Wireless Sensor Network, 2010, 2, 746-754
doi:10.4236/wsn.2010.210090 October 2010 (http://www.SciRP.org/journal/wsn/).
Copyright © 2010 SciRes. WSN
Published Online
An Application-Oriented Network Model for Wireless
Sensor Networks*
Xiaoliang Cheng, Zhidong Deng#, Zhen Huang
State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science
and Technology, Department of Computer Science, Tsinghua University, Beijing, China
E-mail: chengxl06@mails.tsinghua.edu.cn, michael@mail.tsinghua.edu.cn, chinaheart2003 @qq.com
Received June 29, 2010; revised August 2, 2010; accepted September 10, 2010
Abstract
Wireless sensor networks (WSNs) are energy-constrained networks. The residual energy real-time monitor-
ing (RERM) is very important for WSNs. Moreover, network model is an important foundation of RERM
research at personal area network (PAN) level. Because RERM is inherently application-oriented, the net-
work model adopted should also be application-oriented. However, many factors of WSNs applications such
as link selected probability and ACK mechanism etc. were neglected by current network models. These fac-
tors can introduce obvious influence on throughput of WSNs. Then the energy consumption of nodes will be
influenced greatly. So these models cannot characterize many real properties of WSNs, and the result of
RERM is not consistent with the real-world situation. In this study, these factors neglected by other re-
searchers are taken into account. Furthermore, an application-oriented general network model (AGNM) for
RERM is proposed. Based on the AGNM, the dynamic characteristics of WSNs are simulated. The experi-
mental results show that AGNM can approximately characterize the real situation of WSNs. Therefore, the
AGNM provides a good foundation for RERM research.
Keywords: Wireless Sensor Networks, Personal Area Network (PAN), Network Model, Throughput
Analysis
1. Introduction
With the rapid development of WSNs [1-3], the interac-
tion manners between the human being world and the
physical world have been changed greatly. Utilizing well-
deployed WSNs, we can sense the selected physical world
at anytime; then we could exert some customized influ-
ences on the physical world. Therefore, WSNs are attract-
ting increasing interests of people.
However, WSNs are resource-constrained networks.
These constraints are embodied almost at every aspect of
WSNs [4]. The large-scale deployment of WSNs is con-
strained by these factors, especially in terms of energy.
To monitor the energy consumption of WSNs, the RERM
research becomes an urgent task. Moreover, network mo-
del is the fundamental infrastructure of RERM research
at the PAN-level. Because the RERM research is inher-
ently application-oriented, the network model adopted
should be application-oriented too.
There are lots of factors that can influence the energy
consumption of WSNs. These factors have a large transi-
tional range in link quality that is characterized by sig-
nificant levels of unreliability and asymmetry [5]. More-
over, these characteristics have also been verified in our
previous study [6]. However, these properties of WSNs
have not been handled by the network models adopted by
other previous RERM researches reported [7-10]. This
becomes the main reasons of the inconsistent between
RERM results and the real WSNs.
To solve this problem, based on real platforms, a new
perspective of PAN was investigated by us when analy-
zing the fundamental causes of unreliability and asym-
metry. This model takes into account factors such as link
selected probability and ACK mechanism, etc. Then, an
application-oriented general network model (AGNM) used
for RERM research was proposed. The simulative results
showed that AGNM can approximately characterize the
real situation of WSNs.
The rest of this paper is organized as follows. A brief
introduction of the research platform is introduced in
*Supported by the National High Technology Development 863 Pro-
gram of China under Grant No. 2006AA040102.
X. L. CHENG ET AL.747
Section 2. AGNM is proposed in Section 3. In Section 4,
some simulation experiments are carried out to testify the
effectiveness of AGNM. Section 5 concludes this paper
and suggests some future research topics.
2. Research Platform
The RERM research should be application-oriented. To
effectively study RERM, an application-oriented general
network model for WSNs (AGNM) should be proposed
first. The AGNM model should be established based on
appropriate platform and real application environment.
To our best knowledge, the ZigBee/802.15.4 specifica-
tion reflects the basic characteristics of WSNs better than
other specifications [4,11]. The BeeStack protocol stack
is complied with ZigBee/802.15.4 [12]. So, the ZigBee/
802.15.4 and BeeStack protocols are selected as our re-
search platforms.
ZigBee [13] is based on 802.15.4 [14]. The medium
access control (MAC) layer and physical layer (PHY)
were defined by 802.15.4; and the upper layers from
network layer (NWK) were defined by ZigBee. Espe-
cially, the NWK layer of ZigBee provides full support
for Star, Cluster-Tree and Mesh topologies.
In the ZigBee specification, nodes are categorized into
three types: coordinator (ZC), router (ZR) and end device
(ZED). ZC creates and maintains a PAN. ZRs route data
to ZC and help maintaining a PAN. ZEDs sense the phy-
sical world and send information to ZC with the help of
ZRs. Moreover, each node maintains a neighbor table
locally. After the node has joined a PAN, its neighbor
table will be used to store relationship and link-state in-
formation about neighbor nodes. The table entry of a node
should be updated when any frame is received from its
neighbors.
Based on this platform, some assumptions can be drawn
out. Then, an application-oriented network model can be
established.
3. Application-Oriented General Network
Model
If all the nodes have good consistency, then the energy
consumption of each node is mainly determined by its
throughputs. Moreover, the throughput is influenced by
many other factors. From a perspective of a PAN, these
factors can be categorized into two classes: PAN-outside
factors (electromagnetic environment etc.), PAN-inside
factors (topology, ACK mechanism etc.).
For simplicity, only the PAN-inside factors are dis-
cussed here. The PAN-inside factors can be subdivided
into two subclasses: the topology factors and the opera-
tional factors. Both of them are dynamic and uncertain,
especially in the case of Mesh topology.
3.1. Modeling of Topology Factors
All the monitoring frameworks proposed in [7-10] can-
not provide any support for Mesh topology. Moreover,
they cannot be used for the mobile nodes. Hence, their
scalability decreased greatly. To solve these problems,
this subsection will propose a dynamic topology model
based the analysis of ZigBee Mesh topology.
1) Analysis of ZigBee Mesh Topology: A typical Zig-
Bee Mesh topology was introduced as Figure 1.
In Figure 1, dark circle denotes ZC node; gray cir-
cles denote ZR nodes; white circles denote ZED nodes.
Lines denote bidirectional radio links. Especially, links
among node-1, 2, 3 and 4 form a typical mesh structure.
Note that a path loop among nodes should be forbidden,
i.e., a frame should not pass through the same node
more than once in a delivery path. Let the length of
path from nodeto ZC bei, and the minimum hops
from node to ZC be, then we adopt the follow-
ing constraint:
iL
1D
ii
D
ii i
DL
.
In Figure 2, the paths of query-message are depicted
by downward arrow lines that start from node-1 (ZC).
The relationships among neighbor nodes are created
during topology formation. In ZigBee, there are three
relationship types: parent, child and sibling. Here, a
parent emits a unidirectional arrow line; a child is in-
jected by a unidirectional arrow line; siblings are con-
nected by bidirectional arrow line, because sibling is a
mutual relationship type. For convenience, some addi-
tional relationship types are defined by us.
Figure 1. A typical ZigBee Mesh topology.
Figure 2. Topology-construction and message-query in Zig-
Bee Mesh topology (downlinks).
Copyright © 2010 SciRes. WSN
X. L. CHENG ET AL.
Copyright © 2010 SciRes. WSN
748
Definition 1: Given the node , all its children (de-
noted as) and the descendants of its children are
named as descendants of node i(denoted as),
then
i
()ch i
)(ide

()(),(())([1, ])de ich ide ch iin
i
(1)
Definition 2: Given the node , the neighbors of
node (denoted as) comprise all the nodes that can
communicate with node within one hop distance,
then
i()ne i
i

()(),(),()([1,])ne ipa isi ich iin
()pai
(2)
where denotes the parents of node i;
denotes the siblings of node .
)(isi
i
In Figure 3, the paths of report-messages are de-
picted by upward arrow lines that start from ZEDs/
ZRs and direct to node-1 (destination). For example,
when a message is sent from node-4 to node-1, there
are five path options: 41, 421, 431,
4231 and 4321.
According to, the optional paths are
reduced to three ones: 41, 421, 431. Differ-
ent from the case of Cluster-Tree topology, the selection
of next hop node in Mesh topology is a probability event
1
ii i
DLD
Figure 3. Message-report in ZigBee Mesh topology (uplinks).
(a)
(b)
Figure 4. The link selected probability distribution in a Zig-
Bee Mesh topology. (a) Case of downlinks. (b) Case of up-
links.
[15]. So the state of network topology behaves with
evident dynamic characteristics during running time,
especially in the case of uplinks. Therefore, the link
selected probability is chosen to model the link state
(see Figure 4).
The bidirectional link of Figure 1 is subdivided into
an uplink and a downlink in Figure 4. Both of them are
attached with a selected probability. Specifically, the
links 2←→3, 2←→4 and 3←→4 of Figure 4(b) are
all uplinks, e.g. 3←→4 denotes two uplinks: 34 and
34.
When a message is sent from node-4 to node-1, the
optional paths include: 41, 421 and 431.
The link selected probability distribution of the next
hop is {p4,1 = 0.6, p4,2 = 0.2 and p4,3 = 0.2}. Note that
according to1
ii i
DLD
, when node-1 has been
selected as the next hop of node-4, the link selected
probability distribution should be {p2,1 = 1, p1,3 = 0 and
p2,4 = 0}, instead of {p2,1 = 0.8, p1,3 = 0.1 and p2,4 = 0.1}.
2) ZigBee Mesh Topology Model: Based on the dis-
cussion above, the mathematical models for undirected
links, node relationships and link selected probabilities
are discussed separately in the following.
a) Undirected Link Model: Based on Graph Theory
[16], the undirected link model (see Figure 1) can be
defined as an undirected graph. Here, is
a finite nonempty set, and the elements of is called
vertices; is a set of two element subsets of , and
the elements ofare called edges. In a static topology
model, each node corresponds to a vertex; and each
link corresponds to an edge. Also, an edge directed
from to
(, )
t
GVEV
V
EV
E
i
v
j
v is denoted as. ,
ij
vv
n
Suppose the number of vertices is, (, )
tEGV
can be expressed as a adjacency matrixGt
nn
A
.
The elements ofGt
A
are determined by Formula (3).
1,
0,
ij
ij
ij
ifv vE
aifvvE


(3)
Note that in an adjacency matrix, the sum of row
is named as out-degree (denoted as), which de-
notes the number of emitted links from nodei; the sum
of columni is named as in-degree (denoted asi),
which denotes the number of links injected into nodei.
Also, the sum of out-degree and in-degree is named as
degree of , i.e. =+.
i
)
od( )
i
v
id( )
i
v
id(v
Gt
ideg( )
i
vod()
i
v
A
is a
symmetric matrix, so, =.
od(v)id(v
i i
b) Node Relationship Model: The Node Relationship
Model (see Figures 2,3) can be defined as a directed
graph
)
(, )
r
GVE
. It can be expressed as a nn
adjacency matrixGr
A
. The elements ofGr
A
are deter-
mined by Formula (4).
1,
0,
ij
ij
ij
ifv vE
bifv vE


(4)
X. L. CHENG ET AL.749
When and, is a parent of, andis
a child of; whenij ji, and are siblings.
1
ij
b
i
0
ji
b
bb
i
1
j j
ij
Gr
A
is an asymmetric matrix.
c) Link Selected Probability Model: Because down-
links (see Figures 2 and 4(a)) take very low portion in
the lifetime of WSNs, only the uplink selected prob-
ability model is discussed here.
An uplink selected probability model (see Figure
4(b)) can be defined as a selection-weighted directed
graph . An uplink selected probability
as a weight is attached to corresponding edge.
()( ,)
we
GuV E
Definition 3: For uplinks, given the node, only the
parent and siblings of node can be selected as the
next hop. The set of uplink next hop nodes of node
is denoted as, then
i
i

i
i
Nu
(),()([1, ])
i
Nupa isi iin
)
(5)
Suppose the selected probability of an uplink from
node to node is, then ij()ij
pu
[0,1] ()
() 0(
i
ij
i
jNu
pu jNu
(6)
Moreover,
() 1
i
ij
jNu
pu
(7)
According to Formulas (6) and (7), ()( ,)
we
GuV E
(see Figure 4(b)) can be expressed as a asym-
metric adjacency matrix
nn
Ul
A
.
3.2. Modeling of Operational Factors
The operational factors comprise ACK and retransmis-
sion mechanisms, etc. For simplicity, only the influ-
ence caused by ACK mechanism is discussed here.
1) Analysis of Throughput: From the perspective of a
node, the throughput can be divided into two classes:
Throughput of neighbors and throughput of current node.
There is a competition between them. The throughput of
current node can be further subdivided into in-throughput
and out-throughput. Moreover, both in-throughput and
out-throughput of current node are influenced by its
neighbors.
To guarantee reliable delivery, a fully acknowledged
mechanism was adopted by ZigBee/802.15.4. By this
mechanism, an ACK frame will be triggered by a suc-
cessful reception of a DATA frame. The ACK frame
must be sent back to its direct source node. As a result,
the throughputs of the two parts in communication
would be increased by the ACK mechanism. When the
receiver sends an ACK frame, its out-throughput will
increase; when the sender receives the ACK frame, its
in-throughput will increase too.
2) Throughput Model of Uplink: After a ZigBee Mesh
network has been constructed, the uplink (see Figure 3)
is mainly used. And in the case of uplink communica-
tion, the majority of frames yielded and being deliv-
ered are DATA and ACK frames. So, based on the
Mesh topology model (see 3.1) and the ACK mecha-
nism, the mathematical model for throughput in the
case of uplink is proposed as follows.
Suppose that all the DATA frames yielded at node
i([2,])in
are destined to node-1 (ZC), and all the
frames can be transmitted and received successfully.
Definition 4: In uplinks, all the nodes that can yield
frames and be routed by node are named as the up-
link source nodes of node (denoted as), then
i
i()Su i
())i()(), (),(Suide isiidii
()Su i
(
e s[2, ])n (8)
The DATA frames yielded at would be
routed by node with a probability.
i((0,1])
uu
pp
a) In-throughput of Uplink: First, all the input DA-
TA frames of node during a time slice S
T con-
tribute to the uplink DATA in-throughput of node
(denoted as
i
in
i()
data
up
TP i
). Suppose the DATA frame
yield rate at node is
i()
u
i
. Here, ()
u
i
takes the
same value for any node . Note that, be-
cause node-1 is a ZC node, the DATA frame yield rate
at node-1 is
i([2,i])n
(1) 0
u
, but the ACK frame can still be
yielded and emitted at node-1 as other nodes. Then
()(())
()(( )(()))
data
up inkiuS
ksii ldesik
TP ip uiT



()
(() )
uS
jdei
iT

(, ,())jkl Sui (9)
where the first item denotes the number of DATA fra-
mes that come from ()
s
ii ; the second item denotes the
number of DATA frames that come from . Here,
()de i
(())
(() )
uS
ldesik
iT
denotes the number of DATA fra-
mes that come from to
((de si i)) ()
s
ii .
Second, all the input ACK frames of node during
S contribute to the uplink ACK in-throughput of
node (denoted as ). Then
i
T
i()
ack
up in
TP i
data
()() ()
ack
up inup inuS
TP iTP iiT

 (10)
where ()
uS
iT
denotes the number of ACK frames
corresponding to the DATA frames yielded at node .
i
Finally, all the input frames of node during
contribute to the uplink total in-throughput of node
(denoted as
iS
T
i
()
total
up in
TP i
). Then
()
total
TP i() ()
data ack
up inup inup in
TP iTPi

(11)
b) Out-throughput of Uplink: First, all the output
DATA frames of node during S
T contribute to the
uplink DATA out-throughput of node (denoted as
). Then
i
T
i
T
()
data
up out
TP i
()() ()
data data
up outup inuS
TP iP ii

 (12)
where ()
uS
iT
denotes the number of DATA
frames yielded at node , which will be emitted.
i
Copyright © 2010 SciRes. WSN
X. L. CHENG ET AL.
Copyright © 2010 SciRes. WSN
750
Second, all the output ACK frames of node dur-
ing S contribute to the uplink ACK out-throughput
of node (denoted as ). Then
i
T
i()
ack
up out
TP i
()
ack TP i() data
up outup in
TP i (13)
Finally, all the output frames of node during
contribute to the uplink total in-throughput of node
(denoted as). Then
i
ck
S
T
i
()
total
up out
TP i
()
total
TP i() ()
data a
up outup outup out
TP iTPi

 (14)
c) Total Throughput of Uplink: All the throughput
(frames) of node during S
T contribute to the uplink
total throughput of node (denoted as). Then
i
tal
i
()
t
i
()
total
up
TP i
total
() ()
to
upup inup out
TP iTPTP i
otal
 (15)
According to Formulas (9)-(15), the uplink total
throughput of node can be expressed as follows:
i
()
()4(2()((() )
total
up Suu
jdei
TP iTii


()(())
(()(( )))))
ki u
ksii ldesik
pu i


 (16)
Finally, by modeling link selected probability and
dynamic throughput of nodes etc., a comprehensive
AGNM used for RERM is proposed.
4. Simulation Experiments
As mentioned above, the energy consumption is mainly
determined by the throughput. The AGNM is designed
for RERM. So its capability in characterizing dynamic
throughput should be testified.
4.1. Experiment Settings
In the Cartesian coordinate plane (x, y), simulated no-
des are 1(50, 50), 2(75, 0), 3(75, 100), 4(100, 50),
5(150, 50), 6(175, 0), 7(175, 100), 8(100, 150) , 9(0,
50), respectively. The ZRs (No.2-5) and ZEDs (No.6-9)
sense environment information every 5 seconds. All
the sensed information would be delivered to ZC
(No.1).
The network topology adopted is a ZigBee Mesh
topology (see Figure 1). The undirected link model
can be expressed as an adjacency ma-
trix
(, )
t
GVE
Gt
A
.
011100001
101100000
110100010
111010000
000101100
000010000
000010000
010000000
100000000
Gt
A

The nodes relationship model (see Fig-
ures 2,3) can be expressed as adjacency matrix
(, )
r
GVE
Gr
A
.
011100001
001100000
010100010
011010000
000001100
000000000
000000000
000000000
000000000
Gr
A
(18)
The uplink selected probability model ()( ,)
we
GuV E
(see Figure 4(b)) can be expressed as adjacency ma-
trix Ul
A
.
0 0 0 000000
0.8000.100.100 0000
0.800.1000.100 0000
0.600.200.20 000000
000 1.00 0 0000
0 0 0 01.000000
0 0 0 01.000000
00 1.0000 0000
1.000 0 000000
Ul
A
(19)
4.2. Experimental Results
For simplicity, we assumed that the electromagnetic en-
vironment was ideal and the throughput of each node
was affordable, i.e. there was no delivery error.
1) Characteristics of Throughput: the characteristics of
throughput in WSNs mainly include: dynamic through-
put and dynamic components.
a) Dynamic Throughput: The AGNM can partially
characterize the running state of WSNs, especially in
terms of link selected probability and ACK mechanism.
The dynamic throughput is an intuitive reflection of
them.
(17)
Figure 5 shows the throughputs of nodes at time-slice
(TS, 1TS = 2hours) 1 and 12. Comparing the cases of
TS-1 with TS-12, the throughputs of node 1 (ZC) and
node 6-9 (ZEDs) are static, and the throughputs of node
2-5 (ZRs) are dynamic. According to AGNM, the dy-
namic throughputs are caused by link selected probabil-
ity (see Figure 4 (b)).
b) Dynamic Components: Because ACK mechanism is
taken into account, the components of throughput have
four types: DATA-out, ACK-out, ACK-in and DATA-in.
X. L. CHENG ET AL.
Copyright © 2010 SciRes. WSN
751
static, and the components at node 2-5 (ZRs) are dy-
namic. Moreover, the changes of different components at
node 2-5 (ZRs) from TS-1 to TS-12 are temporal proc-
esses (see Figure 7). According to the AGNM, the dy-
namic components were caused by link selected prob-
ability.
2) Performance Comparison: Compared with the net-
work models (non-ACK supported) adopted by [7-10],
the AGNM (ACK supported) have the advantage of cha-
racterizing the real situation of throughput (see Figures
8,9). So, the AGNM is a more application-oriented than
those used in [7-10].
3) Analysis of Generality: The AGNM is a Mesh-
supported model. Because link selected probability is
adopted, this model can be easily generalized to a Clus-
ter-tree-supported model by setting some link selected
probabilities to 0 in Figure 4(b), e.g. {p2,1 = 1, p2,3 = 0, p2,4
= 0, p3,1 = 1, p3,2 = 0, p3,4 = 0, p4,1 = 1, p4,2 = 0 and p4,3 = 0}.
So, the AGNM is more general than those used in [7-10].
(
a) (b)
Figure 5. Throughputs of nodes. (a) at TS-1; (b) at TS-12.
Figure 6 shows the components of throughputs at TS-1
and TS-12. First, the components at node 1 (ZC) have no
DATA-out and ACK-in, and the components at node 6-9
(ZEDs) have no DATA-in and ACK-out. After a PAN
have been constructed, the cases shown in Figure 6 are
normal in a ZigBee application (environment monitoring,
etc.). Second, comparing the cases of TS-1 with TS-12,
the components at node 1 (ZC) and node 6-9 (ZEDs) are
4) Usage in RERM: The AGNM is mainly designed
for RERM. So, it should be used in our RERM research
first. The energy model adopted in this experiment was a
simplified version of our previous work [6] (see Formula
(20)).
(a)
(b)
Figure 6. Components of throughput. (a) at TS-1; (b) at TS-12.
X. L. CHENG ET AL.
Copyright © 2010 SciRes. WSN
752
Figure 7. Components of throughput from TS-1 to TS-12.
Figure 8. Throughput from TS-1 to TS-12.
Figure 9. Accumulated throughput.
X. L. CHENG ET AL. 753
( 266.57184.1158
dep senrec
EN N 
6
1.35(7.2 103.291
s
en
N 
3
0.842)) /10N
sen
Where dep denotes the depleted energy,
(mJ) (20)
E
s
en denotes the
out-throughput of a node, rec denotes the in-throughput
of a node. Besides, all the constants are computed based
on MC13213 datasheet [17].
N
N
Suppose the initial energy reservation of a node (de-
noted as init ) is 300 mAh, and let the residual energy
of a node be , then we have
E
E
EE
res
( 266.57184.1158
res initsenrec
N N 
6
1.35(7.2 103.291
s
en
N 
3
0.842)) /10
sen
N (mJ) (21)
Based on the AGNM and Formula (20), the energy
consumption of WSNs is simulated (see Figures 10,11).
Based on the AGNM and Formula (21), the residual
energy of WSNs is simulated (see Figure 12) also.
Because node 1(ZC) has permanent power supply, its
residual energy is always the same as .
init
E
Figure 10. Energy consumption from TS-1 to TS-12.
Figure 11. Contour of energy consumption at TS-1.
Figure 12. Contour of residual energy at TS-12.
In summary, because the AGNM can well characterize
the link selected probability and ACK mechanism, the
real situation of throughputs and energy consumption can
be depicted in certain degree. Furthermore, the real situa-
tion of energy consumption can be partially characterized
by the ANGM model.
5. Conclusions and Future Works
An application-oriented general network model (AGNM)
designed for RERM research was proposed in this paper
by encoding link selected probability and ACK mecha-
nism etc. Different from the existing models, AGNM
was built based on the practical Mesh topology, and it
can be easily generalized to a Cluster-tree-supported one
by setting some link selection probabilities to zero. The
simulation results show that AGNM can approximately
characterize some real properties of WSNs.
However, the throughputs of nodes are also influenced
by other factors such as retransmission, which is intro-
duced by heavy throughputs of neighbors and harsh elec-
tromagnetic environment etc. To better modeling the real
situation of throughput, our future works will be focused
on AGNM based retransmission inference and prediction
algorithms.
6
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