Wireless Sensor Network, 2009, 1, 358-364
doi:10.4236/wsn.2009.14044 Published Online November 2009 (http://www.scirp.org/journal/wsn).
An Energy-Efficient MAC Protocol for WSNs:
Game-Theoretic Constraint Optimization with
Multiple Objectives
Liqiang ZHAO, Le GUO, Li CONG, Hailin ZHANG
State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an, China
Received March 23, 2009; revised June 2, 2009; accepted June 10, 2009
Abstract
In WSNs, energy conservation is the primary goal, while throughput and delay are less important. This re-
sults in a tradeoff between performance (e.g., throughput, delay, jitter, and packet-loss-rate) and energy con-
sumption. In this paper, the problem of energy-efficient MAC protocols in WSNs is modeled as a
game-theoretic constraint optimization with multiple objectives. After introducing incompletely cooperative
game theory, based on the estimated game state (e.g., the number of competing nodes), each node independ-
ently implements the optimal equilibrium strategy under the given constraints (e.g., the used energy and QoS
requirements). Moreover, a simplified game-theoretic constraint optimization scheme (G-ConOpt) is pre-
sented in this paper, which is easy to be implemented in current WSNs. Simulation results show that
G-ConOpt can increase system performance while still maintaining reasonable energy consumption.
Keywords: Wireless Sensor Network, MAC, Energy Efficiency, Game Theory, Constraint Optimization
1. Introduction
As an emerging technology, Wireless Sensor Networks
(WSNs) have a wide range of potential applications in-
cluding environment monitoring, smart spaces, medical
systems and robotic exploration. Performance analysis
and optimization of WSNs, especially its Medium Access
Control (MAC) protocols, have attracted much research
interests. Traditional MAC protocols for wireless ad hoc
networks are designed to maximize throughput and
minimize delay. As sensor nodes are generally bat-
tery-operated, to design a good MAC protocol for WSNs,
the first attribute that has to be considered is energy con-
sumption [1]. Other important attributes (such as
throughput and delay) are generally the primary concerns
in traditional wireless ad hoc networks, but in WSNs they
are secondary.
IEEE 802.11 Distributed Coordination Function (DCF),
the basic MAC protocol in Wireless LANs (WLANs), is
based on Carrier Sense Multiple Access with Collision
Avoidance (CSMA/CA), one of typical contention-based
MAC protocols. CSMA/CA uses an acknowledgment
(ACK) mechanism for verifying successful transmissions
and optionally, an RTS/CTS handshaking mechanism for
decreasing collisions overhead. In both cases an exponen-
tial backoff mechanism is used. Before transmitting, a
node generates a random slotted backoff interval, and the
number of the backoff slots is uniformly chosen in the
range [0, CW-1]. At the first transmission attempt, the
contention window, CW, is set equal to a value CWmin
called the minimum contention window. After each un-
successful transmission, CW is doubled up to the maxi-
mum value CW max. Once CW reaches CWmax, it will re-
main at the value until the packet is transmitted success-
fully or the retransmission time reaches retry limit. While
the limit is reached, retransmission attempts will cease
and the packet will be discarded. Currently, CSMA/CA
has been the de facto MAC standard for wireless ad hoc
networks, widely used in almost all of the testbeds.
Moreover, low-power, low-rate Wireless PANs (WPANs)
such as IEEE 802.15.4 utilizes CSMA/CA too. However,
the energy consumption using CSMA/CA is very high
when nodes are in an idle mode. It is mainly called prob-
lem of idle listening. CSMA/CA-based S-MAC is explic-
itly designed for WSNs to solve this problem [2]. The
basic idea of S-MAC is that used energy is traded for
throughput and delay by introducing an active/sleep duty
period. Some researchers are attempting to improve the
performance of S-MAC [3–6]. To handle load variations
in time and location, T-MAC introduces an adaptive duty
cycle by dynamically ending its active part. This reduces

L. Q. ZHAO ET AL. 359
the amount of energy wasted on idle listening, in which
nodes wait for potentially incoming messages, while still
maintaining a reasonable throughput [7].
Recently, game theory [8] becomes a very good tool to
analyze and improve the performance of contention-based
protocols. Game-theoretic approaches were proposed to
solve the problem of security, query routing, and power
control respectively in distributed sensor networks
[9–12].
When using game theory in WSNs rather than mathe-
matics or economics, much attention should be paid to the
context of WSNs. For example, explicit cooperation
among nodes is clearly impractical in WSNs as it causes
additional energy and bandwidth consumption. We pre-
sented a novel concept of incompletely cooperative game
theory to improve the performance of MAC protocols in
WSNs without any explicit cooperation among nodes
[13–14].
In this paper, the preliminary results presented in
[13–14] will be substantially extended. The problem of
energy-efficient MAC protocols for WSNs is modeled as
game-theoretic constraint optimization with multiple ob-
jectives, e.g., energy consumption and QoS metrics.
2. Game-Theoretic Constraint Optimization
A node starts a game process when a new packet arrives
at the node’s transmission buffer and ends it when the
packet is moved out of the buffer (i.e., transmitted suc-
cessfully or discarded). Each game process includes many
time slots and each time slot corresponds to one game
state. In each time slot, each player (i.e., node) estimates
the current game state based on its history. After estimat-
ing the game state, the player adjusts its own equilibrium
strategy by tuning its local contention parameters. Then
all the nodes take actions simultaneously, i.e., transmit-
ting, listening, or sleeping. Although the player does not
know which action the other nodes (i.e., its opponents)
are taking now, it can predict its opponents’ actions ac-
cording to its history.
In the game, each player takes a distributed approach of
detecting and estimating the current game state, and tun-
ing its local contention parameters to the estimated game
state.
In economics, normally, the optimal target of the
player is to maximum its own profits. However, in WSNs,
the target of each player is to maximum the system per-
formance under certain limits, e.g., energy consumption
and QoS requirements.
In the game for WSNs, the utility function of the player
(i.e., node i) is represented by

,
iiii

s
sμμ . The pa-
rameters of the vector, μi,j correspond to its energy con-
sumption and QoS requirements, e.g., bandwidth, delay,
jitter, and packet-loss-rate. Obviously, there are some
limits on its utility function, called max
i
μ
, e.g., the maxi-
mum energy consumption, the tolerant minimum band-
width, maximum delay, jitter, or packet-loss-rate. If we
do not consider its opponents, the strategy of the player, si,
includes three possible actions: transmitting, listening or
sleeping.
The strategy profile of its opponents (i.e., all the other
n neighbors) is defined as

121 1
, ,...,,,...,
iiin
s
sss ss

.
Similarly, we can get the utility function of its opponents
that


,
iiii
μ
s
s  . Also, there are some limits on the
above utility function, called max
i
μ.
In many game-theoretic models, a player is a node con-
tending for the channel. As there may be many nodes in a
WSN and each node may contend for the channel repeat-
edly, a very complicated method is needed to determine
the strategy. Hence, in the game, a player is not always a
node. If we analyze the equilibrium strategy of node i,
Player 1 is node i, and Player 2 (i.e., its opponents) is all
the other n-1 nodes. In fact, it is possible for Player 1 to
estimate Player 2’s state, and difficult for Player 1 to es-
timate the states of each node in Player 2. In a formal
description, we are looking for


*
,,
*m
*
,
*
,, *m
*
,
arg min
arg min
i
i
ij ij
ii
sjij
ij ij
ii
sjij
s
s















μμ
μμ
ax
ax
i
i
(1)
Obviously, Player 1 adjusts its strategy si not to obtain
its own optimal utility (), but to help Player 2 get the
optimal utility (
*
i
μ
*
i
μ
); vice verse. Hence, it indicates that all
the nodes play the cooperative game based on the esti-
mated game states. On the other hand, the two players
help each other get the optimal utility under their own
limits respectively. It indicates that all the nodes play the
constrained game.
As Player 2 includes all the other n-1 competing nodes
except Player 1, collisions may happen among the n-1
competing nodes even not considering Player 1. So Player
2 includes four possible actions: successful transmission,
failed transmission, listening or sleeping, even if we do
not consider Player 1. Table 1 is the strategy table with 2
players (i.e., n nodes).
With regard to the payoff of Play 1 in a given time slot,
there are four possibilities when considering the two
players. Firstly, Player 1 sleeps with the probability of
, whose payoff is , where j corresponds to the
j-th parameter of the utility function. Secondly, Player 1
listens to the channel with the probability of
i
w,wj
c




11
i
wi


, whose payoff is . Here
,ij
ci

is the con-
ditional transmission probability of Player 1. Thirdly,
Player 1 fails to transmit its packets due to the collision
etween the two players with the probability of b

360 L. Q. ZHAO ET AL.
Table 1. Strategy model with n+1 nodes.


ii
cc ,


si
cc ,


fi
cc ,


is
cc ,


ff
cc ,
Transmitting
Playe
r
2
/
O
p
ponent
(all the other n nodes)
Player 1
(node i)
Listening
Sleeping
Sleeping


ww
cc ,
Listening
Failed
Transmission
Successful
Tran smission


fw
cc ,


iw
cc ,


wi
cc,


wf
cc ,






11
ii ii
www  
i

, whose payoff is ,
f
j
c. Here i
w
and i

are the sleeping probability and the conditional
transmission probability of Player 2 respectively. Finally,
Player 1 transmits successfully with the probability of

111
ii ii
ww
ets due to the collisions between the two players or
among the n-1 nodes within Player 2 with the probability
of






11 11
iiii iiii
wwpw   w
, whose
payoff is ,fj
c. Finally, Player 2 transmits successfully
with the probability of




1111
ii iii
wpw




,
whose payoff is ,
s
j
c. Here, i p is the conditional colli-
sion probability of Player 2, which is the function of the
probability i

[14].


 
, whose payoff is ,
s
j
c.
With regard to the payoff of Player 2 in a given time
slot, there are four possibilities too after considering the
two players. Firstly, Player 2 sleeps with the probability
of i
w, whose payoff is ,wj
c Secondly, Player 2 listens to
the channel with the probability of
.

1
i
1
i
w

e
payoff is

, whos
,ij
c. Thly, Player 2 fails to transmit its pack-
Hence, the optimal strategies of the two players under
the given constraints are expressed as
ird

   





  



,, ,
*max
*
,,
,, ,,
*max
*
,,
111111 11
arg min1
111 11
arg min1
ii
ii
iiijii iisji iiiiiifjiwj
iii
wjij
iiiisjiijiii ifjiwj
iii
wjij
wc pwcwpwwcwc
s
wwcc wwcwc
s


 



 
 



 





μμ
μμ
,
ided into super-frames and
every super-frame has two parts: an active part and a
sle
where τ is the frame transmission prob
If solving the above equation w
(2)
In general, the contention-based MAC protocol in
WSNs is modelled as a game-theoretic constraint optimi-
zation with multiple objectives. Based on the estimated
game state, each node achieves the global optima by ad-
justing its transmission and sleeping probability simulta-
neously.
eping part. During the active part, each node contends
for the channel in the incompletely cooperative game.
During the sleeping part, each node turns off its radio to
preserve energy. The time length of the active and sleep-
ing part is adjusted according to the estimated game state
too.
In the game, firstly, a node estimates the current state
of the game, e.g., the number of its opponents n-1. When
th
3. A Simplified Game-Theoretic Constraint
Optimization Scheme for WSNs e node is transmitting its frame, if any other node
transmits at the same time slot, the frame will be collided.
So the frame collision probability of the node p is ob-
tained as follows:

1
11 n p 

  (3)
Unfortunately, the above problem has been proven to be
NP-hard [15], so we cannot hope an algorithm that can
find the theoretical optimum and runs in polynomial time.
Hence, we present a simplified game-theoretic constraint
optimization scheme (G-ConOpt) in this section. In
G-ConOpt, we optimize the performance (e.g., the system
throughput, delay, jitter, and packet-loss-rate) under the
limited energy consumption.
In G-ConOpt, time is div
ability of the node.
ith respect to n, we ob-
tain:



log 1
1p nlog 1



(4)

L. Q. ZHAO ET AL. 361
Secondly, the node adjusts its e.g
the minimum contention windomin
m
quilibrium strategy, e.,
w (CW ), to the esti-
ated number of its opponents (ˆ
n), as follows [14]:


min ˆ7,8CWn rand

(5)
where rand (x, y) returns a rando value between x amnd y,
and [z] returns the floor function of z .
However, Vercauteren et al [16] showed that (4) is ac-
curate only under saturated conditions (i.e., each node
always has a packet waiting for transmission), and far
from being accurate under unsaturated conditions if not

filtered, e.g., for burst traffic. Bianchi and Tinnirello [17]
presented two run-time estimation mechanisms, i.e., auto
regressive moving average (ARMA) and Kalman Filters.
The two mechanisms are very accurate even in unsatu-
rated conditions. However, they are too complex to im-
plement in sensor nodes.
We provided an auto degressive backoff mechanism to
implement the game in current WLANs [14], which can
be implemented easily in sensor nodes.
In the active part, after transmitting or discarding a
packet, i.e., at the end of each game process, to maintain
the current contention level, the player adjusts CWmin as

min
min
max,/2The prevCW CW
CW CW


max
ious packet is transmitted successfully
The previous packet is discarded
(6)
The parameter CWmin, CWmax, and CW at the right of (6)
re the values of the nominal CWmin, CWmax and the final
o s
In G-ConOpt, after transmitting a packet, no matter it is
transmitted successfully or not, the player does not start
th
a
c ntention window ued in the previous game process
respectively. The parameter CWmin at the left of (6) is used
in the current game process to transmit a new packet.
In CSMA/CA, a node starts a contention process al-
ways with the nominal CW min, e.g., in IEEE 802.11b
CWmin=32. So CSMA/CA has one main drawback: in a
high load network the increase of the value of CW is ob-
tained at the cost of continuous collision.
e next game process with the nominal CWmin, as shown
in Figure 1. Given that the previous packet is transmitted
successfully, the final value of CW is the optimal one.
The best strategy for the player is to set CWmin=CW/2, to
make use of the channel effectively. On the contrary,
given that the previous packet is discarded, the best strat-
egy for the player is to set CWmin=CWmax, to decrease col-
lisions.
Figure 1. Auto degressive backoff mechanism.

362 L. Q. ZHAO ET AL.
Obviously, compared with the gam
ve feature of G-ConOpt is that it is simple to implement.
i
Moreover, at the end of the active part, the node
of the active part (Tactive) and the next
pe
e, the most attrac-ergy consumption.
ti
Frstly, no estimation mechanism is needed. Secondly, it
is not needed to compute the optimal value of CWmin.
That is to say, G-ConOpt would not cause any more en-

changes the length
riod (Tnext), according to the estimated game state, as
follows:


,min
0.
ˆ
min,2, /0.1
active
nextcurrentcurrentcurrent current
activeactive activenextactive
next
active act
TT TTTnnTT
TT


 
currentnext current
ivesleep sleep
TT else




,max
max ,
next current
activeactive activenext
TTTT  



ˆ
5, /0.5
currentcurrent current
TnnTT 

(7)
where max(x, y) and min(x, y) return the larger value and
e smaller value between x and y respectively. The pa-
an that in the last
ac
rotocol G-ConOpt, the fol-
wing simulations are made in an ideal channel. The
channel
rate
aSlot Time retry limit MAC PHY
header
The packets will be discarded only due to the re-
transmission time reaches the retry limit, and do not
coe dt.ary withe
cooor anvices, where eacnerates
n sizs under a Poocess and
tr
th
rameters current
active
T and current T are the time length of the
active part and the period in the current period. Tactive,max
and Tactive, the m and minimum length of
the active part. next
active
T and next T are used in the next
period. α is a predetermined integer, n is the last esti-
mated number of eting n, and ˆ n is the current
estimated number of competing nodes.
At the end of the current active part, if the estimated
number of competing nodes is larger th
min, areaximum
p ocomdes
tive part, it indicates many nodes still have packets to
send. So the time length of the next active part equals to
that of the current active part plus α but not longer than
the maximum active part size. The time length of the next
period is half that of the current period; thereby the nodes
can wake up more frequently to reduce the delay of
communication. On the other hand, if the estimated num-
ber of competing nodes is smaller than that in the last
period, the time length of the next active part equals to
that of the current active part minus α but not shorter than
the minimum active part size. The time length of the next
period is twice that of the current period, so the nodes
need not wake up frequently.
4. Simulation Results
To evaluate the proposed p
lo
values of the parameters used to obtain numerical results
for simulations are specified in IEEE 802.11b protocol,
as shown in Table 2.
Table 2. Simulation parameters.
header
1Mb/s 20μs 7 144μs 192μs
ACK SIFS
nsider th
rdinat
elay limi
d 50 de
We set a st topolog
h device ge
on
ew fixed
a
e packetisson pr
nsmit them to the coordinator. The packet arrival rate
is initially set to be lower than the saturation case, and it
is subsequently increased so that, at the end of the simu-
lation time, all nodes are almost in saturation conditions
[18].
CSMA/CA is considered as the worst case: it has no
energy saving features at all. The radio of each node does
not go into the sleep mode. It is either in the listen-
ing/receiving mode or transmitting mode. S-MAC is con-
sidered as the basic contention-based MAC protocol in
WSNs. It includes the periodic active and sleeping time to
achieve energy savings. For simplicity, the length of the
active and sleeping part are fixed at 500ms in the follow-
ing simulations. Compared with S-MAC, T-MAC can
adapt to the load variations in time and location, and can
end the active part according to the traffic loads.
Figure 2 shows that the four protocols have almost the
same system throughput under light traffic loads, and
under heavy traffic loads, the system throughput of
G-ConOpt is a little higher than that of CSMA/CA,
which is about 2 times that of S-MAC and a little higher
than T-MAC.
0 2040608010012014016018
0.0
0.1
0.2
0.3
0.4
0.5
0.6
put
G-ConOpt
S-MAC
T-MAC
CSMA/CA
DIFS
5
T Receiving Listen Power Sleeping
Power
27.45mW 13.5mW 13.5mW 0.015mW
CWmin CWmax
112μs 10μs 0μs 32 1024
ransmit
Power Power
System through
Sim u la tio n time(sec)
0
Figure 2. System throughput.

L. Q. ZHAO ET AL. 363
Figure 3 shows that delay in G-ConOpt, CSMA/CA
and T-MAC are much lower than that in S-MAC. Under
light traffic loads, delay in G-ConOpt is a little larger
than that in CSMA/CA, which is due to the periodic
active/ sleeping period in G-ConOpt. Under heavy traf-
fic loads, delay in G-ConOpt is lower than that in
CSMA/CA and T-MAC, which is due to the game in
G-ConOpt.
Figure 4 shows that jitter in S-MAC is much higher
than that in the other 3 protocols.
Figure 5 shows that packet-loss-rate in G-ConOpt al-
most keeps zero, which is much lower than that in S-
MAC and CSMA/CA. Meanwhile, packet-loss-rate in G-
ConOpt is a little lower than that in T-MAC, which is du
to the game in
F
s larger than that in S-MAC
un
C protocol, S-MAC has higher energy
eff
e
G-ConOpt.
igure 6 shows that the energy consumption in
S-MAC is near to one half that in CSMA/CA, which is
due to the periodic active/sleeping scheme. Energy con-
sumption in T-MAC is a little lower than that in
S-MAC under light traffic loads, for nodes in T-MAC
sleep longer than that in S-MAC. However, energy
consumption in T-MAC i
der heavy traffic loads, since nodes in T-MAC sleep
shorter than that in S-MAC. The energy consumption in
G-ConOpt is the lowest one in the four protocols, which
is due to the dynamic duty cycle strategy and the game
in G-ConOpt.
As an energy-efficient MAC protocol, G-ConOpt
considers not only energy consumption but also energy
efficiency (i.e., the ratio of the successfully transmitted
bit rate to energy consumption). Figure 7 shows that
energy efficiency in G-ConOpt is much higher than that
in S-MAC and CSMA/CA and T-MAC. As an en-
ergy-aware MA
iciency than CSMA/CA under light traffic loads.
However, the advantage of S-MAC over CSMA/CA
decreases with the increasing of traffic loads. Under
heavy traffic loads, energy efficiency in S-MAC is al-
most equal to that in CSMA/CA. Energy efficiency in
T-MAC is always larger than that in S-MAC and
T-MAC.
020406080100 120 140 160 180
0
5
10
15
20
25
30
Delay(sec)
Simulation time(sec)
G-ConOpt
S-MAC
T-MAC
CSMA/CA
020406080100 120 140 160 180
0
1
2
3
4
5
6
7
Jitter(s
Simulation time(sec)
ec)
G-ConOpt
S-MAC
T-MAC
CSMA/CA
Figure 3. Delay. Figure 4. Jitter.
020406080100 120 140 160 180
0.0 00
0.0 05
0.0 10
0.0 15
0.0 20
0.0 25
0.0 30
0.0 35
Packet-loss-rate
Simulation time(sec)
G-ConOpt
S-MAC
T-MAC
CSMA/CA
020406080100 120 140 160 180
0
10
30
40
50
60
20
Energ nsumption(mj)
Simu la tio n tim e (s e c )
G-ConOpt
S-MAC
T-MA C
y co
CS MA/CA
Figure 5. Packet-loss-rate. Figure 6. Energy consumption.

364 L. Q. ZHAO ET AL.
020406080100 120 140 160 180
6
7
8
9
10
11
12
13
14
15
16
Energy efficiency(kb/s/mj)
Si mu la tion time (s e c)
G-ConOpt
S-MAC
T-MAC
CSM A/CA
Figu
5. Conclusions
In this paper, firstly, the incompletely cooperative game
is used to model the MAC protocol of WSNs. Secondly,
after considering the context of WSNs, e.g., the require-
ments on energy consumption, the problem of the MAC
protocols of WSNs is modeled as a game-theoretic con-
straint optimization problem. Moreover, one simple f
mulation is presented for the problem. Finally, a simpli-
fied protocol, G-ConOpt is proposed, which can be eas-
ily implemented in current WSNs. Based on G-ConO
each nodes can achieve independently the optimal per-
formance under limited energy consumption. The sim
lation results show that G-ConOpt is an appropriate too
to improve ther certain con
only provide a simplified meth
ddress the sleeping probability. We are developing
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Acknowledgement: This work is supported by the 111
Project (B08038), State Key Laboratory of Integrated
Services Networks (ISN090105), Program for New
Century Excellent Talents in University (NCET-08-
0810), National Natural Science Foundation of China
(No. 60772137), and UK-China Science Bridges: R&D
on 4G Wireless Mobile Communications.
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