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[Pre-print version] DOI:10.1109/WCNC.2011.5779189 https://ieeexplore.ieee.org/document/5779189
Maximizing Throughput-Fairness Tradeoff in MAC
for ad hoc Networks
Miguel Lu´
ıs†§, Rodolfo Oliveira†, Luis Bernardo†, Rui Dinis†§
†CTS, Uninova, Dep.ode Eng.aElectrot´
ecnica, Faculdade de Ciˆ
encias e Tecnologia, FCT,
Universidade Nova de Lisboa, 2829-516 Caparica, Portugal
§IT, Instituto de Telecomunicac¸ ˜
oes, Portugal
Abstract—In the last years, there has been an increasing
interest in developing and testing Medium Access Control (MAC)
protocols for ad hoc networks based on optimal methods. Sev-
eral solutions do not take into account the throughput-fairness
tradeoff, presenting high throughput performance but under-
performing in terms of medium access fairness. This work
presents a novel MAC scheme, which is designed to maximize
the network throughput-fairness performance 1. In our scheme,
all nodes adopt a common optimal contention window, which is
based on a common view of the channel. Our proposal improves
the access fairness because the contention window is similar to all
nodes, and its behavior does not depend on previous MAC states.
Departing from the optimal throughput for a saturated network,
we devise a scheme to estimate the number of nodes, which
is a prime parameter to regulate the medium access control.
We show that each node is suitable to estimate the number of
competing nodes by using both its own medium access probability
and the idle slot probability observed from the channel. Several
simulation results evaluate the throughput-fairness performance
of our proposal with several state-of-the-art MAC protocols, such
as AOB, Idle Sense, GDCF and the well known IEEE 802.11. The
results indicate that our approach presents the highest value of
medium access fairness among the simulated protocols, meaning
that its throughput is closer to the optimal theoretical throughput
obtained for a fair network. 2
Keywords: Medium Access Control, Wireless LANs, MAC
Performance Evaluation, MAC Optimization.
I. INTRODUCTION
The wireless ad hoc networks are characterized by the
lack of an infrastructure able to centralize their medium
access control (MAC). Although the lack of infrastructure
is an obvious advantage, because it allows fast and costless
network deployment, it also increases the complexity of the
MAC protocols: if multiple nodes simultaneously access to the
channel, their mutual interference corrupts both transmissions,
which are unsuccessful. A MAC protocol should allow channel
access to every node in an efficient way. This means that MAC
protocols should be designed to maximize the throughput and
allow the nodes to access the channel in a fair way.
1The source code of our proposal was written for the
network simulator ns-2.33, and is available to download at
http://tele1.dee.fct.unl.pt/downloads/miop_MAC.tar.gz,
allowing the community to evaluate their own scenarios and compare it with
other protocols.
2This work was supported in part by the FCT/MCTES (UNINOVA
plurianual funding), MPSAT project [PTDC/EEA-TEL/099074/2008] and
OPPORTUNISTIC-CR project [PTDC/EEA-TEL/115981/2009].
The most successful MAC techniques used in ad hoc
networks are contention-based. The time is divided into con-
secutive slots and the nodes are able to sense the channel.
Each node adopts an initial medium access probability, which
is determined by its contention window (W). A given number
of slots (randomly chosen from the interval [0, W −1]) is
assigned to a contention counter (cc), representing the number
of slots that should be sensed before accessing to the channel.
A collision occurs if at least two nodes access the channel in
the same slot. Otherwise, the transmission succeeds.
The MAC protocols based on throughput-fairness optimiza-
tion generally explore the relation between the time wasted
in the contention period and the period of time in which
the node effectively occupies the medium, subjected to a
constraint that imposes access fairness. Several proposals are
based on Network Utility Maximization (NUM) [1], [2],
[3]. These works start to define an access utility function
that quantifies the reward that a node earns by accessing
to the channel in a given circumstance. However, the utility
functions must comply with several requirements before being
used in multi-criteria optimization techniques, provided by
several optimization theories. The optimal solution is then
relaxed into an implementable algorithm. Both [1] and [2]
require extensive message passing among the nodes, wasting a
significant amount of throughput on it. The relaxation process
described in both works decreases the optimization efficiency,
as several approximations are used to translate the solution into
a feasible algorithm. The work in [3] avoids message passing.
But the authors only prove that the algorithm converges for
a large number of nodes and consider a few non-realistic
assumptions: infinite backlogs and frequent message exchange
among the nodes, which is a requirement to estimate the packet
error rate of the communication channel.
The well-known MAC scheme denominated ”Asymptoti-
cally Optimal Backoff” (AOB) [4] presents a methodology
to optimize the IEEE 802.11 [5] throughput. AOB assumes
that the optimal medium access is almost independent of the
number of active stations, which is a rough approximation,
namely for a small number of nodes. Idle Sense (IS) [6]
tries to adapt the node’s access behavior that maximizes the
throughput by minimizing the time wasted in contention and
collisions, and thus increasing the available time for transmis-
sions. IS concludes that the optimal throughput is maximized
when 5.68 consecutive idle slots are sensed, independently of
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[Pre-print version] DOI:10.1109/WCNC.2011.5779189 https://ieeexplore.ieee.org/document/5779189
the number of nodes competing for the medium.
The previous works exemplify how difficult is to find an
optimization criteria without adopting a simplification that
translates the optimization solution. Other MAC protocols
only define simple heuristics to adapt the contention window
without optimal policy. IEEE 802.11 [5] adopts this solution.
Another heuristic-based protocol, GDCF [7], improves the
IEEE 802.11 performance, motivated by the fact that IEEE
802.11 sharply cuts the contention window after a successful
collision, independently of the level of contention in the
medium. GDCF adopts a heuristic that incorporates a more
conservative approach: a node does not change its contention
window after a successful transmission. Moreover, if eight
consecutive idle slots are observed during the contention
period, the window is halved and a new value ccis randomly
chosen.
This work presents a novel MAC scheme, which is designed
to maximize the network throughput-fairness performance.
Each node estimates the channel utilization (idle slot probabil-
ity) as well as the number of nodes competing for the channel.
These parameters are available by only observing the channel,
and thus no message passing is needed. All nodes have a
shared knowledge of these parameters. Our proposal presents
high access fairness since the contention window is similar to
all nodes, and it does not depend on prior individual behaviors.
Departing from the optimal throughput for a saturated network,
we devise a scheme to estimate the number of nodes, which is
a prime parameter to regulate the medium access control. We
present an extensive comparison of several simulation results
to evaluate the performance of our proposal with several state-
of-the-art MAC protocols, such as AOB, Idle Sense, GDCF
or the well known IEEE 802.11. The results indicate that
our proposal presents the highest degree of fairness and its
throughput is closer to the optimal one. This indicates that
our scheme performs better than the compared protocols.
The rest of this paper is organized as follows. In the next
section we introduce our MAC scheme. Section III describes
several implementation details. Simulation results shown in
Section IV compares the performance of our approach with
several MAC protocols. Finally, a few conclusions are given
in Section V.
II. SYS TEM DESCRIPTION
We consider the set Nof nnodes and, at each time
instant, at most one node is allowed to transmit to the shared
medium, otherwise there exists a collision. All nodes are
traffic-saturated. When a node has a new packet to transmit,
it senses the channel activity. If the channel is sensed idle
for a given period of time (we denote it Distributed Inter-
Frame Space (DIFS)) the node transmits the packet to the
channel. Otherwise, if the channel is sensed busy, the node
starts a random contention period to minimize the packet
collision probability. In the contention period, a node starts to
charge a contention counter with the number of slots randomly
chosen according to a uniform distribution in the range (0,
W-1], where Wis the Contention Window. The contention
counter is decremented as long as the channel is sensed idle,
stopped when a transmission is detected, and resumed when
the channel is sensed idle again for a period equal to a
DIFS interval. The transmission only occurs when the backoff
counter reaches the value zero.
The behavior described above is similar with IEEE 802.11’s
behavior. But contrarily to IEEE 802.11, where the contention
window is doubled when the node transmission collides, in
our scheme the nodes use a window that is close to the
optimal one, which is regulated in the end of each transmission
attempt. In our proposal, the nodes always use a single
contention window that does not depend on the previous
transmission state (collision or success) as is the case with
IEEE 802.11 exponential backoff.
A. Packet Transmission Probability
Let us define τas the probability that a node transmits
in a randomly chosen slot time. Since the system behaves
like IEEE 802.11 when only one backoff stage is used, the
stationary probability τof our approach is only a function of
W[8]:
τ=2
W+ 1.(1)
B. Throughput
Let Sbe the normalized system throughput that represents
the amount of channel capacity successfully used. To compute
Swe must describe the probability of finding slots where the
channel may be found idle, with a probability
pi= (1 −τ)n,(2)
or busy with a successful transmission probability
ps=nτ(1 −τ)(n−1) (3)
or busy due to collisions with probability
pc= 1 −ps−pi.(4)
The system throughput is defined as the ratio of the amount
of time that the channel is successfully used, over the expected
contention duration [8]:
S=psE[p]
piE[Ti] + psE[Ts] + pcE[Tc],(5)
where E[Ts],E[Tc]and E[Ti]denote the expected duration
of a successful transmission, collision and idle slot, respec-
tively. E[p]denotes the expected frame’s duration. After some
mathematical manipulations, and considering that the expected
durations are constants (E[p] = P,E[Ts] = Ts,E[Ti] = Ti,
E[Tc] = Tc), Scan be rewritten as
S=P
Ts−Tc+Tc+pi(Ti−Tc)
ps
.(6)
Sis maximized by finding the optimal access probability τ?
that solves the following equation:
(1 −τ?)n(Tc−Ti)+(nτ?−1)Tc= 0.(7)
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[Pre-print version] DOI:10.1109/WCNC.2011.5779189 https://ieeexplore.ieee.org/document/5779189
The optimal throughput S?is achieved by imposing to each
node the access probability τ?, which can be written as a
function fof the number of nodes
τ?=f(n).(8)
In this way, the optimal medium access probability τ?only
depends on the number of nodes competing for the medium
and f(n)is a decreasing function for n > 0. Equation (8)
stresses the importance of having an estimate of the number
of nodes, because if the number of nodes is known we can
solve (7) to find the optimal medium access probability.
C. Estimation of the number of nodes
A node can measure the probability of finding an idle slot,
denoted by ˜pa, by observing the state of the slots during the
period of contention. To keep ˜pain a slowly time varying
value, and consequently close to its steady state, we filter the
slot samples as is detailed in the next section. If the network
is operating near a stable point, all nodes adopt the medium
access probability τ?. When this occurs, a node listens to an
idle slot if the remaining n−1nodes do not transmit, meaning
that pa= (1 −τ?)(n−1). By this way, the number of nodes
can be estimated by minimizing the squared error between
the measured probability (˜pa) and the optimal one (pa). The
estimated number of nodes ˆncan be approximated by
ˆn= argmin
n∈N q˜pa−(1 −τi)n−12.(9)
However, there is an open question: the nodes do not know
what is the stable point of operation, and τiin the equation (9)
is unknown. Since all nodes use the same contention window,
in the steady state a node nacan use its own probability of
medium access to estimate the number of nodes (τi=τa). If
the network is operating far from the stable point, the accuracy
of the estimates decrease and this approach is only valid if τa
converges to the stationary optimal point of operation τ?. Thus
we must validate the following hypothesis:
H-Is it possible to design a MAC scheme where a node
nauses its own medium access probability τain (9) to
determine the optimal access probability (τ?given by (8)) and
simultaneously guarantee that its medium access probability
converges to the optimal value?
D. MAC Scheme
We start to consider the medium access probabilities vector
T(k) = (τ1(k), τ2(k), ..., τn(k)), which describes the proba-
bilities applied by each node at a time instant k. The vector
Tis initialized with a given probability 0< τinit <1, and
all nodes use the first contention window given by Winit =
2/τinit −1. This window is used by each node until having the
first measure ˜pa. After this moment, a node starts to adapt the
medium access probability each time the contention counter
reaches zero. The adaptation process is illustrated in Figure 1.
In the instant ka node uses the expression (9) with the measure
˜paand τi=τinit to obtain the estimate for the number of
competing nodes (ˆn(k)). Then it uses ˆn(k)in equation (8) to
obtain the system reference ˜τ(k)that is later imposed by the
controller C(˜τ(k)). The controller output τ(k+ 1) is then used
to define the contention window W(k+ 1) = 2/τ (k+ 1) −1
used for the next contention period. Note that for the con-
tentions k= 3,4, ..., m the measure ˜pa(k)is obtained by
using τi=τ(k= 2), τi=τ(k= 3), ..., τi=τ(k= (m−1)),
instead of using τi=τ(k= 1) = τinit.
)
ˆ
(nf
n
ˆ
)(
ˆkn )(
~
k)1(k
)
~
(C
p
~
)(k
a
Fig. 1. Block diagram for the MAC scheme.
To validate the hypothesis Hwe employ the technique of
Lyapunov drift, which has been successfully used to stabilize
several systems, such as packet switch systems (e.g: [9]). This
allows us to deduce the stability-in-the-mean of the system,
and because the MAC scheme is markovian, such stability is
equivalent to the existence of a steady state distribution.
Using a quadratic Lyapunov function L(T) = Pn
i=1 τ2
i, and
assuming that T(k)evolves according to some probabilistic
law, the MAC scheme is strongly stable if there exists con-
stants B > 0and > 0, such that for all time instants kwe
have [10]
E{L(T(k+ 1)) −L(T(k))|T(k)} ≤ B−
n
X
i=1
τi(k).(10)
When the condition (10) holds, then for any
δ > 0, the Lyapunov drift, denoted by ∆(T(k)) ,
E{L(T(k+ 1)) −L(T(k))|T(k)}, satisfies ∆(T(k)) ≤ −δ
whenever Pn
i=1 τi(k)≥(B+δ)/. In other words, the
condition (10) ensures that the Lyapunov drift is negative
whenever the sum of the medium access probabilities is
sufficiently large. Intuitively, this property ensures MAC
scheme stability because, whenever the vector Tleaves the
bounded region {T≥0|Pn
i=1 τi(k)≤(B+δ)/}, the
negative drift eventually drives it back to this region [10].
Validation of the hypothesis H
To prove the stability of our MAC scheme, and consequently
the validity of the hypothesis H, we study the Lyapunov
drift for two different cases: 1) the case when the number
of network nodes increases; 2) the case when the network
nodes decrease. These cases are representative of the network
changes where our MAC scheme must guarantee convergence
to the steady state optimal medium access probability.
1) The number of network nodes increases: Considering
that at instant k−1the network is operating with n=Ke
nodes and, from k−1to k,Kanodes are added to the network,
such that n=Ke+Ka. Admitting that the existing Kenodes
are close to the steady state optimal point of operation, when
the Kanodes access to the medium, they will decrease the
measured probability ˜paused in (9). Since Kenodes use its
current medium access probability τ(k)to determine τ(k+
1), from (9) we conclude that if ˜pa(k)<˜pa(k−1) then
ˆn(k)>ˆn(k−1). Since the decreasing function f(n)is used
to determine τ(k+ 1), then τ(k+ 1) < τ(k). In this way, the
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[Pre-print version] DOI:10.1109/WCNC.2011.5779189 https://ieeexplore.ieee.org/document/5779189
Lyapunov drift is negative, meaning that the existing nodes
will successfully decrease their medium access probability to
adapt to node’s increase.
2) The number of network nodes decreases: In the same
way, we consider that at instant k−1the network is op-
erating with n=Kenodes and, from instant k−1to
instant k,Kd< Kenodes stop transmitting, such that
n=Ke−Kd. Admitting that the existing Kenodes are close
to the steady state optimal point of operation, when Kdnodes
stop transmitting they will increase the measured probability
˜paused in (9). Because the remaining Ke−Kdnodes
use its current medium access probability τ(k)to determine
τ(k+ 1), from (9) we conclude that if ˜pa(k)>˜pa(k−1)
then each node observes that ˆn(k)<ˆn(k−1). Since the
decreasing function f(n)is used to determine τ(k+ 1), then
τ(k+ 1) > τ (k). For future steps k+ 2, k + 3, ..., k +G
the nodes will increase its medium access probability, while
˜pa(k+ 2) >˜pa(k+ 1), ..., ˜pa(k+G)>˜pa(k+G−1),
because the filter used to sample ˜paintroduces a delay. But
after G+ 1 periods, the measure ˜pa(k+G+ 1) <˜pa(k+G),
since the nodes are increasing its medium access probability.
When this happens, the condition ˆn(k+G+ 1) >ˆn(k+G)
holds, and consequently, the transmission probability for the
instant (k+G+2) will guarantee a negative drift that stabilizes
our MAC scheme: τ(k+G+ 2) < τ (k+G+ 1).
III. MAC PROTOC OL IMPLEMENTATION
In this section, we present a novel MAC protocol, designed
to maximize the network throughput and increase the channel
access fairness. These improvements are achieved because we
assure that all nodes adopt the optimal access probability. As
seen in the previous section, the optimal access probability can
be computed in four stages: 1) idle slot probability measure-
ment, 2) estimation of the number of nodes, 3) optimal access
probability computation and 4) access probability control.
Stages 1) and 4) are detailed next.
As mentioned in Section II-D, the idle slot probability
can be measured by observing the state of the slots during
the period of contention. We define the following relative
frequency
1
B
B
X
i=1
Sloti,(11)
where Slotiis equal to 0 if the i-th slot is sensed idle, or equal
to 1 if during the i-th slot the channel is sensed busy. Bis the
number of observed slots. To obtain a slowly-varying measure
of ˜pawe used an Auto Regressive Moving Average (ARMA)
filter. This filter uses the relative frequency from (11), and is
given by
˜pa(k+ 1) = α˜pa(k) + 1−α
B
B
X
i=1
Sloti,(12)
where αrepresents the filter memory.
To parameterize the ARMA filter we have simulated a
scenario in which the number of terminal nodes in the network
changes on every 100 seconds (the nodes were changed to 2,
5, 10, 25, 15, 5 and 25). We set the contention window used by
each node to the optimal value for a network with 25 nodes.
Figure 2 represents ˜pameasured using B= 1000 and α=
0.75. As we can see, the chosen filter parameters leads ˜pa
closer to the steady state value pa. For a small number of
nodes ˜pais accurately measured and the standard deviation
is low. However, for a large number of nodes, ˜paexhibits a
higher standard deviation because the number of samples per
time decreases (e.g.: the number of samples from 300 to 400
sis smaller than the number of samples from 0 to 100 s, since
the average contention slot duration increases with the number
of network nodes).
0 100 200 300 400 500 600 700
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Simulation Time [s]
Idle Probability [%]
Measured
Steady state
Fig. 2. Idle slot probability for the case when the nodes use a fixed contention
window.
Having a slowly-varying measure of ˜pa, it is possible to
estimate the number of nodes applying (9). After that, we can
use (8) to compute the optimal access probability. Knowing
that the filter (12) introduces a slower dynamic due to the
memory parameter, the reference ˜τobtained through (8) is not
directly adopted by each node. For that, we use a Proportional-
Integral Controller, which is represented by C(˜τ)in Figure 1.
In this way, the controller simply adapts the individual medium
access probability according to the reference ˜τ(k)and the
ARMA filter dynamics. Figure 3 illustrate the block diagram
of our PI Controller, where the Set Point is the optimal access
probability computed in the previous phase.
)(k
~
+Process
1
sT
I
KP
-
)
1
(k+
Fig. 3. PI Controller C(˜τ).
To parameterize KPand TI, the proportional gain and the
integral time respectively, we simulated a scenario to study the
process response to a unit step that represents a change in the
number of network nodes (the nodes were changed from 0 to
25). The response of the system (˜pa) was measured in an open
loop to evaluate the time needed to reach the steady state value.
Applying the classical Ziegler-Nichols tuning methodology,
KPand TIbecame approximately 0.6 and 23.81, respectively.
Figures 4 and 5 represent ˜paand ˆnwhen the number of
network nodes is changed according to the same pattern used
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[Pre-print version] DOI:10.1109/WCNC.2011.5779189 https://ieeexplore.ieee.org/document/5779189
in Figure 3, and the medium access probability is regulated
according to our scheme. Winit was set to 500. In Figure 4
we observe that the measurement of the idle slot probability
follows the steady state probability. Smaller accuracy is ob-
served when the number of network nodes changes because
of the transient periods while the medium access probability
is converging to the optimal steady state value.
0 100 200 300 400 500 600 700
0.75
0.8
0.85
0.9
0.95
1
Simulation Time [s]
Idle Probability [%]
Measured
Steady state
Fig. 4. Idle slot probability when the contention window is regulated by our
approach
Figure 5 compares the number of network nodes estimated
with our approach. The estimation error increases as the num-
ber of network nodes increases because the ˜pameasurement
obtained with the ARMA filter is less accurate. When the
number of nodes increases ˆn’s accuracy decreases within a
short period, being a direct consequence of using the individual
medium access probability to estimate the number of nodes.
This is because the individual medium access probability is
not yet adapted to the real number of nodes, but as the
medium access probability converges to the optimal value, the
estimated number of nodes becomes more accurate.
0 100 200 300 400 500 600 700
0
10
20
30
40
50
60
70
Simulation Time [s]
Number of Nodesd [n]
Estimated
Real
Fig. 5. Estimated number of nodes (ˆn).
IV. PERFORMANCE ANA LYSIS
A. Simulation Setup
In this section, we present a performance analysis of the
proposed MAC protocol, evaluating the throughput and the
channel access fairness. We compare the performance of our
approach with other four MAC protocols: AOB, IEEE 802.11,
GDCF and Idle Sense. Their throughput is also compared with
the optimal one. The simulations were performed with the
network simulator ns-2 [11]. We have simulated a scenario
where the network transmitting nodes changes on every 100
seconds according to the pattern (2, 5, 10, 25, 15, 5 and 25).
Each transmitting node has always a frame to transmit. The
parameters used in the simulations are described in Table I.
TABLE I
COMMON PARAMETERS USED IN THE SIMULATED PROTOCOLS.
SIFS 10 µs Data Rate 11 Mbps
DIFS 50 µs Propagation Delay 2 µs
EIFS 364 µs φ 416 µs
Slot Time 20 µs Sampling Window Size (B) 1000
Winit 500 Frame Size 1500 bytes
Figure 6 compares the instantaneous throughput obtained
for each protocol. While we present the absolute throughput,
it can be normalized by dividing it by the transmission rate
(11Mbps). The results show that our approach performs better
in the first 100 s. This is because only 2 nodes are transmitting,
and for a small number of competing nodes the medium access
probability approach used by AOB and IS are less accurate.
For a larger number of nodes AOB presents a better throughput
when compared to the other protocols. However, the difference
between AOB and our approach never exceeds approximately
150 kbps (from 600 to 700 seconds). Finally, we observe that
for heuristic-based protocols the throughput clearly depends on
the number of nodes, namely for IEEE 802.11. The protocols
that use an optimal principle to regulate its medium access
probability, such as AOB, IS and our approach, are less
dependent on the number of nodes.
0 100 200 300 400 500 600 700
5.4
5.5
5.6
5.7
5.8
5.9
6
6.1
6.2
6.3
6.4 x 106
Simulation Time [s]
Throughput [bps]
AOB
GDCF
IEEE 802.11
Idle Sense
Our Approach
Optimal
Fig. 6. Instantaneous throughput when the number of network nodes is
changed.
From Figure 6 we can also observe that most of the MAC
protocols present throughput values that are higher than the
optimal one. This is because the optimal throughput computed
by (5), assumes that the medium access is fairly distributed by
the nodes. If the medium access is not fair, some nodes can
have shorter contention periods, and the network throughput
can be higher than the optimal value. In the limit, if a single
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[Pre-print version] DOI:10.1109/WCNC.2011.5779189 https://ieeexplore.ieee.org/document/5779189
node adopts the maximum medium access probability (equal to
1) and the remaining nodes inhibit their access, the throughput
equals the maximum network usage, which outperforms the
optimal throughput for perfect fair medium access.
Figure 7 compares the throughput performance for a differ-
ent number of nodes. As the number of nodes increases, we
observe that our approach presents a performance close to Idle
Sense, and slightly below AOB and GDCF. All these protocols
present a throughput higher than the optimal one, denoting
that they are not perfectly fair. Note that our approach and IS
are closer to the optimal throughput, indicating that eventually
they are fairer.
0 10 20 30 40 50 60
4.8
5
5.2
5.4
5.6
5.8
6
6.2
6.4 x 106
Number of nodes [n]
Throughput [bps]
AOB
GDCF
IEEE 802.11
Idle Sense
Our Approach
Optimal
Fig. 7. Average throughput for different network nodes.
We also evaluated the performance of our MAC scheme
in terms of fairness. We used the well known Jain’s fairness
index [12] for different fairness window sizes (to distinguish
from short to medium/high-term analysis). Figure 8 compares
the fairness performance of our approach for a network with
25 nodes. Initially, we used a short fairness window size
(to analyze the short-term) increasing it up to 2500 channel
accesses. Figure 8 indicates that our approach presents the
highest fairness index for the fairness window sizes considered
in the analysis. This is because our MAC approach imposes
a similiar channel access probability (τ) to all network nodes,
0 500 1000 1500 2000 2500
0.4
0.5
0.6
0.7
0.8
0.9
1
Fairness Window
Jain Average Index [%]
AOB
GDCF
IEEE 802.11
Idle Sense
Our Approach
Fig. 8. Jain’s fairness index for a network with 25 nodes.
which is close to the optimal value. AOB exhibits the highest
throughput, however it presents a smaller fairness index when
compared to our approach and to Idle Sense. This analysis
also indicates that higher values of fairness lead to throughput
values that are close to the optimal ones.
Now that we have analyzed both throughput and fairness
results, we can conclude that our approach outperforms the
compared protocols since it exhibits higher access fairness and
its throughput is closer to the optimal curve.
V. CONCLUSIONS
In this paper, we proposed a distributed throughput-fairness
optimal scheme for ad hoc wireless networks, which is mo-
tivated by the shared view of the channel. The main novelty
of our scheme is its simplicity and the use of the individual
medium access probability and the probability of idle slot to
estimate the number of competing nodes. Several simulations
show that our scheme successfully adapts to the number of
the network nodes. Since each node shares the same channel
view, and because the contention window mainly depends on
it, the simulation results confirm that our scheme achieves
better access fairness when compared to AOB, IS, GDCF and
IEEE 802.11. Moreover, its average throughput is closer to the
optimal curve. The simplicity and the results achieved with
our approach clearly ranks it as a strong candidate for future
networks.
REFERENCES
[1] J. Lee, A. Tang, J. Huang, M. Chiang, and A. R. Calderbank. Reverse-
Engineering MAC: a non-cooperative game model. Selected Areas in
Communications, IEEE Journal on, 25:1135–1147, 2007.
[2] J. Lee, M. Chiang, and A. R. Calderbank. Utility-optimal random-access
control. Wireless Communications, IEEE Transactions on, 25:1135–
1147, 2007.
[3] A. Hamed Mohsenian Rad, J. Huang, M. Chiang, and Vincent W. S.
Wong. Utility-optimal random access without message passing. Wireless
Communications, IEEE Transactions on, 8(3):1073–1079, 2009.
[4] L. Bononi, M. Conti, and E. Gregori. Runtime optimization of IEEE
802.11 wireless LANs performance. Parallel and Distributed Systems,
IEEE Transactions on, 15:66–80, 2004.
[5] ANSI/IEEE 802.11 Standard. IEEE Standard for Information technology
– Telecommunications and information exchange between systems –
Local and metropolitan area networks-Specific requirements – Part 11:
Wireless LAN Medium Access Control (MAC) and Physical Layer
(PHY) Specifications, 2007.
[6] M. Heusse, F. Rousseau, R. Guillier, and A. Duda. Idle sense: An
optimal access method for high throughput and fairness in rate diverse
wireless LANs. In ACM SIGCOMM, pages 121–132. ACM Press, 2005.
[7] C. Wang, B. Li, and L. Li. A New Collision Resolution Mechanism to
Enhance the Performance of IEEE 802.11 DCF. Vehicular Technology,
IEEE Transactions on, 53:1235–1246, 2004.
[8] G. Bianchi. Performance analysis of the IEEE 802.11 distributed
coordination function. Selected Areas in Communications, IEEE Journal
on, 18(3):535–547, March 2000.
[9] P.R. Kumar and S.P. Meyn. Stability of queueing networks and schedul-
ing policies. Automatic Control, IEEE Transactions on, 40(2):251 –260,
February 1995.
[10] L. Georgiadis, J. Michael, and R. Tassiulas. Resource allocation and
cross-layer control in wireless networks. In Foundations and Trends in
Networking, pages 1–149, 2006.
[11] Information Sciences Institute. NS-2 Network Simulator (version 2.33).
Software Package retrieved from http://www.isi.edu/nsnam/ns/, 2010.
[12] R. Jain, D. Chiu, and W. Hawe. A Quantitative Measure Of Fairness And
Discrimination For Resource Allocation In Shared Computer Systems.
Technical Report TR-301, DEC Research, September 1984.
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