughput improvement is the fact that vehicles cross the

intersections in platoons. Further, smaller enhancements can

be generated by signal aware platoon control [15], [21],

[22], [24] and a coordinated control strategy of the traffic

lights [20], [51], which entails considerable system complex-

ity in proportion to the achieved benefit. In this work we will

show that simply applying CDG in platoons in oversaturated

conditions can further increase the throughput by a similar

order of magnitude as platooning itself. However, we will

also give indications how CDG platooning in oversaturated

grid networks could be aligned with the signal schema.

III. SINGLE TRAFFIC LIGHT PERFORMANCE

In this section we investigate the performance of CDG on

a single traffic light, before considering whole intersections

and traffic systems in the subsequent sections. For this pur-

pose, we first need to define a baseline for comparison with

other spacing policies and how performance can be measured.

In this regard, we define the research scope of this

work, including preliminary assumptions. From this scope,

we derive the working parameters for all policies; e.g., the

standstill distance, as these parameters have a major influence

on system performance. Once these parameters are identified,

we use real world data to calibrate them. Finally, we describe

the implementation of the policies that we use for simulation

with the PHABMACS simulator [13] and we evaluate the

results.

A. RESEARCH SCOPE

The most relevant metric to assess traffic light performance

is capacity, which is defined by its maximum throughput,

i.e., the maximum possible number of vehicles passing per

time unit [26]. In order to measure the capacity, we consider

traffic-lights in an oversaturated condition only (e.g., during

rush-hour), which implies that there are always more vehicles

waiting in the queue than can pass in one green phase.

The relevant relationship between throughput and platoons

passing the traffic-light is the number of vehicles per platoon

length. The portion of the platoon length pertaining to each

vehicle in a CTG platoon is dependent upon the parameters

depicted in Fig. 1. The constant portion is the vehicle length

plus the standstill distance. The dynamic portion is the time

gap, which grows with the platoon velocity. The dynamic

VOLUME 10, 2022 43769

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

FIGURE 1. A platoon of i vehicles, where liis the length, riis the

standstill distance, hiis the time gap, ngiis the net gap, and ggiis the

gross gap of the ith vehicle in the platoon.

part is zero in CDG platoons, i.e., the CDG platoon length

is always the same like in standstill, which makes the CDG

so effective.

Another relevant parameter, especially for the start-up at

traffic lights, is the drivers’ reaction time. This time refers

to the delayed start-up of a vehicle in the platoon with

regard to the start-up of its preceding vehicle. In contrast to

CTG, which is similar to human drivers’ vehicle following

behavior, CDG can hardly be realized by humans. Thus,

for CDG we assume a fully automated longitudinal control

with no driver in the loop. This consideration is especially

relevant for the start-up at traffic lights, as human reaction

time would make notable difference here. Since the objective

is to compare the following behavior of CDG with other

policies, we neglect the reaction time for all policies in this

work.

Accordingly, in order to compare CDG with CTG, we need

to parametrize the constant portion, vehicle length and the

standstill distance with the same values. Furthermore, these

values should be chosen as realistic as possible for com-

parison, as their ratio to the time gap makes a considerable

difference. Finally, we also need to parameterize the time gap

of CTG as realistically as possible.

Indications for all these parameters could be derived

from Highway Capacity Manual (HCM) [26] and the

German equivalent HBS [27]. The HCM indicates a capac-

ity of 2400 vehicles per hour on open roadways, while the

HBS indicates 2000 vehicles per hour. Besides the fact that

both values differ considerably (gross gap between vehicles

of 1.8 s and 1.5 s) we have no indication on how to split

that time in the dynamic and the constant portion. Recent

work [14], on the other hand, indicates that time gaps for CTG

of below 0.6 s can be realized for string stable platoons with

automated CACC, (0.25 s in [41]).

Remark: In this study we do not use the theoretical param-

eters used in the above reports, but rather real measurements.

We assumed for this study, that future CACC distance behav-

ior in series production will be of similar performance as

skilled human drivers and with no reaction time. For this

purpose, we derive our baseline (time gap and standstill

distance) from real world data collected during the field trial

simTD [28]. For the sake of fairness, in this section, we will

also present results of using parameterization of achieved

time gaps in current research. We further assume that the

velocities in our study are low enough so that an automated

system can keep the CDG standstill distance.

The resulting parametrization is presented in the next sub-

section. Recall, the hypothesis of this work is to apply CDG

only in few driving situations, realized by a context aware

switch between CTG and CDG. This switch is dependent

from the current importance of traffic throughput, platoon

length, and speed. With the focus on starting platoons at

traffic-light-controlled intersections, we consider this context

to be always given at all simulations presented in this work

because:

•Traffic throughput is of crucial importance at intersec-

tions as they are the bottlenecks in traffic.

•The platoon length is inevitably limited due to the signal

phases cutting platoons.

•Most traffic light scenarios are located in urban areas and

we limit our study to velocities below 50 Km/h.

As earlier mentioned, CDG should not be applied at arbi-

trary high velocities due to safety aspects and stability issues

arising when the one-vehicle-look-ahead communicationpat-

tern is applied. Thus, there is a speed limit at which the CDG

spacing policy is required to be switched to CTG. For the

threshold of this speed limit we chose 50 Km/h and 30 Km/h

as parameters to be studied in simulation, due to the fol-

lowing considerations. While in German cities 50 Km/h is

the speed limit for general safety considerations, 30 km/h

is the speed limit for areas of increased safety demand.

These values provide a good indication for different lev-

els of velocity related safety in our study. Thus, we define

and study two different Policies. For the 50 Km/h thresh-

old we can apply CDG without switching in simulation of

urban environments. In addition, we define another policy

that switches from CDG to CTG at 30 Km/h. This policy

will be referred to as SWITCH in the remainder of this

work.

The specific velocity thresholds of future real world appli-

cation should be derived from real world working parameters,

e.g., the achieved performance of the underlying longitudinal

controller and the current reliability of communication link.

The same applies for the optimal standstill distance in real

world, which should be chosen as small as possible in order

to gain efficiency and large enough regarding the named real

world parameters. Note that, keeping a standstill distance

of 2.95 m, as we will use in our study, might seem challenging

in terms of user experience, even below 30 Km/h. However,

we assume that with the advent of automated driving, users

will gain trust in that technology in the future. This also

applies for CTG with very small time gaps, as [41] shows

in simulation with a resulting distance of 3.25 m at 30 Km/h

and 3.75 m at 50 Km/h.

As earlier stated, this study considers the one-vehicle-look-

ahead communication pattern only, which does not require

a formal platoon architecture and provides the best pos-

sible communication stability for high frequent real time

applications like CACC. We assume this pattern to be the

most suitable in oversaturated multi-intersection-scenarios

with a high proportion of V2X enabled vehicles. However,

in cases where one-vehicle-look-ahead communication can

43770 VOLUME 10, 2022

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

be employed successfully, it can reduce the time headway of

CTG notably and make CDG overall string stable.

B. CALIBRATION OF SIMULATION ON REAL WORLD DATA

As motivated in the previous subsection, we employ real

world data to calibrate the policy parameters for simulation,

as well as the baseline for evaluation. The data we used

has been captured at simTD [28], a large scale field trial

for testing V2X applications conducted over a period of six

month, including a test fleet of 100 controlled vehicles. For

the calibration of the simulation model, we consider start-up

situations at traffic lights. The relevant calibration data for

parameterization includes the acceleration profile in order to

model the first vehicle of a platoon, the standstill distance and

the time gap. Therefore, we filtered situations from the logged

test data according to the following constraints:

•start-up after standstill, preceding vehicle is present;

•vehicle accelerates, target speed 40km/h – 65 km/h;

•accelerator is not released during the situation.

The filtered data included 3,546 start-up situations from

27,642 logged trips driven by 98 different drivers (73 male,

25 female). Fig. 2 depicts the resulting data, inspired by

the model matching process for acceleration maneuvers

described in [13]. All situations were aligned time-wise,

at the point time when the preceding vehicle starts moving.

The resulting curves of velocity and distance to the preced-

ing vehicle were averaged. The averaged time gap settles

at 0.87 s and the average standstill distance is 2.95m. We used

these values to feed our simulation models. The black dot-

ted lines represent the 95% confidence intervals of distance

and velocities, which mark the band for simulation model

validity according to [13]. The simulation is considered as

valid if it stays within the confidence band. We calibrated the

acceleration profile of the platoon leader in our simulation to

match the average speed trajectory of real world data. The

speed profile in simulation matches the confidence band of

the real world data, except for some dents in the graph during

gear shifts. Thus, we consider the simulation model as valid

representation of the real world data. In this way we were

able to determine all relevant parameters as defined for our

research scope, except for the vehicle length. For the vehicle

length we assume 5.15 m due to the following considerations.

According to [29] in 2011 we can assume an average length

of passenger vehicles of 4.75 m. We add further 0.4 m to

represent the increased length of vehicles since 2011 and

some heavy duty traffic.

C. SPACING POLICIES

Using the parameters derived in the previous subsection,

we can now define the following policies for studies in

simulation.

1) CDG-CONSTANT DISTANCE GAP

The constant distance gap policy CDG is defined by the

vehicle length of 5.15 m and the stand still distance of 2.95 m

determined in the previous subsection.

FIGURE 2. Velocities, following distances, and confidence bands

processed from real world start-up situations to derive CDG and CTG

controller parameters.

2) CTG-CONSTANT TIME GAP

According to the calibration with real world data we define

the baseline policy for this work with 0.87 s time gap, in the

following referred to as CTG-Ref. At 50 Km/h a gap of 15 m is

reached. This is close to match the American HCM at speeds

in urban areas (50 Km/h). Assuming the gross gap between

vehicles of 1.5 s (HCM at 2400 vehicles per hour) together

with vehicle length and standstill distance (as defined above),

this results in a time gap of 0.92 s. CTG-HBS represents

the German HBS with 2000 vehicles per hour, a time gap

of 1.22 s.

3) SWITCH

Based on the parameters of CDG and CTG-Ref, we define two

polices to switch between CDG and CTG-Ref at a predefined

velocity of 30 Km/h. SWITCH1 renders the time gap using

the difference between the current velocity and 30 Km/h, i.e.,

at 50 Km/h a gap of 7.8 m is reached. SWITCH2 increases

the gap from 0 m at 30 Km/h to 15 m at 50 Km/h, so that the

same distance as with CTG-Ref is reached.

4) MIX

In order to enable studying a certain rate of CDG penetration,

we define the Mix policy. The penetration rate (fraction of

vehicle adopting the policy) is set to 50% with a randomly

alternating pattern on CDG and CTG-Ref.

D. REALIZATION

All spacing policies described above have been implemented

in the PHABMACS simulator [13], for subsequent evalua-

tion. Furthermore, all policies rely on the one-vehicle look-

ahead communication pattern [25]. The evaluation scenario

consists of a straight single lane road with a single traffic

light, generated manually. In order to measure the maximum

achievable throughput of all policies, we create the same

oversaturated initial condition for each policy simulated. All

vehicles are queued up to at the stop line. Once the traffic light

turns green, the platoon starts accelerating up to 50 Km/h.

Vehicles passing the stop line are counted for evaluation.

VOLUME 10, 2022 43771

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

1) CTG

The basis controller for the vehicles is a Java implementation

of the cascaded PID framework presented in [30] (see Fig. 3),

integrated as longitudinal controller in the PHABMACS driv-

ing controller hierarchy (see [13] for explanation). As the

controller design is discussed in detail in [30], we just briefly

describe its main components. Girepresents the low-level

controller LL acting on the vehicle modeli, where irepre-

sents the ith vehicle in the platoon. LL is different from the

low-level controller in [5] and was initially presented in [31].

The input of LL is the control value uirepresented by the

desired acceleration of the vehicle, while the output is the

desired torque for the engine and the brake, which are fed

directly to the vehicle model as described in [13]. Ci,ACC is

a PD-type feedback controller that acts on a locally sensed

distance to the preceding vehicle with a simulated sensor

delay of 150 ms. Hiimplements the spacing policy. For CTG

the policy Hiis defined by 1 +hd,is[30] (here, s is the

Laplace transform variable) which is the transfer function

representation of dr,i=ri+hd,iviin the time domain,

where dr,iis the desired spacing, riis the standstill distance,

hd,iis the time gap and vithe velocity. Ci,CACC is a feed-

forward filter described in [30] using the communicated

information (with a simulated delay of 50 ms at 25 Hz) of

the directly preceding vehicle, i.e., the current and desired

acceleration ai−1and ui−1, as well as the current time lag

of the vehicle model τi−1. In contrast to [30] we treat τias

a dynamic value for each vehicle, which is taken online from

a calibrated map depending on the current gear, requested

torque (drive/brake), and current engine rotational speed.

FIGURE 3. Control structure of the longitudinal model.

2) CDG

For the CDG policy, there are two differences from the

setup described above. The spacing policy Hiis expressed by

dr,i=riin the time domain and Hi=1 in the frequency

domain. The feedforward controller Ci,CACC is the implemen-

tation of the system depicted in Fig. 4. An acceleration curve

is predicted for the preceding vehicle, based on the received

information ai−1(t), ui−1(t), and τi−1(t). Taking the latest

measured communication delay into account, uiis calculated

so that aimeets ai−1in a predefined time interval in the future.

This controller has been tested in real world test vehicles and

will be presented in detail in future work.

3) SWITCH

By combining CDG and CTG according to the parameters

described above, we realized SWITCH1 and SWITCH2 as

FIGURE 4. Concept of the predictive CDG feed forward controller, where

tnow is the current point in time, tnow+1is the next future point in time,

tdelay is the communication delay, n is the length of the acceleration

trajectory [atϕ..atϕCn].

FIGURE 5. Throughput comparison for the different spacing policies.

a simple change between both policies at 30 Km/h, with

accordingly defined time gaps. As stated in the research scope

(section III.A), we consider the context for switching to CDG

to be always given at all simulations presented in this work

and the only parameter to be varied in the simulation is the

velocity threshold. Consequently, we can simplify the switch

by formulating it in one policy SWITCH1 as dr,i=ri+

hd,imax(0,vi−vlim), where vlim is the threshold of 30 Km/h.

For SWITCH2 the time gap is larger with hd,i=2.5hd,i.

E. EVALUATION

Fig. 5 depicts the results of eight simulation runs with one

graph each for the eight described polices. The graphs can be

interpreted as a counter of vehicles passing the traffic light

stop line over time. The counter starts at time 0 when the

traffic light turns green after red. The vertical lines in the

figure mark the throughput at different green phase lengths.

Their offset to the time scale is caused by the yellow phase

of three seconds. The throughput of the alternative spac-

ing policies for a specific green phase length can be read

from the figure at the point where its vehicle counter graph

crosses the vertical lines. For instance, the number of passing

vehicles at a green phase of 15 s is 20 for CDG, 15 for

43772 VOLUME 10, 2022

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

SWITCH1, 13 for MIX, 11 for CTG-Sota, 9 for CTG-Ref.,

and 8 for CTG-HBS. In order to make the performance of Mix

comparable to the other policies at each green phase in Fig. 5,

we need to create the same portion of CDG/CTG at each point

in time. Thus, we applied a deterministic alternating pattern

on the Mix policy for this simulation, while a random pattern

is applied in subsequent sections. Note that at time 15 s the

platoon leader reaches maximum speed of 50 Km/h. In case

of the CDG policy that means the whole platoon is already at

maximum speed and CDG can fully exhibit its performance

benefit. Accordingly, its throughput graph becomes linear.

On the other hand, in the case of CTG, vehicles start moving

one by one, while the CDG platoon is moving as a whole

from the point in time when the platoon leader starts up. This

is the key effect which makes CDG effective at traffic lights.

For a more performance oriented analysis of the results,

Fig. 6 compares the throughput improvement of all policies

with the baseline CTG-Ref over time. While the throughput

improvement of SWITCH1/2 and MIX reach their saturation

around 50% near 20 s, CDG approaches an improvement

of about 140%. In order to illustrate the impact of different

standstill distances, we ran one simulation with the double

standstill distance of 6 m (CDG-6m). It improved the through-

put by 70%. We note that, 6 m is an (artificial) large standstill

distance and more than one vehicle length so a reduction in

efficiency is expected. Clearly, as one increases the gap, the

steady state throughput gain decreases proportionally.

FIGURE 6. Throughput improvement of the different spacing policies.

F. CONCLUSION — SINGLE TRAFFIC LIGHT PERFORMANCE

Our studies of CDG on start-up at a single traffic light

show a performance benefit over CTG and the other poli-

cies. This performance benefit grows with the green phase

length, reaches 120% at 10 s green time and then saturates

at approximately 140% for longer green phases. A pene-

tration rate of 50% CDG in a mix with the baseline pol-

icy only reaches 45%, i.e., the CDG benefit does not scale

linearly with the penetration rate. In order to provide a

comparison between the policies, the baseline parameters of

the policies were calibrated on real world data and human

reaction time was neglected. It must be noted, that for

green phases of more than 30 s, the CDG platoon exceeds

a length of 43 vehicles, which already could give rise to

string stability issues. For that reason, for a real world

implementation, counter measurements such as splitting up

FIGURE 7. Four way, reference intersection layout for simulation.

into mini-platoons must be considered [3], which may also

affect the performance. The SWITCH1 policy, which switches

from CDG to CTG at 30 Km/h reaches a performance gain

of 60%.

IV. SINGLE INTERSECTION PERFORMANCE

In this section we expand the analysis of CDG from a single

traffic light to a whole intersection. The very good perfor-

mance of CDG policies, described in the previous section,

is to a large extent due to the fact that the platoon could

pass the traffic light in a free flow. However, at whole inter-

sections the impact of traffic flow reducing factors needs

to be taken into account for performance comparison. This

includes reduced velocities while turning, stops due to giv-

ing way while turning, as well as the fact that green light

phases cannot be arbitrary long as they share the full cycle

time with cross traffic and turn phases. We start with the

definition of an intersection layout that covers all aspects

relevant for this research. Subsequently, we define further

metrics to assess CDG performance at intersections and

we finally evaluate results gained from simulating a whole

intersection.

A. INTERSECTION LAYOUT AND SIMULATION SETUP

Intersection layouts in urban areas include many possible

combinations of elements where each element might have a

different impact on the performance of CDG [26], [32]. As we

have to handle and permute many parameters apart from the

layout, our objective now is to define a reference layout that

covers as many layout related aspects as possible and can be

a fixed parameter for further studies.

Note: A literature review failed to reveal results on

the question of what are realistic portions of turning

vehicles.

We, thus, decide to permute both as parameters of the

simulation. Fig. 7 depicts our reference layout with two lanes

in each direction. Each right lane mixes straight driving with

protected right turning vehicles, as there are no pedestrians.

Each left lane mixes straight driving with unprotected left

turning vehicles, which always need to wait for oncoming

vehicles. This is ensured as the intersection is oversaturated

according to the scope defined in the previous section, i.e.,

there are always more vehicles waiting in front of red traffic

lights from each direction than can pass it during the green

phase. This oversaturation at the intersection inlets is also

necessary to allow the different policies to exploit its full

VOLUME 10, 2022 43773

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

potential of passing vehicle per green light phase. Leftturning

vehicles entering the intersection consequently block their

lane until the end of the green light phase. This reduces the

random effects in the resulting throughput, independently

from the desired parameterization of the simulation. The

radius of the intersection is 20 m and turning velocity is

7 m/s which results from a maximum lateral acceleration of

2.5 m/s2[33]. We choose this particular intersection layout

due to the following considerations. We should cover pro-

tected turning (turning signal phase - no yielding required)

due to the reduced velocity while turning and unprotected

turning (yielding required) due to its blocking effect on the

following vehicles. We do not need to consider dedicated

turning lanes, as they would just shift the blocking effect to

occur at a higher portion of turning vehicles. We also do not

need to consider dedicated traffic light phases for turning,

as we already cover protected turning. We also decide to

avoid lane changes in the whole scenario, in order to exclude

the impact of lane changes on the simulation results. Lane

changing is difficult to model, it depends on many parameters

of random character, and we have no ground truth for cali-

bration. Lane changing would further enlarge the parameter

space for our simulation, while having a considerable random

influence on the results. For the metrics discussed in the next

subsection, missing lane changes are only relevant for the

travel time of single vehicles on the blocked left lane when the

right lane is free. However, we assume these to be averaged

out by faster vehicles on the right lane. Thus, the results in

real world would differ only slightly from the simulation.

B. METRICS

To compare the performance of CDG and CTG at intersec-

tions, we measure the maximum intersection capacity [27]

for both. The intersection configuration parameters to be

permuted are the green phase length and the ratio of left

and right turns per lane. While oversaturating the intersection

inlets, we choose to measure the following metrics:

•Throughput (vehicles passing per time)

•Travel time (average time vehicles need to pass)

•Density (portion of road meters occupied by vehicles)

The throughput is needed to derive the intersection capac-

ity, while the travel time experienced is a quality of ser-

vice (QoS) measure. We also measure the density to analyze

the efficiency of road utilization, which is foremost relevant

when whole traffic systems are considered in the following

subsections.

C. EVALUATION

As earlier stated, our goal is not to find an optimization for

the traffic light setup but to study the performance of CDG

vs. CTG under all potentially occurring traffic conditions.

In order to map this span of conditions, the simulation ran

with 504 permutations of the following conditions, as moti-

vated in the previous subsections.

•Intersection layout is fixed.

•Traffic flow at the intersection inlets is oversaturated,

so that there are always more vehicles waiting at a red

light than can pass during one green phase.

•Portion of right (0%, 10%, 30%) and left turns (0%, 5%,

15%, 30%) are permuted.

•Penetration rate of CDG and CTG are permuted with

(0%, 10%, 25%, 37%, 50%, 75%, 100%).

•Green light phase is permuted from 5 s to 30 s. In one

permutation, the green time is the same for all directions.

•Simulation time is five full traffic light cycles.

The portion are a sample of possible permutations to illus-

trate trends. Additional measurements can easily be incor-

porated. The intersection layout and the simulation setup as

described in Section IV-A, as well as the policies as described

in Section III-C were implemented in the PHABMACS vehi-

cle simulator [13]. Fig. 8 depicts a view on the intersection

during simulation. The colored circles represent the radius

for travel time measurement (40 m) and density (20 m). The

travel time of each vehicle is measured from the point in time

when it enters the named radius until it leaves the radius.

The density is calculated for each second of a simulation

run by dividing the length of available lane meters within

the named radius by the cumulated length of all vehicles

currently being inside the radius. For the evaluation, the

measured travel times and densities are averaged over one

simulation run. Throughput is calculated from the number

of vehicles leaving the 20 m radius per time. To generate

randomness and equally distribute turnings and penetration

ratios, PHABMACS employs the Mersenne Twister algo-

rithm [35]. On average around 160 vehicles were in the

simulation at the same time, 40 vehicles per direction.

FIGURE 8. Simulation of a single intersection in PHABMACS simulator.

The results of the simulations for 15 s green phase, cap-

tured in accordance with the previous section, are depicted

in Fig. 9. The throughput of different CDG penetration rates

is depicted in vehicles per hour on the vertical axis, for

each permutation of left and right turn rate on the horizontal

axis. The highest throughputs were measured with no turning

43774 VOLUME 10, 2022

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

FIGURE 9. Simulation results on a single intersection CDG vs. CTG

throughput, travel time, density.

vehicles, at 11,550 CDG and 5,254 CTG-Ref, an improve-

ment of 120%. The lowest throughput at 30% right turns

and 30% left turns is at 4,281 CDG and 3,016 CTG-Ref,

an improvement of 42%.

The improvement without turning is similar to the

improvement measured at a single traffic light in the previous

section. With a ratio of 30% right turns on the right lane, the

improvement falls to 88% due to the reduced velocity while

turning. An additional 30% left turns on the left lane almost

stops the throughput on the left lane, i.e., all vehicle passing

the intersection are affected by the reduced speed of the right

turns, which results in a drop of the improvement to 42%.

The travel time drops from 55 s (CTG-Ref) to 34 s

(CDG), which corresponds to a travel time reduction of 38%.

TABLE 1. Throughput improvement of CDG at single intersection.

The lowest time reduction of 12% results with 30% left

turns and 30% right turns. Throughput improvement and

travel time reduction correlate with an increased density on

the intersection. While the average density of CTG-Ref is

around 35% for all permutations, the density of CDG depends

visibly on the turning ratios. With no turns, the density for

CDG peaks at 47%. For different CDG penetration rates,

the same superlinear effect becomes apparent on throughput,

travel time and density. At the first glance all graphs seem

to follow an approximately uniform course. However, there

are some irregularities recognizable in the pattern due to

the randomness in the simulation. For instance, at 5% left

turns, 10% right turns and 50% penetration, the throughput

is the same as with 25% penetration. Moreover, although

the travel time falls with an increasing CDG penetration,

the travel time gain is of less magnitude as the throughput

improvement. This is due to the fact that during the red signal

for all directions portion of the traffic light cycle, no time

benefit can be achieved by CDG. Discretization effects of

the traffic light queue, become apparent at 15% left turns and

25% penetration with a higher throughput than CTG-Ref, yet

with a higher travel time.

Table 1 summarizes the throughput improvement over

CTG-Ref (throughput of the considered policy divided by

throughput of CTG-Ref) at all green light phases simulated.

All values are rounded to the depicted number of digits. For

the sake of simplicity, the table only lists the extreme values

of 100% (CDG) and 50% (Mix) penetration. The penetra-

tion dependent improvement ratio (PIR) on the throughput

is calculated by Mix

CDG to compare the improvement of CDG

and Mix. Accordingly, the PIR is an indicator for the relative

benefit of CDG, i.e., the benefit of each single CDG vehicle

among CTG vehicles in relation to absolute benefit. At 15 s

green phase length with left and right turns, the PIR peaks at

0.55, i.e., 50% CDG penetration were able to gain 55% of the

improvement of 100% CDG penetration. With no turns and

30 s green time, only 27% percent were gained. While the

absolute improvement of CDG falls with falling green phase

and increasing turning rates, the PIR grows for short green

phases and high turn rate.

VOLUME 10, 2022 43775

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

D. CONCLUSION—SINGLE INTERSECTION PERFORMANCE

In this section we broaden the study of CDG from a sin-

gle traffic light to a whole intersection, including different

rates of protected and unprotected turning. As expected, the

presence of turnings at the intersection reduced the benefit

of CDG compared with a single traffic light. The lowest

benefit was measured at 10 s green phase length, where the

throughput improvement shrank from 81% without turning

to 27% with turnings. The specific impact of turnings depends

on presence and length of turning lanes. In our studies we

omit such lanes in order to reduce parameter space. Thus,

in our studies, one turning vehicle already blocks a complete

lane.

Summary of Section IV: Vehicle simulations, including of

up to 160 vehicles, showed that the presence of turnings at

the intersection can lower the CDG throughput improvement

to 27% in worst case, compared with 140% at a single

intersection. The CDG penetration rate among CTG has a

superlinear effect on its absolute benefit. This fact is a poten-

tial hurdle for market-introduction. However, with falling

absolute benefit of CDG, due to high turning rates and short

green phases, the relative benefit of CDG penetration rate

increases. Relative benefit means the benefit of each single

CDG vehicle among CTG vehicles in relation to absolute

benefit.

V. MODEL CALIBRATION FOR MACROSCOPIC

SIMULATION

The next step for our studies on CDG is to evaluate its impact

on whole traffic systems, i.e., on multiple mutually influenc-

ing intersections. As motivated earlier, development and eval-

uation of control systems like CACC in simulation requires

realistic mapping of vehicle dynamics. Fine differences

in mapping physics and the control system interacting

with its environment may lead to considerable differences

to the resulting behavior. Thus, for studying CDG at a

single traffic light, the sub-microscopic vehicle simulator

PHABMACS is the appropriate tool (for explanations of

the terms microscopic, mesoscopic, macroscopic, and sub-

microscopic simulation models, see [13] or [37]). Thanks to

its ability to scale out physics and control algorithms, simu-

lating a whole intersection including hundreds of vehicles for

hundreds of simulation runs is enabled [13].

However, in order to research whole traffic systems includ-

ing many thousands of vehicles, PHABMACS becomes out

of scope. Mapping that many vehicles would still require

considerable time and computation capacity. Furthermore,

traffic systems under research observed from a macroscopic

perspective may also produce realistic results, provided that

an appropriate model is leveraged, which maps the micro-

scopic behavior sufficiently in a macroscopic scale.

We use the methodology proposed in [42] to calibrate and

validate a sub-microscopic simulation model against a micro-

scopic simulation model, in order to enable macroscopic

traffic analysis including several thousand vehicles. We use

this methodology to match the implementation of CACC

controllers in PHABMACS and its validated vehicle model to

the SUMO [34] traffic simulator. Calibration and validation

are essential here in order to ensure that the traffic simulation

model in SUMO generates the same results regarding relevant

metrics as the vehicle dynamics simulation model in PHAB-

MACS. All simulations presented in Section Vto VII were

done using SUMO version 0.32.0. In order to make the results

reproducible, all information about our modelling and about

parametrization different from default values are given in this

in this paper and its references.

VI. MULTI INTERSECTION PERFORMANCE

In this section, we use synthetic simulation scenarios to reveal

traffic hindrance situations caused by CDG, which lead to a

decreased performance of CDG in a traffic system, compared

with the single intersection analyzed earlier. Two main factors

lead to such a lowered performance. First, congested inter-

section outlets that lead to obstructed off-flowing traffic, and

second, reduced in-flowing traffic. Thus, the main question to

be discussed in this context is the impact of CDG on the traffic

system, or more precisely on multiple mutually influencing

intersections.

To proceed, for consistency with our previous discussion,

we consider the same intersection layout. We combine this

layout to two synthetic simulation scenarios, an arterial sig-

nalized corridor [38] with five intersections and acoordinated

grid network [38] of 25 intersections. The intersections are

aligned along the dimensions of an even grid with the dis-

tance of 276.5m NW bound and 192.5m SE bound. These

dimensions originate from the area depicted in Fig. 10. These

constant intersection interspaces enable isolating the impact

of interspace length on the simulation results from the other

simulation parameters. Although this area in real world con-

sists of one-way streets partially, we unify the simulation

scenario with two-way streets.

Including up to 5500 simultaneously, both scenarios are

simulated with multiple permutations of traffic light config-

urations and turning ratios. With regard to simulation run-

time, we can afford such a number of vehicles and this span

of permutations, thanks to the calibration of the CDG and

CTG model with the traffic simulator SUMO. The results

are calculated counting vehicles entering/leaving the simu-

lation 20 m far from the outer intersections, i.e., excluding

the unbound queues. All trips end outside this area. Final

values are captured when all metrics increased to a steady

state level and keep it for five hours simulation time. For all

simulation scenarios, we assume an oversaturated traffic flow

at the inlets and an unobstructed outflow of the traffic system.

We permute the parameters of the traffic light system in order

to reveal possible drawbacks of CDG /CTG related to specific

setups. Finally, we model a real world road network simu-

lation scenario using a real world traffic layout and traffic

light configurations in the following section. All information

needed to reproduce these simulations done with SUMO

are either standard parametrization of SUMO or provided

throughout sections IV to VII.

43776 VOLUME 10, 2022

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

FIGURE 10. The synthetic simulation scenarios arterial and grid combine

the intersection layout of the previous sections with two way streets (one

lane per direction) along the dimensions of an urban area in, San

Francisco, CA.

A. TRAFFIC HINDRANCE SITUATIONS

Applying CDG at the intersections arranged in this way,

leads to three general traffic hindrance situations depicted in

Fig. 11. For a better understanding of the simulation results,

the disturbance effects resulting from these three situations

are described in the following

1) SITUATION 1 — JUNCTION BLOCKING

We start by assuming the traffic backlog from a traffic light

reaches the adjacent intersection as shown in Fig. 11 (a).

Under certain circumstances vehicles come to a stop on the

middle of the intersection and do not leave before the traffic

light switches to the phase for the cross traffic. In this situa-

tion, the cross traffic has to wait for a full traffic light cycle

until the intersection is clear again. Due to the close distances

in a CDG platoon and the one-vehicle look-ahead pattern,

this event occurs more often than with CTG. CTG by its very

nature creates a contraction of the platoon while stopping and

thereby more space on the intersection area. In order to create

spaces on the intersection, CDG would require a coordina-

tion between vehicles, such as described in [36]. In SUMO

there is a heuristic mechanism (no-block-heuristic) that helps

vehicles to anticipate a possible hold at a position which

blocks the cross traffic. However, as in the real world, in some

specific situations, this predictive mechanism does not always

work out.

2) SITUATION 2 — TURN BLOCKING

Even if vehicles stop to prevent a junction blocking, traffic

backlogs might prevent vehicles from turning. In this case,

as depicted in Fig. 11 (b), the cross traffic behind the turning

vehicle is blocked for the current traffic light cycle. This

applies for right and left turning vehicles. This event is also

more likely to happen with CDG than with CTG for the

aforementioned reasons.

FIGURE 11. Traffic hindrance situations.

3) SITUATION 3 – GRIDLOCK

If situation 2 occurs at four intersections at the same time, this

leads to a complete standstill beyond subsequent traffic light

cycles (see Fig. 11 (c)). For such situations, SUMO offers

a mechanism (teleport [39]) to model the real-life behavior

of eventually finding a way around the blocking vehicle and

so resolving the gridlock. For all experiments in this study,

we set the waiting time in SUMO for each vehicle to resolve

gridlocks and turn blockings to three full traffic light cycles.

Solving junction blockings is set to the time of two green light

phases.

B. ARTERIAL SIGNALIZED CORRIDOR — SIMULATION

SCENARIO

The arterial scenario consists of five adjacent intersections

of a major street with a distance of 192.5 m, as depicted in

Fig. 12. The two lane layout of Section IV-A, as depicted

in Fig. 7, is applied. The arrows in Fig. 12 mark the traffic

inflows. As described earlier, lane changes are suppressed

in order to exclude the impact of a lane change model on

the simulation results. This scenario represents coordinated

intersections on a major street. Thus, the green light portion

of the cycle time is longer for the major street than for the

minor streets. The following parameters were applied for the

simulation:

FIGURE 12. Layout arterial signalized corridor with five intersections.

•turning rates on minor roads: left 20%, right 40%;

•turning rates on main road is permuted with two dif-

ferent parameterizations: 1 (no turning), 2 (left 10%,

right 20%);

•penetration rates are permuted with 0% (CTG),

50% (Mix), and 100%(CDG);

VOLUME 10, 2022 43777

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

•green light portion for the major street is permuted with

25 s, 30 s, and 35 s with corresponding 10 s, 7 s, and 5 s

for the minor streets (this also defines the traffic flow

ratios);

•offset time (time shift between the traffic light cycles)

between intersections is permuted with 0 s and 15 s.

1) IMPACT OF GREEN PHASE AND OFFSET TIME BETWEEN

COORDINATED INTERSECTIONS FOR CDG ON ARTERIALS

For a better understanding of the arterial scenario simulation

results, we present some preliminary remarks in the follow-

ing. The performance of CDG in such a scenario is heavily

influenced by the ratio of platoon length and intersection

interspace. Assuming that there are no turnings and lane

changes, the platoon length is indirectly controlled by the

green light phase. Fig. 13 depicts four different situations to

be distinguished regarding the named ratio:

FIGURE 13. Impact of green phase and offset time between coordinated

intersections for CDG on arterials.

Situation 1 – Fig. 13 (a) - Platoon length (81.5 m at 10 s

green phase) is shorter than intersection interspace and traffic

lights are synchronized, i.e., of same cycle time and no offset

between their cycles. After starting up, the platoon needs

about 15 s to travel to the next intersections at 50 Km/h.

However, as the full cycle time is 36 s, additional waiting

time at the next intersection results in a travel time of 36 s

per intersection.

Situation 2 – Fig. 13 (b) - The parameters are the same

as in Situation 1 with an additional offset between the traffic

light cycles of 15 s (from left to right in Fig. 13). This offset

reduces the travel time to 15s per intersection inone direction,

as the platoon does not need to stop. In the opposite direction,

the platoon still needs to stop, however, the waiting time is

reduced by 15 s to 21 s. This results in an average travel time

for both directions of 18 s per intersection. This shows that

synchronized traffic lights are always the worst case in terms

of travel time. Any offset has a positive impact.

Situation 3 – Fig. 13 (c) - Platoon length is longer than the

intersection interspaces (in our case for green times longer

than 15 s). The platoons stopping at a traffic light pro-

trude into the adjacent intersection, which leads to the traffic

hindrance situations of junction blocking and turn blocking

(see previous subsection). This leads to a falling traffic

throughput and an increased travel time compared with

Situation 1 and 2.

Situation 4 – Fig. 13 (d) - Relatively long green times on

the major road lead to a platoon length which spans multiple

intersections and result in a flushing effect. While junction

blocking still occurs, its negative effect on throughput and

average travel time is compensated by the flushing of traffic.

The throughput increases due to the short red time (long green

time) portion on the major road and the travel time falls as

vehicles do not need to stop at each intersection.

2) RESULTS

Fig. 14 depicts the simulation results without turnings on the

major road. Fig. 15 depicts the simulation results done with

10% left turnings and 20% right turnings on the major road.

In both figures, sub-figures a, b, c depict the throughput,

travel time and density measured for CDG,CTG, and Mix.

Sub-figures d, e, f depict the improvement of CDG and Mix

over CTG. In each sub-figure the relevant metric is plotted

at the vertical axis on a ground plane which represents the

permutation of green time and offset. The calculation of the

metrics is done in accordance with Section IV using

the boundaries for counting as described at the beginning of

this section. In the following, we present a brief discussion

of the main findings while a more detailed discussion is

presented in [42], Sec.VI.B.2)].

a: RESULTS WITHOUT TURNINGS

CTG and CDG throughput in Fig. 14 (a) and (d) both increase

with green time length, while an offset has a slightly neg-

ative effect on both above 30 s green time. CDG shows

an improvement of around 50% in average, while Mix is

around 35%. This means that in contrast to a single traffic

light scenario, the CDG improvement for this scenario scales

better than linear with the penetration rate. However, the

overall improvement is lower, since all green times simulated

are above 15 s, which means in all cases the disturbance

effects of junction blocking and turn blocking occur.

A separate simulation without turnings on the minor

streets, not depicted in the figures, resulted with a CDG

throughput improvement of 65% at 25 s green time and 85%

at 35 s green time. We measured the same throughput with

and without offset for each green time length. This simula-

tion revealed that without turnings, the positive offset impact

on the junction blocking could completely compensate the

negative offset impact on flushing.

While the travel time (see Fig. 14 (b) and (e)) of CTG

is approximately equal for all green times and offsets,

CDG travel time notably benefits from offset. The travel

time improvement of CDG and Mix over CTG are both

43778 VOLUME 10, 2022

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

FIGURE 14. Arterial scenario simulation results without turnings.

around 20% without offset and around 30% with offset.

In general, high green times have a positive impact for both.

Here, CDG increases the throughput at the expense of density

and travel time. Another indicator for this relationship is

shown by the fact that throughput of CDG is higher than

Mix, while their travel times are almost equal. The most

remarkable permutation regarding travel time is at 25 s green

time without offset. This permutation results in the highest

travel time for CDG, mainly caused by the turn blocking

problem. Turnings from the minor streets cannot enter the

main street, which is mitigated when offset is present and

compensated in average by the flushing effect at higher green

times.

b: RESULTS WITH TURNINGS

An increased throughput (Fig. 15 (a) and (d)) for CDG can

be seen in the results with additional turnings present on the

main street. While the CTG throughput is in saturation at 30 s

green time, the CDG throughput increases linearly with the

green time length. Its improvement over CTG peaks at 110%

at 35 s green time. The difference to the case without turnings

is caused by vehicles leaving gaps on the main street platoons

when turning. In this way the platoons can contract at red

lights, which mitigates the junction blocking and turn block-

ing effect. CTG on the other hand is negatively influenced

by the turnings, especially at longer green times. The offset

FIGURE 15. Arterial scenario simulation results with turnings.

shows the earlier explained influence on the flushing effect

for CDG. Its positive impact on blocked turnings at minor

streets does not come into effect, as the gaps on the major

street already mitigate turn blocking.

Introducing turnings on the major street results in halving

of the density in simulation for all policies. This leads to an

overall reduced travel time in Fig. 15 (b) and (e). The travel

time improvement of CDG ranges from 20% to 45%, while

Mix goes in saturation around 30% at 30 s green time. Here,

CDG travel time is not affected by the offset, while there is a

slightly negative impact on CTG.

3) ARTERIAL SIGNALIZED CORRIDOR SIMULATION

RESULTS SUMMARY

From the simulation results we observe the following facts

about CDG applied in traffic system (specifically at adjacent

and mutually influencing intersection on arterial streets).

•In contrast to single (or isolated) intersections, the high

traffic density caused by the CDG platoons may lead

to the disturbance effects, junction blocking and turn

blocking.

•These effects lower the room for improvement of CDG

over CTG. Lower penetration rates (Mix) are less vul-

nerable to these effects, which increases their relative

benefit.

VOLUME 10, 2022 43779

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

FIGURE 16. Grid scenario simulation results without turnings.

•The overall high density on the major street is usually

mitigated by turnings leaving gaps in the platoons on the

major street.

•The traffic density is lower in the presence of offsets or

green times which create platoons that are shorter than

intersection interspaces.

•Long green times that entail platoons spanning multiple

intersections cause a flushing effect in the major street

that improves throughput and travel time. Despite that,

vehicles on minor streets still suffer from disturbance

effects.

•Offsets, in general, reduce travel time for CDG and can

reduce disturbance effects in one direction, however they

reduce the flushing effect.

C. GRID SCENARIO

The grid scenario includes all 25 intersections marked

in Fig. 10. Again, the two-lane layout of Section IV-A,

as depicted in Fig. 7, is applied and lane changes are sup-

pressed. Oversaturated traffic inflows are specified at the

20 inlets. This scenario represents a coordinated grid net-

work [38] of intersections that connect major streets. Thus,

the green light portion of the cycle time is equal for both

directions. The following parameters were applied for the

simulation:

•Turning rates are permuted with two parameterizations:

1 (no turnings), 2 (left 5%, right 10%).

FIGURE 17. Grid scenario simulation results with turnings.

•Penetration rates are permuted with 0% (CTG),

50% (Mix), and 100% (CDG).

•Green light portion permuted with 5 s, 10 s, 15 s, 20 s.

•Offset time between intersections is permuted with 0 s,

5 s, 10 s, and 15 s.

1) RESULTS

Fig. 16 depicts the grid simulation results done without turn-

ings and Fig. 17 with 5% left turnings and 10% right turnings.

The sub-figure structure and the method of calculating the

presented metrics is similar to Fig. 14/Fig. 15.

a: RESULTS WITHOUT TURNINGS

CTG and CDG throughput both increase with green time

length (see Fig. 16 (a) and (d)). While CTG goes in saturation

at 15 s green time, CDG shows a kink at 15 s, which is

caused by the junction blocking beginning on the shorter axis

of the grid. Along the longer axis, junction blocking occurs

from 20 s green time onwards. However, we see a further

increase in the throughput. The improvement of CDG has

its maximum of 100% at 10 s green time and approaches

70% above 20 s. This value matches the results of the arterial

scenario without turnings on the minor streets (not depicted

in the figures). The offset has no notable influence on all

policies.

The travel time (see Fig. 16 (b) and (e)) increases for CTG

from 2.5 min at 5 s green time to 3.3 min at 20 s green

43780 VOLUME 10, 2022

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

time, due to the increased cycle times. Up to 10 s green time

CDG saves travel time as expected, while above 15 s green

time, the junction blocking lead to a considerably increase

in traffic density and, thus, to an increased travel time. Here,

throughput is increased to the expense of travel time again.

In contrast to the arterial scenario, junction blocking effects

both directions. Thus, the average travel time is affected in

both directions by many vehicles which need to wait two

cycles at the same intersection. Mix has no significant travel

time improvement, and the offset has a positive impact in all

policies.

b: RESULTS WITH TURNINGS

CTG shows similar characteristics to the case without turn-

ings but with approximately 20% lower throughput (see

Fig. 17 (a) and (d)). For CDG the throughput drops sig-

nificantly at 15 s green time. This drop results from grid-

locks occurring in addition to the junction blocking and turn

blocking as discussed earlier. While Mix shows an average

throughput improvement to about 20%, CDG drops from

60% to 20% at this significant threshold. Without an off-

set between the traffic light phases, Mix even generates a

higher throughput than CDG at 20 s green time. An offset

between the traffic light phases shows an overall positive

impact on CDG as it creates free spaces and so counteracts

gridlocks. In contrast to the arterial scenario, longer green

times do not lead to platoons spanning multiple intersections,

i.e., intersections are not cleared which in turn contributes

to the emergence of gridlocks. Rather, gridlocks are a local.

This becomes apparent by observing the traffic density, which

is even lower on average than in the case without turnings.

CTG and Mix do not suffer from gridlocks in this scenario.

At short green times the travel time (see Fig. 17 (b) and (e))

is for all policies higher than without turnings. This is

explained by the fact, that without turnings, the vehicles need

to stop once at each intersection. Vehicles turning inward

from cross traffic enlarge the platoons, so that the whole

platoon cannot pass in one traffic light cycle. The travel

time improvement of CDG and Mix, as well as the impact

of the offset show similar characteristics to the case without

turnings.

2) GRID SCENARIO SIMULATION RESULTS SUMMARY

The following points summarize the findings of our simula-

tion on mutually influencing intersection in a grid.

•In contrast to arterial scenarios, gridlocks may occur

when CDG platoons are longer than intersection inter-

spaces arise.

•Gridlocks drastically reduce the benefit of CDG (in our

scenario down to 15%) with a simultaneous increase in

travel time.

•Gridlocks do not occur in the presence of short green

times when platoons are shorter than intersection inter-

spaces. The same effect could be achieved by lim-

iting the platoon length accordingly as part of the

CDG controller.

•Offsets can mitigate gridlocks for one travelling

direction.

•At very short green times, travelling times increase con-

siderably, which is the case for all policies studied.

•Lower CDG penetration rates (Mix) are less vulnerable

to gridlocks and of little potential for improvement in

grids.

D. VULNERABILITY OF CTG AND CDG WITH RESPECT TO

GRIDLOCKS

From the grid layout simulation we observed that likelihood

of gridlock of the traffic flow increases with longer green

times, high inflow rates (maximum possible in our case) and

turn rates. This applies for CDG as well as for CTG and Mix.

However, CDG is more sensitive in this regard. The high

traffic density caused by the dense CDG platoons provides

no buffer space like the CTG platoons which contract while

slowing down. Hence, with CTG the traffic flow is stable,

in the sense that gridlocks do not occur, for higher turn rates

at oversaturated inflow rates than with CDG. For limited

inflows, the traffic flow is more stable regarding gridlocks

with CDG than with CTG. Offsets appear to have a nega-

tive influence on traffic flow stability with CTG. We further

explored this relationship in [42], Sec. IV.D.

E. CONCLUSION — MULTI INTERSECTION PERFORMANCE

Fig. 18 compares the throughput improvement of the grid

scenario (Fig. 16 / Fig. 17) with single intersection (Fig. 9)

and the arterial scenario (Fig. 14 /Fig. 15) with the single

traffic light (Fig. 5). Min and max refer to the offset with the

best and the worst improvement, respectively.

The performance of CDG in the grid without turnings

is approximately the same as for a single traffic light up

to 10 s green times. Above 10 s, the disturbance effects

(see Section VI-A) result in a considerable performance drop.

A similar picture can be observed with turnings, with an

additional performance drop when no offset is present. Addi-

tionally, the gridlock impact is higher with turnings at longer

green times. The performance drop of Mix is less for all cases.

An exceptional case is 5 s green time where we have a very

high performance at the single traffic light. This is due to

discretization effects in the green times and the small number

of vehicles passing per green phase. Note that 5 s is a very

short value used for minor streets in real world. We included

it to address a range of different ratios of green times and

intersection interspaces in the grid. Green times above 20 s

in the grid resulted with the simulation full of gridlocks and

gave no further insight.

In the arterial scenario with 25 s to 35 s green time, distur-

bance effects are present for all CDG permutations. As CTG

is less affected by them, we see an overall worse through-

put improvement of CDG here. Additionally, CTG shows

comparably high throughput in absolute numbers at long

green times, which makes the impact of disturbance effects

on the performance comparison with CDG grow. Thus, the

arterial chart without turnings apparently is an extension of

VOLUME 10, 2022 43781

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

FIGURE 18. Results of arterial and grid scenario simulation.

the grid chart. With turnings, the CDG benefit comes to the

fore notably, as the flushing effect (see Section VI-B) gets

interrupted more often by the turning vehicles and CDG can

reap the benefits of more start-ups similar to shorter green

times.

In conclusion we found that CDG and CTG performance in

multi intersection scenarios is influenced by many different

effects. Their impact can be observed as a superposition in

the measured metrics. In addition to the results presented

in this work, the authors conducted further studies on each

effect in order to explain them correctly. However, isolating

each effect requires many more simulation scenarios, chart

analytics and visual observation of simulations, which is

beyond the scope of this work.

Remark: For some cases in both scenarios, grid and arte-

rial, we observed that an improved throughput of CDG over

CTG, comes with a smaller improvement in travel time.

Actually one would assume intuitively that travel time and

throughput should be improved approximately proportion-

ally. However, this is not the case when different inter-vehicle

distances are considered in signalized networks. If e.g., for

situation 1 and 2 in Section VI-B1 the distances are halved,

the throughput is approximately doubled, while traveling

through the intersections takes the same time for each vehicle,

except for a little less waiting time at the first queue.

Our objective in this section was to present the over-

all benefit of one-vehicle look-ahead CDG in oversaturated

multi-intersection-scenarios. Our most relevant findings are

summed up as follows.

•If the ratio of intersection interspaces and green time

length is too high, CDG leads to disturbance effects in

the traffic flow in the form of junction and turn blocking.

FIGURE 19. Real world scenario: arterial road with nine intersections in

Berlin.

•In oversaturated grid scenarios these disturbances create

gridlocks, with a probability that is more likely than

with CTG. For limited inflows, CDG is less sensitive for

gridlocks than CTG.

•Offset positively counteracts such disturbance effects

•CDG penetration rates below 100% are less sensitive

to the disturbances. This improves the ratio between

penetration rate and performance benefit of CDG con-

siderably over single intersection scenarios. For some

edge cases, a penetration of 50% CDG even outperforms

100% of CDG penetration.

•For all scenarios and parameter permutation tested,

CDG improves traffic throughput. However for some

situations, this improvement of CDG is bought by

higher travel times due to its vulnerability to disturbance

effects.

Summary of Section VI: The performance of CDG in

grids and arterial scenarios is sensitive to the traffic light

configuration in relation to intersection interspaces. Green

times above a certain threshold may lead to disturbance

effects (junction blocking and turn blocking). An offset posi-

tively counteracts such disturbance effects. CDG showed an

improvement over the CTG baseline, in all cases. Finally,

we emphasi ze that discussed disturbance effects could be

prevented by adding a cooperative aspect to CDG. If CDG

limited the platoon length to be shorter than intersection

interspaces or the vehicles in a platoon could anticipate

an unintended stop within the intersection area, the general

performance of CDG could be improved considerably and

grid locks could be prevented.

VII. REAL WORLD ROAD NETWORK

In order to confirm the results observed in Section IV to VI

using synthetic simulation scenarios, we now attempt to

assess the real world performance of CDG. For this purpose,

we model a simulation scenario covering a heavily frequented

arterial road in Berlin, Germany, as depicted in Fig. 19.

This includes the Bismarckstraße between Theodor-Heuß-

Platz and Ernst-Reuter-Platz with ten traffic light coordinated

intersections with interspaces between 160 m and 500 m

(266 m on average). The main difference to the synthetic

scenarios in the previous section is the real world intersection

layout, interspaces, and traffic light program including offset.

43782 VOLUME 10, 2022

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

TABLE 2. Berlin simulation scenario configuration.

While the road layout and the traffic light configuration are

captured from real data, we again assume a maximum pos-

sible traffic inflow and an unobstructed outflow. In accor-

dance with Section VI, the simulation results are calculated

by counting vehicles entering/leaving an area that encloses

all intersections together with an outer margin of 20 m, i.e.,

excluding the unbound queues of vehicles entering the area.

All trips end outside this area. Furthermore, we assume the

following:

•No pedestrians are blocking vehicles while turning.

•While assuming a capable cooperation concept to

enable negotiation of lane changes between vehicles

at high penetration rates of CDG, we excluded lane

changing by respective route design in the previous

sections. We now employ the SUMO lane changing

model [34] without validating it analogous to Section V.

As this model does not support opening gaps for

merging parallel traffic, we accept a performance drop

of CDG.

•Due to traffic backlog and quite large intersection inter-

spaces, platoons of very large size appear, which in

reality needs to be split to achieve platoon stability

(see Section II-B for explanation). This splitting would

slightly lower the performance of CDG.

A. SIMULATION SETUP

The traffic light program was observed on week-days

between 10 am and 12 am. Public authorities indicated a

fixed schedule for this period (dynamic priority phases e.g.,

for buses neglected). Table 2 lists the phase times of the

program for each intersection in the following order: 1) green

on major road, 2) yellow, 3) clearance interval, 4) protected

left turning major road, 5) green on minor road, 6) yellow,

7) clearance interval. The base ratio for turning was estimated

by observation at 80%, 12%, 8% (straight, right, left) on

average on the major roads and 75% / 16% / 9% on the minor

roads. The final turning configuration was adjusted based

on the number of lanes per direction at each intersection,

as listed in Table 2 using JTRRouter [39]. Combining the

real world traffic light program with this setup leads to a

FIGURE 20. Simulation results real world scenario Berlin CDG / CTGS.

FIGURE 21. Simulation results real world scenario Mix / Switch1 /

Switch2.

simulation setup using SUMO’s default driver model, with

all lanes evenly occupied and without traffic jams. All other

parameters were left at default values.

B. EVALUATION

Fig. 20 compares the results of two simulation runs with

CDG and CTG for the first two hours simulation time.

In addition to the metrics used before, the figure also sep-

arately indicates the ingoing traffic flow from east, west,

and from the minor roads (north and south). CTG reaches

a steady state level for all metrics after 15 minutes simu-

lation time, with a throughput of around 210 vehicles per

minute. CDG reaches around 380 vehicle per minute, how-

ever the density and the travel time keep rising slightly.

After minute 65 the metrics begin to stabilize while the

throughput drops slightly to around 355 vehicle per minute.

This behavior is the result of an east bound traffic backlog

VOLUME 10, 2022 43783

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

at Suarezstr. The traffic light there shows a slightly lower

capacity than Kaiser-Friedrich-Str. in the simulation scenario.

As CDG leverages the longer green times better than CTG,

assuming a maximum possible traffic inflow, this leads to

a larger capacity difference and, thus, to a rising backlog.

The backlog reaches Am Schillertheater at minute 54 and

finally reaches the east traffic inflow at minute 65. This

becomes apparent with the declined inflow rate east. Once

the traffic jam emerges, vehicles have difficulties finding

gaps for lane changes, due to the close vehicle interspaces

of CDG and missing cooperative behavior. Thus, some vehi-

cles reach the intersection in the wrong lane and block that

lane for a whole cycle. This further reduces the intersection

capacity and the traffic jam cannot be dissolved. However,

even with the named drawbacks, in terms of throughput,

CDG still outperforms CTG. Applying, a switch to CTG

at 30 Km/h solves this problem completely. As shown in

Fig. 21, SWITCH1 reaches the same throughput on average

as CDG.

C. CONCLUSION — REAL WORLD ROAD NETWORK

In the previous section, we used synthetic simulation sce-

narios to reveal the relationship of specific constellations of

road topology and traffic light configuration. This real world

road network scenario in contrary shows the performance of

CDG in a real world traffic system that mixes a plethora

of such constellations at the same time. Moreover, in the

previous section we neglected the impact of lane changes by

route design, as we assume a cooperative merging feature

coming with 100% penetration of CDG. In this section we

included uncoordinated lane changing which led to a jammed

condition for CDG. However, we showed that this effect

would not necessarily occur in real world, as it is due to

the non-cooperative character of merging in the simulation

models of SUMO combined with small gaps. Besides that,

even with a part of the scenario in a jammed condition, CDG

still outperforms CTG in terms of traffic throughput. While

the travel time raises by 60%, the CDG throughput is 70%

higher than CTG. The following considerations pertain to the

performance of CDG before the jamming occurred. Regard-

ing throughput improvement of CDG, the real world road

network scenario matches the results of the arterial scenario in

Section VI-B, for the configuration of 25 s green time and no

offset. The throughput improvement of MIX is slightly lower.

We observe no negative impact by the presence of offset

and no considerable disturbance effects (see Section VI-A)

before minute 65. This becomes apparent in particular by

the steady inflow from the minor roads. The absence of

disturbance effects is a result of the very well balancing of

traffic light configuration to the intersection interspaces done

by the Berlin traffic management. Given the assumption that

we usually find such well balancing in traffic management,

CDG can exploit much of its potential in traffic systems, not

only at single intersections. Surprisingly, the travel time is

almost equal for all policies. Even by visual inspection of the

simulation, we could not find a clear cause for this effect.

The most reasonable explanation here is the following. As we

learned from the previous section, CDG can buy throughput

by travel time. Therefore, the specific configuration of the

scenario might lead to levelling out the travel time by different

throughputs and densities for each policy.

Summary of Section VII: In a real world network with a

well-balanced traffic light configuration, CDG can exploit

much of its potential in traffic systems, not only at single

intersections. Comparing the performance of SWITCH1 and

CDG in this scenario and in Section III, we could deduce the

following finding. In dense, urban traffic systems a switch

from CDG to CTG at 30km/h is recommended in order to

create gaps for lane changes. At single intersections, for

example, on crossing rural roads, this is not required and

CDG without switching results with a considerably better

performance.

VIII. CONCLUSION AND FUTURE WORK

In this paper, we comprehensively investigated the impact of

applying a constant distance gap (CDG) policy for starting

platoons at traffic lights. The applicability of CDG in real traf-

fic is limited, due to its demand on communication topologies

in order to achieve string stability. However, we were able

to show its capability to increase the capacity of signalized

intersections.

As a baseline for comparison, we calibrated a constant

time gap (CTG) policy in the vehicle dynamics simulation

PHABMACS using real word driving data. Compared with

this baseline, CDG increased the capacity of a single inter-

section by up to 140%, depending on the green light time and

the ratio of turning vehicles. The penetration rate of CDG

in mixtures with CTG does not have a linear impact on the

capacity enhancement on single intersections, which is a clear

downside. A penetration of 50% still peaked with a capacity

enhancement of 40%.

For large scale analysis of CDG performance on multi-

ple adjacent intersections in traffic systems, we employed

traffic simulation with several thousand vehicles. To achieve

this scaling, we proposed a method for calibrating and val-

idating traffic simulation against vehicle dynamics simula-

tion. This calibration enables traffic simulation to render

the same results as vehicle dynamics simulation regarding

the relevant metrics. This study and its references provide

all information needed to reproduce the simulations done

with SUMO.

The large scale analysis yielded the following conclusions:

•Compared to single intersections, a full penetration of

CDG reaches a lower performance at arterial roads and

grids with multiple intersections due to occurring distur-

bance effects. This performance drop is less pronounced

at lower CDG penetration rates.

•CDG outperformed CTG regarding throughput in all

cases observed in this work. Although, a 50% penetra-

tion rate of CDG has less potential for improvement,

it is less vulnerable to disturbance effects and appears

as stable as CTG in traffic systems.

43784 VOLUME 10, 2022

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

•While CDG is more prone to gridlocks in traffic grids at

maximum traffic inflow, it is less prone to gridlocks than

CTG if the inflow is limited. Thus, CDG should either

limit the platoon length to be shorter than intersection

interspaces or the vehicles in a platoon should beenabled

to anticipate an unintended stop within the intersection

area.

•CDG gains a considerable travel time improvement on

arterial roads. However, the increased throughput of

CDG comes with a higher density in traffic grids, which

may lead to an increased average travel time.

After exposing some edge cases using synthetic scenar-

ios with uniform parameterization, we finally modeled a

real world road network scenario which includes a mix-

ture of parameterizations. This mixture originates from the

heterogeneous road geometry in Berlin, Germany and its

well calibrated traffic light configuration. CDG improved

the traffic throughput by 80% at the same average travel

time as CTG. Given the average green light time and turn-

ing rates, this improvement confirms the results of a single

intersection.

The simulation results revealed a potential performance

drop of CDG originating from prevented lane changing and

blocked intersections due to missing coordination and small

gaps. Both problems could be tackled by a close range coordi-

nation between vehicles [36], to create gaps for merging and

prevent entering intersections when a stop within the inter-

section area is likely. Given such coordination, the potential

of performance improvement for CDG in a traffic system

seems similar to the single intersections. Finally, it should

be noted, that the CDG performance is largely dependent on

the distance between vehicles. The steady state throughput

gain decreases proportionally with increasing gaps, as shown

in Section III.

Our future work includes implementing a coordination

strategy as described above and a real world road network sce-

nario for traffic grids. Replacing the maximum traffic inflow

by real world traffic flows at rush hours will reveal infor-

mation about the benefit of CDG by a market introduction

in today’s traffic. As a countermeasure to potentially arising

string stability issues, CDG platoons should be split up into

mini-platoons [3]. Future studies on switching between CDG

and CTG should incorporate this splitting as an additional

parameter to find the optimal platoon lengths. While in this

paper we focus on platoons of homogenous vehicle dynamics,

dynamics heterogeneity has a relevant impact on inter vehicle

distances in real world applications. In future work, we will

show the ability of the predictive controller, presented in

Section III, to handle such heterogeneity.

ACKNOWLEDGMENT

The authors would like to thank Pietro Ferraro for lan-

guage editing, and proofreading of the manuscript. They

would also like to acknowledge support by the German

Research Foundation and the Open Access Publication Fund

of TU Berlin.

REFERENCES

[1] S. E. Shladover, C. Nowakowski, X. Y. Lu, and R. Ferlis, ‘‘Coopera-

tive adaptive cruise control (CACC) definitions and operating concepts,’’

Transp. Res. Board, vol. 2489, pp. 145–152, Nov. 2014.

[2] Press Information: Daimler Trucks invests half a Billion Euros in Highly

Automated Trucks, [2] Daimler North America, Portland, OR, USA,

Jan. 2019.

[3] D. Swaroop and J. K. Hedrick, ‘‘Constant spacing strategies for platooning

in automated highway systems,’’ J. Dyn. Syst. Meas. Control, vol. 121,

no. 3, pp. 462–470, 1999.

[4] Y. Sugiyama, ‘‘Traffic jams without bottlenecks—Experimental evidence

for the physical mechanism of the formation of a jam,’’ New J. Phys.,

vol. 10, Mar. 2008, Art. no. 033001.

[5] G. J. L. Naus, R. P. A. Vugts, J. Ploeg, M. J. G. van de Molengraft, and

M. Steinbuch, ‘‘String-stable CACC design and experimental validation:

A frequency-domain approach,’’ IEEE Trans. Veh. Technol., vol. 59, no. 9,

pp. 4268–4279, Nov. 2010.

[6] J. Ploeg, ‘‘Analysis and design of controllers for cooperative and

automated driving,’’ Ph.D. dissertation, Technische Universiteit

Eindhoven, Eindhoven, The Netherlands, 2014. [Online]. Available:

https://research.tue.nl/en/publications/analysis-and-design-of-controllers-

for-cooperative-and-automated-, doi: 10.6100/IR772224.

[7] A. Geiger, M. Lauer, F. Moosmann, B. Ranft, H. Rapp, C. Stiller, and

J. Ziegler, ‘‘Team AnnieWAY’s entry to the 2011 grand cooperative driving

challenge,’’ IEEE Trans. Intell. Transp. Syst., vol. 13, no. 3, pp. 1008–1017,

Sep. 2012.

[8] S. E. Shladover, ‘‘Longitudinal control of automated guideway transit

vehicles within platoons,’’ J. Dyn. Syst., Meas., Control, vol. 100, no. 4,

pp. 302–310, Dec. 1978.

[9] A. A. Peters, ‘‘Stability and string stability analysis of formation con-

trol architectures for platooning,’’ Ph.D. dissertation, Nat. Univ. Ireland

Maynooth, Maynooth, Ireland, 2015.

[10] J. Wang and R. Rajamani, ‘‘Should adaptive cruise control systems be

designed to maintain a constant time gap between vehicles?’’ IEEE Trans.

Veh. Tech., vol. 53, no. 5, pp. 1480–1490, Sep. 2004.

[11] Y.-H. Chiang and J.-C. Juang, ‘‘Longitudinal vehicle control with the

spacing policy in consideration of brake input limits,’’ in Proc. IEEE Int.

Conf. Syst., Man Cybern., Oct. 2007, pp. 1705–1710.

[12] T. Kim and D. J. Lovell, ‘‘Observation of real driving behavior in car-

following: Preliminary results,’’ in Proc. IEEE 61st Veh. Technol. Conf.,

Stockholm, Sweden, May 2005, pp. 2939–2943.

[13] K. Massow and I. Radusch, ‘‘A rapid prototyping environment for coop-

erative advanced driver assistance systems,’’ J. Adv. Transp., vol. 2018,

pp. 1–32, Mar. 2018.

[14] J. Ploeg, E. Semsar-Kazerooni, A. I. M. Medina, J. F. C. M. de Jongh,

J. van de Sluis, A. Voronov, C. Englund, R. J. Bril, H. Salunkhe, Á. Arrúe,

and A. Ruano, ‘‘Cooperative automated maneuvering at the 2016 grand

cooperative driving challenge,’’ IEEE Trans. Intell. Transp. Syst., vol. 19,

no. 4, pp. 1213–1226, Apr. 2018.

[15] Z. Wang, G. Wu, P. Hao, and M. J. Barth, ‘‘Cluster-wise cooperative eco-

approach and departure application for connected and automated vehicles

along signalized arterials,’’ IEEE Trans. Intell. Vehicles, vol. 3, no. 4,

pp. 404–413, Dec. 2018.

[16] H.-J. Gunther, S. Kleinau, O. Trauer, and L. Wolf, ‘‘Platooning at traffic

lights,’’ in Proc. 4th IEEE Intell. Veh. Symp., Jun. 2016, pp. 1047–1053.

[17] E. V. Nunen, M. R. J. A. E. Kwakkernaat, J. Ploeg, and B. D. Netten,

‘‘Cooperative competition for future mobility,’’ IEEE Trans. Intell. Transp.

Syst., vol. 13, no. 3, pp. 1018–1025, Sep. 2012.

[18] J. Wang, Y. Bian, B. Xu, H. Qin, M. Hu, and B. Huang, ‘‘V2I-based start-

up assistance system at signalized intersections,’’ Adv. Mech. Eng., vol. 7,

no. 8, pp. 1–11, 2015.

[19] S. E. Li, S. Xu, X. Huang, B. Cheng, and H. Peng, ‘‘Eco-departure of

connected vehicles with V2X communication at signalized intersections,’’

IEEE Trans. Veh. Technol., vol. 64, no. 12, pp. 5439–5449, Dec. 2015.

[20] Q. He, K. L. Head, and J. Ding, ‘‘PAMSCOD: Platoon-based arterial multi-

modal signal control with online data,’’ Transp. Res. C, Emerg. Technol.,

vol. 20, pp. 164–184, Feb. 2012.

[21] H. Yang, F. Almutairi, and H. Rakha, ‘‘Eco-driving at signalized inter-

sections: A multiple signal optimization approach,’’ IEEE Trans. Intell.

Transp. Syst., vol. 22, no. 5, pp. 2943–2955, May 2021.

[22] L. Kang, H. Shen, and A. Sarker, ‘‘Velocity optimization of pure electric

vehicles with traffic dynamics consideration,’’ in Proc. IEEE 37th Int.

Conf. Distrib. Comput. Syst. (ICDCS), Jun. 2017, pp. 2206–2211.

VOLUME 10, 2022 43785

K. Massow et al.: Numerical Study on Constant Spacing Policies for Starting Platoons at Oversaturated Intersections

[23] B. Liu and A. El Kamel, ‘‘V2X-based decentralized cooperative adaptive

cruise control in the vicinity of intersections,’’ IEEE Trans. Intell. Transp.

Syst., vol. 17, no. 3, pp. 644–658, Mar. 2016.

[24] J. Lioris, R. Pedarsani, F. Y. Tascikaraoglu, and P. Varaiya, ‘‘Doubling

throughput in urban roads by platooning,’’ in Proc. IFAC Symp. Control

Transp. Syst., Istanbul, Turkey, vol. 49, no. 3, 2016, pp. 49–54.

[25] Y. Zheng, S. E. Li, J. Wang, L. Y. Wang, and K. Li, ‘‘Influence of

information flow topology on closed-loop stability of vehicle platoon with

rigid formation,’’ in Proc. 17th Int. IEEE Conf. Intell. Transp. Syst. (ITSC),

Oct. 2014, pp. 2094–2100.

[26] Highway Capacity Manual, Transp. Res. Board, Washington, DC, USA,

2010.

[27] Handbuch fuer Bemessung von Straβenverkehrsanlagen: HBS (German

Highway Capacity Manual), Forschungsgesellschaft fuer Strassen- und

Verkehrswesen, Cologne, Germany, 2015.

[28] H. Stübing, M. Bechler, D. Heussner, T. May, I. Radusch, H. Rechner, and

P. Vogel, ‘‘SimTD: A car-to-X system architecture for field operational

tests,’’ IEEE Commun. Mag., vol. 48, no. 5, pp. 54–148, May 2010.

[29] W. Schnabel and D. Lohse, ‘‘Grundlagen der straβenverkehrstechnik

und der verkehrsplanung,’’ Deutsches Institut für Normen e.V., Berlin,

Germany, Tech. Rep., 2011. [Online]. Available: https://trid.trb.org/

view/988635

[30] S. Öncü, J. Ploeg, N. van de Wouw, and H. Nijmeijer, ‘‘Cooperative

adaptive cruise control: Network-aware analysis of string stability,’’ IEEE

Trans. Intell. Transp. Syst., vol. 15, no. 4, pp. 1527–1537, Aug. 2014.

[31] S. Bunk, A Situation Aware Vehicle Dynamics Controller Hierarchy.

Berlin, Germany: TU-Berlin, 2016.

[32] K. Fitzpatrick, M. D. Wooldridge, and J. D. Blaschke, ‘‘Urban inter-

section design guide,’’ Texas Transp. Inst., College Station, TX, USA,

Tech. Rep. FHWA/TX-05/0-4365-P2, 2005.

[33] S. Schmidl, ‘‘Untersuchung des fahrverhaltens in unterschiedlichen

kurvenradien bei trockener fahrbahn,’’ M.S. thesis, BOKU Wien, Vienna,

Austria, Tech. Rep., 2011. [Online]. Available: https://epub.boku.ac.at/

obvbokhs/content/titleinfo/1083118 and https://epub.boku.ac.at/

obvbokhs/download/pdf/1083118?originalFilename=true

[34] P. A. Lopez, E. Wiessner, M. Behrisch, L. Bieker-Walz, J. Erdmann,

Y.-P. Flotterod, R. Hilbrich, L. Lucken, J. Rummel, and P. Wagner, ‘‘Micro-

scopic traffic simulation using SUMO,’’ in Proc. 21st Int. Conf. Intell.

Transp. Syst. (ITSC), Nov. 2018, pp. 2575–2582.

[35] M. Matsumoto and T. Nishimura, ‘‘Mersenne twister: A 623-dimensionally

equidistributed uniform pseudo-random number generator,’’ ACM Trans.

Model. Comput. Simul., vol. 8, no. 1, pp. 3–30, Jan. 1998.

[36] IMAGinE-Konsortium, Kooperative Funktionen. Accessed: May 31, 2020.

[Online]. Available: https://imagine-online.de/kooperative-funktionen/

[37] S. Krauss, ‘‘Microscopic modeling of traffic flow: Investigation of collision

free vehicle dynamics,’’ Ph.D. dissertation, Universität zu Köln, Cologne,

Germany, 1998.

[38] T. Urbanik, A. Tanaka, B. Lozner, E. Lindstrom, K. Lee, S. Quayle,

S. Beaird, S. Tsoi, P. Ryus, D. Gettman, and A. Z. Phoenix, ‘‘Signal timing

manual,’’ Nat. Cooperat. Res. Program, Tech. Rep. 812, 2014, pp. 3–103.

[Online]. Available: https://nap.nationalacademies.org/catalog/22097/

signal-timing-manual-second-edition and https://www.webpages.uidaho.

edu/trafficsignalsystems/stm/ch01.pdf

[39] SUMO User Documentation. Accessed: Dec. 29, 2021. [Online]. Avail-

able: http://sumo.dlr.de/docs/

[40] S. Ellwanger and E. Wohlfarth, ‘‘Truck platooning application,’’ in

Proc. IEEE Intell. Vehicles Symp. (IV), Jun. 2017, pp. 966–971, doi:

10.1109/IVS.2017.7995840.

[41] H. Xing, J. Ploeg, and H. Nijmeijer, ‘‘Compensation of communication

delays in a cooperative ACC system,’’ IEEE Trans. Veh. Technol., vol. 69,

no. 2, pp. 1177–1189, Feb. 2020, doi: 10.1109/TVT.2019.2960114.

[42] K. Massow, I. Radusch, and R. Shorten, ‘‘On constant distance spacing

policies for cooperative adaptive cruise control,’’ 2019, arXiv:1909.10913.

[43] A. Zhou, S. Gong, C. Wang, and S. Peeta, ‘‘Smooth-switching control-

based cooperative adaptive cruise control by considering dynamic infor-

mation flow topology,’’ Transp. Res. Rec., J. Transp. Res. Board, vol. 2674,

no. 4, pp. 444–458, Apr. 2020.

[44] J. Ploeg, E. Semsar-Kazerooni, G. Lijster, N. van de Wouw, and H. Nijmei-

jer, ‘‘Graceful degradation of cooperative adaptive cruise control,’’ IEEE

Trans. Intell. Transp. Syst., vol. 16, no. 1, pp. 488–497, Feb. 2015.

[45] C. Wu, Z. Xu, Y. Liu, C. Fu, K. Li, and M. Hu, ‘‘Spacing policies for

adaptive cruise control: A survey,’’ IEEE Access, vol. 8, pp. 50149–50162,

2020.

[46] A. Ali, G. Garcia, and P. Martinet, ‘‘Minimizing the inter-vehicle distances

of the time headway policy for urban platoon control with decoupled

longitudinal and lateral control,’’ in Proc. 16th Int. IEEE Conf. Intell.

Transp. Syst. (ITSC), Oct. 2013, pp. 1805–1810.

[47] C. Flores, V. Milanes, and F. Nashashibi, ‘‘A time gap-based spacing policy

for full-range car-following,’’ in Proc. IEEE 20th Int. Conf. Intell. Transp.

Syst. (ITSC), Oct. 2017, pp. 1–6.

[48] B. Bayar, S. A. Sajadi-Alamdari, F. Viti, and H. Voos, ‘‘Impact of different

spacing policies for adaptive cruise control on traffic and energy con-

sumption of electric vehicles,’’ in Proc. 24th Medit. Conf. Control Autom.

(MED), Jun. 2016, pp. 1349–1354.

[49] S. Darbha, S. Konduri, and P. R. Pagilla, ‘‘Vehicle platooning with constant

spacing strategies and multiple vehicle look ahead information,’’ IET Intell.

Transp. Syst., vol. 14, no. 6, pp. 589–600, Jun. 2020.

[50] D. Swaroop, J. K. Hedrick, C. C. Chien, and P. Ioannou, ‘‘A comparision of

spacing and headway control laws for automatically controlled vehicles,’’

Vehicle Syst. Dyn., vol. 23, no. 1, pp. 597–625, 1994.

[51] M. B. Younes and A. Boukerche, ‘‘Intelligent traffic light controlling

algorithms using vehicular networks,’’ IEEE Trans. Veh. Technol., vol. 65,

no. 8, pp. 5887–5899, Aug. 2016.

KAY MASSOW received the Diploma degree in

computer engineering from the Technical Univer-

sity of Berlin, Berlin, Germany, in 2008. In the

past, he has worked at Daimler and Volkswagen of

America, Inc. He is currently the Team Leader at

the Department of Automotive Services and Com-

munication Technologies, Fraunhofer Institute for

Open Communication Systems, Berlin. He is also

assists teaching and research at the Daimler Center

for Automotive Information Technology Innova-

tions, a joint initiative of Daimler AG, and the Technische Universität Berlin.

He is working in the fields of intelligent transport systems, cooperative

driving applications, digital high definition maps, and automotive big data

analytics.

ILJA RADUSCH received the Ph.D. degree in

engineering from the Technische Universität

Berlin, Berlin, Germany. He is currently the

Head of the Department for Automotive Services

and Communication Technologies, Fraunhofer

Institute for Open Communication Systems,

Berlin, and the Managing Director of the Daimler

Center for Automotive Information Technology

Innovations, Technische Universität Berlin. His

teaching and research interests include (secure)

car-to-X communications, internet-based telematics services, and simulation

for cooperative vehicles.

ROBERT SHORTEN (Senior Member, IEEE)

received the B.E. degree in electronic engineer-

ing and the Ph.D. degree from University Col-

lege Dublin, Dublin, Ireland, in 1990 and 1996,

respectively. From 1993 to 1996, he was the holder

of a Marie Curie Fellowship. He was with the

Daimler-Benz Research, Berlin, Germany, to con-

duct research in the area of smart gear-box sys-

tems. Following a brief spell with the Center for

Systems Science, Yale University, working with

Prof. K. S. Narendra, he returned to Ireland as a European Presidency

Fellowship, in 1997. He is the Co-Founder of the Hamilton Institute, National

University of Ireland, Maynooth, Ireland, where he was a Full Professor, until

March 2013. He was also a Visiting Professor with the Technical University

of Berlin, from 2011 to 2012. From 2013 to 2015, he led the Control

and Optimization Team at IBM Research, Dublin. He was a Professor of

control engineering and decision science with University College Dublin,

from 2015 to 2019, and IBM Research. He is currently a Professor of

cyber-physical systems design at Imperial College London. His research

spans a number of areas. He has been active in computer networking,

automotive research, collaborative mobility (including smart transportation

and electric vehicles), basic control theory, and linear algebra. His research

interest includes the study of hybrid dynamical systems.

43786 VOLUME 10, 2022