An Application-Oriented Network Model for Wireless Sensor Networks

doi:10.4236/wsn.2010.210090

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Wireless Sensor Network, 2010, 2, 746-754

doi:10.4236/wsn.2010.210090 October 2010 (http://www.SciRP.org/journal/wsn/).

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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:

ii i



.

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).

X. L. CHENG ET AL.

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

()ch i

)(ide



()(),(())([1, ])de ich ide ch iin

(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



()(),(),()([1,])ne ipa isi ich iin

()pai

(2)

where denotes the parents of node i;

denotes the siblings of node .

)(isi

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: 4→1, 4→2→1, 4→3→1,

4→2→3→1 and 4→3→2→1.

According to, the optional paths are

reduced to three ones: 4→1, 4→2→1, 4→3→1. Differ-

ent from the case of Cluster-Tree topology, the selection

of next hop node in Mesh topology is a probability event

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: 3←4 and

3→4.

When a message is sent from node-4 to node-1, the

optional paths include: 4→1, 4→2→1 and 4→3→1.

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

(, )

GVEV

v is denoted as. ,

vv

Suppose the number of vertices is, (, )

tEGV



can be expressed as a adjacency matrixGt

nn



The elements ofGt



are determined by Formula (3).

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. ＝＋.

)

od( )

id( )

id(v

ideg( )

vod()



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

)

(, )

GVE



. It can be expressed as a nn



adjacency matrixGr



. The elements ofGr

are deter-

mined by Formula (4).

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.

b

bb

1

j j

 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.

()( ,)

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



(),()([1, ])

Nupa isi iin

)

(5)

Suppose the selected probability of an uplink from

node to node is, then ij()ij

[0,1] ()

() 0(

jNu

pu jNu









(6)

Moreover,

() 1

jNu





 (7)

According to Formulas (6) and (7), ()( ,)

GuV E



(see Figure 4(b)) can be expressed as a asym-

metric adjacency matrix

nn

.

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()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])

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()

data

TP i



). Suppose the DATA frame

yield rate at node is

i()



. Here, ()



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





, 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











()

(() )

jdei







(, ,())jkl Sui (9)

where the first item denotes the number of DATA fra-

mes that come from ()

ii ; the second item denotes the

number of DATA frames that come from . Here,

()de i

(())

(() )

ldesik









denotes the number of DATA fra-

mes that come from to

((de si i)) ()

ii .

Second, all the input ACK frames of node during

S contribute to the uplink ACK in-throughput of

node (denoted as ). Then

i()

ack

up in

TP i

data

()() ()

ack

up inup inuS

TP iTP iiT







 (10)

where ()





denotes the number of ACK frames

corresponding to the DATA frames yielded at node .

Finally, all the input frames of node during

contribute to the uplink total in-throughput of node

(denoted as

()

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

()

data

up out

TP i

()() ()

data data

up outup inuS

TP iP ii







 (12)

where ()





denotes the number of DATA

frames yielded at node , which will be emitted.

X. L. CHENG ET AL.

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()

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

()

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

tal

()

total

TP i

total

() ()

upup inup out

TP iTPTP i



otal

 (15)

According to Formulas (9)-(15), the uplink total

throughput of node can be expressed as follows:

()

()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

(, )

GVE

.

011100001

101100000

110100010

111010000

000101100

000010000

010000000

100000000

A











The nodes relationship model (see Fig-

ures 2,3) can be expressed as adjacency matrix

(, )

GVE



011100001

001100000

010100010

011010000

000001100

000000000

A



























































(18)

The uplink selected probability model ()( ,)

GuV E



(see Figure 4(b)) can be expressed as adjacency ma-

trix Ul



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

00 1.0000 0000

1.000 0 000000

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.

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.

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 

1.35(7.2 103.291

N 

0.842)) /10N

sen

Where dep denotes the depleted energy,

(mJ) (20)

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].

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

res

( 266.57184.1158

res initsenrec

N N 

1.35(7.2 103.291

N 

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

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.

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