1

Distributed Rate and Power Control in Vehicular
Networks

arXiv:1511.01535v1 [] 4 Nov 2015

Jubin Jose, Chong Li, Xinzhou Wu, Lei Ying and Kai Zhu

Abstract—The focus of this paper is on the rate and power
control algorithms in Dedicated Short Range Communication
(DSRC) for vehicular networks. We first propose a utility maximization framework by leveraging the well-developed network
congestion control, and formulate two subproblems, one on rate
control with fixed transmit powers and the other on power
control with fixed rates. Distributed rate control and power
control algorithms are developed to solve these two subproblems,
respectively, and are proved to be asymptotically optimal. Joint
rate and power control can be done by using the two algorithms
in an alternating fashion. The performance enhancement of our
algorithms compared with a recent rate control algorithm, called
EMBARC [1], is evaluated by using the network simulator ns2.

I. I NTRODUCTION
Dedicated Short Range Communication (DSRC) service [2]
is for vehicle-to-vehicle and vehicle-to-infrastructure communication in the 5.9 GHz band. Among the 75 MHz allocated to
DSRC, the channel 172 (5.855 GHz – 5.865 GHz) is assigned
for critical safety operations, which allows vehicles to periodically exchange Basic Safety Messages (BSM) to maximize
the mutual awareness to prevent collisions. Such messages
typically include the GPS position, velocity of the vehicle.
By receiving these BSM messages from surrounding vehicles,
all participating vehicles in the DSRC safety system can assess
the threat of potential collisions and provide warnings to the
driver, if necessary. United States Department of Transportation (USDOT) reported that the DSRC safety system based
on this simple mechanism can address 80% of the traffic
accidents on the road today and thus has potentially huge
societal benefit. On the other hand, such benefit is possible
only when timely and reliable information exchange among
vehicles using DSRC can be guaranteed in all deployment
scenarios.
DSRC is based on IEEE 802.11p standards [3] at PHY and
MAC layer. It has been well known that DSRC vehicular networks exhibit degraded performance in congested scenarios. In
particular, excessive packet loss can be observed at high node
density even between vehicles which are in close proximity
to each other [4], which can severely undermine the safety
benefit targeted by deploying such networks. Performance
improvement in such scenarios has been one of the key
challenging issues for the success of DSRC. The industry and
academics have contributed various solutions to this issue in
a collaborative way over the last decade, e.g., [5], [6], [7].
J.Jose, C. Li and X. Wu are with Qualcomm Research; L,Ying and K. Zhu
are with School of Electrical, Computer and Energy Engineering, Arizona
State University. The authors are listed in alphabetical order

The key system parameters one may control at each vehicle
are the transmit power and transmit rate, i.e. the periodicity
of the BSM messages, to alleviate the system congestion, i.e.
lower transmit rate and power reduces the footprint and also
the number of messages a DSRC device may generate and
thus reduce the congestion level in the critical safety channel.
On the other hand, both rate control and power control are
critical for system performance as the transmit power of a
vehicle determines the number of surrounding vehicles which
can discover the vehicle and higher transmit rate of the BSM
message can improve the accuracy the of collision estimation
between two vehicles by having more message exchanges.
Thus, a key problem to be addressed in the DSRC system is:
How to choose the transmit rate and power for each vehicle in
a distributed manner such that the overall system performance
is maximized without creating excessive network congestion,
i.e. observing very high channel load in some locations of the
network?
Both rate control and power control have been studied in
the literature (e.g. [8], [9]). However, most of these works
propose heuristic methods to adjust the rate and (or) power
in simplistic scenarios, e.g. single bottleneck scenarios (i.e.,
there is only one congested channel in the network). Further,
some of the methods [6], [1] rely on the existence of global
parameters for algorithm convergence, which leads to system
resource under-utilization in some scenarios.
The focus of this paper1 is to propose a network resource
allocation framework for rate and power control in vehicular
network, by leveraging existing network congestion control
framework [11] established in the context of wireline and
wireless networks, and then develop optimal distributed rate
and power control algorithms to achieve such a goal. The main
contributions of this paper are summarized below:
• We propose a utility maximization framework for rate and
power control in DSRC. In general, the utility maximization is a non-convex optimization problem with integer
constraints. We separate the problem to two subproblems:
rate control problem and power control problem, where
the rate control problem is to find the optimal broadcast
rates when the transmit power (i.e., the transmit ranges)
of vehicles are fixed and the power control problem is to
find the optimal transmit power (or transmission range)
when the broadcast rates are fixed.
• We develop a distributed rate control algorithm which
is similar to the dual algorithm for the Internet congestion control and prove that the time-average total utility
1 Partial

version of this paper has appeared in [10].

2

obtained under the proposed rate control algorithm can
be arbitrarily close to the optimal total utility with fixed
transmission power.
• The power control problem is a non-convex optimization
problem. We reformulate the problem as an integer programming problem. After relaxing the integer constraints,
we develop a distributed power control algorithm based
on the dual formulation. Interestingly, it can be shown that
one of the optimal solutions to the Lagrangian dual, when
fixing the dual variables, is always an integer solution.
That implies that the distributed algorithm derived from
the relaxed optimization problem produces a valid power
control decision and the relaxation is performed without
loss of optimality (more details can be found in Section
IV). Based on that, we prove that the time-average
total utility obtained under the proposed power control
algorithm can be arbitrarily close to the optimal total
utility with fixed broadcast rates.
The paper is organized as follows. In Section II, a utility
maximization framework is provided for congestion control in
DSRC. Then asymptotically optimal distributed rate control
algorithm and power control algorithm are derived respectively
in Section III and IV. In the end, simulation results are
presented in Section V to verify our algorithms. The proofs in
the paper are provided in the Appendix.
A. Discussion on Related Work
The design of rate and power control algorithms in DSRC
is one of most critical problems in ITS. Error Model Based
Adaptive Rate Control (EMBARC) [1] is a recent rate control protocol which integrates several existing rate control
algorithms including the Linear Integrated Message Rate
Control (LIMERIC) [6], Periodically Updated Load Sensitive
Adaptive Rate control (PULSAR) [12], and the InterVechicle
Transmission Rate Control (IVTRC) [13]. LIMERIC allocates
the wireless channel equally among all vehicles that share
the same bottleneck link while guaranteeing the channel
load is below a given threshold. IVTRC generates messages
and adapts transmission probabilities based on the Suspected
Tracking Error (STE) calculated based on vehicle dynamics to
avoid collisions. In EMBARC, the message rates are controlled
by LIMERIC and are further modified to satisfy the STE
requirement.
A parallel work [14] introduced a network utility maximization (NUM) formulation on the rate control problem when
specified to safety-awareness. A distributed algorithm was
proposed to adjust the rate with the objective to maximize
the utility function. Similarly, [15] also provided a NUM
formulation on the rate control problem and proposed a fair
adaptive beaconing rate for intervehicular communications
(FABRIC) algorithm, which essentially is a particular scaled
gradient projection algorithm to solve the dual of the NUM
problem.
Other related work includes the database approach proposed
in [9], where the optimal broadcast rates and transmission
power are calculated offline based on the network configurations. Also, [16] proposed an environment and context-aware

distributed congestion control (DCC) algorithm, which jointly
control the rate and power to improve cooperative awareness
by adapting to both specific propagation environments (such
as urban intersections, open highways, suburban roads) as well
as application requirements (e.g., different target cooperative
awareness range). However, the stability and convergence of
the algorithm are not proved mathematically. Besides the rate
control algorithm IVTRC, the authors also proposed range
control algorithms in [17], [18], [8] where the objective is to
adapt the transmission ranges to achieve a specific threshold.
The motivation of limiting channel loads below the threshold
is to control channel congestion to maximize effective channel
throughput. However, fair resource allocation among vehicles
to increase the safety awareness of all vehicles are not considered, and the stability of the algorithms is subject to certain
conditions [8].
II. P ROBLEM F ORMULATION
In this section, we formally define the utility maximization
framework for the DSRC congestion control problem. We first
introduce the set of notations used throughout this paper.
• µi : the message broadcast rate of vehicle i;
• pi : the transmit power of vehicle i;
• αij : the minimum transmit power required for node i’s
message to be decoded by node j;
• βij : the minimum transmit power required for node i’s
message to be sensed by node j, i.e. the received energy
is above the carrier sensing energy detection threshold;
• I : indicator function.
Note αij is not necessarily the same as βij , as in IEEE802.11
standards, packet header decoding happens at a much lower
energy level than energy based detection in carrier sensing.
From the definition of αij and βij , it is easy to see that
• Vehicle j can receive the message from vehicle i if pi ≥
αij ;
• Vehicle j can detect (but not necessarily decode) the
message from vehicle i if pi ≥ βij .
We assume αij and βij are constants within the time frame
for the distributed rate and power control algorithm, which is
reasonable as the nominal BSM update rate is 10Hz, i.e. 10
transmissions in every second.
In DSRC, a vehicle can control rate µi and power pi . We
consider the following utility maximization problem for rate
and power control:
P P
General − OPT maxµ,p i j Ipi ≥αij Uij (µi ) (1)
P
∀j
(2)
subject to:
i µi Ipi ≥βij ≤ γ
µi ≥ 0, pi ≥ 0

∀i.

(3)

Now we explain the particular choice of the objective
function and constraints above. In the objective function (1),
X
Ipi ≥αij Uij (µi )
j

is the total utility associated with vehicle i, which depends on
the number of vehicles who can receive the transmissions of
vehicle i, i.e., the size of the set

(4)
j : Ipi ≥αij = 1

3

and the utility function Uij (µi ) associated with each ordered
pair (i, j), which is a concave function and can be interpreted
as the level of j ′ s awareness of i when j receives messages
from i with rate µi . Obviously, higher transmission rate µi
should lead to higher value of Uij in DSRC. The neighborhood
size (4) is controlled by the transmit power pi and the value
of utility Uij (µi ) is determined by rate µi .
Remark 1. A widely used utility function [19] is called the
α-fair utility function which includes proportional fairness,
minimum potential-delay fairness as special cases and is given
by
µ1−αi
Ui (µi ) = wi i
, αi > 0,
(5)
1 − αi
where wi represents the weight of node i, determined by
its local information such as relative velocity, instantaneous
location in the application of vehicular network. Notice that
this utility function, given in a generic form, is independent
of communication links (from j). In other words, each vehicle
only knows its own utility function. As will be seen later, a
choice of such a form of utility function further simplifies the
proposed distributed algorithms because there is no need of
obtaining neighbors’ utility functions.
i
For αi = 2, the utility function turns to be Ui (µi ) = − w
µi
which implies weighted minimum potential delay fairness in
network’s resource allocation. For αi = 1, the utility function
behaves as Ui (µi ) = wi log(µi ) which leads to weighted
proportional fairness. We refer interested readers to [20] for
details.
The constraint (2) states that the channel load at any vehicle
j should be below a target channel load γ. In CSMA based
systems, high γ value indicates channel congestion, which
implies high packet collision rate and low effective channel
throughout [17], [9]. In [17], the authors have observed that the
curve of information dissemination rate versus channel load
remains almost the same under different configurations. In [9],
the authors also found that the effective channel throughput is
maximized when the channel load is around 0.91 under various
settings. Thus, it is natural to impose such a constraint (2) to
limit the congestion level in the system.
A. Problem decomposition
General-OPT is difficult to solve because the objective
function (1) is not jointly convex in (µ, p). We therefore
separate the problem into rate control problem and power
control problem as defined below.
• Assume the transmit power is fixed at each vehicle. Then
we can define
Ri = {j : pi ≥ αij },
i.e., the set of vehicles who can receive the messages
from vehicle i, and
Ii = {j : pi ≥ βij },
i.e., the set of vehicles whose channel load can be affected
by vehicle i′ s transmissions. When transmit power pi is

•

fixed, both Ri and Ii are fixed. In this case, general-OPT
becomes the following Rate-OPT
P P
Rate − OPT : ρ = maxµ i j∈Ri Uij (µi ) (6)
P
subject to:
∀ j. (7)
i:j∈Ii µi ≤ γ

Assuming the broadcast rates are fixed, i.e., µi ’s are fixed,
OPT becomes the following Power-OPT:
P
Power − OPT : ρ = maxp i,j Ipi ≥αij Uij (µi )(8)
P
(9)
subject to:
i µi Ipi ≥βij ≤ γ.

B. Iterative joint rate and power control
In light of the above decompositions, a (suboptimal) solution of General-OPT can be obtained by iterating Rate-OPT
and Power-OPT. The initial set of rate or power parameters for
the iterative algorithm can be appropriately chosen according
to certain practical constraints. The stopping criterion at step k
is typically set to be ρ(k + 1) − ρ(k) ≤ ǫ for ǫ > 0. It is worth
noting that in each step of iterations the utility value ρ(k) is
non-decreasing and ρ(k) is bounded above for all ∀k, given
a well-defined utility function. Therefore, the convergence of
the iterative algorithm is guaranteed.
In the following sections, we will develop distributed algorithms to solve Rate-OPT and Power-OPT separately. The
optimal rate control algorithm directly follows from the welldeveloped network congestion control while the optimal power
control algorithm is innovative and rather technical.
III. R ATE C ONTROL A LGORITHM
In what follows, we study the rate control problem and
develop a distributed rate control algorithm that solves (6).
Note that Rate-OPT is similar to the network utility maximization (NUM) problem for the Internet congestion control
(see [11] for a comprehensive introduction of the NUM
problem for the Internet congestion control). Each vehicle i
may represent both a flow and a link onPthe Internet, and
µi is the data rate of flow i. Regarding j∈Ri Uij (µi ) as
the utility function of vehicle i, the objective is to maximize
the sum of user utilities. We may further say that flow i
uses link j when j ∈ Ii . Then constraint (7) is equivalent
to the link capacity constraint that requires the total data
rate on link j to be no more than the link capacity γ.
To this end, Rate-OPT can be viewed as a standard NUM
problem for the Internet congestion control. The distributed
rate control algorithm below is based on the dual congestion
control algorithm for the Internet congestion control [11],
which consists of rate control and congestion price update. The
congestion price update monitors the channel load of vehicle
j. The congestion price λj increases when the channel load
at vehicle j exceeds the threshold γ and decreases otherwise.
The rate control algorithm adapts the broadcast rate µi based
on the aggregated congestion price from all vehicles who can
sense the transmissions from vehicle i, i.e., the vehicles whose
channel loads are affected by vehicle i.
Rate Control Algorithm

4

1) Rate control algorithm at vehilce i : At time slot t, vehicle
i broadcasts with rate µi [t] such that
µi [t]
= min




arg max
µ



X

X

Uij (µ) − ǫµ

j∈Ri

λj [t − 1], µmax





j∈Ri

(10)

where ǫ ∈ (0, 1] is a tuning parameter.
2) Congestion price update at vehicle j : At time slot t,
vehicle j updates its congestion price λj to be

+
X
λj [t] = λj [t − 1] +
µi [t − 1] − γ  .
(11)
i:j∈Ii

This rate control algorithm is developed based on the dual
decomposition approach [11]. Specifically, the Lagrangian of
optimization (6) is
L(µi , λ)
=

X X
i

=

X
i

X

λj 

Uij (µi ) − ǫµi

X

Uij (µi ) − ǫ

j

j∈Ri




X



j∈Ri

j∈Ii

X

i:j∈Ii



µi − γ 

λj  − γ

X

λj ,

j

min g(λ) = min max L(µi , λ)
λ

µi

When λ is fixed, the µi should maximize
X
X
Uij (µi ) − ǫµi
λj ,
j∈Ri

j∈Ii

which motivates the rate control algorithm (10). The congestion price update (11) is designed by taking derivative of g(λ)
over λ and then the optimal λ, as a mean to optimize the dual
problem, can be achieved by using a gradient search in (11).
The next theorem shows the rate control algorithm is
asymptotically optimal.
Theorem 2. Denote by µ∗i the optimal solution to problem (6)
and assume µmax > µ∗i for all i. Then there exists a constant
B > 0, independent of ǫ, such that under the proposed rate
control algorithm
lim inf
T →∞

1
T

T
−1 X
X
t=0

i

X

j∈Ii

Uij (µi [t]) ≥

XX
i

xij = Ipi ≥αij

∀ βik ≤ αij (15)
∀i, j
(16)

yij ∈ {0, 1}

∀i, j.

xij ≥ xik
yik ≥ xij

(17)

∀ αij ≤ αik (20)
∀ βik ≤ αij (21)

0 ≤ xij ≤ 1
0 ≤ yij ≤ 1

∀i, j
∀i, j.

(22)
(23)

Now by including constraint (19) in the Lagrangian, we
obtain
P
P
P
maxx,y i,j xij Uij (µi ) − ǫ j λj ( i yij µi − γ)
s.t.:
xij ≥ xik ∀ αij ≤ αik
yik ≥ xij ∀ βik ≤ αij
0 ≤ xij ≤ 1 ∀i, j
0 ≤ yij ≤ 1

j∈Ii

The proof of the theorem is similar to the proof of Theorem
6.1.1 in [11], and is omitted in thisP
paper. Remark that if the
objective function utility function j∈Ri Uij (µi ) is strictly
concave, the optimal solution of Rate-OPT is unique since the
search space is convex. As a consequence, the above algorithm
converges to the unique optimal solution.

yik ≥ xij
xij ∈ {0, 1}

Recall αij is the minimum transmit power for vehicle j to
receive messages from vehicle i. So constraint (14) states
that if vehicle j requires a smaller minimum transmit power
of vehicle i than vehicle k, then vehicle j can receive from
vehicle i if vehicle k can do so. Constraint (15) is similarly
defined.
Next, we relax the integer constraints (16) and (17) to obtain
the following linear programming problem.
P
maxx,y i,j xij Uij (µi )
(18)
P
∀j
(19)
subject to:
i yij µi ≤ γ

Uij (µ∗i ) − Bǫ.


and yij = Ipi ≥βij .

The Power-OPT problem is equivalent to the following integer
programming problem:
P
(12)
maxx,y i,j xij Uij (µi )
P
∀j
(13)
subject to:
i yij µi ≤ γ
xij ≥ xik
∀ αij ≤ αik (14)



where ǫ is a tuning parameter. Then the dual problem is
λ

IV. P OWER C ONTROL A LGORITHM
In this section, we develop a distributed power control algorithm that solves (8). The power control problem is developed
by formulating the Power-OPT as an integer programming
problem. After relaxing the integer constraint, we develop a
distributed power control algorithm using the dual approach.
Interestingly, it turns out the solution obtained from the
Lagrangian dual is always an integer solution. In other words,
the power control algorithm based on the linear approximation
always gives a valid power control solution and is proved to
be asymptotically optimal for Power-OPT.
We first introduce new variables x and y such that

∀i, j.

where ǫ is a tuning parameter. Note that constraints (20)
and (21) impose conditions on x and y related to the same
transmitter i. Therefore, given λ, the Lagrangian dual problem
above can be decomposed into the sub-problems for each given
i:
P
(24)
maxx,y j xij Uij (µi ) − ǫλj µi yij
subject to:

xij ≥ xik

∀ αij ≤ αik

5

yik ≥ xij

∀ βik ≤ αij

0 ≤ xij ≤ 1 ∀j
0 ≤ yij ≤ 1 ∀j.
Next we will show that one of the optimizers to the problem
(24) is an integer solution. For a fixed vehicle i, we sort the
vehicles in a descendent order according to αij and divide
them into groups, called G-groups and denoted by Gg , such
that αij = αik if j, k ∈ Gg , and αij < αik if j ∈ Gg and
k ∈ Gg+1 . Associated with each group Gg , we define α̃g to
be common α in the group. We further define H-groups
Hg = {m : α̃g−1 < βim ≤ α̃g }.
This is the set of vehicles that can sense the transmission
of vehicle i when the transmit power is α̃g and cannot if
the power is α̃g−1 . Furthermore, let g(j) denote the G-group
vehicle j is in and h(j) the H-group vehicle j is in. The
following lemma proves that one of the optimal solution to
(24) is an integer solution. The proof is presented in the
Appendix.

1. Note that the optimization problem can be further simplified
for specific utility functions, e.g., Ui,j (µi ) = wi log(µi ).
Based on the discussion and lemma above, we develop the
following power control algorithm, which consists of congestion price update and power update. The congestion price
update monitors the channel load and the power update adapts
the transmission power pi based on the aggregated congestion
price from all vehicles who can sense the transmissions from
vehicle i.
Power Control Algorithm
1) Power control at vehicle i : Vehicle i chooses the transmission power to be
pi [t + 1] = α̃gi′ ,
where gi′ is defined in Lemma 3 with λ = λ[t].
2) Congestion price update at vehicle j :

+
X
λj [t + 1] = λj [t] +
µi − γ  .

(25)

(26)

i:j∈Ii

Lemma 3. Given λ, one of optimizers to optimization problem
(24) for given vehicle i is the following integer solution


1, if g(j) ≤ gi′
1, if h(j) ≤ gi′ Remark 4. Notice that the second step of the power control,
xij =
and yij =
, congestion price update, is identical to that in the rate control.
0, otherwise.
0, otherwise.
P
In practice, the value of i:j∈Ii µi can be approximated by
where
measured/sensed channel load of individual vehicle2 . Further

more, as shown in Lemma 3, the congestion prices of vehicles
X
Uij (µi )
gi′ = max g :
in the sensing range Ii are required in the power control (25)

j∈∪q:k≤q≤g Gq
while
only the prices of vehicles in the receiving range Ri are

needed
in the rate control. Unlike the price acquisition in the

X
receiving range, which can be piggybacked in the broadcasted
λj µi > 0 ∀0 ≤ k ≤ g .
−ǫ

BSM, the price information of vehicles in the sensing range
j∈∪q:k≤q≤g Hq
cannot be decoded. The approach of obtaining congestion

prices in the sensing range is not discussed in this paper since
it is rather implementation-specific and out of the scope of this
Algorithm 1 Sample algorithm for Lemma 3
paper.
Input: gmax , λj .
The next theorem shows the asymptotic optimality of the
Output: gi′
P
P
proposed
distributed power control algorithm.
1: Define fp =
j∈Hp λj µi , p =
j∈Gp Uij (µi ) − ǫ
1, 2, · · · , gmax .
Theorem 5. Denote by p∗ the optimal solution to Power-OPT.
2: for all g ∈ {gmax , gmax − 1, · · · , 1} do
There exists a constant M > 0, independent of ǫ, such that
3:
k ← g and f lag ← 1.
under the proposed power control algorithm,
4:
while f lag
=
1
and
k
≥
0
do
Pg
T −1
X
1 XX
5:
Fg ← p=k fp ;
lim inf
Ip∗i ≥αij Uij (µi ) − ǫM.
Ipi [t]≥αij Uij (µi ) ≥
6:
if Fg > 0 then
T →∞ T
t=0 i,j
i,j
7:
k ←k−1

8:
else
9:
f lag = 0
10:
end if
V. P ERFORMANCE E VALUATION USING NS 2
11:
end while
In this section, we evaluate the performance of the dis12:
if f lag = 1 then
tributed
rate and power control algorithm developed in this
13:
gi′ ← g; break;
paper,
and
compare the performance with EMBARC [1]. We
14:
end if
used
the
ns2
platform to simulate the asynchronous IEEE
15: end for
802.11p media access control algorithm with the associated
The optimization in Lemma 3 can be solved by low complexity algorithms. A sample algorithm is given in Algorithm

2 The channel load of DSRC is measured by carrier sensing technique which
is widely implemented in CSMA network

6

Fig. 1: Deployment of 6-lane highway vehicles

Number of packet delivered per second

7

5
4
3
2
1
0
0

1
EMBARC
Joint rate&power control

0.8
Channel Load

EMBARC
Rate control
Joint rate&power control

6

50

100
Distance (m)

150

200

Fig. 3: Number of successful received packets per second v.s.
distance between transmitter and receiver

0.6
12
10

0.4
Rate

8
6
4

0.2
0

2

4

6
8
Time (s)

10

12

2

14

0

0

200

400

600

800
1000 1200
Location (m)

1400

1600

1800

2000

0

200

400

600

800
1000 1200
Location (m)

1400

1600

1800

2000

Fig. 2: Convergence of channel load

lower layer functions. The 802.11MacExt package in ns2 is
adopted.
To simulate congestion at high densities, we constructed a
6-lane scenario where each lane is 4 meters wide and 2000
meters long. We use a wrap-around model of a network along
the length of the road (see Figure 1). In each lane, 300 vehicles
are deployed in a dense-sparse-dense-sparse fashion as a grid.
Specifically, the first 120 vehicles are spaced with either 4 or
5 meters distance between any adjacent vehicles. Similarly,
the next 30 vehicles are spaced with either 16 or 17 meters
distance. The last 150 vehicles are deployed by following the
same rule. A comprehensive list of simulation parameters is
summarized in Table I.
number of vehicles
packet size
carrier frequency
noise floor
carrier sense threshold
contention window
transmission rate
carrier sensing period

1800
300 Byte
5.9 GHz
-96 dBm
-76 dBm
15
6 Mbps
0.25 s

TABLE I: Simulation Parameters
We now briefly review the EMBRAC algorithm, of which
the transmission rate is a function of both channel load
(using LIMERIC component) and vehicle dynamics (using the
suspected tracking error component). In our ns2 simulations,
we did not consider vehicle dynamics and assumed that the
relative positions of the vehicles are static, which can be
justified using a time-scale separation assumption under which
the dynamics of the rate and power control algorithms are at

Radius (m)

300

200

100

0

Fig. 4: Broadcast rates and transmission ranges of the vehicles
in the first lane under the joint rate and power control
algorithm

a much faster time scale than the relative dynamics of the
vehicles. Therefore, the suspected tracking error component
of EMBARC was not simulated and EMBARC turns to be
LIMERIC. According to [1], LIMERIC is a distributed and
linear rate-control algorithm and the rate of vehicle i is
evolving as follows,
ri (t) = (1 − α)ri (t − 1) + β(rg − rc (t − 1)),

(27)

where rc is the total rate of all the K vehicles and rg is the
target total rate. α and β are parameters that tunes stability,
fairness and steady state convergence. In EMBARC, however,
rc is defined to be the maximum channel load reported by all
the 2-hop neighbors in order to achieve global fairness [1].
For the implementation of our rate and power control
algorithm, the sum rate from the interfering vehicles in the
congestion price update equations (11) and (26) can be replaced by the measured channel load at vehicle j. Therefore,
each vehicle only needs to piggyback its congestion price
in the safety message in broadcasting. Further, we chose the

7

following utility function for evaluation
Uij (µi ) =

max{vij , α}
log µi .
dij

Awareness
0.7

(28)

Joint rate&power control
EMBARC

0.6

0.5

This specific choice of utility functions is motivated from
the collision avoidance perspective, which we explain in
Appendix. In simulations, the target channel load is set to
be 0.6.

0.4

0.3

0.2

0.1

A. Convergence to Target Channel Load
0

The evolving equation (27) shows that in steady state
LIMERIC converges to a value strictly smaller than rg [6].
In other words, the target channel load can not be achieved in
steady state. However, our algorithm leads to full utilization
of the target channel load. See Figure 2. Furthermore, our
algorithm converges less than 4 seconds while in EMBARC
oscillations still occur after 10 seconds.

0

50

100

150
200
Number of nodes

250

300

Fig. 5: Awareness distribution of joint rate and power control
Coverage
0.7

0.6
Joint rate&power control
EMBARC
0.5

B. Packet Reception Rate

0.4

We compare the number of successful received packets per
second between EMBARC (with α = 0.1 and β = 0.001)
and our joint congestion control algorithm, which motivates
the need of congestion control algorithms in DSRC. To be
fair with (rate-control only) EMBARC, we simulated our
standalone rate control algorithm as well. Figure 3 shows that:

0.3

1) our rate control algorithm performs uniformly better
than EMBARC because of full utilization of the target
channel load. Specifically, our rate control guarantees the
convergence of measured channel load of each vehicle to
the target channel load while EMBARC is proved to have
inevitable gap in its steady state (27);
2) the joint congestion control algorithm provides significant
gain in short distance regime (safety-sensitive zone). This
is because both rate and transmission range are adjusted
according to the deployment topology, as shown in Figure
4. Specifically, the transmission range increases in the
sparse segments and achieves maximum at the center
vehicle, while the range is constantly short in the dense
segments. Note that 80% vehicles have short range, e.g.,
50m, which leads to the performance gain in the shortrange regime.

C. Coverage and Awareness
Figures 5 shows the distribution of the number of vehicles
that a vehicle can receive messages from, called awareness.
Figure 6 shows the distribution of the number of vehicles
within a vehicle’s transmission range, called coverage. Under
EMBARC, there are two peaks at 35 and 145 in both coverage
and awareness, respectively associated with two different
densities in the network. The joint algorithm only has one
peak since the algorithm dynamically allocates the resources
based on the network topology, achieving fairness in terms of
both coverage and awareness.

0.2

0.1

0

0

50

100

150
200
Number of nodes

250

300

350

Fig. 6: Coverage distribution of joint rate and power control

VI. C ONCLUSIONS
In this paper, we proposed a utility maximization framework
for joint rate and power control in DSRC, and formulated
two optimization problems, named Rate-OPT and PowerOPT, where Rate-OPT deals with rate control with fixed
transmit power and Power-OPT deals with power control
with fixed rates. We developed both distributed rate control
and power control algorithms and proved the algorithms are
asymptotically optimal. Evaluations using ns2 showed that our
algorithms outperform EMBARC at several relevant aspects
including channel utilization, packet reception rate, coverage
and awareness.
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[1] G. Bansal, H. Lu, J. B. Kenney, and C. Poellabauer, “EMBARC: error
model based adaptive rate control for vehicle-to-vehicle communications,” in Proc. ACM Int. Workshop on Vehicular Inter-Networking,
Systems, and Applications (VANET), Taipei, Taiwan, 2013, pp. 41–50.
[2] J. B. Kenney, “Dedicated short-range communications (DSRC) standards
in the United States,” in Proc. IEEE, vol. 99, no. 7, pp. 1162 –1182,
Jul. 2011.
[3] IEEE 802.11p Part 11: Wireless LAN Medium Access Control (MAC)
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performance analysis of csma based broadcast protocol in vanets,” in
in Proc. of IEEE Conference on Computer Communications, 2013, pp.
2805–2813.

8

[5] ETSI TS 102 687: Decentralized Congestion Control Mechanisms for
Intelligent Transport Systems operating in the 5 GHz range; Access
layer part, 2011.
[6] G. Bansal, J. Kenney, and C. Rohrs, “Limeric: A linear adaptive message
rate algorithm for dsrc congestion control,” IEEE Trans. Veh. Technol.,
vol. 62, no. 9, pp. 4182–4197, 2013.
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[9] T. Tielert, D. Jiang, H. Hartenstein, and L. Delgrossi, “Joint power/rate
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[10] J. Jose, C. Li, X. Wu, L. Ying, and K. Zhu, “Distributed rate and
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[11] R. Srikant and L. Ying, Communication Networks: An Optimization,
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[12] T. Tielert, D. Jiang, Q. Chen, L. Delgrossi, and H. Hartenstein, “Design
methodology and evaluation of rate adaptation based congestion control
for vehicle safety communications,” in Proc. IEEE Vehicular Networking
Conf. (VNC), Amsterdam, The Netherlands, 2011, pp. 116–123.
[13] C.-L. Huang, Y. P. Fallah, R. Sengupta, and H. Krishnan, “Intervehicle
transmission rate control for cooperative active safety system,” IEEE
Trans. on Intelligent Transportation Systems, vol. 12, no. 3, pp. 645–
658, 2011.
[14] L. Zhang and S. Valaee, “Safety context-aware congestion control
for vehicular broadcast networks,” in Signal Processing Advances in
Wireless Communications (SPAWC), 2014, pp. 399–403.
[15] Egea-Lopez, Esteban, and P. Pavon-Mariño, “Distributed and fair beaconing congestion control schemes for vehicular networks,” arXiv
preprint arXiv:1407.6965, 2014.
[16] B. Aygün, M. Boban, and A. M. Wyglinski, “Ecpr: Environment- and
context-aware combined power and rate distributed congestion control
for vehicular communications,” arXiv preprint arXiv:1502.00054, 2015.
[17] Y. P. Fallah, C.-L. Huang, R. Sengupta, and H. Krishnan, “Congestion
control based on channel occupancy in vehicular broadcast networks,”
in Proc. IEEE Vehicular Technology Conf., Ottawa, Canada, 2010, pp.
1–5.
[18] C.-L. Huang, Y. P. Fallah, R. Sengupta, and H. Krishnan, “Adaptive
intervehicle communication control for cooperative safety systems,”
IEEE Network, vol. 24, no. 1, pp. 6–13, 2010.
[19] J. Mo and J. Walrand, “Fair end-to-end window-based congestion
control,” IEEE/ACM Transactions on Networking, vol. 8, no. 5, pp. 556–
567, 2000.
[20] R. Srikant, The mathematics of Internet congestion control. Springer
Science & Business Media, 2012.

A PPENDIX
A. Proof of Lemma 3
Recall that the optimization problem (24) is for fixed i and
λ. Define
X
xij Uij (µi ) − ǫλj µi yij .
Fi (x, y) =
j

Let (x̂, ŷ) denote an optimal solution. We first have the
following two observations:
• According to constraint (20), x̂ij = x̂ik if dij = dik ,
which implies that
x̂ij = x̂ik
•

j, k ∈ Gg .

if

(29)

To maximize the objective (24), y should be chosen as
small as possible. So
ŷik =

max

j:βik ≤αij

x̂ij .

(30)

Since x̂ij ≥ x̂ik when αij < αik , (30) is equivalent to
ŷik = x̂ij ′

where j ′ = arg

min

j:βik ≤αij

αij ,

which further implies that
ŷik = x̂ij

if k ∈ Hg and j ∈ Gg .

(31)

In other words, x̂ij and ŷik are equal if j ∈ Gg and
k ∈ Hg for the same g. This is easy to understand because
the define of H-group Hg is the set of vehicles that can
sense the transmission of vehicle i when the vehicles in
G-group Gg can receive messages from vehicle i.
Now suppose that x̂ij is not an integer solution. Initially,
˜ = x̂. Identify vehicle j ′ is the vehicle has the maximum
let x̂
αij among all vehicles such that 0 < x̂ij < 1, i.e.,
j ′ = arg

max

j:0<x̂ij <1

αij .

According to observations (29) and (31), we have x̂ij = ŷik =
x̂ij ′ for j ∈ Gg (j ′ ) and k ∈ Hg(j′) . Therefore,
X
X
x̂ij Uij (µi ) − ǫ
λk µi ŷik
j∈Gg(j′ )



If

= 

k∈Hg(j′ )

X

Uij (µi ) − ǫ

j∈Gg(j′ )

X

Uij (µi ) −

j∈Gg(j′ )

X

k∈Hg(j′ )

X



λk µi  x̂ij ′ .

λk µi ≤ 0,

k∈Hg(j′ )

then we define x̂˜ij = ŷ˜ik = 0 for j ∈ Gg (j ′ ) and k ∈ Hg(j′) .
˜ij = ŷ˜ik = x̂ib for j ∈ Gg (j ′ ) and
Otherwise, we define x̂
k ∈ Hg(j′) where b ∈ Gg(j ′ )−1 . It is easy to see that the
following inequality holds:
˜
˜ ŷ).
Fi (x̂, ŷ) ≤ Fi (x̂,
Now for the second scenario discussed above, we have
X
X
˜ij − ǫ
Uij (µi )x̂
λk µi ŷ˜ik
j∈Gg(j′ ) ∪Gg(j′ )−1

k∈Hg(j′ ) ∪Hg(j′ )−1

9





P
2
Note that ( i yij [t]µi − γ) ≤ (nµmax + γmax )2 , where n is

=
Uij (µi ) − ǫ
λk µi x̂ibthe
. maximum number of vehicles whose transmissions can be
j∈Gg(j′ ) ∪Gg(j′ )−1
k∈Hg(j′ ) ∪Hg(j′ )−1
sensed by vehicle j, P
since 0 ≤ yij [t] ≤ 1 and 0 ≤ γ ≤ γmax .
2
′
Defining
M
=
˜
˜
i (γmax + nµmax ) and denoting by
Similarly, we define x̂ij = ŷik = 0 for j ∈ Gg(j ′ ) ∪ Gg(j ′ )−1
∗ ∗
(x̃ , ỹ ) the optimal solution to problem (18), we have
and k ∈ H
∪H
if
X



X

g(j′)

g(j′)−1

X

X

Uij (µi ) − ǫ

j∈Gg(j′ ) ∪Gg(j′ )−1

∆V [t] =

λk µi ≤ 0;

k∈Hg(j′ ) ∪Hg(j′ )−1

≤

˜ij = ŷ˜ik = x̂ic for j ∈ Gg(j ′ ) ∪ Gg(j ′ )−1
and otherwise define x̂
and k ∈ Hg(j′) ∪ Hg(j′)−1 , where c ∈ Gg(j′)−2 . Similarly, we
also have
˜
˜ ŷ).
Fi (x̂, ŷ) ≤ Fi (x̂,

=

j∈∪g:g≤g′ Gg



−ǫ

Uij (µi )

λj µi > 0 ∀k < g




B. Proof of Theorem 5
P
Defining V [t] = j λ2j [t], we have

.

≤

X

λj [t] +

=

λj [t] +

=

X

2λj [t] +

X
j

X

!2

yij [t]µi − γ

i

j

=

yij [t]µi − γ

i

j

X

I(pi [t]≥βij µi − γ

i

j

X

X

2λj [t]

X
i

yij [t]µi − γ

!

!
+

−

−

X

λ2j [t]

j

X

Note that

λ2j [t]

X

yij [t]µi − γ

!

X

yij [t]µi − γ

!2

i

PT −1

≤

∆V [t] = V [T ] − V [0], so
P
′
∗
(V [T ] − V [0]) − ǫM
i,j Uij (µi )x̃ij
2 +
P
P
T −1
1
t=0
i,j Uij (µi )xij [t],
T

t=0

ǫ
2T

j

i

!

which implies
X
X
ǫ
Uij (µi )xij [t],
Uij (µi )x̃∗ij ≤
(∆V [t] − M ′ ) +
2
i,j
i,j

V [t + 1] − V [t]
!2

.

(34)
(35)

(36)

According to Lemma 3, (33) + (34) ≤ 0. Further, since
(x̃∗ , ỹ ∗ ) is a feasible solution to problem (18), we have (36) ≤
0. Hence, we conclude
2X
2X
Uij (µi )x̃∗ij +
Uij (µi )xij [t],
∆V [t] ≤ M ′ −
ǫ i,j
ǫ i,j

∆V [t]

=

−γ

i

!

i

j



j∈∪q:k≤q≤g Hg

λj [t]

∗
ỹij
µi

X
X
2X
∗
ỹij
µi − γ
λi [t]
Uij (µi )x̃∗ij − 2
ǫ i,j
i
j
2X
2X
−
Uij (µi )x̃∗ij +
Uij (µi )xij [t]
ǫ i,j
ǫ i,j
!
X
X
∗
ỹij
µi − γ .
λi [t]
+2
+

j∈∪q:k≤q≤g Gg

X

X

(33)

where
X

X

∆V [t] ≤ M ′
(32)
!
X
X
2X
yij [t]µi − γ
λi [t]
Uij (µi )xij [t] + 2
−
ǫ i,j
i
j

From the discussion above, the integer optimizer is


1, if g(j) ≤ g ′
1, if h(j) ≤ g ′
xij =
and yij =
,
0, otherwise.
0, otherwise.

g:

i

By rearranging the terms above, we obtain

˜ ŷ).
˜
Fi (x̂, ŷ) ≤ Fi (x̂,

g ′ = min

yij [t]µi − γ

i

j

j

and x = 0 otherwise. Therefore, from any optimizer (x̂, ŷ) we
˜ ŷ)
˜ such that
can construct an integer solution (x̂,




λj [t]

!

2X
2X
Uij (µi )x̃∗ij −
Uij (µi )x̃∗ij
ǫ i,j
ǫ i,j
2X
2X
Uij (µi )xij [t] −
Uij (µi )xij [t]
+
ǫ i,j
ǫ i,j
!
X
X
∗
ỹij µi − γ
λj [t]
+2
−2

j∈∪g:g≤g′ Hg

i

X

+

j∈∪g:g≤g′ Hg

It is easy to see that we should choose x = 1 if
X
X
Uij (µi ) − ǫ
λj µi > 0.

M′ + 2

j

X
j

Repeating the same argument, we can conclude that there
˜ij = x if
exists g ′ such that x̂˜ij = 0 if g(j) > g ′ and x̂
′
g(j) ≤ g . Therefore,


X
X
˜ ŷ)
˜ =
Fi (x̂,
Uij (µi ) − ǫ
λj µi  x.
j∈∪g:g≤g′ Gg

V [t + 1] − V [t]
!
X
X
′
yij [t]µi − γ
λj [t]
M +2

which implies
.

−

T −1
1 X X ηij
ǫV [0] ǫM ′ X
Uij (µi )x̃∗ij ≤
xij [t].
−
+
2T
2
T t=0 i,j dij
i,j

10

The theorem holds by choosing M = M ′ /2 and because
X
X
Uij (µi )x∗ij .
Uij (µi )x̃∗ij ≥
i,j

i,j

C. Selection of Utility Function (28)
Note that given distance dij and relative speed vij , vehicles
dij
i and j on a line would collide after vij
units of time if they
d

ij
do not change their speeds. We therefore call vij
reaction time
of pair (i, j). To prevent the collision, vehicles i and j need to
communicate at least once during this reaction time. Assume
each message is reliably received with probability p, then the
probability that vehicle j receives at least one message from
vehicle i during the reaction time is
dij

1 − (1 − p) vij

µi

.

Imposing a lower bound pmin on this probability is equivalent
to requiring that
dij
log(1 − pmin )
µi ≥
.
vij
log(1 − p)

(37)

These pairwise safety constraints may not always be feasible
depending on the network density and the geographical distribution of the vehicles.

Fig. 7: Vehicle 1 and vehicle 2 are both approaching vehicle
3 with different speeds
Therefore, we consider a different requirement also from the
collision avoidance perspective. Consider a scenario shown in
Figure 7, where both vehicle 1 and vehicle 2 are approaching
vehicle 3 with different speeds. A fair resource allocation
should equalize the reaction time to avoid collisions, i.e., to
have
d23
d13
µ1 =
µ2 .
(38)
v13
v23
In a general scenario, this objective could also be difficult
to achieve. We note that if we assume all vehicles share a
single-bottleneck link, e.g., in the scenario in Figure 7 where
all vehicles can hear each other, then solving the following
optimization problem
v23
v13
log µ1 +
log µ2
(39)
max
µ d13
d23
results in the solution
v23 1
v13 1
=
,
(40)
d13 µ1
d23 µ2
which is equivalent to (38). This motivated the objective function in (28), where each link dij is associated with a weighted
max{vij ,α}
log-utility
log µi . Since vij may be negative, we
dij
define the weight to be max{vij , α} for some α > 0.

