Energy-Efficient Data Aggregation Hierarchy for Wireless Sensor Networks
Yuanzhu Peter Chen Arthur L. Liestman Jiangchuan Liu
∗
School of Computing Science
Simon Fraser University
8888 University Drive, Burnaby, British Columbia, Canada
{yzchen, art, jcliu}@cs.sfu.ca
Abstract
A network of sensors can be used to obtain state-based
data from the area in which they are deployed. To reduce
costs, the data, sent via intermediate sensors to a sink, is of-
ten aggregated (or compressed). This compression is done
by a subset of the sensors called aggregators. Since sen-
sors are usually equipped with small and unreplenishable
energy reserves, a critical issue is to strategically deploy an
appropriate number of aggregators so as to minimize the
amount of energy consumed by transporting and aggregat-
ing the data.
In this paper, we first study single-level aggregation and
propose an Energy-Efficient Protocol for Aggregator Selec-
tion (EPAS). Then, we generalize it to an aggregation hier-
archy and extend EPAS to a Hierarchical Energy-Efficient
Protocol for Aggregator Selection (hEPAS). We derive the
optimal number of aggregators with generalized compres-
sion and power-consumption models, and present fully dis-
tributed algorithms for aggregator deployment. Simulation
results show that our algorithms significantly reduce the en-
ergy consumption for data collection in wireless sensor net-
works. Moreover, the algorithms do not rely on particular
routing protocols, and are thus applicable to a broad spec-
trum of application environments.
1 Introduction
A wireless sensor network is a collection of sensors in-
terconnected by wireless communication channels. Each
sensor node
1
is a small device that can collect data from
its surrounding area, carry out simple computations, and
∗
Supported in part by a Canadian NSERC Discovery Grant 288325, an
NSERC Research Tools and Instruments (RTI) Grant 613276, and an SFU
President’s Research Grant.
1
We assume that each sensor node has only one sensor, and hence, in
the rest of this paper, sensor and sensor node are used interchangeably [28]
communicate with other sensors or with the controlling au-
thorities of the network. Long distance communications are
achieved in a multi-hop fashion. Such networks have been
realized due to recent advances in micro-electro-mechanical
systems and are expected to be widely used for such appli-
cations as environment monitoring, intrusion detection, and
earthquake warning [28].
In many of these applications, the data to be collected is
state-based, that is, it consists of measurements of ambient
surroundings. Significant redundancies often exist in such
data due to spatial-temporal correlations. These local re-
dundancies can be removed prior to sending the over-sized
raw data to the sink and draining the limited sensor energy
store. This process, referred to as data aggregation or data
fusion, is quite attractive as it is often infeasible or costly to
replenish the batteries of the deployed sensors.
It is worth noting, however, that the amount by which
the data size may be reduced by aggregation depends on
the application. For example, simple statistical values such
as sum, mean or deviation, can be easily aggregated into
a single scalar or vector. On the other hand, a tempera-
ture map of a region would allow more limited reduction.
For example, a wavelet scheme separately computes the
wavelet transform for each subregion first, and then merges
the resulting wavelet coefficients of subregions to obtain the
wavelet transform of the entire region. Here, the number of
wavelet coefficients of a subregion may increase as does the
number of sensors therein.
In this paper, we investigate energy-efficient aggregator
deployment in wireless sensor networks. A unique fea-
ture of our study is that we consider a general compres-
sion model for data aggregation, which is more realistic
than the infinite compression [11, 3, 18] allowed in previ-
ous studies. We begin by using only a single level of ag-
gregation. With this restriction, we calculate the number
of aggregators needed to minimize the amount of total en-
ergy consumed in the network. A practical Energy-efficient
Protocol for Aggregator Selection (EPAS) is presented to
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achieve the target number of aggregators. Next, we demon-
strate that multiple levels of aggregation can further reduce
energy consumption. EPAS is then extended to hEPAS (Hi-
erarchical EPAS) to provide a multiple level solution. We
give fully distributed algorithms for aggregator deployment
in the above protocols, which are applicable to a broadspec-
trum of state-based data collection applications in sensor
networks.
The performance of these algorithms are examined by
experiments. Our results demonstrate that EPAS conserves
energy consumed both by the entire network and by the
most heavily loaded sensors. The energy consumption can
be further reduced by using hEPAS. The number of levels in
the hierarchy is also a critical factor, and our results provide
a general guideline toward desirable settings of the aggre-
gation levels.
The remainder of this paper is organized as follows. In
Section 2, we provide some background and review related
work. An energy-efficient protocol for aggregator selection
(EPAS) for one-level data aggregation is presented in Sec-
tion 3. In Section 4, we generalize EPAS to accommodate
aggregation hierarchies, called hEPAS. The performance of
these protocols is examined in Section 5. Finally, Section 6
concludes the paper and offers some future research direc-
tions.
2 Background and Related Work
Wireless sensor networks have received much attention
due to the number of potential applications of this tech-
nology. Many data communication protocols have been
proposed lately, such as DD [12], TAG [16], TTDD [25],
GRAB [26], Pilot [15], LEACH [11], and LAF [20]. Re-
cent surveys by Akkaya and Younis [1], by Akyildiz et al.
[2], and by Tilak, Abu-Ghazaleh and Heinzelman [23] in-
clude information on these and other protocols. There are
three types of data collection in sensor networks. Event-
based data, such as intrusion detection or object tracking,
is collected when an event at a particular venue within the
deployment region occurs. The event is confirmed by de-
tecting sensors using local consensus and reported to the
control authority [6, 19]. Focused state-based data is col-
lected in response to a query sent to selected sensors re-
questing relevant data [12, 26]. Global state-based data,
such as temperature or humidity, is collected by sensors all
over the deployment area and transmitted to the sink [17].
Our interest here is in global state-based data.
Bhardwaj, Garnett, and Chandrakasan [4] provided an
upper bound on the lifetime of sensor networks that are en-
gaged in event detections. In their model, the energy con-
sumed for a node to relay (that is, to receive and transmit)
a unit of data to another node at distance d is denoted by
α
1
+ α
2
d
l
, where α
1
and α
2
depend on the hardware im-
plementation of the sensors and l is the path attenuation ex-
ponent (usually in the range 2 ≤ l ≤ 4). The distance
from one sensor to the next that minimizes the energy con-
sumed is the characteristic distance, denoted d
char
, where
d
char
=
l
q
α
1
α
2
(l−1)
. This value depends only on the hard-
ware design specifications and the environment.
For state-based data collection, Heinzelman, Chan-
drakasan and Balakrishnan [11] presented a clustering al-
gorithm (LEACH) to aggregate the data from sensors. In
LEACH, each sensor becomes a clusterhead with a fixed
probability during startup and every non-clusterhead sensor
joins the cluster of a nearest clusterhead. The clusterheads
act as aggregators. As clusterheads are likely to consume
more energythan non-clusterheads, LEACH allows rotation
of clusterhead status. Alternatively, unequal-sized clusters
can be used to balance the sensor energy consumption [21].
Mhatre and Rosenberg [18] consider two types of nodes:
regular sensors (type 0) and more powerful sensors (type
1) that can serve as clusterheads. Their work focuses on
determining the numbers of type-1 sensors in a single ag-
gregation level. A hierarchical clustering algorithm is pro-
posed by Bandyopadhyay and Coyle [3]. In their model,
they calculate the number of aggregators in each level for
energy conservation. Clustering sensors and mobile ad hoc
nodes, in general, has been an intensively studied area, see
[5, 6, 7, 8, 13, 22, 24, 27].
Our hierarchical aggregator selection protocol (hEPAS)
is motivated by these studies. In particular, Bandyopadhyay
and Coyle [3] show that the use of a hierarchical structure
can help conserve energy. However, we consider a more
realistic compression model, and propose a general hierar-
chical frameworkto minimize the total energy consumed by
both communication and aggregation.
3 One Level Aggregation
We begin by allowing only one level of data aggregation.
Sensor nodes are partitioned into clusters, each with a clus-
terhead. The sensors within each cluster periodically send
their data to the clusterhead. The clusterhead compresses
the data collected from all members and sends the aggre-
gated data to the sink. We first construct an ideal model,
where the sensors and the aggregators are uniformly dis-
tributed over the region. Then we present a distributed algo-
rithm, EPAS, to select the aggregators under practical con-
straints.
3.1 System Model and Notations
We first state our assumptions and introduce some nota-
tion to be used. A summary list of the notation used in this
paper is given in Table 1.
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Symbol Meaning
a Radius of the network deployment region
a
i
Radius of a level i cluster
b
Coverage radius of an aggregator
c
Data compression overhead
d
char
Characteristic distance,
l
q
α
1
α
2
(l−1)
E
a
Energy consumed by aggregating data in a single
cycle in single-level context
E
ai
Energy consumed by aggregating data in a single
cycle in level i
E
ci
Energy consumed by transporting data from
level i to level i + 1 in a single cycle
f
a
(·) Aggregation energy consumption function
g(·)
Data compressibility function
h
Number of levels in the hierarchy
k
Number of aggregators in single-level context
k
i
Number of aggregators in level i
l
Propagation loss exponent
n
Number of sensors in the network
r
Sensor data rate
r
i
Level i aggregator data rate
α
1
Circuit energy consumption coefficient
α
2
Antenna energy consumption coefficient
α
α
1
+α
2
d
l
char
d
char
β Aggregation energy consumption coefficient
γ
Data compression ratio
Table 1. List of notation.
Consider a network of n sensors uniformly distributed
over a region. Many large-scale sensor networks such as
environment monitoring sensors dropped from aircraft have
this property [2, 28]. Route calculation is carried out during
the initial setup after the aggregators (clusterheads) are se-
lected, and the sensors send packets to their respective clus-
terheads using multi-hop paths (if necessary). Each hop in
these paths is roughly of characteristic distance d
char
[4].
That is, each node forwards the data to a node that is ap-
proximately d
char
closer to the destination.
We assume that data collection is synchronized by cy-
cles, where each cycle consists of a roundof data collection,
transmission, and aggregation. During each cycle, sensors
collect data. The data generated is then sent to the aggre-
gator as a packet of r bits. Each aggregator compresses the
data it receives from the sensors of its cluster and then for-
wards the data to the sink. We assume that, by relaying
packets via hops of the characteristic distance, transporting
one unit of data a distance d consumes α×d units of energy,
where α =
α
1
+α
2
d
l
char
d
char
[4]. That is, to send one unit of data
a distance one requires the sender to expend α
2
d
l
char
units
of energy to transmit the message. The sender and receiver
together use a total of α
1
units of energy internally.
We use a generalfunction g(x) to representthe data com-
pressibility at aggregators. Basically, g(x) gives the data
volume after compression as a function of the input data
volume x. When g(x) is a constant, this is the infinite com-
pression assumed in many of the previous studies [11, 3].
We use f
a
(x) to denote the energy consumed by compress-
ing x data units. This is generally proportional to x but
need not be. Although in practice the energy consumed by
compressing a unit of data may be significantly less than
that consumed by transmitting it (see [28]), we include this
cost in our model for completeness, e.g., to accommodate
advanced algorithms like Wavelet compression [28].
3.2 Optimal Number of Aggregators
We would like to determine the number of clusterheads
(aggregators) that minimizes the total energy consumed by
transmitting and aggregating data under our model. For
simplicity, we assume that the sensors are deployed in a cir-
cular region A of radius a meters with the sink located at
the center of the circle. Our solution can be easily extended
to accommodate other region shapes or sink locations.
Let E
c0
denote the total energy consumed by all of the
sensors sending data to their respective aggregators in a
single cycle. Consider the area covered by cluster C cen-
tered at (x
c
, y
c
). The total distance that the data pack-
ets travel from all members of C to (x
c
, y
c
) is
n
πa
2
×
RR
(x,y)∈C
p
(x − x
c
)
2
+ (y − y
c
)
2
dxdy, where
n
πa
2
is the
sensor density.
If each sensor chooses the closest aggregator as its clus-
terhead, the sensors essentially form a Voronoi diagram
of the network region where each cluster corresponds to a
Voronoi cell. For large k, a typical cluster can be approx-
imated as a circle of radius
a
√
k
[14]
2
with the aggregator
at the center. With this, the above expression evaluates to
2an
3k
3
2
. Thus, after factoring in the α coefficient to obtain the
energy consumption, the sensor data rate r, and summing
over the k aggregators, we have
E
c0
=
2αanr
3k
1
2
. (1)
Let E
a
denote the total energy consumed by data aggre-
gation in a single cycle. Since the aggregator receives data
at an average rate of
nr
k
bits per cycle, we have
E
a
= k × f
a
nr
k
. (2)
Let E
c1
denote the total energy consumed by all of the
aggregators sending this data to the sink in a single cycle.
2
More details on the problem of covering geometric spaces with
spheres can be found in Conway and Sloane [10].
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Since the data is sent by an aggregator at a rate of g
nr
k
bits per cycle and the aggregator density is
k
πa
2
, we have
E
c1
= g
nr
k
×α×
k
πa
2
×
RR
(x,y)∈A
p
x
2
+ y
2
dxdy, which
evaluates to
E
c1
= g
nr
k
×
2kαa
3
. (3)
Summing up Equations (1), (2) and (3), we have
2αanr
3k
1
2
+ k × f
a
nr
k
+ g
nr
k
×
2kαa
3
. (4)
Consider a typical circuit power-consumption model
where the aggregation energy consumption is proportional
to the volume of the data to be compressed, that is, f
a
(x) =
βx, for some constant β. Also consider a typical linear com-
pression model, g(x) = γx + c, where γ (0 ≤ γ ≤ 1) is
the compression ratio and c is the compression overhead
[9]. It follows that the number of aggregators that mini-
mizes the energy consumption of the network in a single
cycle (that is, Equation (4)), is k =
nr
2c
2
3
. Substituting
g(x) = γx + c into Equation (3), we see that the energy
consumed by transporting the data from k aggregators to
the sink is proportional to nrγ + ck. Thus, the contribution
of γ to the value of Equation (3) (and (4)) is independent of
k.
Thus, to minimize energy consumption, there should be
nr
2c
2
3
aggregators. This conclusion also applies to the spe-
cial case of β = 0, that is, where the energy required to
compress data is negligible (as assumed in many existing
sensor systems [28]).
3.3 Distributed Aggregator Selection – EPAS
In this section, we propose a practical Energy-Efficient
Protocol for Aggregator Selection (EPAS) that follows our
optimal solution in the previous subsection.
EPAS is a randomized and fully distributed algorithm
that consists of two phases. In the first phase, each sensor
chooses to be a clusterhead (aggregator) with probability
p
1
independently for some p
1
∈ [0,
k
n
]. Suppose that each
clusterhead has a fixed coverage radius ofb meters. (See
Section 3.4 for discussion of determining the value of b.) In
the second phase, each sensor that is not within the coverage
radius of some clusterhead declares itself to be a clusterhead
with probability p
2
.
By careful choice of p
1
and p
2
, we can ensure that the
expected number of aggregators is k. To do that, we lever-
age the following propositions.
Lemma 1 After phase 1 of EPAS, the probability that a sen-
sor c is not covered is (1 − p
1
)
1 −
p
1
b
2
a
2
n−1
, where p
1
is
the phase-1 selection probability, and b and a are the cov-
erage and network region radii, respectively.
Proof. Let X be a random variable denoting the num-
ber of sensors other than c that are contained in a cir-
cle of radius b centered at c. Thus, we have P rob[X =
i] =
n
i
b
2
a
2
i
1 −
b
2
a
2
n−i−1
, for i = 0, 1, . . . , n−1.
Further, (1− p
1
)
X
is a random variable indicating the prob-
ability that c is not covered by any selected clusterhead after
phase 1. Its expected value is
E
h
(1 − p
1
)
X
i
=
n
X
i=0
(1 − p
1
)
i
× P rob[X = i]
=
n
X
i=0
(1 − p
1
)
i
„
n
i
«„
b
2
a
2
«
i
„
1 −
b
2
a
2
«
n−i−1
=
„
1 −
p
1
b
2
a
2
«
n−1
.
This is also the probability that c is not covered by any se-
lected clusterhead. Factoring in the probability that c does
not select itself, we have the expected probability that sen-
sor c is not covered: (1 − p
1
)
1 −
p
1
b
2
a
2
n−1
.
For the expected number of clusterheads generated by
EPAS to be k, the selection probabilities of the two phases
should satisfy the following condition.
Theorem 2 The expected number of clusterheads gener-
ated by EPAS is k iff p
1
and p
2
are chosen such that
p
1
+ p
2
(1 − p
1
)
1 −
p
1
b
2
a
2
n−1
=
k
n
.
Proof. Let random variable Y denote the number of clus-
terheads generated by EPAS. Let binary random variable Y
i
be 1 if and only if sensor c
i
(i = 1, 2, . . . , n) becomes a
clusterhead. Thus we have E[Y
i
] =
E[Y ]
n
=
k
n
. Let binary
random variables Y
i,1
and Y
i,2
denote the fact that c
i
be-
comes a clusterhead in phases 1 and 2, respectively. Since
the events that c
i
becomes a clusterhead in either phase are
mutually exclusive, we have
E[Y
i
] = P rob[Y
i
= 1]
= P rob[(Y
i,1
= 1) ∪ (Y
i,2
= 1)]
= P rob[Y
i,1
= 1] + P rob[Y
i,2
= 1]
= E[Y
i,1
] + E[Y
i,2
].
We know that E[Y
i,1
] = p
1
. In addition, we have
E[Y
i,2
] = p
2
× P rob[c is not covered in phase 1]. Based
on Lemma 1, we have P rob[c is not covered in phase 1] =
(1 − p
1
)
1 −
p
1
b
2
a
2
n−1
. As a result, we have
k
n
=
E[Y
i,1
] + E[Y
i,2
] = p
1
+ p
2
(1 − p
1
)
1 −
p
1
b
2
a
2
n−1
.
After phase 2, the expected number of aggregators is k.
Each sensor that is not an aggregator selects the closest ag-
gregator as its clusterhead. Thus, the clusters essentially
form a Voronoi partitioning of the network.
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3.4 Discussion
Given the number of sensors, deployment area, compres-
sion ratio, characteristic distance, and other network param-
eters, we can calculate the optimal number of aggregators
k. Given this target number of aggregators, we can choose
appropriate probabilities p
1
and p
2
offline. After deploy-
ment, the sensors select k aggregators. Each of the aggre-
gators broadcasts its status to all sensors within coverage
radius b. For large k, k circles of radius b =
q
3
√
3
2π
a
√
k
≈
1.0996 ×
a
√
k
can cover the entire region of area πa
2
[14].
We use a larger coverage radius b =
2a
√
k
to ensure that most
of the sensors are within the coverage radius of at least one
aggregator while keeping the broadcast radius small. In
Section 5, we report on a set of experiments to determine
how many sensors lie outside the coverage areas for k ag-
gregators with coverage radius b =
2a
√
k
.
4 Hierarchical Aggregation
We now consider a more general framework that orga-
nizes the aggregators in a hierarchy. We begin with all sen-
sors in level 0 of the hierarchy. From those sensors, we
select a subset as aggregators for level 1. From the level 1
aggregators, we select a subset to act as level 2 aggregators.
Similarly, we select a subset of the aggregators at each level
to act as aggregators at the next higher level. Finally, the
sink (which may not be an aggregator of any of the other
levels) is the only aggregator of level h + 1.
Once the aggregation hierarchy is established, sensors
collect data and send it to the nearest level 1 aggregator.
The level 1 aggregators collect this data from their sensors,
aggregate it, and forward it to the nearest level 2 aggregator.
This process continues until the level h aggregators forward
the data to the sink.
In this section, we modify the method of Section 3 to de-
termine the optimal number of aggregators in each level of
the hierarchy. Then we extend EPAS to hEPAS, its hierar-
chical version.
4.1 Optimal numbers of aggregators in the hier-
archy
We denote the number of aggregators in level i by k
i
(i = 0, 1, ..., h + 1). Note that k
0
= n and k
h+1
= 1. The
data is sent out of a level i aggregator to its clusterhead at a
rate of r
i
bits/cycle and r
0
= r. As before, the data com-
pression rate is described by function g(·).We assume that
aggregators in each level are distributed uniformly. That is,
a level i aggregator receives data from
k
i−1
k
i
level (i − 1)
aggregators. The data rate r
i
can be expressed as:
r
i
=
(
r if i = 0
g
r
i−1
×
k
i−1
k
i
i = 1, 2, . . . , h.
Let E
ai
be the total energy consumed by the compres-
sion done by all of the aggregators of each level i in a single
cycle. We have E
ai
= k
i
× f
a
k
i−1
k
i
× r
i−1
.
We now consider E
ci
, the total energy consumed by
transporting data from level i aggregators to level (i + 1)
aggregators (i = 0, 1, . . . , h) in a single cycle. As be-
fore, a typical level (i + 1) cluster C can be approxi-
mated with a circle of radius a
i+1
= a/
p
k
i+1
, centered
at (x
c
, y
c
), and the density of the level i aggregators is
k
i
πa
2
. The portion of E
ci
within this cluster is r
i
× α ×
k
i
πa
2
×
RR
(x,y)∈C
p
(x − x
c
)
2
+ (y − y
c
)
2
dxdy =
2αak
i
r
i
3k
3
2
i+1
.
Therefore, summing over the k
i+1
level (i + 1) clusters, we
have E
ci
=
2αak
i
r
i
3k
1
2
i+1
.
Thus, the total energy consumed in a single cycle is
h
X
i=1
E
ai
+
h
X
i=0
E
ci
, (5)
which is a function of the k
i
.
Given values of r, a, α, γ and c for a particular sys-
tem, the values of k
i
minimizing the above total energy con-
sumption can be calculated. These values can then be used
to configure the aggregator selection protocol.
4.2 Hierarchical EPAS
Here, we propose a Hierarchical Energy-Efficient Pro-
tocol for Aggregator Selection (hEPAS). We assume that
the optimal number of aggregators in each level i is k
i
(i = 1, 2, . . . , h) as calculated above. The protocol selects
an expected k
i
sensors as the level i aggregators. hEPAS
executes for h iterations. Each iteration is similar to EPAS
(Section 3.3). During iteration i, a level (i − 1) aggrega-
tor chooses to become a level i aggregator with probability
p
i
∈ [0,
k
i
n
] in the first phase. Each chosen aggregator has
a coverage radius of b =
2a
√
k
i
. In the second phase, a level
(i− 1) aggregator that is not covered by any level i aggrega-
tor chooses to become a level i aggregator with probability
p
2
, where p
1
and p
2
satisfy the condition described in The-
orem 2 for k = k
i
. After the aggregators of all levels are
chosen, each level i aggregator (i = 0, 1, . . . , h) joins the
cluster of the nearest level (i + 1) aggregator.
5 Performance Evaluation
We evaluate the performance of EPAS and hEPAS
through simulations using our custom simulator. We first
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