考量能源效益與傳輸量之無線感測網路中繼點佈建方式

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考量能源效益與傳輸量之無線感測網路

中繼點佈建方式

On Energy-Efficient Traffic-Aware Deployment of a

Wireless Sensor Network

研 究 生：高志偉

指導教授：曾煜棋 教授

On Energy-Efficient Traffic-Aware Deployment of

a Wireless Sensor Network

Student: Chi-Wai Kou

Advisor: Prof. Yu-Chee Tseng

Department of Computer Science

National Chiao-Tung University

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某些缺點，這是因為他們的 網路拓樸是由Steiner tree建成的，而當中的Steiner tree是一

種方_{法可保證用最短的距離把整個網路連起來。} 因_{此，在這篇研究裏，首先，我們會介紹為什麼建Steiner tree作為有考慮流量大小} 的網路拓樸會產生問題。接下來，我們會針對在考慮網路流量大小的網路拓樸中進行 中繼點_{佈建的這個問題上，提出一個“權重移動演算法”來解決這個問題，而這個演算法} 我_{們是透過非線性規 劃(NLP)來處理。可是，因為非線性規劃不能保證程式可以在多項} 式時間下結束，所以我們另外提出了兩個啟發式方法來處理這個佈建的問題。最後，

在我們的模擬結果中，我們會呈現我們提出的方法以及以前在中繼點佈建中提出的方 法的數_{據。當中，我們察覺到我們的方法一定比以前的方法來得省電，因此網路的壽} 命也相對的比較長，而且我們的方法的改進效果在不同的情況下都可以維持在一個很 好的_範圍內。 關 關 關鍵鍵鍵字字_{字 : 省電、中繼點佈建、考慮流量、無線通訊與無線感測器網路。}

On Energy-Efficient Traffic-Aware Deployment

of a Wireless Sensor Network

Student: Chi-Wai Kou Advisor: Prof. Yu-Chee Tseng

Department of Computer Science

National Chiao Tung University

ABSTRACT

There are many different kinds of studies discussing how to achieve extending lifetime on

sensor network. Among them, relay nodes deployment is a way to enlarge lifetime by reducing

the communication range of sensor nodes. And in the early studies, they are usually concerned

with placing minimum number of relay nodes into homogeneous or heterogeneous WSNs to

meet certain connectivity and survivability requirements. However, some researchers start to

consider the traffic volume in the network when they deploy relay nodes. And there is a study

which the relay node deployment is related to the traffic volume and ensures the network

con-nectivity. But, we have found some drawbacks on it since its network topology is based on

Steiner tree, which can guarantee to connect the network with the minimum distance.

In this paper, we will first explain the problems about constructing Steiner tree as

traffic-aware network topology. Then, we will propose a weighted moving algorithm using non-linear

programming (NLP) to solve this traffic-aware relay node deployment problem. Since NLP

can not guarantee to terminate in polynomial time, we also propose two heuristic approaches

to solve this traffic-aware relay node deployment problem. In our simulation results, we have

shown that both of our approaches must consume less energy than previous studies and obtain

Keywords: energy efficient, relay node deployment, traffic-aware, wireless communication,

誌

謝

Contents

List of Figures viii

List of Tables ix 1 Introduction 1 2 Related Works 5 3 Problem Definition 7 4 Deployment Algorithms 9 4.1 Basic Ideas . . . 9

4.2 Weighted Moving Algorithm . . . 11

4.3 Heuristic Approaches . . . 14

4.3.1 Constrained Heuristic (CH) . . . 18

5 Simulation 22

6 Conclusions 28

Bibliography 29

List of Figures

1.1 An example of relay node deployment: (a) connectivity (b) traffic-aware (c)

connectivity and traffic rate. . . 3

4.1 An illustration of relay node deployment for single source q traffic flows with length of edge L and k extra nodes . . . 10

4.2 An example of improving case for relay node deployment. . . 12

4.3 An example of the block-by-block network topology. . . 15

5.1 Normalized network lifetime. . . 23

5.2 Normalized residual energy. . . 24

5.3 The performance improvement of CH and SSNLP with different numbers of sensor nodes. . . 25

5.4 The performance improvement of CH and SSNLP with different numbers of relay nodes. . . 26

List of Tables

Chapter 1

Introduction

The rapid progress of wireless communication and embedded micro-sensing MEMS

technolo-gies has made wireless sensor networks (WSNs) possible. A WSN usually needs to configure

itself automatically and support ad hoc routing. A lot of research works have been dedicated to

WSNs, including power management [12], routing [3], sensor deployment and coverage issues.

In WSNs, each sensor node has the capability to sense the environment (e.g., temperature,

pres-sure, light, humidity, etc.) and process the data. And in recently, more and more researchers

adopt WSNs to create a smart home, such as, intelligent lighting devices [13][14]. In general,

WSNs have an ad hoc topology, and each node is capable of relaying the data toward the sink.

Since most of the sensor nodes are battery-constrained, one of the design objective is to prolong

the network lifetime. There is a lot of research studying how to extend the network lifetime,

such as data aggregation, duty-cycle scheduling, energy-aware routing, relay node deployment,

etc. And there are various ways to define the lifetime of a WSN. It can be defined as the time

at which the first node runs out of energy. This time is equivalent to the time at which the first

routing path is disconnected. It can be defined as the time at which a region within the WSN is

not covered by any nodes.

In relay node deployment, the researchers have proposed to deploy lots of relay nodes which

WSN. And these studies can prolong network lifetime while meeting the certain network

spec-ifications. Most of the relay nodes deployment problem are focus on maintaining the network

connectivity and survivability [6][8][9][11][15]. In connected relay node deployment, we place

a minimum number of relay nodes to ensure that sensor nodes and the sink node are connected.

In survivable relay node deployment, we place a minimum number of relay nodes to ensure that

sensor nodes and the sink nodes are bi-connected. In the previous studies[6][8][9][11][15], they

only consider the connectivity of the network but not traffic flows in a WSN. However, in relay

node deployment, the network lifetime is limited by the relay node battery power. And this

bat-tery power consumption closely depends on the communication distance and traffic volume. So,

[10] has brought up an idea that the location of the relay node assigned to the network should

not only consider the distances but also the traffic volume. Unfortunately, the network topology

of [10] is based on Steiner tree, which is the optimal solution for 1-connected relay node

de-ployment. However, Steiner tree only considers the total length of entire network but not traffic

rate in the network. Inspired by this situation, we believe that we can modify the topology of

Steiner tree to find out some proper locations for Steiner points which retain connectivity and

consider traffic rate as well. After constructing the new network topology, we can deploy the

relay nodes on each edge depended on its traffic volume to get a better result than previous

works. In Fig. 1.1, there are N relay node will be deployed. We consider two sensor nodes s1 and s2with traffic rate0.6 and 0.3, respectively, and the sink node s0which can collect the data from s1 and s2. In Fig. 1.1(a) only considers the connectivity for deployment. We can observe that the traffic distance from s1to v, s2to v and v to s0is less than the distance which the sensor nodes direct connected to the sink. Fig. 1.1(b) is the result of [10] which considers traffic-aware

for deployment. It means that we can move some relay nodes from less traffic intensive section

(a) (b) N 3 1 N 3 1 N 3 1 N ) 3 1 ( ' N ) 3 1 ( ' N 3 1 N ' L 3 3 L 3 3 L 3 3 N ) 3 1 ( ' N ) 3 1 ( ' N 3 1 N ' L ) ' ' 3 3 ( ' L 3 3 L ) ' 3 3 ( ' (c)

Figure 1.1: An example of relay node deployment: (a) connectivity (b) traffic-aware (c) con-nectivity and traffic rate.

connectivity and traffic rate for deployment. By the numerical analysis, we can observe that the

topology of Fig. 1.1(c) can get better performance than Fig. 1.1(b) and Fig. 1.1(a) because the

location of intersection v′is involved with the traffic volume.

In this thesis, we will propose one non-linear programming(NLP) algorithm and two

heuris-tic approaches to solve the relay node deployment problem which must be considered network

connectivity and traffic volume of the network. In NLP, we will find all proper locations for

Steiner points at the same time. It considers the entire network topology at the same time so

its complexity will be higher if the original network topology is complicated. Next, since the

complexity of NLP may be high, we propose two heuristic approaches that is low complexity

with acceptable performance. In heuristic approaches, we will divide the entire network into

several blocks and solve them separately.

about relay node deployment. In Section III, we define the problem definition of the relay node

deployment. In Section IV, we describe our relay node deployment algorithms. Simulation

Chapter 2

Related Works

In WSNs, the mainly energy consumption of a sensor node is wireless communication, which is

proportional to the data rate and the communication distance. Since the communication distance

can be adjustable, lots of research has been studied this property to achieve topology control

with given node deployment, such as power-aware routing, relay node deployment, etc.

Relay node deployment for WSNs have been studied in various contexts. In [7], it was first

shown that the connectivity for relay node deployment is NP-hard and it proposed a minimum

spanning tree (MST) based 5-approximation algorithm. Later, the authors[4] also proposed a

3-approximation algorithm for this problem. In relay nodes deployment for WSNs, most of the

studies were focused on the connectivity of the network. It meant that they had to guarantee

that the given relay nodes should be connected to all sensor nodes and the sink node after their

deployment. In [15], they not only considered the connectivity of the network in relay node

deployment, but also proposed to create a network with fault-tolerant, which is k-connectivity

network, by relay nodes. The connectivity problem had developed from 1-connected to

k-connected. After that, the work[8] extended the fault-tolerant problem by considering that the

relay nodes can only be placed at some given locations and considered the reality and the

ap-plication requirement. Moreover, the work[6] provided fault-tolerance with higher network

transmission radii. Work[9] not only considered deploying relay nodes into the network to

miti-gate network geometric deficiency and prolong network lifetime, but also provisioned additional

energy on the existing nodes for a two-tier wireless sensor network. The deployment studies

which we mentioned before were placed by their algorithm. But in [11], they developed three

random deployment strategies for relay nodes in a heterogeneous WSN by impact of random

device deployment on system lifetime not stressed enough.

But the strategy of the deployment in previous studies is evenly deployed relay nodes

ac-cording to the length of the distance. So, in [10] has shown us that the strategy of the relay node

deployment should be considered the traffic flows, and its performance is better than others.

Unfortunately, the network topology of [10] is a Steiner tree, and Steiner tree only considers the

total length of entire network but not traffic rate in the network. Hence, in our work through

con-sidering the traffic volume, we will move the Steiner points to some proper locations to satisfy

Chapter 3

Problem Definition

We consider a wireless sensor network with three types of nodes: sensor node, relay node, and

sink node. A sensor node is a device which can report environment data (such as temperature,

humidity, and light intensity), but has no communication capability. A relay node is a device

which has only communication capability, but no sensing capability. A sink node is a special

relay node which is designed to collect all sensor nodes’ data. We assume that there are one sink

node, denoted by s0, M sensor nodes, denoted by s1, s2, . . . , sM, and N relay nodes, denoted by r1, r2, . . . , rN, in the network, where M ≤ N. The locations of s0, s1, . . . , sM are already known, but the locations of r1, r2, . . . , rN are yet to be determined. The data generating rate of sj, j = 1 . . . M, is also known and is denoted by βj.

Our goal is to design a deployment scheme to place these relay nodes to form an

energy-efficient topology and forward sensing data. Since sensor nodes have no communication

capa-bility, each of them has to be accompanied by a relay node (this is why M ≤ N). We thus need

to decide the locations of the rest of the N− M relay nodes. Let liand tibe the location and the transmission distance of ri, respectively, i = 1 . . . N. We assume that each ti is controllable, but must satisfy

For each sensor sj, j = 1 . . . M, we also need to find a path

pj = rj1rj2. . . rjhs0,

such that rj1 is located at sjand the distance between rjiand rji+1, denoted by dist(rji, rji+1), is

≤ tji, for i = i . . . h − 1, and dist(rjh, s0) ≤ tjh.

To calculate the energy cost, we denote energy incurred to riby path pj by ˆ

E(ri, pj) = ˆEtx(ri, pj) + ˆErx(ri, pj),

where ˆEtx(ri, pj) and ˆErx(ri, pj) are the transmit and receive costs, respectively,

ˆ Etx(ri, pj) =  βj(tαi + etx), if ri ∈ pj 0, otherwise, ˆ Erx(ri, pj) =

 βjerx, if ri ∈ pj and riis not the head of pj 0, otherwise, ,

where α is the power attenuation factor (2 ≤ α ≤ 6), and etxand erxare manufacture-dependent constant of transmit and receive factors, respectively. The total energy incurred on ri is:

ˆ E(ri) = X ∀j ˆ E(ri, pj).

Our relay node deployment problem is to find li, ti, and pj for i= 1 . . . N and j = 1 . . . M with the following objective function:

min{max

Chapter 4

Deployment Algorithms

Below, we first make some observations based on an existing work [10]. Then we show how to

improve it by presenting our non-linear programming algorithm and some heuristics.

4.1

Basic Ideas

The work [10] shows that an efficient deployment should find a Steiner tree to connect all sensor

nodes and the sink node and then evenly place relay nodes along each Steiner edge according to

some weighting mechanism. The following lemma shows how relay nodes should be deployed

along a Steiner edge.

Lemma 1. Given two relay nodes raand rb, suppose that ra has received a certain amount of data to be delivered to rb. If there are k extra relay nodes available, the best way to deploy these k relay nodes is to evenly distribute them along the line connecting raand rb.

Proof. There are two ways for us to deploy k extra relay nodes. At first, we can divide the data volume of ra into q parts and relay these q traffic flows separately by assigning ni relay nodes, where i= 1 . . . q andPq

i=1ni = k. Secondly, we can just relay all the data of raby using only one traffic flow with k relay nodes. By the result of [10], we know that we would rather to use

the latter one, and must deploy k relay nodes evenly on this flow.

L k Relay nodes ͙ Traffic q outflow Traffic 1 outflow ͙ Traffic q inflow Traffic 1 inflow ͙

Figure 4.1: An illustration of relay node deployment for single source q traffic flows with length of edge L and k extra nodes .

and outflow are L. The best way to deploy relay nodes is to evenly distribute them among edge

L.

Based on the above Lemma 1, the work[10] proposes to solve the deployment problem as

follows:

1. Construct a graph of Steiner tree G = (V, E) to connect all sensor nodes and the sink

node because Steiner tree can guarantee to interconnect a network with the shortest length

where the length is the sum of lengths of all edges, by adding some new vertices which

are known as Steiner points. And it is the optimal solution for 1-connected relay node

deployment.

2. After the Steiner tree G has constructed, we have to calculate the traffic rate λek of each

Steiner edge k, where λek is the sum of data generating rates of the traffic flows passing

through the edge k.

3. In Lemma 1, we understand we should deploy relay nodes evenly on each edge k. Hence,

the energy of each relay node in edge k must be the same. We can formalize the energy

model as

ˆ

Eek = ˆE(ri),

and since both terms erxand etxare quite small than tαi, we can simplify the above equa-tion as

And our target is tomin{max∀i{ ˆE(ri)}}, it can also mean to min{maxei∈E{ ˆEek}} by

given N relay nodes. Therefore, we can let ˆEe1 = ˆEe2 = ... = ˆEek, and it can be

expressed as follows, λe1( Le1 ne1 )α = λe2( Le2 ne2 )α = . . . = X ek∈E λek( Lek nek )α. (4.1)

Though Eq. (4.1), we can calculate nek for each edge k.

4. After calculating nek, we deploy nek relay nodes on edge k evenly with communication

range tek =

Lek

nek

. And the first relay node must be placed on the location of the head node

of edge. The head node of edge must be sensor node or Steiner point.

Although [10] proposed a pretty good algorithm for traffic-aware relay node deployment,

it still has some drawbacks. Fig. 4.2 shows an example. In Fig. 4.2(a), we deploy two sensor

nodes and one sink node by [10]. As shown in Fig. 4.2(b), we move the Steiner point v to the

new location v′. By numerical analysis, we observe that the energy consumption of each relay node in Fig. 4.2(b) is smaller than Fig. 4.2(a). From the example, we know that there must exist

a better network topology for a traffic-aware WSN. Hence, we try to move all Steiner points to

proper locations in order to obtain the better topology. In the following, we will show how to

move all Steiner points to proper locations and assign appropriate relay nodes on each edge to

prolong network lifetime.

4.2

Weighted Moving Algorithm

From above section, we know that moving Steiner points may prolong network lifetime. Here,

we propose a weighted moving method which can move the Steiner points according to the

nodes’ traffic rates. The moving scheme is based on a non-linear programming. Through the

(a) (b) 0.6

S

S

S

v

S

S

S

ǀ͛

Figure 4.2: An example of improving case for relay node deployment.

In the beginning of relay node deployment problem, we just know the locations of sensor

nodes and the sink node, and they are not connected. So, our objective is to connected all

sensor nodes and the sink node with minimum energy consumption. And our xxxx algorithm

are organized as follows:

1. Construct a graph of Steiner tree G = (V, E) to connect all sensor nodes and the sink

node by using heuristic method proposed in [1], where V = {v0, v1, . . . , vM, vM +1, . . .}, and E = {e1, e2, . . .}. Here, we define vertices vi = si for i = 0 . . . m, and vj is called Steiner point, j ≥ m + 1. Let e1, e2, . . . represent the edges connect the vertices in V , where traffic flows are unidirectional.

2. After the Steiner tree G has constructed, we have to calculate the traffic rate λek of each

edge k, and λek is the sum of data generating rates of the traffic flows passing through the

edge k.

3. Now, we need to find a proper network topology and relay node deployment. In the

following, we will propose a non-linear programming to solve this problem. Since the

locations of vi, i = 0 . . . m, i.e., sensor nodes and the sink node, are fixed, we can only modify the locations of vi, i = M +1 . . ., i.e., Steiner points, to achieve our target. Hence,

we can modify Eq. (4.1) into λe1( q (XA_e1 − XB_e1)2+ (YA_e1− YB_e1)2 ne1 )α _{= . . .} = X ek∈E λek( q (XA_ek − XB_ek)2+ (YA_ek − YB_ek)2 nek )α _(4.2) where XA_ei, YA_ei, XB_ei and YB_ei represent the x-axis and y-axis location of two vertices, i.e., Aeiand Bei of edge ei, and the vertices can be sensor nodes, Steiner points or the sink

node. In the following, we call the Steiner point as merge vertex. According to Eq. (4.2),

we model this problem, which can guarantee both the minimum energy for transmitting

traffic flows and the network connectivity, as follows.

minimize X ek∈E λek( q (XA_ek − XB_ek)2+ (YA_ek − YB_ek)2 nek )α subject to X ek∈E nek = N min(Xv0, . . . , Xvm) ≤ Xvi ≤ max(Xv0, . . . , Xvm), i = M + 1, M + 2, . . . min(Yv0, . . . , YvM) ≤ Yvi ≤ max(Yv0, . . . , Yvm), i = M + 1, M + 2, . . . (4.3) Rmin ≤ q (XA_ek − XB_ek)2+ (YA_ek − YB_ek)2 nek ≤ Rmax, ∀ek∈ E λej( q (XA_ej − XB_ej)2+ (YA_ej − YB_ej)2 nej )α ₌ λej+1( q

(XA_ej+1 − XB_ej+1)2+ (YA_ej+1 − YB_ej+1)2 nej+1

)α, j = 1 . . . k − 1

where k is amount of total edges

The constraint 1, it ensures that given N relay nodes must be used completely and

as-signed to each edge. Constraint 2 and 3 can guarantee the locations of merge vertices

must be inside a boundary. Constraint 4 guarantees that the communication range of each

relay node must not be over the boundary and also guarantees the connectivity. The last

re-sult of the NLP, we can find out all the proper locations for merge vertices and the number

of relay nodes nek assigned on each edge k.

4. After we have decided nek, and the locations of merge vertices, we can deploy nek relay

nodes on edge k evenly with communication range tek =

Lek

nek

. And the first relay node

must be placed on the location of the head node of edge. The head node of edge must be

sensor node or Steiner point. Our algorithm can be summarized as Algorithm 1.

Algorithm 1 Weighted Moving algorithm

Input: s0, . . . , sm, Xs0, . . . , XsM, Ys0, . . . , YsM,

β1, . . . , βM, N relay nodes, RminandRmax.

Output: G′(V′ , E′

)

1. Construct a Steiner tree G(V, E) with heuristic approach.

2. Calculate the traffic rate λek based on the G(V, E), where ek∈ E

3. By Eq. (3), we can calculate the approximative solution G′ (V′

, E′

) with nek,

Xvm+1, XvM +2. . ., YvM +1, YvM +2. . . to decide where the merge vertices are so as to minimize

and balance the relay node energy, ek∈ E′.

4. Deploy nek relay nodes on edge k evenly with communication range tek =

Lek

nek

.

4.3

Heuristic Approaches

In above section, we use non-linear programming algorithm to model our problem and also

find out the proper locations of merge vertices. From the Algorithm 1, we realize that it can

find approximative solution. However, since it considers the entire topology to find the proper

locations of merge verteices, the complexity of it is depended on how many variables are there.

If there are m merge vertices and n edges, the variables are 2m+n. It means that the more merge

vertices and Steiner edges there are, the higher complexity it is. Therefore, in this section, we

will propose some heuristic approaches that are lower complexity with acceptable improvement.

1

2

3

4

(a) Original topology

1

2

3

4

(b) After finding all proper locations of merge vertices

1. We construct a Steiner tree G(V, E) to connect all sensor nodes and the sink node with

heuristic approach.

2. Then, we can calculate the traffic rate λek based on G(V, E) for each Steiner edge.

3. For decreasing the complexity of Algorithm 1, we need to reduce the number of variables

of it. Hence, we firstly divide the network topology into blocks and are going to solve

them separately in the following two approaches. Each block is a triangle and composed

of four nodes. The merge vertex is a node which is connected three neighbor nodes in the

same block, and other three nodes can be sensor nodes, merge vertex or sink node. Each

block can be considered as an independent 4-points tree, and we can only modify the

location of merge vertex in each block. The traffic-rate of merge vertex can represent its

block’s rate, and we will cope with the blocks in order by pre-defined priorities sequence.

The higher rate the block is, the higher priority it is. Fig. 4.3 shows an example of five

sensor nodes with different data generating rate and one sink node in the network. In

Fig. 4.3(a), we divide the network into four blocks, and each block is a triangle with

4-points tree. We can observe that the block with the highest rate is4, thus priority of block

4 is the highest priority. And the next highest is block2. Finally, we can set the order as (4, 2, 3, 1) in this network. Then, we will find the proper location of each merge vertex of

each block in orderly.

4. After dividing the network into blocks, we propose two methods to find the proper

lo-cation of each merge vertex. The first method is “constrained heuristic” which can be

finished in polynomial time but its performance worse than Algorithm 1, and the second

one is “small-scale nonlinear programming” which can get better performance than the

And we will explain these two methods in detail later. Fig. 4.3(b) shows the result after

we have solved all blocks in Fig. 4.3(a).

5. In these two methods, we only find the proper location of each merge vertex of each block.

Since we solve the relay node deployment problem locally do, not actually calculate how

many nodes should be assigned on each Steiner edge. Hence, we can not ensure the

com-munication range of each relay node is in the boundary and also guarantee the network

connectivity. Therefore, we must check the network connectivity. We use Eq. (4.1) to

calculate ne1, ne2, . . . for each Steiner edge and deploy nek relay nodes on Steiner edge

k evenly with communication range r = Lek

nek

.. If the network is connected, the

commu-nication range of each relay node must be satisfied the boundary,_Rmin ≤ Lek

nek

≤ Rmax, where ek∈ E. And the result can be the candidate of our final solution.

6. In Fig. 4.3(b), we can observe that the boundary of each block is different from the

bound-ary in Fig. 4.3(a). This is because the boundbound-ary of a block can be influence by the

loca-tions of the merge vertices in close blocks of that block. Therefore, we realize that if all

merge vertices have been changed once, the boundaries of each block may be enlarged or

reduce. It means that we may find a better location of each merge vertex in the second

round. So, we will repeat step3, 4, 5 in T iterations to find a better solution, where T is a

user-setting parameter.

7. After executing T iterations, we will choose the candidate with minimum energy

con-sumption and connected network as our final solution.

Next, we will explain the two methods which we use to find out the proper location of merge

4.3.1

Constrained Heuristic (CH)

In Algorithm 1, the complexity is very high if there are many merge vertices or Steiner edges.

It may not be terminated in polynomial time. Hence, we show the first method which can

guarantee to be finished in polynomial time.

In the object function of Eq. (4.3), since there are only three edges in one block, we can

modify the object function as,

min 3 X k=1 λek( q (XA_ek − XM V)2+ (YA_ek − YM V)2 nek )α_, (4.4)

where e1, e2, e3 represent the three edges connected to the merge vertex, XM V and YM V are location of merge vertex, XA_ekand YA_ek represent the locations of three vertices connected with the merge vertex, and these three vertices can be sensor nodes, sink node or the merge vertices

of other blocks. In this approach, we assume α = 2, ne1 : ne2 : ne3 = 1 : 1 : 1, and

ne1 + ne2 + ne3 = C, where C is a constant. Hence, ne1 = ne2 = ne3 =

C

3. The Eq. (4.4) can be modified as, min 3 X k=1 λek( q (XA_ek − XM V)2+ (YA_ek − YM V)2 C 3 )2 (4.5)

Since we want to minimize Eq. (5), we can omit constant C₃. And when we extend Eq. (5), we can observe that the solution of it is center of gravity of the triangle of Ae1Ae2Ae3. It is

proved by following equations,

min 3 X k=1 λek((XAek − XM V) 2 + (YA_ek − YM V)2) (4.6) min 3 X k=1 λek(X 2 M V + Y 2 M V) − 2XM V( 3 X k=1 λekXA_ek) − 2YM V( 3 X k=1 λekYA_ek) + K (4.7) P3 λ X P3 λ Y

where K and K′ are constant. From Eq. (8), when XM V and YM V are equal to P3 k=1λekXAek P3 k=1λek and P3 k=1λekYA_ek P3 k=1λek

, Eq. (8) will get minimum.

Theorem 2. Considering one block in relay deployment problem, if α = 2, ne1 : ne2 : ne3 =

1 : 1 : 1, and ne1 + ne2 + ne3 = C, where C is a constant. The best location of merge vertex

must be the center of gravity of the triangle Ae1Ae2Ae3.

4.3.2

Small Scale Non-linear Programming (SSNLP)

In the first approach, although we can solve the problem in polynomial time if α = 2 and ne1 : ne2 : ne3 = 1 : 1 : 1, the performance may not improved more because the proper location

is only related to the traffic rate and the length of Steiner edge. What we really need is to find

a proper location of merge vertex which is involved with the traffic rate, the length of Steiner

edge and the ratio among ne1, ne2 and ne3. And it is suitable for any cases. As can be seen that

the reason why the complexity of Algorithm 1 is high because it considers the entire topology

at the same time. But, in the previous heuristic approach, we show that we can divide the whole

topology into blocks and solve them orderly. Therefore, we can modify Eq. (4.3) into

minimize 3 X k=1 λek( q (XA_ek − XM V)2+ (YA_ek − YM V)2 nek )α subject to ne1 + ne2 + ne3 = C XM V, YM V ∈ triangle(XA_ek, YA_ek), k = 1, 2, 3 (4.9) λej( q (XA_ej − XM V)2+ (YA_ej − YM V)2 nej )α ₌ λej+1( q (XA_ej+1 − XM V)2+ (YA_ej+1 − YM V)2 nej+1 )α, j = 1, 2 ,

where C is a constant, e1, e2, e3 represent the three edges connected with the merge vertex, XA_ekand YA_ek represent the locations of three vertices connected with the merge vertex, and

these three vertices can be sensor nodes, sink or the merge vertices of other blocks, and where

XM V and YM V are the location of merge vertex. Since we solve the relay node deployment locally, we can only calculate the ratio among ne1, ne2 and ne3 in constraint 1. Constraint 2

ensures the proper location of merge vertex must be inside the block. Constraint 3 can guarantee

all energy consumption of relay nodes on three Steiner edges of the block must be the same.

In Eq. (4.9), we only find the proper location of merge vertex, i.e., XM V and YM V, and the ratio among ne1, ne2 and ne3, so the number of variables of Eq. (4.9) is only 5. The

num-ber of variables is fixed and will not change due to different network topology. Although the

complexity of second method is little higher than the first one, the performance of it must be

better.

Now, let us summarize our heuristic approaches briefly. Before we start to execute the

heuristic approaches, we first check whether the given N relay nodes can connect the Steiner

tree or not by Eq. (4.1). If N relay nodes are enough to connect the Steiner tree, the heuristic

approaches can be executed. Otherwise, since the given N relay nodes is less than minimum

requirement, we can not find a solution for this problem. Then, after finding out all proper

locations of merge vertices, we will check whether the new network topology can be connected

by N relay nodes or not. If the new topology can be connected, it will be the candidate of

our final solution. Then we will repeat the above steps in T times. After that, we choose the

candidate with minimum energy consumption and connected network as our final solution. Our

Algorithm 2 Heuristic

Input: s0, . . . , sM, XS0, . . . , XSM, YS0, . . . , YSM,

β1, . . . , βM, N relay nodes, RminandRmax, method.

Output: G(V, E)

1. Construct a Steiner tree G(V, E) with heuristic approach.

2. Calculate the traffic rate λek based on the G(V, E), where ek∈ E

if CheckConnectivity(N, G(V, E)) then

Calculate ˆE.

for i:= 1 to T do

Partition the network topology into blocks.

switch (method)

case 1: Execute constrained heuristic

case 2: Execute small scale non-linear programming

end switch

Use Eq. (1) to calculate ne1, ne2, . . . and calculate ˆE

′ . if( ˆE′ < ˆE) and CheckConnectivity(N, G′ (V′ , E′ )) then ˆ E = ˆE′ ; G(V, E) = G′ (V′ , E′ ); end if end for

Use Eq. (1) to calculate nek for edge k, ek ∈ E

Deploy nek relay nodes on edge k evenly with communication range tek =

Lek

nek

.

else

The given N relay nodes can not connect the Steiner tree.

Chapter 5

Simulation

In this section, we will evaluate the performance of our algorithms by numerical analysis. Since

NLP can not guarantee to solve this problem in polynomial time, we just evaluate our two

heuristic approaches, i.e., CH and SSNLP. We have deployed5 to 25 sensor nodes by random

distribution in a field of5000m × 5000m with the sink node settled at the center (2500, 2500).

And the normalized data rate of each sensor node is randomly chosen from (0, 1]. For each

number of sensor node, we generated 10 topologies for analysis. In this network, there are

only250 relay nodes for us to deploy. We set the power attenuation of relay nodes α = 2, the

maximum communication range of relay nodes_Rmax = 500m, and minimum one Rmin = 10m. The above simulation environment is shown in Table 5.1.

For comparison, we implement two deployment approaches from [10][15], namely

Connectivity-only, denote as CO, and Traffic-aware, denote as TA. CO is chosen from a state-of-the-art scheme proposed in [15], which optimizes the system performance by considering

connectivity-Table 5.1: Simulation Environment

Sensor nodes 5, 10, 15, 20, 25

Data generating rate [0.1, 0.2, . . . , 1]

Maximum communication range of relay node 500m

Minimum communication range of relay node 10m

Deployment area 5000 ∗ 5000m2 Location of sink node (2500, 2500)

1 2 3 4 5 6 25 20 15 10 5

Normalized Network Lifetime

Number of Sensor Nodes CO

TA SSNLP CH

Figure 5.1: Normalized network lifetime.

only. In [15], there are multiple versions of scheme. Here, we use the1-connectivity version

and construct a Euclidean Steiner minimum tree [1] for the network topology, and CO serves

as a baseline. TA is chosen from [10] which is the first study accommodate the heterogeneous

traffic flows in relay node deployment for WSN.

We use network lifetime, defined as the lifetime of the first depleted relay node, as our

metrics for evaluation. The first depleted relay node can serve as a good indicator for the end

of the network lifetime because if the first relay node is out-of-battery, the data of some sensor

nodes can not be relayed to the sink node in1-connected WSN. In the following simulation

results, they are normalized by the base-line scheme CO. We use MATLAB [2] as our simulation

tools, and the interior point methods[5] to solve non-linear problems. Fig. 5.1 shows the results

of the network lifetime with different number of sensor nodes. When the number of sensor

nodes increases, the lifetime of both SSNLP and CH increases and is higher than lifetime of TA.

Since SSNLP has considered traffic rate, length of edge and ratio of relay nodes among three

150 160 170 180 190 200 25 20 15 10 5

Normalized Residual Energy

Number of Sensor Nodes TA

SSNLP CH

Figure 5.2: Normalized residual energy.

have also evaluated the residual energy among these approaches. Since CO can not guarantee

the energy consumption of each relay node is the same, we only evaluate the residual energy of

TA, SSNLP and CH when the lifetime of CO is finished. And the total residual energy can be

estimated as ˆ Eresidual = X ek∈E [ ˆE− λek( Lek nek )αT] · nek,

where T is the network lifetime of CO, and the result is shown in Fig. 5.2. When the number of

sensor increases, the normalized residual energy of TA, SSNLP and CH increases. And because

the energy consumption of SSNLP and CH is less than TA, the normalized residual energy of

them is higher than TA’s.

Fig. 5.3(a) and Fig. 5.3(b) show that the improvement from TA to SSNLP and CH,

respec-tively. We observe that SSNLP can always obtain8 ∼ 10% improvement with different number

of number of sensor nodes, and CH can obtain5 ∼ 7% improvement. Although the averages of

0 5 10 15 20 25 5 10 15 20 25 Improvement Percentage

Number of Sensor Nodes (TA-SSNLP)/TA (a) 0 5 10 15 20 25 5 10 15 20 25 Improvement Percentage

Number of Sensor Nodes (TA-CH)/TA

(b)

Figure 5.3: The performance improvement of CH and SSNLP with different numbers of sensor nodes.

0 5 10 15 20 25 1000 500 250 100 Improvement Percentage

Number of Relay Nodes (TA-SSNLP)/TA (a) 0 5 10 15 20 25 1000 500 250 100 Improvement Percentage

Number of Relay Nodes (TA-SSNLP)/TA

(b)

Figure 5.4: The performance improvement of CH and SSNLP with different numbers of relay nodes.

be23% and the minimum can be 5% in SSNLP. How many improvement percentages obtained

by SSNLP and CH is decided by the configuration of the network topology.

Next, we fix the network topology with only5 sensor nodes, and set the number of relay

nodes from 100 to 1000. Fig. 5.4(a) and Fig. 5.4(b) show that the improvement from TA to

SSNLP and CH, repsectively. We can observe that no matter how many relay nodes there

are, CH and SSNLP can also retain a pretty good improvement. SSNLP can maintain the

improvement percentage around 10 ∼ 13%, and CH can keep the improvement percentage

around6 ∼ 8%.

From the above results, we realize that only considering connectivity is the worst case for

relay node deployment, and only considering traffic volume based on Euclidian Steiner tree

also is not the best way. The results show us that we should construct a traffic-aware network

topology and the strategy of the relay node deployment must be according to the traffic volume

Chapter 6

Conclusions

In this thesis, we showed some problems about deploying relay nodes on Euclidian Steiner

tree. We proposed some algorithms to modify the existing Euclidian Steiner tree to adapt the

traffic volume in reality. Firstly, we proposed a weighted moving algorithm. In this algorithm,

we modeled the relay node deployment problem as a non-linear programming. In this

pro-gramming, we could guarantee that the network is connected and also accommodate the traffic

volume. But the non-linear programming could not ensure to solve the problem in polynomial

time, so we had proposed two heuristic approaches, which could finish in polynomial time,

to compare with the previous studies by MATLAB. According to the simulation results, we

observed that the performance of these two heuristic approaches was better than all previous

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Vita

Chi-Wai Kou

Contact Information

Department of Computer Science

National Chiao Tung University

1001 Ta Hsueh Road, Hsinchu, Taiwan 300

Email: [email protected], [email protected]

Education

M.S.: Network Engineering, National Chiao Tung University (2008.9∼ 2010.7)

B.S.: Computer Science, National Tsing Hua University (2004.9∼ 2008.6)

Awards

Publication Lists

Journals

1. L. W. Yeh and C. Y. Lu and C. W. Kou and Y. C. Tseng and C. W. Yi, “Autonomous

Light Control by Wireless Sensor and Actuator Networks”, IEEE Sensors Journal, To