Design Methodology and Evaluation of
Rate Adaptation Based Congestion Control
for Vehicle Safety Communications
Tessa Tielert
∗
, Daniel Jiang
†
, Qi Chen
†
, Luca Delgrossi
†
and Hannes Hartenstein
∗
∗
Institute of Telematics and Steinbuch Centre for Computing, Karlsruhe Institute of Technology
Email: {tessa.tielert, hannes.hartenstein}@kit.edu
†
Mercedes-Benz Research & Development North America, Inc.
Email: {daniel.jiang, qi.chen, luca.delgrossi}@daimler.com
Abstract—Vehicle Safety Communications (VSC) is advancing
rapidly towards product development and field testing. While a
number of possible solutions have been proposed, the question
remains open as how such a system will address the issue
of scalability in its actual deployment. This paper presents a
design methodology for congestion control in VSC as well as the
description and evaluation of a resulting rate adaption oriented
protocol named PULSAR. We start with a list of design principles
reflecting the state of the art that define why and how vehicles
should behave while responding to channel congestion in order t o
ensure fairness and support the needs of safety applications. From
these principles, we derive protocol building blocks required
to fulfill the defined objectives. Then, the actual protocol is
described and assessed in detail, including a discussion on the
intricate features of channel load assessment, rate adaptation
and information sharing. A comparison with other state-of-the-
art protocols shows that “details matter” with respect to the
temporal and spatial dimensions of the protocol outcome.
I. INTRODUCTION
Vehicle Safety Communications (VSC) research and de-
velopment is rapidly advancing to a stage where the focus
shifts more and more to the actual deployment of the system.
A key concern in this context is the question of system
scalability. VSC based on Dedicated Short Range Communi-
cations (DSRC) will be dominated by pervasive and periodic
safety message broadcasts, typically denoted as Basic Safety
Messages (BSMs) in the U.S. and Cooperative Awareness
Messages (CAMs) in Europe or generally as beacons, from
all vehicles to their neighbors for cooperative awareness and
tracking. Experiments have demonstrated that channel con-
gestion can occur even in relatively simple traffic scenarios
[1]. Therefore, it is important to introduce congestion control
mechanisms to r egulate vehicles’ BSMs in order to prevent
them from actually drowning out each other.
Looking back at about 10 years of research in vehicular com-
munications, a large number of dedicated congestion control
solutions have been proposed, tailored not only towards VSC
but also for traffic efficiency applications. These approaches
often have differing design objectives and control dimensions,
which makes it difficult to compare them and to eventually
decide for one solution in the standardization process.
In this work, we t ake one step back and provide:
1) A consolidated view on the design principles and require-
ments for congestion control for VSC. To integrate the views
of previously proposed ideas, we review existing solutions
with respect to these design principles and show that especially
fairness aspects and safety applications’ requirements are often
not covered sufficiently (Sections II and III).
2) An overall design methodology that takes into account
the required transmission (Tx) range as an input from safety
applications and optimizes the Tx rate with respect to a target
Channel Busy Ratio (CBR) (Section IV).
3) Building blocks required to implement the design principles
following the suggested methodology as well as an in-depth
study of their r espective configurations. We introduce a Tx rate
adaptation based approach for VSC congestion control named
PULSAR (Periodically Updated Load Sensitive Adaptive Rate
control) as a direct implementation of the design principles
and building blocks. We analyze thoroughly channel load
assessment, rate adaptation and information sharing with its
many intricate features and pitfalls particularly with r espect to
timing issues (Section V).
4) An Evaluation and comparison of PULSAR in dynamic
scenarios with heterogeneous vehicular traffic densities. We
show that even seemingly similar protocols show significant
differences in behavior (Section VI).
We summarize our findings and conclusions in Section VII.
II. CONGESTION CONTROL PRINCIPLES FOR VSC
In this section, we summarize the state of the art in general
design principles for congestion control in VSC. Note that
these principles are tailored specifically towards controlling
the channel load generated by BSMs. Therefore, the objective
of congestion control is to ensure that safety applications’
requirements are fulfilled rather than to maximize end-to-end
throughput like for example in MANETs or sensor networks.
Also, the focus is not on mitigating the broadcast storm prob-
lem resulting from retransmissions of multi-hop (emergency)
messages or on regulating the channel load introduced by non-
safety applications. Finally, we focus on the design of concrete
algorithms rather than a general framework for the integration
and regulation of different message types and priorities. We
consider such efforts, e.g. [2], to be complementary to this
work. In Section III, we are going to review the related work
with respect to the proposed principles.
1) Decentralization: DSRC-based VSC is meant to func-
tion in ad-hoc mode. Thus, it is straightforward that congestion
control should be distributed. This principle is followed by all
related approaches and is only stated for completeness.
2) Participation: In order to ensure fairness, it is intuitively
clear that all nodes who contribute to congestion at a certain
location should participate in congestion control. Commonly,
the so-called Carrier Sense (CS) range is used as a boundary
for this purpose. It is defined as the distance from a trans-
mitting radio up to which the received signal strength can
be distinguished from the noise floor by a receiving radio.
Typically, it is calculated as a fixed distance assuming deter-
ministic propagation [3][4][5][6]. An important implication of
this principle is that all relevant nodes have to be aware of
their contribution to congestion within their CS range.
3) Local fairness: Nodes near each other share the same
channel. Therefore, it follows intuitively that nodes located
physically close to each other should have similar congestion
control levels. This principle is typically assumed implicitly
in the related work, but not stated explicitly. Note that, as we
will discuss later, this principle does not necessarily require
nearby nodes to have the same Tx parameters.
4) Global fairness: [7] discusses the suitability of the
proportional and max-min fairness notions for VSC. The
authors conclude that, from a safety point of view, it does
not make sense to increase the overall BSM throughput while
potentially throttling individual nodes. These nodes who are
not able to make themselves heard sufficiently may become a
danger to others who are not aware of their presence. However,
due to the unbounded and probabilistic nature of wireless
communications, it is difficult to apply the max-min principle
literally. Therefore, we use the term global fairness for a best-
effort approach to fulfill max-min fairness.
5) Deference to safety applications: The objective of trans-
mitting BSMs is to create a mutual awareness among vehicles.
Thus, recent works increasingly demand to base congestion
control measures on safety applications’ requirements in dif-
ferent driving contexts. [8] suggests to adapt the Tx rate based
on a vehicle’s own movement, vehicle density and dangerous
traffic situations. [9] describes a protocol which determines the
min. required Tx rate based on the estimated tracking error of
other vehicles. [10] goes one step further and derives the re-
quired Tx parameters by determining a min. warning distance
based on a sample application’s requirements. The overall
channel load, however, is not controlled. [11] concludes that
both, congestion and “awareness control”, should be integrated
into one solution. [2] suggests a general framework in which
the application layer provides constraints within which the
congestion control module can adapt the Tx parameters with
respect to the channel load. We summarize these findings in
the last principle: Congestion control should defer to and work
with guidance from safety applications on the space available
for control adjustments. Note that this principle implies that
the adjustment space may be different for individual vehicles.
III. RELATED WORK
Some recent approaches suggest to regulate beacons as
well as event-driven messages based on their utility for the
network [12][13]. They prioritize messages in the Tx queue
based on factors like the distance to an event, message age,
vehicle speed and the new area covered by a (re-)transmission.
However, the term “beacon” in this context does not refer
to BSMs but to periodic messages generated by non-safety
applications, e.g. in order to disseminate road-state informa-
tion. BSMs on the other hand contain information like a
vehicle’s current position and heading which is useful only for
a very brief period of time after being generated. Therefore,
it is preferable to avoid the queueing of outgoing BSMs by
adapting their generation to channel conditions and safety
applications’ requirements.
The channel load resulting from BSMs is typically controlled
by adapting Tx rate, power or both. Data rate and packet size
are usually fixed following [14] and standardization guidelines.
The dynamic adaptation of 802.11 parameters such as Clear
Channel Assessment (CCA) threshold [2] and contention win-
dow size [15] is primarily suitable to prioritize packets and is
therefore not considered here.
As detailed in [11], congestion control in VSC can be im-
plemented as feedforward (proactive) or feedback (reactive)
control. Proactive protocols estimate the future channel load
and try to avoid congestion in the first place. One of the
most cited solutions for VSC congestion control is D-FPAV
[3] which focuses on proactive Tx power adaptation. In order
to avoid congestion, vehicles running D-FPAV cooperatively
calculate the max. Tx power for each individual while ensuring
max-min fairness and not violating a system wide channel
load threshold. The original D-FPAV design introduces a large
overhead that is mostly reduced through a segment based
information aggregation mechanism in [4].
For an actual deployment, it may be more practicable to react
to congestion that has actually occurred, since this solution
depends less on highly accurate information and suitable
models for prediction. Therefore, the remainder of this paper
focuses on reactive congestion control.
The protocol introduced in [9] determines the min. required
Tx rate based on the estimated tracking error of other vehicles.
In a second loop, Tx power is scaled to extend range until a
defined CBR threshold is reached. Thereby, all information
used for control i s obtained locally, i.e., without information
sharing. Consequently, some nodes may contribute to conges-
tion at a location without being aware of it, since their own
location is not congested.
The authors of [5] introduce a joint rate and power adaptation
protocol designed to achieve fairness by assigning a fraction
of resources to each node. That is, if a node increases its
Tx power, it has to decrease its Tx rate and vice versa in
order to occupy the same amount of resources. However, the
same share of bandwidth does not necessarily imply the same
amount of safety benefit for different vehicles [10]. Therefore,
the underlying fairness assumption i s likely too restrictive.
In [16], the authors regulate the BSM Tx rate based on MAC
0
0.1
0.2
0.3
0.4
0.5
100 200 300 400 500
Avg. packet inter-reception time [s]
Distance to sender [m]
Tx = 200m, 21.1 Hz
Tx = 300m, 14.3 Hz
Tx = 400m, 10.7 Hz
Tx = 500m, 8.57 Hz
Tx = 600m, 7.10 Hz
Tx = 700m, 6.10 Hz
Tx = 800m, 5.35 Hz
Tx = 900m, 4.78 Hz
Fig. 1. Tx range and rate combinations resulting in 0.6 CBR (Rayleigh)
blocking, i.e., stopping all transmissions if the CBR exceeds
a defined threshold. Based on congestion events, nodes adapt
their Tx rate using Additive Increase Multiplicative Decrease
(AIMD). The protocol is designed to maximize traffic gen-
eration fairness but does not take into account the awareness
requirements of safety applications.
[6] and [17] are probably the most closely related approaches
to the protocol presented in this work. Thus, a detailed
description, analysis and evaluation as well as a comparison
with our approach will be provided in Section VI.
IV. PROTOCOL DESIGN METHODOLOGY
Typically, the objective of VSC congestion control is to
keep the channel load generated by BSMs below a certain
threshold in order to reserve bandwidth for event-driven emer-
gency messages [3][5][9]. In this context, the question is how
transmission parameters, i.e., Tx rate and range, should be
adapted to meet safety applications’ requirements.
The underlying general optimization problem, i.e., to find the
“optimal” Tx rates and ranges for a certain metric given the
safety requirements of each individual vehicle as well as vehi-
cle density and context parameters, is highly complex. Thus, a
computationally tractable and distributed way of tackling the
optimization problem is desirable. In the following, we outline
the rationale of the proposed methodology in comparison to
related work. Particularly, we focus on which metrics to select
and which parameters to fix first.
In [18], the authors of [9] use the i nformation dissemination
rate (IDR), i.e., the number of packets received successfully by
a node’s neighbors, as a metric for application performance.
They analyze different combinations of Tx rate and range
and show that the max. achievable IDR i s always the same,
concluding that therefore IDR can be maximized through a
separate control of both parameters. Furthermore, the authors
analyze the relationship of IDR and CBR, i.e., the fraction
of time the medium was sensed busy by the radio. They
observe that any combination of Tx rate and range results
in the same IDR vs. CBR curve. Thus, they conclude that
CBR is a suitable feedback measure for maximizing IDR.
Based on these conclusions, the authors present a design
methodology for congestion control which first fixes Tx rate
based on vehicle tracking performance and then adapts Tx
range based on CBR. However, the authors face the problem
that the optimal choice of the Tx range depends not only on
the current Tx rate but also on vehicle density. Since vehicle
density is hard to estimate correctly in reality, the authors
“resort to a robust but suboptimal design” by adjusting the
0
100
200
300
400
500
600
700
800
900
1000
1100
100 150 200 250 300 350 400
0
2
4
6
8
10
12
14
16
18
20
Theoretical Tx-range [m]
Tx-rate [Hz]
Distance to sender [m]
Optimal Tx range 200 nodes/km
Optimal Tx range 100 nodes/km
Optimal Tx rate 200 nodes/km
Optimal Tx rate 100 nodes/km
Fig. 2. Optimal Tx rate and range allocations for 0.6 CBR (Rayleigh)
channel load between a min. and max. CBR value of 0.4 and
0.8, even though they identified 0.65 as the optimal CBR value.
In this work, we take a different approach by first fixing
Tx range and then adapting Tx rate wit h respect to CBR
measurements. VSC applications based on BSMs are typically
associated with a certain range up to which information is
required to be received at high probability [10][19][20]. This
target range is typically in the order of 100 to 300 meters
[21]. A common metric for application performance in this
context is the average packet Inter-Reception Time (IRT), i.e.,
the average amount of time between two subsequently received
messages for a sender-receiver pair [22]. Figure 1 illustrates
the IRT for different pairs of Tx range
1
and rate which result
in a CBR value of 0.6. The result was obtained from ns-
2 simulations using a 20 km long circular linear road with
a uniform node distribution of 100 nodes/ km and Rayleigh
fading (Nakagami model with m = 1). We observe that the
optimal Tx rate/ range combinations in terms of minimizing
the IRT for each distance from the sender form a linear line.
Figure 2 plots these points as the optimal Tx rate and range
with respect to the distance from the sender, i.e., the target
range, for node densities of 100 and 200 nodes/ km. The result
indicates that, while the optimal choice of Tx rate depends on
node density, the optimal Tx range does not. Therefore, our
approach is to fix Tx range first depending on the currently
required target range and to adapt Tx rate in a second step
depending on channel conditions. Note that, since the target
range changes with respect to a vehicle’s driving context, the
Tx range is also adapted dynamically based on guidance from
the application layer. However, we expect these changes to
occur at a lower pace than the adaptation of the Tx rate.
Given a fixed Tx range, the Tx rate can be used to adapt the
IRT within the target range. Safety applications typically have
a max. IRT value beyond which no further safety benefit can
be achieved. Thereby, safety benefit could be expressed in dif-
ferent metrics, e.g., “awareness probability” [20], “application
reliability” [10] or “vehicle tracking error” [18]. At the same
time, there is likely to be a min. requirement below which the
application cannot work. Depending on the driving context of
a vehicle, we expect the s afety benefit curve with respect to
the Tx rate to resemble the ones shown in Figure 3. From
this consideration, a min. and max. Tx rate requirement can
be derived for each vehicle depending on its driving context
as illustrated in the figure. If channel conditions don’t allow
1
The term (theoretical) Tx range denotes the distance at which the transition
from reception to non-reception occurs using deterministic propagation.
Fig. 3. Schematic illustration of safety benefit vs. Tx rate
for all vehicles to transmit at their max. rate r equirement,
it would be fair to provide everyone with the same relative
“safety benefit”, i.e., to restrict each vehicle to a rate which
corresponds to x% of their min/ max Tx rate interval.
V. PROTOCOL DESCRIPTION
In this section, we translate the principles from Section II
into actual protocol mechanisms following t he methodology
described in the Section IV and introduce PULSAR as a
resulting reactive congestion control protocol for VSC. Note
that, even though PULSAR is designed to support different
Tx ranges and min/ max Tx rate interval settings per node, in
this work we focus on uniform configurations of all vehicles
in order to better illustrate the characteristics of the different
mechanisms. An extended description of the protocol is going
to be presented in future work.
A. Channel Load Assessment
While some protocols use metrics like the number of col-
lisions and SNR as a metric for channel load [13], PULSAR,
like most other approaches [5][6][9][16], makes use of CBR
measurements. In [18], the authors conclude that CBR is
a suitable feedback metric for maximizing the number of
received packets (IDR) and recommend a CBR target value of
0.65. Our own analysis has shown that, independent of packet
size and the fading model used, a CBR value between 0.6 and
0.7 achieves the best results in terms of IDR. In this work, we
use a CBR target value of 0.6. Note that any CBR value is
only meaningful considering the underlying CCA threshold.
While some approaches use values near -85 dBm [5][23], our
analysis has shown that a lower CCA-threshold results in better
per-message reception performance. Today’s radios can set
the CCA threshold very close to the noise floor. Assuming
a noise floor of -99 dBm (-107 dBm thermal noise at 5.9 GHz
and 5 dB hardware noise) and a tolerance of 4 dB, we use a
CCA threshold of -95 dBm which is consistent with [18].
In PULSAR, the arrival of a new CBR measurement triggers
a Tx rate adaptation. A key parameter in this context is the
length of the interval during which the busy indications of the
physical layer are evaluated. [17] uses a node’s Tx interval for
this purpose. However, this approach can lead to (global) un-
fairness, for example since nodes using a lower Tx rate get less
chances to increase their share. PULSAR therefore uses a fixed
length Channel Monitoring and Decision Interval (CMDI) for
all nodes. Since the CMDI influences the convergence time of
the protocol, its length should be minimized. However, due
to fading, CBR measurements are subject to a probability
distribution whose variance is inversely proportional to the
length of the CMDI. Our analysis has shown that a reasonable
trade-off between variance and reaction time is between 200
and 400 ms. In this work, we use a CMDI of 250 ms.
In order to reduce the probability of reacting to a “false alarm”,
PULSAR additionally uses a first-order digital low-pass fil-
ter to reduce measurement noise. The smoothed out value
CBR
avg
is calculated from a new measurement CBR
new
as
CBR
avg
= 0.5 ∗ CBR
avg
+ 0.5 ∗ CBR
new
.
B. Rate Adaptation
When a new CBR measurement arrives at the end of
each CMDI, PULSAR compares the measured value against
the target value. In a binary decision, a node’s Tx rate is
either decreased if there is excess channel load or increased
otherwise. Thereby the Tx rate is adapted within the min.
and max. Tx rate limits provided by the application layer.
The actual rate increment or decrement is calculated using
Additive Increase Multiplicative Decrease (AIMD) and the
target rate mechanism described below. The combination of
both mechanisms ensures local and global fairness as well as
sufficient convergence time when vehicles are moving fast.
In [24], the authors show that, for wired networks, AIMD is
favorable over the other three combinations of additive and
multiplicative increase and decrease since it ensures max-min
fairness. An analysis by the authors of [25] has shown that
this also holds for VSC. However, in some cases, AIMD may
not converge to fairness if nodes are not synchronized i n their
measurements [26]. PULSAR therefore assumes that all nodes
are (loosely) synchronized in their CMDI, e.g., using GPS. We
are currently evaluating LIMERIC [25], which does not have
this restriction, for usage in PULSAR.
In terms of controlling a system, it is desirable that control
measures take effect immediately. However, when adapting
the Tx rate at the end of each CMDI, nodes typically have
already scheduled their next transmission based on the old
Tx rate. In addition, a node’s current Tx interval may be
longer than the CMDI. PULSAR therefore uses a rescheduling
mechanism for already scheduled transmissions. Let i
orig
,
i
new
and i
rest
denote the original and newly calculated
Tx interval and the remaining part of i
orig
, respectively.
The pending transmission is canceled and rescheduled using
time
rescheduled
= time
now
+
i
rest
i
orig
∗ i
new
.
Vehicular networks are characterized by a high dynamic in
node topology. In order to ensure especially local fairness, the
rate adaptation mechanism is required to have a sufficiently
short convergence time. Given a fixed-length CMDI, one way
would be to tune AIMD parameters aggressively, i.e, to take
into account large fluctuations of Tx rate and CBR. Another
way is to make use of the average Tx rate of a node’s
neighbors. PULSAR uses a node’s target rate, i.e., an average
of the Tx rates of its neighbors, as a gravitation pull when
calculating Tx rate adjustments. That is, when increasing, the
increment is doubled if the vehicle’s current rate is below
target rate. Else, if the current rate is already above target
rate, the increment is halved. In opposite direction, the same
principle applies to the decrement. The target rate itself is
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 200 400 600 800 1000 1200 1400 1600 1800
PDF
Distance to sender [m]
Theoretical
Tx-range
Carrier sense range
Recv. 1 out of 1 msg.
Recv. 1 out of 2 msg.
Recv. 1 out of 4 msg.
Recv. 1 out of 8 msg.
Rcv. 1 out of 16 msg.
Rcv. 1 out of 32 msg.
Carrier sensing
Fig. 4. Piggybacking efficiency at 0.6 CBR, Tx = 500 m
calculated as an exponentially weighted moving average of
the Tx rate information r
c
contained in received BSMs (e.g.,
using δ = 0.1): r
target
= (1 − δ) ∗ r
target
+ δ ∗ r
c
. Compared
to an average derived, e.g., from a neighbor table, fading
results in an implicit weighting within the target rate, favoring
close neighbors over distanced ones and large groups of
neighbors over small groups. In our analysis, the target rate
mechanism has shown a smoother convergence behavior than
a simple neighbor average derived from a neighbor table. This
mechanism is going to be further evaluated and improved in
future work.
C. Information Sharing
In the related work, there is no consensus on whether or
not information on channel conditions needs to be exchanged
among vehicles. While some approaches share channel state
information [16][17], others rely on local measurements only
[5][6][9][13]. The latter approach features less overhead. How-
ever, it may lead to a violation of the local and global fairness
principle. Due to fading, CBR measurements are subject to
a certain r andomness. Therefore, even neighboring nodes can
come to different assessments of the channel state. For exam-
ple, consider a situation i n which node A detects congestion,
while its neighbor B does not. In this case, A would increase
its rate, while B would decrease, making room for A to
increase again and so on. Over time, this effect can result in
imbalance and unfairness. In addition, nodes can contribute to
congestion at a distant location without measuring congestion
themselves. Thus, while from a system point of view the
objective of controlling channel load can be met with local
measurements only, the participation and fairness principles
require the exchange of channel state information.
The participation rule suggests that all nodes within a certain
range, e.g., CS range, from a congested location need to
be informed of their contribution in order to participate in
congestion control. A CCA threshold of -95 dBm results in
a CS range which has approximately twice the length of
the (theoretical) Tx range. Therefore, for uniform Tx range
settings, it is not possible to notify all nodes within CS range
of an occurring congestion by using 1-hop piggybacking. One
way would be to send a high-power message containing the
required information, another one is to piggyback information
over two hops. Unless an increment of the Tx power is
required anyway, the latter approach is likely to introduce less
additional load to the channel.
Figure 4 illustrates the feasibility of constructing a 2-hop
information dissemination mechanism for congestion control
A B C
A measures congestion
B receives information
A transmits information
C receives information
B transmits information
1 sliding window
1 sliding window
CAT + propagation
CAT + propagation
approximately
2 sliding windows
Fig. 5. Max. age of 2-hop piggybacking information
over a Rayleigh channel. The vertical bars in the figure
illustrate the underlying Tx range (500 m) and CS range
(1021 m). The figure also shows that, with Rayleigh fading,
there is a non-trivial chance that a generated message is carrier
sensible beyond the nominal Tx range and even CS range.
For fairness, it is therefore necessary to propagate congestion
information at least up to CS range. While the probability
of reception is relatively low for a single transmission under
channel load (the red/leftmost curve in the figure), generally
more than one vehicle measures and reports congestion. It is
sufficient to receive just one out of the messages transmitted
by all of these vehicles in order to receive the contained
congestion information. Therefore we can assume that, with
high probability, the nominal Tx and CS range can be covered
in one and two piggybacking hops, respectively.
When constructing a 2-hop piggybacking scheme as outlined
above, the most straightforward approach is to react to the
congestion indication received from local measurement, 1-
hop and 2-hop information within the last CMDI. However,
in doing so, we would not take into account the resulting
information dissemination delay: Nodes measuring congestion
themselves would decrease their Tx rates first, while others
contributing to congestion might not yet be aware of doing so,
increasing their Tx rates even further. To avoid this violation
of the global fairness principle, the propagation delay has to
be taken into account when reacting to local and reported
congestion. The general objective is for all nodes to react to
the same state of the system at the same time.
In PULSAR, each node attaches its own congestion state based
on its last CBR measurement as well as the max. congestion
state it has received from nodes within range R and time frame
T to each beacon. Assuming non-deterministic propagation, R
is an adjustable parameter which determines the size of one
piggybacking hop and therefore also the participation range,
i.e., the distance from a congested location at which nodes
participate in congestion control. T is a sliding window of
the same length as the CMDI in order to prevent the relayed
information from being older than one CMDI.
Figure 5 sketches a scenario of 3 nodes (A, B and C) in a
unit disc graph model where B and C are not congested but
contributing to the congestion at A. However, A cannot reach
C directly. The figure illustrates that the max. age of the 2-
hop information received at C is approximately two sliding
windows, i.e., two CMDIs. In order to have all nodes react to
the same system state, PULSAR delays a node’s reaction by a
max. of two CMDIs. To be precise, at the end of CMDI t, C
reacts to the max. congestion state of its local measurement of
t-2, it s 1-hop information received between t-1 and t-2 and its
2-hop information received between t and t-2, but generated
at t-2. I n order to determine in which CMDI the reported 2-
![Fig. 9. [6] w.r.t. time](/figures/fig-9-6-w-r-t-time-51ut2rey.webp)
