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Electronic Theses, Treatises and Dissertations The Graduate School

2016

Energy Efficient Routing Algorithms inWireless Sensor NetworksYizhou Dong

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FLORIDA STATE UNIVERSITY

COLLEGE OF ENGINEERING

ENERGY EFFICIENT ROUTING ALGORITHMS

IN WIRELESS SENSOR NETWORKS

By

YIZHOU DONG

A Dissertation submitted to theDepartment of Electrical and Computer Engineering

in partial fulfillment of therequirements for the degree of

Doctor of Philosophy

2016

Copyright c⃝ 2016 Yizhou Dong. All Rights Reserved.

Yizhou Dong defended this dissertation on November 18, 2016.The members of the supervisory committee were:

Ming Yu

Professor Directing Dissertation

Zhenghao Zhang

University Representative

Bruce Harvey

Committee Member

Petru Andrei

Committee Member

The Graduate School has verified and approved the above-named committee members, and certifiesthat the dissertation has been approved in accordance with university requirements.

ii

TABLE OF CONTENTS

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

1 Introduction 1

1.1 Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Energy-efficiency and lifetime of WSN . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Energy Harvesting Wireless Sensor Networks . . . . . . . . . . . . . . . . . . 3

1.2 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Problem Statement and System Modeling of Application-Specific Routing 10

2.1 Network modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 An example of our model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 Theoretical analysis of the optimization problem . . . . . . . . . . . . . . . . . . . . 132.5 Proposed Flow-Lifetime Routing (FLR) Algorithm . . . . . . . . . . . . . . . . . . . 142.6 Simulation Results of Flow-lifetime Routing . . . . . . . . . . . . . . . . . . . . . . . 16

3 Prediction-based Energy-efficient Routing Design for EHWSN 23

3.1 System Models for EHWSN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1.1 Network model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1.2 Energy harvesting model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1.3 Prediction model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 Problem Statement and Optimization Modeling . . . . . . . . . . . . . . . . . . . . . 263.2.1 A general modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.2 A comprehensive modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.3 Theoretical analysis of the optimization problem . . . . . . . . . . . . . . . . 31

3.3 A New Energy-Efficient Routing Algorithm . . . . . . . . . . . . . . . . . . . . . . . 343.3.1 Prediction-based Energy-Efficient Routing (PEER) Algorithm . . . . . . . . . 343.3.2 Theoretical analysis on time complexity . . . . . . . . . . . . . . . . . . . . . 34

3.4 Simulation Results of PEER algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4 Conclusion and Future Work 50

4.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Biographical Sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

iii

LIST OF FIGURES

1.1 Energy sources of EHWSN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Demonstration of flow lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Distribution of network lifetime by using flow lifetime method . . . . . . . . . . . . . 18

2.3 Lifetime Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 Energy Utilization Rate Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5 Lifetime by varying flow rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.6 Lifetime by varying node numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.7 Lifetime by varying update interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1 flow chart of PEER algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2 Energy percentage by different flow rates . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3 Harvested energy by different flow rates . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.4 Network lifetime by different flow rates . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.5 Network throughput by different flow rate . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.6 Energy percentage by different network coverage . . . . . . . . . . . . . . . . . . . . . 42

3.7 Harvested energy by different network coverage . . . . . . . . . . . . . . . . . . . . . . 43

3.8 Network lifetime by different network coverage . . . . . . . . . . . . . . . . . . . . . . 44

3.9 Network throughput by different network coverage . . . . . . . . . . . . . . . . . . . . 45

3.10 Energy percentage by different updating intervals . . . . . . . . . . . . . . . . . . . . 46

3.11 Harvested energy by different updating intervals . . . . . . . . . . . . . . . . . . . . . 47

3.12 Network lifetime by different updating interval . . . . . . . . . . . . . . . . . . . . . . 48

3.13 Network throughput by different updating interval . . . . . . . . . . . . . . . . . . . . 49

iv

LIST OF SYMBOLS

G(N,L) directed graphn node numberN set of sensor nodes in network G(N,L)L set of all links in network G(N,L)P (i, j) route path between node i and jEi(0) initial energy of the node iER

i (t) residual energy of node i at time tetij energy consumption in transmitting a unit of data

erji energy consumption in receiving a unit of data

egi energy consumption in sensing and collecting a unit of data at node ifij assigned flow in data rate (bits/sec)Fij the amount of flow going through (i, j)Tlij the lifetime of link lijTp the lifetime of path pTFij

the lifetime flow fijTsys the network lifetimecost(i,j) the cost function of link lijB route update intervalEH

i (t) the energy harvesting rate of node i at time tλi(t) data generation rate of node i at time t in EHWSNxi,j(t) data rate of transmission from node i to node j at time tBi(t) indicate the data rate derived from the buffered data in node i at time tXt current observation in the prediction modelsXt−1 previously smoothed value in the prediction modelsYt+1 prediction value for time t+ 1 in prediction modelsCi(t) consumed energy for node i at time tEH harvested energyV (T ) volume of collected data at time THi(t+ 1) predicted energy by using prediction modelFP (Hi(t) abstract prediction model for energy harvestingα(t) the factor to dynamically adjust the energy spent on receivingβ(t) the factor to dynamically adjust the energy spent on transmissionγ(t) the factor to dynamically adjust the energy spent on generation

v

LIST OF ABBREVIATIONS

WSN WirelessSensorNetworksEHWSN EnergyHarvestingWirelessSensorNetworksDTN DelayTolerantNetworkAODV AdhocOnDemandDistanceV ectorEDM EnergyDissipationModuleEHM EnergyHarvestingModuleESM EnergyStorageModuleECM EnergyConsumptionModuleSMA SimpleMovingAverageEWMA ExponentialWeightedMovingAverageWCMA WeatherConditionedMovingAverageSD SourceDestinationLP LinearProgrammingPEER Prediction− basedEnergy − EfficientRoutingPEERA Prediction− basedEnergy − EfficientRoutingAlgorithmFLR FlowLifetimeRoutingNLR NodeLifetimeRoutingFLRA FlowLifetimeRoutingAlgorithmNP − hard Non− deterministicPolynomial − timehard

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ABSTRACT

A wireless sensor network (WSN) consists of a large number of low-cost sensors that can com-

municate to each other for specific applications. Sensor nodes are spatially distributed in a large

region and operated in an autonomous manner. Each sensor node in the network is battery-limited

and irreplaceable for most applications. Compared to the existing ad-hoc networks, significant

problems have been raised. How to efficiently consume the energy to obtain a long lifetime of the

network? How to design routing algorithms to adaptively accommodate the change in energy?

How to reconsider the energy-efficiency issue if the renewable energy devices are involved? How

to mathematically model these problems and validate solutions by simulations and experiments?

We investigate these questions and present our models, designs, algorithms, and results in the

dissertation.

Research on WSNs is driven by specific applications but the applications of WSN have been

widely divergent in recent years. Environmental monitoring and surveillance is a major application,

in which the WSN is implemented to monitor a large geographic area that is usually unexplored or

potentially dangerous area, such as forests, rivers, and desert. It is especially challenging when the

infrastructure of the environment is unknown. The sensors for this application are irreplaceable and

thus the battery life becomes crucially important. Military applications are designed to support

communications among soldiers, military vehicles, and headquarters. For example, in a battlefield,

the coordination among a groups of soldiers has to be well-established in any complicated situation.

An interesting paradigm is animal monitoring, in which small sensors are placed on animals to

surveil their habitat. The sensors carried by animals form a mobile ad hoc network to collect

and transmit data. The difficulties of this application are that the sensors must be lightweight

enough for animals while the topology of the network is always changing. Also, there are other

emerging applications like body health monitoring, disaster recovery, and underwater robot-assisted

exploration.

In this work, we have two major related research topics. One is the energy-efficient design and

optimization of the application-specific routing protocols to maximize the network lifetime of a

WSN. Another is the optimization and design of the routing protocol for energy harvesting wireless

sensor network (EHWSN) by predicting the condition of energy harvesting in the near future.

vii

For the first topic, the key issue is how to conserve energy to maintain the network connectivity

as long as possible, or maximize the lifetime of the network. One common solution is to design a

routing algorithm that can cope with the changes of network conditions and dynamically adjust

the routing strategy or switch the operation modes to save energy. Many routing metrics have to

be considered including transmission distance, residual energy, link capacity, etc. Energy-efficient

routing protocols have been well investigated with the goal of maximizing the network lifetime,

which is usually defined as the time when the first node dies. Once a node becomes unavailable

due to energy depletion, its data transmissions in the network are assumed to fail. In our work,

we consider the network remains alive as long as the energy is enough to maintain the flows of the

application traffic, which is more reasonable since the network can still function even without those

”dead” nodes. Instead of universally balancing the energy consumption over the entire network,

we aim at locally optimizing the energy-efficiency of the target nodes on the application flows.

Essentially, it’s an energy trade-off between the target nodes and other irrelevant nodes, in which

he former will expend more energy than the latter on the application flows for energy-efficiency.

Therefore, the routing algorithm can be designed to save more energy on routes of the specific

traffic. We present a novel application-specific and energy-efficient routing algorithm to maximize

the lifetime of the application flows in WSNs. Firstly, we formulate the routing problem as a linear

programming problem, which can be converted to a max-min fairness problem. Secondly, the

lifetime of a flow is evaluated in terms of the link metrics including residual energy, transmission

rate, and link distance. Thirdly, a heuristic routing algorithm is proposed to compute the best

route that minimizes the cost of application flows. Simulation results have shown that our routing

algorithm prolong the lifetime of flows around 10%.

For the second topic, compared to a conventional WSN, which is strictly limited by its bat-

tery supply of the sensor nodes, EHWSN is an environmentally powered network that brings new

techniques and challenges to the energy-efficiency topic. By harvesting the ambient or renewable

energy feasible to WSN, a tremendous breakthrough can be made to improve the energy-efficiency

and the network lifetime. Environment usually has a large variety of the energy sources, such as

solar, wind, mechanical, thermal, and biochemical sources. Some major issues have been raised in

order to take advantage of energy harvesting. For instance, how to schedule and allocate the energy

consumption by predicting the energy availability? How to jointly consider the energy-efficiency

viii

and network lifetime? How to design a prediction model for energy harvesting in order to achieve

a better performance?

We find a critical issue in current routing algorithms for EHWSN, in which the calculated

routes are frequently alternating because of the uncertainty of the energy availability in the near

future. Without knowing the future harvesting condition, the current algorithms calculate the

most energy-efficient routes based on the past and current condition. The uncertainty may lead

to energy waste and extra network overheads. In our work, we propose to predict the energy

harvesting condition in the near future and estimate whether the current optimal routes can be

maintained by the harvested energy in a certain time threshold. If yes, we temporarily restrict

the data transmission and receiving to reduce the energy cost by using parameters, which are

determined by the availability and intensity of the future harvesting. Comprehensive factors are

considered to predict the energy condition in near future and help make routing decisions including

residual energy, harvest energy, and energy consumption.

We first give an example to illustrate the motivation of our energy prediction-based routing

problem. Second, we formulate the problem as a linear optimization problem and convex optimiza-

tion problem with analytical proof depending on prediction models. Third, we propose a heuristic

routing algorithm to maximize the volume of collected data from the network. Fourth, the routing

algorithm is implemented and verified by Matlab and OMNET++ simulation. The results indi-

cate that the proposed algorithm can largely improve the energy-efficiency and reduce the network

overheads.

In summary, we propose to solve the energy-efficiency issues in both application-specific WSN

and EHWSN. For application-specific WSN, the network lifetime is extended by our routing al-

gorithm, which aims at minimizing the energy consumption of the target nodes rather than the

entire network nodes. The results shows a 10% improvement on network lifetime. For EHWSN,

the network throughput is increased by a predictable energy-efficient routing algorithm, which con-

sidering the harvested energy in the near future. The results demonstrate that the both network

throughput and lifetime are increased.

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CHAPTER 1

INTRODUCTION

1.1 Wireless Sensor Networks

1.1.1 Energy-efficiency and lifetime of WSN

A wireless sensor networks (WSN) consists of a large numbers of energy-limited sensor nodes

that can communicate to each other for specific applications. The sensor nodes are spatially scat-

tered in a large region and programmed to operate in distributed manner. Each node in the network

is battery limited and irreplaceable for most applications. For such an ad hoc network, the routing

algorithm is critical for the energy-efficient delivery of the packets from sources to destinations.

The key issue is how to minimize the energy consumption in order to maximize the lifetime of the

network. The sensor nodes are distributed in a dynamic topology. The routing algorithm needs

to be flexible to accommodate the energy consumption requirements. Also, it is required to cope

with the changes of network conditions, including transmission distance, residual energy, and link

capacity, and dynamically adjust the routing strategy or switch the operation modes to save energy.

Research on WSN is driven by specific applications. In recent years, the applications of WSN

have been widely divergent. First, military applications are designed to support communications

among soldiers, military vehicles, and headquarters. In a battlefield, the coordination among groups

of soldiers has to be well-established in any complicated situation. Second, environmental monitor-

ing is a major application. It is especially challenging since the infrastructure of the environment is

unknown, in which the WSN is implemented to monitor a large geographic area, such as a forest or

glacier, which is usually unexplored or potentially dangerous. The sensors for this application are

irreplaceable and thus the battery life becomes crucially important. Third, an interesting paradigm

is animal monitoring, in which small sensors are placed on animals to monitor their habitat. The

sensors carried by animals form a mobile ad hoc network to collect and transmit data. The design

of the WSN bears numerous difficulties not only the sensors must be lightweight enough for animals

to carry but also the network topology is changing. Fourth, there are other emerging applications

like body health monitoring, underwater robot-assisted exploration, and disaster recovery.

1

The characteristics and requirements of routing schemes in WSN are distinct from the existing

networks. First, longevity is the most important requirement, which requires the energy-efficient

routing schemes that can extend the lifetime of networks. Second, the mobility of the sensor

nodes determines the design of the routing algorithms to a large extent. The sensor nodes may

be fixed or mobile depending on the specific application. The node mobility needs to be taken

into consideration in the design of routing schemes. Third, the scalability is an inherent feature

of WSN, in which the schemes have to be scalable for large size networks. Topology of the WSN

can be unconstrained and irregular. The routing schemes need to be applicable to various network

topologies. Fourth, the flexibility requirement is that the routing algorithm can adapt to the

changes in the network, such as node failure, energy change, and nodes movement. Some other

characteristics may become also critical for different network applications.

Recently, network lifetime becomes the main performance measurement to evaluate the energy

efficiency of a WSN. Among various definitions, one becomes popular and well-investigated, that is,

the time when the first node dies. However, from an application aspect, the application may be still

feasible to transmit data even if some nodes died. For application-specific flows, a routing algorithm

can be designed to avoid those dead nodes or ignore the energy level of irrelevant nodes, thus prolong

the lifetime of the application. For instance, in a battlefield, soldiers must be warned immediately

if a nearby bomb has been detected. The soldier who noticed the bomb first must send a message

to his commander or captain, who is responsible to make decisions. In this emergent situation,

the message may failed to be delivered to the commander because too many environmental factors

may influence the transmission. Consequently, the commander may miss the moment to make a

decision and prompt an unimaginable consequence. In this scenario, each soldier can be considered

as a sensor node in the network and the commander is the destination. To deal with the scenario,

most existing energy-efficient routing algorithms may fail because the algorithms are designed to

balance the energy level globally, which means all packets in the network are equally considered.

If the routing algorithm fail to deliver this emergent packet, the network can be regarded as dead.

A better solution is that the routing algorithm is designed to merely optimize the flow from the

soldier to the commander, regardless of energy level of irrelevant nodes. This solution motivates

our proposed routing algorithm that locally optimizes the energy-efficiency on target nodes rather

than globally balances the energy consumption over the entire network.

2

1.1.2 Energy Harvesting Wireless Sensor Networks

For a conventional WSN, the limitation on energy capacity of the network nodes is a determi-

nant factor on the lifetime of the networks since the nodes are usually batter-powered and difficult

to be replaced or replenished. A lot of works have been proposed to improve the energy-efficiency

or lifetime by modifying the routing algorithm considering the energy status. EHWSN is an en-

vironmentally powered network and brings new techniques and challenges to WSN. By harvesting

ambient or renewable energy to WSN, a tremendous breakthrough can be made to improve the

energy-efficiency and the network lifetime. Environment provides a large variety of the energy

sources, such as solar, wind, mechanical, thermal, and biochemical sources. However, the availabil-

ity of the sources are uncertain and the energy supply are not stable. For instance, solar-powered

nodes’ energy harvesting depends on diurnal cycle in solar energy and is also affected by weather

conditions, monthly trends, and seasonal patterns. Even, physically co-located nodes can expe-

rience a large difference on harvesting rates if the orientation and position of the PV panels are

different.

As the emerging of EHWSN, new problems and challenges have been noticed and introduced in

recent researches. Several issues have been raised in order to take advantage of energy harvesting

from different aspects. First, the problem that how to schedule and allocate the energy consumption

by predicting the energy availability becomes a critical issue. Note that the issue concentrates on

the energy allocation and scheduling for a single node, not the entire network. Second, routing

algorithms have been investigated extensively to jointly consider the energy-efficiency and network

lifetime. Currently, most of the proposed online algorithms can adaptively change routing paths

according to the energy levels of the network nodes. Also, the network overhead is a crucial

factor to evaluate the performance of the routing algorithms. Third, the prediction model for

energy harvesting techniques has also been well investigated. The common prediction models are

regression analysis, simple moving average, exponential smoothing, double exponential smoothing,

and the ARIMA model. The accuracy and efficiency of the models largely determine how efficient

we can take utilize the harvested energy. The surrounding environment provides us a great variety of

energy sources that can be harvested by using wireless sensor networks. The various sources provide

necessary energy in different amount and formats, including solar, wind, piezoelectricity, thermal,

and wireless. Solar is the most common source for energy harvesting because of its accessibility

3

Forms of Energy

Mechanical Photovoltaic Hybrid

Acoustic Noise

Biochemical

WindThermal

Wireless

ELectrostatic Piezoelectric Solar

Electromagnetic

Inductive

Coupling

RF Energy

Pyroelectric Thermoelectric

Figure 1.1: Energy sources of EHWSN

and reliability. Unlike other energy sources, solar energy is accessible everywhere on earth without

any limitations on location and environment. It provides a decent amount of energy in a relatively

reliable manner. Photovoltaic is a well-developed technology that transforms the photons to DC

current in semiconductors. Wind energy is one of the remarkable sources in large-scale among

various types of renewable energy sources. Wind is a free and clean energy without any pollution

emissions. In many countries like German, Spain, and Denmark, wind energy provides a significant

amount of electricity. However, due to its intermittent behavior, wind energy is not a primary

energy source because it may cause instability issues to the power system. Piezoelectric material

can result external electrical field under mechanical pressure and piezoelectricity is very useful in

many applications that require high voltage. Wireless RF energy can be harvested from ambient

facilities and one advantage of the RF is that the amount of transferred energy can be controlled.

The energy sources of EHWSN are showed in Fig. 1.1.

To design an energy-efficient routing algorithm, a critical issue has been addressed extensively

that the energy of the network nodes consumed unevenly, which may lead to rapid changing of

routing paths. In the latest work for EHWSN routing, the instantaneous status of energy harvesting,

energy consumption, and instant energy level are all considered and the design of the routing

4

algorithm. The common way to handle the energy harvesting condition is to import empirical data

with a probability model to build a harvesting profile. Then, the instantaneous data of energy

harvesting is selected to serve as a factor in optimization model and routing algorithm. In our

point of view, merely considering the instantaneous status of the energy conditions (consumption,

harvesting, and instant level) has two major deficiencies. One is the routing decision that may

not be optimal in terms of energy-efficiency. The reason is that the routing path calculated based

on the harvesting profile is not always accurate. Another one is the network overhead that may

be extremely large. Since the future harvesting condition is unknown, the routing path calculated

based on instant conditions is very different from the path calculated in the next time slot. To our

best knowledge, no research has considered the future energy conditions in the design of the routing

algorithms. Thus, the motivation of our work is to achieve higher energy-efficiency by designing a

routing algorithm by considering both the current and future energy conditions.

1.2 State of the Art

In this section, we categorize the related work on the energy-efficiency of the WSN and EHWSN.

For each category, major contributions and related issues are summarized.

For WSN, the network lifetime is a major problem and extensive research works are accom-

plished [67] [43] [47] [19] [18] [42] [60] [76] [37] [75] [61] [71] [62] [45] [31] [29] [57] [36] [20] [21] [26].

The network lifetime problem is a classical problem in the research of WSN [25].

The problem of maximizing network lifetime was initially formulated as a linear optimization

(LP) problem with a mathematical definition for node lifetime [3]. A flow augmentation routing

algorithm was proposed to solve the problem. Also a new cost function of the link was designed for

the proposed algorithm. The performance of the algorithm is compared with other algorithms and

found significant improvement. The optimal values of the lifetime found in numerical calculation

and network simulation are very close. However, for the cost function, some parameters do not have

physically meaning and cannot be implemented in real-world experiments. A tree-based topology

is proposed for data collection that aims at maximizing the lifetime of the network [20]. A novel

algorithm (e.g., RaSMaLai) was proposed to balance the traffic loads with a low time complexity.

Also, the lifetime maximization problem is proved to be NP-complete. To avoid the energy hole

problem, a cooperative transmission method was introduced to increase the lifetime of networks [23].

5

Whenever the next-hop node along the primary route has a lower residual energy level than the

existing one, the proposed REACT protocol triggers the range extension. The results of network

lifetime and residual energy are presented and compared. The cooperative method can sometimes

maintain the primary route, but the energy consumption is even larger than the method without

cooperation from a long-term perspective. A lifetime vector was defined as the vector of all sensors

lifetimes sorted in ascending order [72]. The motivation of the lifetime vector is reasonable since

the network remains operational even if a few nodes are out of operation. Both centralized and

distributed algorithm were proposed to optimize the lifetime vector. Two subgradient algorithms

were proposed to solve a dual problem in order to compute optimal routes in a fully distributed

manner [59]. The proposed algorithms try to balance the energy consumption for all nodes and

minimize the transmission power for each connection simultaneously. However, many factors and

parameters need to be considered in the cost function. An method was proposed to address both

the network lifetime and the sensing spatial coverage [25]. It determines network lifetime by the

available node numbers and sensing range. Afterwards, a new criterion was proposed to improve the

flow augmentation algorithm with a better lifetime. However, the proposed criterion only depends

on the numbers and sensing range of available nodes, which may not accurate and practical for

real-world applications. Applications in energy-efficient WSNs have brought in new requirements in

scenarios like disaster recovery [77] and surveillance systems [32]. In delay-tolerant network (DTN),

a method was proposed in to maximize the lifetime while a mobile sink is involved [69].

In [7], a method is designed to jointly consider the source sampling rate and energy consumption

rate to maximize the average flow rate. A stochastic model has been proposed to estimate the

likelihood that the data queue or battery energy is no longer available by using the theory of large

deviations of appropriate Markov Chains. One assumption is that the average rate must be equal.

In [14], the authors proposed a routing protocol AODV-EHA, which not only inherits the

advantage of AODV in dealing with the ad hoc manner, but also make use of the harvested energy

to enhance the performance of the routing protocol. In AODV-EHA, the spatial distance and hop-

count are replaced by energy distance and energy count, which are weighted metrics combining the

energy levels and routing metrics. The performance evaluation has been considered in two aspects:

average transmissions cost and average hop-count of a route. The simulation results indicate the

performance improvement by comparing it to other routing protocols AODV and DEHAR.

6

In [50], a predictive energy efficient routing algorithm is designed and implemented based on

AODV and Dijkstras algorithm. The algorithm is simulated in JAVA and the result shows that

the energy depletion rate is different by using the proposed algorithm.

In [77], the rate allocation problem is formulated as a max-min fairness problem in energy

harvesting networks. The objective of the problem is the rate allocation in terms of both nodes

and time slots. Unlike the previous works, this paper focuses on multihop topologies and different

routing methods (e.g., unsplittable routing and fractional routing). It has been shown that the

optimization problem is a max-min fairness problem and proved to be NP-hard. For different

routing methods, the time complexity is evaluated.

In [4], the finite horizon throughput problem is formulated as a convex optimization problem.

A scheme is proposed to compute a shortest-path in terms of the cumulative energy of a single

node. Then authors relax the assumption that the energy harvesting profile is known and propose

an online algorithm. A distributed heuristic energy allocation scheme (e.g., NetOnline) is proposed

and demonstrated via simulations. This paper concerns the finite-horizon problem instead of the

infinite horizon problem since the inefficiencies cannot be made to vanish infinitesimally small

values. The proposed scheme tries to optimize the energy allocation and consumption for a single

node in a shortest-path manner. It doesnt really focuses on routing algorithm.

For EHWSN, a lot of research works are presented recently in many aspects, including routing

algorithms in EHWSN, energy harvesting system and modules, prediction models for energy har-

vesting, and theoretically analysis for the optimization problem [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

[12] [13] [14] [15] [16] [17] [22] [23] [24] [25] [27] [28] [30] [32] [33] [34] [35] [38] [39] [40] [41] [44] [46]

[48] [49] [50] [51] [52] [53] [54] [55] [56] [58] [42] [43] [44] [63] [65] [66] [64] [68] [69] [70] [73] [74] [77].

In [39], an online multi-commodity routing algorithm is proposed for EHWSN. The authors

formulate the routing problem as an LP problem and try to balance two routing objectives of

max-total and max-min energy to prolong the network lifetime. The objective function of the opti-

mization problem is a linear combination of max-total and max-min energy levels. In simulations,

the authors use NS-2 to compare the max-total, max-min, and the proposed MC-OMLU to evaluate

the energy level, and it shows the MC-OMLU improve the performance on energy-effiency.

In [34], authors first summarize the modules for a typical energy harvesting system including en-

ergy dissipation module (EDM), energy harvesting module (EHM), energy storage module (ESM),

7

and energy conversion modules (ECM). Second, a new concept of effective energy dissipation is

introduced to practically evaluate the dissipated energy. Third, three prediction models have been

formulated to predict the harvesting condition in a short period of time. Fourth, an algorithm (e.g.,

MAP-DVFS that evolves from AS-DVFS) is proposed to enhance the accuracy of the prediction by

comparing the miss rate. Also, the performance of different prediction models has been evaluated

including RA, MA, and ES.

In [2], a novel prediction model named Pro-Energy (e.g., PROfile energy) is proposed to provide

accurate estimation of future energy availability. The predictions for short and medium-term are

considered differently. A module named profile analyzer determines the selection of similar profiles.

The authors traced the real-time solar and wind data by interfacing TelosB nodes. Compared

to EWMA and WCMA, it has been shown that the prediction accuracy of the proposed model

outperforms the existing algorithms around 60%.

In [16], a solar energy prediction approach (e.g, SEPAD) was proposed by using additive de-

composition that considers both seasonal and daily trends. The total estimated energy contains

three parts: cyclic solar energy estimation, estimated energy due to seasonal variation, and energy

estimation to incorporate recent solar energy trend. Results have been shown that the proposed

SEPAD is better than other approaches (EWMA, AEM, and WCMA) in terms of absolute error.

1.3 Contributions

In the first part, we aim at prolonging the lifetime of a network flow between a specific source-

destination (SD) pair by redefining the network lifetime as the time when the first flow dies.

Moreover, we propose an energy-efficient routing scheme to maximize the network lifetime. The

major contributions are:

• Define the network lifetime as the time when the first application flow dies. The definition is

based on the flow lifetime, instead of the node lifetime.

• Design a new link cost function in terms of link parameters, i.e., transmission rate, distance,

and energy level.

• Formulate the problem as an LP problem that can be converted to a max-min fairness prob-

lem.

• Propose a heuristic routing algorithm to solve the LP problem.

8

In summary, the proposed energy-efficient routing scheme improve the network lifetime around

10%, which is a notable improvement comparing to the existing works.

In the second part, we aim at achieving high energy-efficiency for the EHWSN by formulating

an optimization problem. We propose a routing algorithm to consider both the current and future

harvesting condition. The major contributions are:

• Propose a model for the problem and formulate it as an optimization problem, which is a

linear programming problem.

• Design a heuristic algorithm, prediction-based energy-efficient routing algorithm, to find a

solution of the optimization problem to increase the network throughput while maximize the

network lifetime.

• Simulate the heuristic algorithm on Matlab for numerical analysis and simulate a distributed

routing algorithm on a packet-level simulation tool.

• Validate the solution methods by extensive simulation results.

In summary, the proposed routing algorithm improve the energy-efficiency of the EHWSN

significantly, while the average network lifetime increased by 29.8% and the average net-

work throughput increased by 31.6%. Also, network overhead for routing updates is reduced

considerably.

9

CHAPTER 2

PROBLEM STATEMENT AND SYSTEM

MODELING OF APPLICATION-SPECIFIC

ROUTING

2.1 Network modeling

We consider a WSN network with a flat topology. All nodes in the network are capable of

generating (sensing) data, transmitting data, and receiving data. The network can be described as

a directed graph G(N,L), where N is the set of nodes (vertices) representing the battery-powered

sensor nodes, denoted by N = {1, 2, ..., n}; and L the set of all links (edges), denoted by L = {lij}.

A link between two nodes can be formed successfully only if the two nodes are within the radio

range of each other and able to communicate directly. We assume that the transmission range is

fixed and not adjustable by power control. Between a source node S and destination node D pair,

there are many possible paths, and the set of paths is denoted as P (i, j).

Let Ei(0) be the initial energy of the node i, also known as the battery capacity of node i.

We denote the residual energy of node i at time t by ERi (t), i.e., the remaining energy of the

node i after some energy is expended on transmission and processing. Except for the source and

destination nodes along a path, the intermediate nodes work as transceivers that can transmit and

receive at the same time. The energy consumption in transmitting and receiving a unit of data can

be denoted by etij and erji, respectively. Also, to sense and collect a unit of data at node i costs

egi energy. The energy consumption of transmission side is calculated as: etij = eT + ξamp · d4ij ,

and the energy consumption of receiving side is erij = eR , where eT = 50nJ/bit, eR = 150nJ/bit,

ξamp = 100pJ/bit/m4.

We only consider the energy spent on transmission and receiving. The energy consumption on

computing, processing, and other operations are much smaller and thus can be ignored.

In this work, we use a multi-commodity case as an example to investigate the lifetime. Flows

(commodity) are assigned to a network according to the application requirements on the network.

Generally, one path or multiple paths can be selected to transmit the data flow at the same time.

10

7 8 6

4

3 2

1 5

SRC DST

f1

f2

f3

p1

p2

p3

Figure 2.1: Demonstration of flow lifetime

We assume the flow is unsplittable, i.e., one path for one flow. For multiple paths, the modeling

and algorithm are more complicated.

We assume that for an SD pair (i, j), the assigned flow is fij in data rate (bits/sec). Over a

period of time T , the amount of flow going through (i, j) is Fij in bits, i.e., Fij = Tfij . Similarly,

the data generated by a node i is denoted by Gi in amount with a data rate of gi.

2.2 An example of our model

We use a simple example to show the modeling of the flow lifetime and motivation of the

energy-efficient routing problem.

In a typical wireless sensor network, we assume that there are n possible paths between the

source node (SRC) and destination node (DST), i.e., p1, p2, ..., and pn, with flow f1, f2, ..., and fn,

respectively. As shown in the Fig. 2.1, for the SD pair between nodes 1 and 5, there are 3 paths,

denoted by p1, p2, and p3, respectively.

We assume that the lifetime of all the links are given. For link lifetime, we consider a link is

no longer available if one of the two nodes of the link is not available for data transmission. To be

simple, the link lifetime can be considered that it is determined by the node lifetime of the nodes on

the link. Compared to the link lifetime, the node lifetime is determined by the initial energy level

and energy consumption rate of the node itself. The rate of energy consumption is time varying

depends on the transmission range, data rate, operation mode, and many other factors.

11

Compared to the existing work, we design the model based on link lifetime instead of node

lifetime. For a link between two nodes, it’s possible that one node remains a lot of energy while the

other nodes almost runs out of energy, which is unsatisfactory in terms of energy efficiency. Thus,

we think that the link lifetime is more reasonable and effective than the node lifetime for WSN.

For example, for the 3 links from node 1, we have Tl12 = 10, Tl14 = 20, and Tl16 = 30,

respectively. The lifetime of the other links is Tlij = 40, for i, j ∈ {2, 3, ..., 8}. On one hand, in

terms of the path lifetime, we have Tp1 = min{Tl12 , Tl23 , Tl35} = 10. Similarly, we have Tp2 = 20 and

Tp3 = 30 for path p2 and p3, respectively. Therefore, the flow lifetime is TF15= max{Tp1 , Tp2 , Tp3} =

30. On the other hand, the network lifetime, Tsys = min{Tlij} = 10, for i, j ∈ N , as defined in [3].

Clearly, the flow lifetime is different from the existing lifetime. We propose to use the flow lifetime

here to demonstrate our system model.

2.3 Problem formulation

In this work, we present the routing problem that aims at maximizing the lifetime of a specific

flow within a network, so that the application carried over the flow can be sustained as long as

possible. Our focus is the flow lifetime routing (FLR) instead of the node lifetime routing (NLR),

which is a common method for routing algorithms in WSN.

Let’s denote by Tlij the lifetime of link lij and Tp the lifetime of path p = (n1, n2, ..., nm)

consisting of node ni, i = (1, 2, ..., n). A path becomes unavailable if any link along the path runs

out of battery. Therefore, we have:

Tp = minTlk , for lk ∈ Lp, (2.1)

where the path lifetime is selected as the minimum lifetime of all the links along the path.

Now we define the lifetime of a flow, denoted by Tf . For an SD pair, a flow may go through

many possible paths between the SD nodes. For example, for fSD, the set of path between the SD

nodes can be denoted by PSD = {p1, p2, ..., pn}, or PSD = {pk|k = 1, 2, ..., n}. In order to maximize

the flow lifetime, the path with the longest lifetime is selected as the flow lifetime. Therefore, we

have:

Tf = maxTpk , for pk ∈ PSD, (2.2)

12

It can be seen that finding the lifetime of a flow is a classical max-min fairness problem, as

shown in Eqns. (2.1) and (2.2).

Let’s denote by Sout(i) and Sin(i) the sets of outgoing and incoming neighboring nodes, respec-

tively; and SD the set of destination nodes. Now we formulate the problem as follows.

maxp∈P

minl∈p

Tl, (2.3)

Subject to:

Fij > 0, ∀(i, j) ∈ L, (2.4)

∑

k∈Sin(i)

Fki + Tlgi =∑

j∈Sout(i)

Fij , ∀i ∈ N −D, (2.5)

∑

k∈Sin(i)

Fki =∑

j∈Sout(i)

Fij , ∀i ∈ D, (2.6)

∑

k∈Sin(i)

eRki∑

F

Fki +∑

j∈Sout(i)

eTij∑

F

Fij ≤ Eoi, (2.7)

The constraint Eqn.(3.12) states that the amount of flow through an SD pair should be larger

than zero. Equations (3.13) and (3.14) are general flow conservation regarding the data generation

for each node. Equation (3.15) indicates that the energy spent on transmitting and receiving cannot

exceed the initial energy.

2.4 Theoretical analysis of the optimization problem

The optimization problem (3.16) is a max-min fairness problem. For a given time-invariant

unsplittable routing path pk, the problem of determining the max-min fair assignment of the rates

Fij is NP-hard.

Data rate assignment in unsplittable routing was studied extensively. The max-min fairness

problem studied in [3][7] was reduced to the problem for eTij = 0, seRki > 0, and T = 1. For T = 1,

it indicates that the routing path is time-invariant and determined at beginning. Moreover, the

rates are constant over time in [3][7]. In [20], the authors considered a more general case, where

the rates are time-variant, fairness is required over both network nodes and time slots. The routing

can be time-variant and given in a form of an unsplittable routing or a routing tree. Determining

13

a max-min fair unsplittable routing as studied in [18] is a special case of our proposed problem for

eTij = 0, eRki > 0, and T = 1. The NP-hardness results from [18] imply the NP-hardness of our

proposed optimization problem.

Thus, we believe that the optimization problem is an NP-hard problem. It’s difficult to find an

accurate solution for the NP-hard problem, and we propose a heuristic routing algorithm in the

next chapter.

2.5 Proposed Flow-Lifetime Routing (FLR) Algorithm

In this section, we propose a cost function that mainly depends on link characteristics in order

to prolong the flow lifetime. We also describe a heuristic algorithm to find the lifetime of a network

with the cost function.

We emphasize that the cost function mainly focuses on the metrics of a link. For link lij , the

metrics are the link distance, flow rate along the link, and energy level of the link. A routing

algorithm needs to update its optimal route frequently based on the cost function consisting of a

link weight and assigned link rate. The cost function is.

cost(i,j) = (Eoi

Eri· eTij +

Eoi

Eri· eRij) ·Rij , (2.8)

where Eoi/Eri is a factor showing the level of the residual energy of node i. The cost will be

extremely high if the node almost runs out of energy. eTij and eRij are the energy consumption

coefficients for transmitting and receiving, respectively, which depend on path loss model and the

transmission range, i.e., the physical distance of link lij . Rij is the flow rate assigned to link lij .

Note that the we consider this flows across the links are bidirectional, thus the flow rate Rij is

different from Rji.

In this way, the algorithm considers not only the current energy level, but also the link char-

acteristics including the link distance and flow rate of this link. To show our heuristic routing

algorithm for flow lifetime, we provide a pseudo code of the algorithm, as shown in Algorithm 1.

We explain some details here. In the input part, we define the route updating interval B as the

time duration when the algorithm starts to run until the routing information is renewed. In step 2,

the cost is calculated by Eqn. (2.8). In step 4, we use Bellman-Ford algorithm to find the path for

each flow based on link cost obtained in step 2. In step 6, every node involved in the application

14

Algorithm 1 Flow Lifetime Algorithm

Input: Network G(V, L); Node number n; Cost metric cost(i,j); Route update interval B;

Output: Flow Lifetime, Tf ; Legacy Lifetime (Node Lifetime), Tn; Percentage of consumed energy,

P

1: while flag do

2: Calculate cost(i,j) based on current network status

3: for all f ∈ F do

4: R← BellmanFord(cost(i,j)) ▷ Find flow route

5: for all i ∈ R do

6: Eri ← Eri − cost(k,i) − cost(i,j) ▷ Update residual energy

7: end for

8: end for

9: for all n ∈ V do

10: if satisfy constraints (3.12),(3.13),(3.14),and (3.15) then

11: flag ← 1 ▷ Flow alive

12: else

13: flag ← 0 ▷ Flow die

14: end if

15: end for

16: end while

17: Calculate the Lifetime Tf and Tn

15

Table 2.1: Simulation Settings

Items Values Description

Network Size 50m× 50m Physical size fornetwork

Node Number 20 40 Number of sensornodes distributed

Flow Number 4 Number of trafficflows

Flow Rate (1kb, 2kb, 3kb, 4kb) Transmission ratefor each flow

Update interval 10 sec Time period forrouting path up-dated

Node Initial Energy 10J Initial energylevel for eachsensor node

flow has to update its energy by subtracting the consumed energy. The overlap of multiple flows has

to be considered in order for the residual energy and cost function to be updated correctly. In step

10, the judging condition is used to determine whether the application flows are still feasible. The

death of a node does not stop the algorithm as long as the flows can be maintained. After all, when

the network finally died, we use a timer t to indicate how many iterations have been conducted

for the application flows. Thus, the flow lifetime is the product of timer t and updating interval

B. After the death of network, the percentage of the energy consumed for the entire network is

P =∑

i∈N Eri/∑

i∈N Eoi.

2.6 Simulation Results of Flow-lifetime Routing

In this section, we use MATLAB 7.10.0 to simulate the performance and flow lifetime of our

algorithm. The settings are given in Table I.

We randomly generate the physical locations of all the sensor nodes in terms of uniform distri-

bution. The network is initialized with the parameter values before the simulation. For example,

30 nodes are uniformly distributed in a 50m× 50m network with 10J initial energy per node. The

updating interval is 10 seconds, i.e., every 10s the network needs to renew flow path and update

16

energy information. We assume that the source nodes constantly generate traffic flow with a se-

lected flow rate until the death of the flow. For each scenario, we run the simulation 100 times and

take the average as our final result.

The setting is only for our first scenario. Other settings may change the parameter values later.

One setting needs to be mentioned, that is, the SD nodes are assumed to have sufficient energy to

sustain the application traffic. The initial energy is set to 100J for the SD nodes. We develop four

scenarios to evaluate the performance. For comparison purpose, we use Flow Lifetime and Node

Lifetime to represent the results of our method and the reference method [3], respectively.

In our first scenario, we compare the results of the two methods in terms of the death of the

first node. In Fig. 2.3, we compare our algorithm to the one in without implementing the lifetime

algorithm. We use the same network settings in both cases in order to compare the performance.

The node number is set as 30 and the flow rate is configured as 2.5kb. For the bars on left side, we

implement the node lifetime algorithm. For the bars on right side, we implement the flow lifetime

in which the first flow death is considered as the network death by using our heuristic algorithm.

The lifetime result is averaged across the simulation runs and topologies. The topology of the

network is randomly generated in which all nodes are scattered randomly in the network and the

source-destination pair is also chosen randomly. The worst case is the minimum lifetime among all

the simulation runs with the same configuration.

Fig. 2.3 shows that our method achieves 3217 seconds at average level that is about 10% better

than the reference method with 2982 seconds. Moreover, in worst case, our method performs much

better than the node lifetime method, i.e., for about 43%. Besides, the average result is much better

than the worst case, which indicates that the network topology is also crucially important for the

energy-efficiency of the network, i.e., the network planning and node allocation are important.

Therefore, the method can explicitly prolong the lifetime of the traffic flows in both the average

and worst case. In summary, the proposed routing method based on flow lifetime improve the

network lifetime for about 10%, which is a great improvement compared to the existing routing

schemes.

Fig. 2.2 shows the distribution of the network lifetime by using the flow lifetime method. The

topology of the network is randomly generated for 100 times and the source-destination pair is

also randomly chosen. The average lifetime of the network is 3217 and the worst lifetime is 1920.

17

The distribution of flow lifetime

1500 2000 2500 3000 3500 4000 4500 50000

2

4

6

8

10

12

Figure 2.2: Distribution of network lifetime by using flow lifetime method

The flow lifetime values are distributed approximately in a normal distribution. We also find that

the node lifetime values are distributed in a similar way. We observe that the network topology

impacts the performance to some extent.

In the same scenario, we inspect the percentage of the consumed energy over the total energy

after the network died. In addition to the lifetime, we also want to improve the energy utilization

of the sensor network. The energy utilization indicates that the percentage of the remaining energy

of the entire network after the network died. As shown in Fig.2.4, energy utilization of our method

reaches 67%, whereas the compared result only has 58%. The proposed flow lifetime algorithm

utilizes more energy than the algorithm of the node lifetime for about 9%, which illustrates that

our method is more energy-efficient than the existing ones. The energy of the entire network can

not be consumed completely and usually 67% is a relatively high utilization value.

We change the flow rates but keep all other configurations the same in order to investigate

the lifetime. As shown in Fig. 2.5, different flow rates are shown in x-axis. We assume that the

link capacity is much higher than the configured flow rate, which means we don’t need to consider

the congestion and queuing problem here. Basically, four flows are transmitted from the source to

destination at a specific flow rate. At the flow rate of 1kb, our algorithm is averagely 3% better than

the node lifetime algorithm. The lifetime drops sharply as the flow rate increases, which means

that the network lifetime decrease as the traffic load increases. The network nodes consume more

energy at high flow rates than that at low flow rates. At 5kb, our algorithm is 12% better than the

18

Node Lifetime Flow Lifetime0

500

1000

1500

2000

2500

3000

3500

4000

Ne

two

rk L

ife

tim

e (

se

c)

Worst case

Average case

Figure 2.3: Lifetime Comparison

Node Lifetime Flow Lifetime0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Perc

enta

ge o

f consum

ed e

nerg

y

Worst case

Average

Figure 2.4: Energy Utilization Rate Comparison

19

0 1 2 3 4 5 61000

2000

3000

4000

5000

6000

7000

8000

Flow rate (kb)

Lifetim

e (

sec)

Node lifetime

Flow lifetime

Figure 2.5: Lifetime by varying flow rate

node lifetime algorithm, which is much better than that in the low flow rate case. Thus, our flow

lifetime algorithm performs better than the node lifetime algorithm especially when the traffic load

is higher.

In Fig. 2.6, we change the node number but keep all other configurations the same. In this

scenario, the network size is fixed as 50m × 50m and the transmission range of sensor nodes is

25m. When the node number is 20, our algorithm is averagely 10% better than the node lifetime

algorithm. As the node number increases, the lifetime rises almost linearly. For the same network

size, the node density increases as the node number increasing. When the node number is 40, our

flow lifetime algorithm is 5% better than the node lifetime algorithm. Therefore, each SD pair

has increased number of choices when selecting routes as the node number increases because the

transmission range is fixed. The shortest routes calculated by the routing algorithm avoid the

low-energy nodes by altering the routes to prolong the network lifetime. Thus, the result shows

that the flow lifetime algorithm extends the network lifetime and also performs better constantly

in terms of network density than the node lifetime algorithm.

20

15 20 25 30 35 40 451500

2000

2500

3000

3500

4000

4500

5000

5500

Node number

Life

tim

e (

se

c)

Node lifetime

Flow lifetime

Figure 2.6: Lifetime by varying node numbers

0 5 10 15 20 25 30 35 40 45 50 552500

2600

2700

2800

2900

3000

3100

3200

3300

3400

3500

Routing update period (sec)

Life

tim

e (

se

c)

Node lifetime

Flow lifetime

Figure 2.7: Lifetime by varying update interval

21

In Fig. 2.7, we investigate the impact of the updating intervals on the flow lifetime. The

updating interval is defined as the time period when the routing algorithm start to run until finishes

the routing information updates. When we increase the updating interval, the frequency to update

the routing information becomes decreased. For the node lifetime method, the lifetime decreases

as the updating interval increases. However, our method achieves a significant improvement. As

shown in the figure, the lifetime almost remains at 3300s when the updating interval is changed

in the range of 5s to 50s. Decreasing the updating frequency brings to the situation in which

the routing algorithm reacts slowly, keeps the traffic on outdated routes, and causes nodes to die

quickly. The improvement is due to the fact that our method focuses on the flow lifetime, which

is independent of the first node death. Our algorithm keeps searching for shortest routes after

some nodes died. However, the lifetime performance can not be maintained further if the routing

updating interval keeps increasing. A fairly large interval can results in bad routing decision because

of the outdated energy information of the network. After the updating interval exceeds 50s, the

network lifetime of the flow lifetime algorithm will decrease sharply to 2600s. This result illustrates

that our algorithm achieves good performance in the range of 5s to 50s. In other words, 50s can be

seen as an optimal value of the routing updating interval in this configuration. In this scenario, we

assume that the network overhead can be ignored to simply investigate the impact of our routing

algorithm on the performance. As the routing updating frequency increases, network overheads

need to be considered, which results in a higher data rate than the case of low interval. The

higher data rate can slightly reduce the network lifetime of flow lifetime algorithm, but the overall

performance of our lifetime is much better than the node lifetime algorithm. Thus, our algorithm

prolong the network lifetime in a certain range of the routing update intervals.

The extensive results have illustrated that our flow lifetime method has better performance

than the node lifetime method with respect to the flow rates, node number, and routing updating

intervals.

22

CHAPTER 3

PREDICTION-BASED ENERGY-EFFICIENT

ROUTING DESIGN FOR EHWSN

3.1 System Models for EHWSN

3.1.1 Network model

We consider an EHWSN network with a flat multi-hop and multi-sink topology. All nodes in

the network are considered capable of harvesting, storing, and consuming energy. The network can

be described as a directed graph G(V,E), where V is the set of vertices representing the sensor

nodes, and E the set of edges representing the links. There is an available link e(i, j) between

nodes i and j only if two nodes are within the radio range of each other and able to communicate

directly. Note that we assume the transmission range is fixed and not adjustable by power control.

Let Ei(0) be the initial energy of the node i, also known as the battery capacity of node i.

We denote by ERi (t) the residual energy of node i at time slot t, i.e., the remaining energy of the

node after some consumptions. Except for the source and destination nodes along a path, the

intermediate nodes are equipped with transceivers that can transmit and receive at the same time.

For node i, the energy consumption in transmitting and receiving a unit of data can be denoted

by eTij and eRji, respectively. Also, to sense and collect a unit of data at node i costs the amount of

energy egi . We use EHi (t) to denote the energy harvesting rate of node i at time t.

Let xi,j(t) be the data rate of transmission from node i to node j at time t, and λi(t) the data

generation rate of node i at time t, which is also called sensing rate. We introduce Bi(t) to indicate

the data rate derived from the buffered data in node i at time t, Bi(t) > 0 if the amount of the

buffered data is increasing at time t while Bi(t) < 0 if it is decreasing at time t.

3.1.2 Energy harvesting model

We assume that each node in EHWSN is considered capable of harvesting, storing, and con-

suming energy. As an example, the architecture of an EHWSN node is shown in Fig.1 from which

we can see that the energy and information flows separately. With the energy harvesting module

23

(EHM), sensor node can harvest external energy from ambient environment. The specific module

is very different depending on the source type of the energy and mechanism to harvest the energy.

Take solar energy as an example, a photovoltaic or solar thermal unit is playing the role of EHM in

the system to harvest solar energy. There is a efficiency factor indicating how much effective energy

can be converted for use. We denote by PH(t) the power output from the energy harvesting module

and ηehm the efficiency of harvesting. The harvesting energy is EH(t1, t2) = ηehm∫ t2t1

PH(t)dt.

The module of energy dissipation module (EDM) of a node is to consume energy for the nodes’

operations. As shown in the figure, this module provides the sensor with the energy spends on trans-

mitting and receiving wireless signal, microprocessor computation, etc. To accurately model the

EDM, we consider two dissipation mechanisms. While the EHM is working, if the harvested energy

is larger than dissipated energy, i.e.,ED < EH , where the dissipated energy is ED = ηedm1 VdIddt.

Similarly, if a sensor has to draw extra energy from battery ,i.e. ED > EH , the dissipated energy is

ED = VHIHdt+ ηedm2 (VdIddt− VHIHdt). The reason we differentiate the two cases is that directly

using the energy being harvested is considered to be more energy-efficient, i.e., ηedm1 > ηedm2 . More

energy will be wasted if extra energy needs to be draw from storage module.

The energy storage module (ESM) is the container to store the energy, usually regarded as a

battery or super-capacitor. The output energy for battery discharge can be expressed as EB =

ηesm∫ t2t1

VSIS(t)dt, where ηesm is the battery’s efficiency factor for the output energy. Similar

formula exists for the battery’s charging process.

3.1.3 Prediction model

Regression Analysis. This method is a popular model often used in prediction, forecasting,

and machine learning. We assume that (x1, z1), (x2, z2), ..., (xn, zn) are n observations for indepen-

dent variable and time, e.g., sunlight intensity and time.

x = bo + b1Z + ε, (3.1)

b1 =

∑ni=1(Zi − Z)

∑ni=1(xi − x)

∑ni=1(Zi − Z)2

, (3.2)

b0 = x− b1z, (3.3)

24

Compared to the other models in this section, regression analysis model has been found to be

the most accurate model within second level horizon.

Simple Moving Averaging. This method has been adopted in early EHWSN research.

The idea is simply average the pervious data equally in a certain time range. This method has

abandoned for it’s inaccuracy.

Y t+1 =Yt + Yt−1 + ...+ Yt−m + 1

m, (3.4)

Exponential Smoothing. This method is also known as exponential weighted moving aver-

age EWMA). It’s an interpolation between current observation Xt and previously smoothed value

Xt−1 controlled by parameter α. To implement the EWMA algorithm, a day is split into 48 sections

and each section holds 30 minutes. The weights are exponentially decreasing and more weight is

given to the most recent value.

Y t = αXt−1 + (1− α)Xt, (3.5)

where Xt is the observed value of the energy harvested in time slot t, and Xt−1 is the average of

the previously stored historical data. α is a weighting factor. Studies have shown that the average

prediction error reaches to minimum when 0.1 < α < 0.2.

This algorithm performs well when solar condition remains consistent. When there is a sharp

transition from sunny to rainy or vice versa, the performance degrades. This model is not feasible

in the frequent alternating weather condition. Also, there is a relatively long time delay between

the prediction and actual condition.

When the weight factor α is close to 1, damping is quick. Similarly, when the α is close to 0,

damping is slow.

Based on initial status of the weather condition, we have a variation of Eqa.(3.5).

Yt = α

t−2∑

i=1

(1− α)i−1Xt−1 + (1− α)t−2Y2, for t ≥ 2, (3.6)

Double Exponential Smoothing.

Yt = αXt + (1− α)(Yt−1 + bt−1), 0 ≤ α ≤ 1, (3.7)

bt = γ(Yt − Yt−1) + (1− γ)bt−1, 0 ≤ γ ≤ 1, (3.8)

25

where bt−1 is the trend of the pervious period to help eliminate the lag between prediction and

actual condition. α and γ are weighting factors that can be obtained via non-linear optimization

algorithms. Compared to EWMA model, this model weights more on current value and the time

delay is relatively short.

Parameterized Exponential Smoothing. This category refers to the variation models

based on EWMA model. Many parameters have been introduced into the model to improve the

accuracy of the prediction.

WCMA is an improved version of EWMAmodel, in which the weight factor for current condition

is modified to provide more accurate prediction.

E(d, n+ 1) = α · E(d, n) +GAP · (1− α)MD(d, n+ 1) (3.9)

where MD(d, n+1) is the mean of D past days at n+1 sample of the day. The weighting factor

GAP is computed:

GAP =V · P∑

P(3.10)

where V contains the quotient of past K samples and the average solar energy available during the

previous D days for those samples. P weights the V values with the distance to the actual point

in time.

SEPAD is the solar energy prediction based on additive decomposition. The model considers

both the seasonal and daily trends of the solar cycle. Two tuning parameters are used to scale the

impact of seasonal and daily data.

Pro-Energy considers both short-term and mid-term prediction by modifying the weight pa-

rameters that determine the influence of the last energy status observed.

3.2 Problem Statement and Optimization Modeling

In this section, compared to the general modeling of the problem in previous section, we formu-

late a comprehensive optimization problem with more specific constraints. In this way, the amount

of data consumed on each module can be finely restricted and controlled, which can improve the

26

energy-efficiency remarkably. We provide analysis for the optimization problem when different

prediction models are applied to the problem.

3.2.1 A general modeling

We model the problem in a general manner to show the intuition and basics of the problem, in

which the objective is to maximize the total amount of collected data in EHWSN with the tolerable

delay.

To maximize the energy efficiency of the networks, usually there are two methods to set the

object of the optimization problem. One is to maximize the lifetime of the networks, or to find

the maximum working time of the network until no energy. Another is to deliver as much data as

possible from sensors to sinks util no energy. In this work, we use the second method to formulate

the problem.

The object of the optimization is to maximize the amount of data collected data from an entire

sensor network to the sinks in time T. We formulate the problem as the follows.

maxx

V (T ) =∑

i∈N

xi,D(t) · T, (3.11)

Subject to:

∑

k∈Nin

xk,i(t) + λi(t) +Bi(t) =∑

j∈Nout

xi,j(t), (3.12)

Ei(t+ 1) = min {Ei(0), Ei(t) +Hi(t)− Ci(t)} (3.13)

Hi(t+ 1) = FP (Hi(t)), (3.14)

λi(t) ≥ 0, xk,i(t) ≥ 0, xi,j(t) ≥ 0, ∀(i, j) ∈ E, (3.15)

The optimization objective is the volume of data collected at destinations. Eqn. (3.12) is

the flow conservation including the buffered data. Eqn. (3.13) states the conservation of energy

including the consumption and harvesting. Eqn. (3.14) indicates an abstract prediction model for

27

energy harvesting, the specific equation could be different. Eqn. (3.15) states the flow rate and

rate of generate data should be larger than zero.

3.2.2 A comprehensive modeling

Optimization objective. To maximize the energy efficiency of the network, we propose to

maximize the amount of data collected from entire sensor network to the sinks during the lifetime

of network. In other words, we try to deliver as much data as possible to the sinks util the network

runs out of energy.

VT =

T∑

t=0

∑

i∈N

xi,D(t), (3.16)

We use VT to indicate the volume or amount of data collected in time T in the network. T is

the lifetime of the network. The data traffic sent to sinks D from all the nodes in network N up to

time T is regarded as the volume or amount of data. Since we focus on the routing layer, the data

loss in PHY and MAC layer are not considered here. (In simulation, the lifetime of a network might

be too long to be implemented. Depending on the applications’ requirements, T can be selected as

a small value to facilitate the simulation.)

Optimization constraints. In the following, we introduce the constraints of the optimization

problem.

∑

k∈Nin

xk,i(t) + λi(t) +Bi(t) =∑

j∈Nout

xi,j(t), (3.17)

Equation (3.17) is for the flow conservation including the buffered data. Bi(t) is the rate of data

generated from the buffer in node i. Bi(t) >= 0 if buffered data increases in time t at node i.

Similarly, Bi(t) <= 0 if buffered data decreases in time t at node i

Hi(t+ 1) = FP (Hi(t)), (3.18)

Equation (3.18) indicates the prediction model for energy harvesting. The specific form of the

equation can be different depending on which prediction model is used.

28

Ei(t+ 1) = min {Ei(0), Ei(t) +Hi(t)−

(αi · eR ·

∑

xk,i(t) + βi · eT ·

∑

xi,j(t) + γi · eg · λi(t)), (3.19)

Equation (3.19) states the conservation of energy including the consumption and harvesting, or the

relation between the instant energy level at time t and t+ 1. Ei(0) is the initial energy status and

also viewed as the capacity of the energy storage. eR ·∑

xk,i(t), eT ·

∑

xi,j(t), and eg ·λi(t) are the

energy consumption on receiving, transmission, and generation, respectively. Factors α, β, and γ

are the weighting factors to restrict the energy consumption for each part.

αi ∽ Hi(t+ 1), 1 ≥ α ≥ 0, (3.20)

βi ∽ Hi(t+ 1), 1 ≥ β ≥ 0, (3.21)

γi ∽ Hi(t+ 1), 1 ≥ γ ≥ 0, (3.22)

Equations (3.20)-(3.22) are the definitions of the weighting parameters, which can be decided

by prediction of the energy harvesting condition at time t + 1. These factors are introduced to

dynamically adjust the energy spent on receiving, transmission, and generation consumptions in

order to optimize the energy-efficiency. All factors should be greater than or equal to zero and less

than or equal to one.

λi(t) ≥ 0, xk,i(t) ≥ 0, xi,j(t) ≥ 0, ∀(i, j) ∈ E, (3.23)

Equation (3.23) states that the rate of flow and generated data should be larger than or equal to

zero.

Logic behind the optimization problem. We rearrange the optimization problem as fol-

lows.

maxx

T∑

t=0

∑

i∈N

xi,D(t), (3.24)

Subject to:∑

k∈Nin

xk,i(t) + λi(t) +Bi(t) =∑

j∈Nout

xi,j(t), (3.25)

29

Hi(t+ 1) = FP (Hi(t)), (3.26)

Ei(t+ 1) = min {Ei(0), Ei(t) +Hi(t)−

(αi · eR ·

∑

xk,i(t) + βi · eT ·

∑

xi,j(t) + γi · eg · λi(t)), (3.27)

αi ∽ Hi(t+ 1), 1 ≥ α ≥ 0, (3.28)

βi ∽ Hi(t+ 1), 1 ≥ β ≥ 0, (3.29)

γi ∽ Hi(t+ 1), 1 ≥ γ ≥ 0, (3.30)

λi(t) ≥ 0, xk,i(t) ≥ 0, xi,j(t) ≥ 0, ∀(i, j) ∈ E. (3.31)

Our motivation is to optimize the amount of data in an energy-efficient manner by predicting

the the level of the energy harvesting. We use the previous and current harvesting profileHi(t) to

estimate the energy harvesting Hi(t+1) in time t+1, which is Eqn. (3.26) and the detailed forms

are presented in the previous section.

By using the prediction of energy harvesting, we use three weighting factors to regulate the

data rate for receiving, transmission, and generating, respectively. The weighting factors can not

only control the data generation rate for each node i in time t, but also regulate the transmission

and receiving sides. For example, if we pick αi(t) = 1, βi(t) = 0, and γi(t) = 0 , then the routing

scheme limits the transmission and generation of data, and only allows receiving. The physical

meaning of the factors is that a node can choose to buffer the received data, queue the received

data, and limit the generated data. Actually, the use of the weighting factors reveal the main idea

of our routing schemes, which aim at optimizing the routing path in an energy-efficient way.

As mentioned before, we try to maintain an optimal routes by using the harvesting energy if

there is enough energy to be harvested. In order to wait for the sensor nodes to harvest the energy,

the energy consumption needs to be reduced by limiting the energy expended on transmission,

receiving, and data generation. For example, if the value of β for node i at time t is 0.8, it means

80% of the transmission data will be delivered to the next hop and 20% of the data will be buffered

in node i. If the value of α is 0.6 for node j, it means only 60% of the data will be received by node

j and 40% of the data from the previous hop will be buffered. The buffered data will be delivered

30

to the next hop later after enough energy is harvested. Therefore, the amount of the data buffered

can be decreased if the transmission rate is larger than the buffering rate plus the receiving rate.

The values of the factors are determined by the prediction of energy to be harvested. If enough

energy will be harvested, the factors can be configured to a relatively large value to finish the data

transmission.

Note that Eqns.(3.26) and (3.28)-(3.30) are equations in a functional manner. The detailed

equations can vary depending on applications.

Next, the analysis of the problem will be presented.

3.2.3 Theoretical analysis of the optimization problem

The novelty of the optimization problem is that the introduction of the weighting factors α, β, γ

to regulate the flow rates for the goal of energy efficiency. The factors are determined by prediction

model of energy harvesting depending on specific applications. The values of factor α, β, and γ

can be chosen as constant or a simple linear function based on the predicted energy Hi(t+ 1). In

our analysis, we provide theoretical insights from abstract to specific depending on the prediction

model. The analysis is structured as follows. We first assume that the prediction model is a linear

model and optimization problem can be formulated into an LP problem which can be easily solved

by simplex method. Second, we assume that the prediction model is a convex/concave model. We

prove that the optimization problem becomes a convex optimization problem. If the problem is a

convex optimization problem, it means that a local optimal solution is definitely the global optimal

solution of the optimization problem. Third, for the three typical prediction models. We present

our analysis on the solutions.

Usually the problem is solved as a disciplined convex optimization problem, but we analyze the

problem as a utility maximization problem. We can easily prove that it is equivalent to a problem

minimizing the negative concave function.

Linear Programming Problem. If the prediction model in Eqn. (3.18) is a linear function

of t, then the optimization problem in Eqn. (3.32) is an LP problem.

Constraint in Eqn. (3.32) is a linear combination of weighting factor β and data flow rate

xi,D(t). Constraint in Eqn. (3.17) is a linear equation indicate the flow conservation considered

the buffered data. Constraint in Eqn. (3.19) is an affine function as the equality constraint. Since

31

parameters eR, eT , and eg are all constant values, and weighting factors α, β, γ are calculated values

limited between zero and one. Constraints in Eqns. (3.20) - (3.22) are inequality constraints to

restrict the values of weighting factors. Constraints in Eqn. (3.23) are typical inequality constraints

commonly used in network optimization. Thus, the objective function and constraints are linear

functions of data rate xi,j(t), thus this problem is a linear programming problem.

If the prediction model is a simple moving average (SMA) model, then the optimization problem

is a linear programming problem. The SMA model is obviously a linear average function, and the

energy-efficiency optimization problem is also a linear programming problem accordingly.

If the prediction model is a SMA model (linear average model equally based on all previous

data), then the optimization problem is a classical LP problem. The LP problem can be easily

solved by simplex method or other relative methods, and we do not provide the details here.

Convex Optimization Problem. Given convex function f : R+ → R, constants eR, eT , eg ∈

R, and ∀t = 0, ..., T . If prediction model in Eqn. (3.18) is a convex function of t, then optimization

problem in Eqn. (3.32) is a convex problem.

The object of the optimization problem (3.32) can be transformed to a standard convex problem

by simply converting to a minimization problem:

minx

−T∑

t=0

∑

i∈N

xi,D(t) (3.32)

Similarly, the constraints in Eqns. (3.17), (3.19), (3.20) - (3.20) are affine functions in equality

constraints that are proved to be affine functions in (3.2.3). Constraints in Eqn. (3.23) are typical

inequality constraints commonly used in network optimization.

Thus, all the constraints and objective satisfy the definition of the standard form of convex

optimization problem.

If the prediction model is an exponential weighted moving average (EWMA) model, then the

optimization problem is a convex problem.

The prediction model is:

32

Ht = (1− α)Ht + αHt−1,

= (1− α)Ht + α[

(1− α)Ht−1 + αHt−2

]

,

= (1− α)Ht + α(1− α)Ht−1 + α2(1− α)Ht−2 + ...,

= α

∞∑

k=0

(1− α)k ·Ht−k,

(3.33)

When k is a parameter to formulate the equation, and it indicates the how many previous estimated

values have been summed up till current t.

Equation (3.33) has been proved to be a strictly convex function in paper (Applications and

Uses of Digital Filters in Finance by Johan Boissard).

Thus, according to the lemma (3.2.3), the energy efficiency optimization problem is a convex

optimization problem if the prediction model is an EWMA model.

If the prediction model is a weather-conditioned moving average (WCMA) model, then the

optimization problem is also a convex problem.

The prediction model is:

Ht = GAP · (1− α)Ht + αHt−1, (3.34)

where GAP is a factor to measure the solar conditions in the present day relative to the previous

days. The definition of GAP is,

GAP =V · P∑

P, (3.35)

where V contains the quotient values of the past samples and average solar energy, and P indicates

the weights of V values with the distance to actual point. Since the values in vector V and P are

all non-negative real constant. Thus, the value of factor GAP is also a non-negative real value.

Similarly, we can find an expression for the WCMA model,

Ht = α

∞∑

k=0

[

GAP · (1− α)]k·Ht−k. (3.36)

Thus, the energy efficiency optimization problem is a convex optimization problem if the prediction

model is a WCMA model.

33

Some other prediction models (e.g., SEPAD) also can be proved to be convex optimization

problem assuming that the parameters or weighting factors are linear functions of real values.

3.3 A New Energy-Efficient Routing Algorithm

3.3.1 Prediction-based Energy-Efficient Routing (PEER) Algorithm

In this chapter, we propose two heuristic algorithms for prediction-based energy efficient routing

(PEER). First, we propose a centralized algorithm that is based on shortest path routing algorithm.

The algorithm calculates the best routing paths in the perspective of global network condition.

Second, we analyze distributed version of the routing algorithm, in which each node has to choose

its next hop based on neighboring information includes energy level and traffic condition. The

prediction of energy harvesting is considered in both algorithms.

We also provide the complexity analysis of the algorithms and compare their performance.

To show our proposed routing algorithm, we first show the flow chart of the PEER algorithm

in Fig 3.1 and then present the pseudocode of the algorithm in Algorithm 2.

About the details of the algorithm 2, in the input part, we provide the prediction model for

energy harvesting. Also, the route updating interval B, the time duration when the routing infor-

mation is renewed, and maximum waiting interval L are imported as the customized parameters.

In Step 2, the cost is calculated by Eqn. (2.8). In Step 4, we use Bellman-Ford algorithm to cal-

culate the path for each flow based on the link cost obtained in Step 2. In Step 6, each node along

the application flow has to update its energy by subtracting the consumed energy. The overlap of

multiple flows has to be considered in order for the residual energy and cost function to be updated

correctly. In Step 10, the judging condition is used to determine whether an application flow is still

feasible. The death of a node does not stop the algorithm as far as the flow can be maintained.

After all, when the network finally died, we use a timer t to indicate how many iterations have

been conducted for the application flow. Thus, the flow lifetime is the product of timer value t

and updating interval B. We are also interested in the percentage of the energy consumed over the

initial network after the death of network, that is, P =∑

i∈N Eri/∑

i∈N Eoi.

3.3.2 Theoretical analysis on time complexity

The complexity of the heuristic algorithm is Θ(V 2 · E · L ·K). V is the number of nodes in the

network. E is the number of edges in the network. L is the time delay allowed for the application.

34

Initial a network

Network Die?

Find the optimal routes

Calculate the energy condition

after rounds by

After harvested after

rounds, if the

can be maintained?

Change the routing

path to

immediately

Keep the path

and wait L rounds for

harvesting

Update the routing information

Keep the path

Yes

No

Yes

No

Yes

No

Calculate the

and Update the

routing every

seconds

Whether the

current

optimal path is

the same as

the previous

path

Figure 3.1: flow chart of PEER algorithm

35

Algorithm 2 Predictable Energy Efficient Routing Algorithm

Input: Network N(V,E); Prediction function of harvested energy Fp(Hi(t)); Route update inter-

val B; maximum waiting interval L;

Output: The total amount of data received at APs VAP ; Network throughput = VAP ; Network

lifetime T ;

1: while flag do

2: Calculate costi,j based on current network status

3: for all Si ∈ V do

4: PSi,APi(t)← OptimalRoute(costSi,APi

) ▷ Find optimal route

5: if PSi,APi(t− 1) = PSi,APi

(t) then

6: Keep the same routing path

7: else

8: Use the prediction model Fp(Hi(t)) to estimate the harvesting condition for next L

rounds

9: Calculate the route after L rounds if the sensors Si ∈ PSi,APi(t) waiting

10: if PSi,APi(t+ L) = PSi,APi

(t) then

11: PSi,APi(t)← PSi,APi

(t− 1) ▷ Wait L rounds to maintain the optimal route

12: else

13: P(Si,APi)(t)← PSi,APi(t) ▷ Change the route immediately

14: end if

15: end if

16: end for

17: for all Si ∈ V do

18: Eri ← Eri − costk,i − costi,j +Hi(t) ▷ Update residual energy

19: end for

20: for all Si ∈ V do

21: if satisfy constraints (3.12),(3.13),(3.14),and Eri > 0 then

22: flag ← 1 ▷ Network alive

23: else

24: flag ← 0 ▷ Network die

25: end if

26: end for

27: end while

28: Calculate the lifetime T , amount of data received at APs VAP and network throughput =

VAP/VAll

36

K is the time complexity of the prediction model. L is usually considered as a constant and K

is also a constant if we use the simple smoothing average model. Then the time complexity of

the algorithm is Θ(V 2 · E). The best case is Θ(V · E) if the Bellman-Ford algorithm can find

the shortest path at the beginning of each round. The optimization problem is complicated and

usually hard to have an optimal solution due to following reasons. 1) The optimization problem

can only be solved either across the nodes or over time since there are actually two variables in the

optimization problem. 2) The values of the proposed three weighting factors can largely influence

the optimality of the solutions. In order to get a quantitative understanding of the optimal solution,

we simplify the model by using simple values in the model. We find that the result is not close to

our simulation results. Thus, we believe the selection of the three weighting factors are related to

the optimal solution.

3.4 Simulation Results of PEER algorithm

We validate our PEER algorithm by both numerical examples (e.g., Matlab) and also packet-

level simulation (e.g, OMNET++). In this section, we investigate the throughput and network

lifetime of our algorithm compared to conventional algorithms. The simulation settings are given

in Table I.

For simplicity, the values of the factors are selected as constant values from 0.2, 0.4, 0.6, and

0.8 depending on the prediction of the energy harvesting for a single node. If enough energy will be

harvested, the factors can be changed to a relatively large values to finish the data transmission.

We evaluate the performance of our algorithms in four perspectives by varying three network

configurations.

Performance with different flow rates:

37

Flow rate (kbps)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Pe

rce

nta

ge

of

co

ms

um

ed

en

erg

y

0

20

40

60

80

100without predictionPEER

Figure 3.2: Energy percentage by different flow rates

The energy percentage indicates the percentage of the total energy consumption of the network

till the network lifetime. It represents the energy utilization rate of the routing algorithm. In Fig.

3.2, the red line illustrates that the PEER algorithm spends less energy in terms of the energy

consumption over the entire network. The energy consumption of the entire network increases

since the increase of traffic load leads to higher energy consumption. When the flow rate is low,

the percentage of energy consumption is above 90%. When the flow rate reaches 4 kbps, the

performance of two algorithms become close, which means that as the flow rate increases to a

certain value the performance can not be enhanced any compared to the method without using

PEER. Note that the harvested energy is deducted from the total consumed energy in order to

accurately show the performance of two algorithms. In short, the PEER algorithm performs better

than the method without PEER in terms of energy percentage by different flow rates.

38

Flow rate (kbps)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Ha

rve

ste

d E

ne

rgy

(J

)

0

20

40

60

80

100without predictionPEER

Figure 3.3: Harvested energy by different flow rates

In Fig. 3.3, the network with PEER algorithm can harvest more energy than the one without

PEER. As the flow rate increases, less energy are harvested because the heavier traffic load leads

to frequent route changes. For example, when flow rate is 1 kbps, the network with PEER can

harvest 24% more energy than the method without using PEER. Similar to the previous result,

the algorithm can not enhance the performance when flow rate increase to 4 kbps. Note that the

harvested energy here is the amount of energy harvested to support our target traffic flows, not

all the energy harvested from the entire network. In short, the PEER can utilize more harvested

energy than the method without PEER by different flow rates.

39

Flow rate (kbps)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Ne

two

rk l

ife

tim

e (

se

c.)

0

1000

2000

3000

4000

5000

6000

7000

8000without predictionPEER

Figure 3.4: Network lifetime by different flow rates

In Fig. 3.4, the network lifetime with PEER is longer than the method without PEER. The

lifetime of the network can be prolonged significantly when the flow rate is low. When the low

rate is 1kbps, the network with PEER algorithm can gain extra lifetime about 21%. When the

flow rate is 4kbps, the lifetime performance of two routing algorithms become similar. As the

flow rate increases, the network lifetime decrease because the heavier traffic leads to higher energy

consumption and more frequent route changes. In short, the network lifetime can be prolonged by

using the PEER algorithm, especially when the flow rate is low.

40

Flow rate (kbps)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Am

ou

nt

of

da

ta r

ec

eiv

ed

(M

bit

)

0

5

10

15

20

25

30

35

40without predictionPEER

Figure 3.5: Network throughput by different flow rate

The network throughput here indicates the amount of data delivered from the sources to des-

tinations till the network lifetime. In Fig. 3.5, the red line indicates that our PEER algorithm

utilizes the energy more efficiently than the one without PEERA. For the same flow rate, the net-

work implemented PEER algorithm can received more data than the one without PEERA around

20%. As the data rate increases, the throughput sightly decreases because the heavier the load

introduced the more energy consumption. The performance with PEER is always better than the

one without PEER even when the flow rate is relatively high.

In summary, as the flow rate increases, the network performance can be greatly improved when

the load is light in terms of energy percentage, harvested energy, network lifetime, and network

throughput. As the rate increases to a threshold, then two algorithms perform similarly. Note that

the 4 kbps is the ”threshold” in our scenario. But the value may not be fixed. It can be changed

if the simulations and configurations are changed.

Performance with different network coverage:

41

Network coverage (m2)

1000 2000 3000 4000 5000 6000 7000 8000 9000

Pe

rce

nta

ge

of

co

ns

um

ed

en

erg

y

0

20

40

60

80

100without predictionPEER

Figure 3.6: Energy percentage by different network coverage

In Fig. 3.6, it indicates that two algorithms perform similarly as the network coverage increases.

When the network coverage is between 2500− 6500(m2), the one with PEER is sightly better than

the other one. For the same number and communication rage of the network nodes, as the network

coverage increases, the percentage of consumed energy decreases because the less link connections

are available for the routing algorithm, which leads to lower energy utilization rate. In short, the

one with PEER can utilize more energy of the network than the one without PEER by different

network scales.

In Fig. 3.7, it shows that two algorithms perform similarly in terms of harvested energy as the

network coverage increases. When the network coverage is small, the harvested energy consumed

on target flows is high because the dense distribution of the network nodes, which means there

are many alternative routes for the data flows. As the network coverage increases, the harvested

energy become less. The performance of PEER method is slightly better than the one without

PEER when the network coverage is between 2500− 6500(m2).

42

Network coverage (m2)

1000 2000 3000 4000 5000 6000 7000 8000 9000

Ha

rve

ste

d E

ne

rgy

(J

)

0

10

20

30

40

50

60

70

80without predictionPEER

Figure 3.7: Harvested energy by different network coverage

In Fig. 3.8, it shows that two algorithms perform similarly in terms of network lifetime as the

network coverage increase. As the network coverage increases, for the fixed transmission range,

the available connections become less. Thus, the network lifetime decreases sharply as the network

coverage increases. The network lifetime of PEER is slightly better than the one without the PEER

when the network coverage is between 2500− 6500(m2).

In Fig. 3.9, it shows that two algorithms perform similarly in terms of network throughput as the

network coverage increases. As the network coverage increases, the available connections become

less, thus the network lifetime become worse. The network throughput of PEER is slightly better

than the one without the PEER when the network coverage is between 2500−6500(m2). Note that

this range of network coverage is the optimal range for this particular network configurations. It

can be changed if the simulations method and network configurations are changed.

In short, for different network coverage, the PEER algorithm performs a little bit better than

the other one. As the network coverage increases and the sparsity of the increases, the available

43

Network coverage (m2)

1000 2000 3000 4000 5000 6000 7000 8000 9000

Ne

two

rk L

ife

tim

e (

se

c.)

0

1000

2000

3000

4000

5000without predictionPEER

Figure 3.8: Network lifetime by different network coverage

links to interconnect the nodes become less, then the overall performance of the network is getting

worse. This result provides an useful conclusion that the PEER is not affected by coverage of the

network. The PEER method performs slightly better than the one without PEER in a certain

range of network coverage.

Performance with different updating intervals:

We point out that the updating interval here is the updating frequency of the routing informa-

tion. By changing it, we can find the speed of the algorithm in searching for the best route at the

moment.

In Figs. 3.10 and 3.11, the consumed and harvested energy are in a same level for both algo-

rithms. This result indicates that the updating interval does not really affect the energy consumed

and harvested over the entire network.

In Fig. 3.12 and Fig. 3.13, the lifetime and throughput of the network reach to a maximum

value when the route updating interval is set to 35 and 45 seconds for two algorithms, respectively.

44

Network coverage (m2)

1000 2000 3000 4000 5000 6000 7000 8000 9000

Am

ou

nt

of

da

ta r

ec

eiv

ed

(M

bit

)

0

1000

2000

3000

4000

5000without predictionPEER

Figure 3.9: Network throughput by different network coverage

This is a significant result which illustrates that there is an optimal value for the algorithm to

improve the network throughput and lifetime. Moreover, the PEER algorithm enables us to set

the frequency of updating the routing information to a high value for a improved performance.

In summary, we investigate the performance of the proposed PEER algorithm by extensive

simulation results. Three major factors are considered in the simulation, including the flow rates,

network coverage, and routing updating intervals. For each factor, we compare the performance

of PEER to the energy harvesting method without prediction in four different aspects, including

consumed energy percentage, harvested energy, network lifetime, and network throughput. We can

conclude that the average network throughput increases by 31.6%. The average network lifetime

increases by 29.8%. The average percentage of consumed energy increases 5.42% and the harvested

energy increases by 8.57%. For different flow rates, the PEER performs much better than the one

without prediction especially when data rates are low. For different network coverage, the results

show that performance of the PEER algorithm is stable while the network coverage increases. For

45

Routing updating interval (sec.)0 10 20 30 40 50 60

Pe

rce

nta

ge

of

co

ns

um

ed

en

erg

y

0

20

40

60

80

100without predictionPEER

Figure 3.10: Energy percentage by different updating intervals

the routing updating intervals, we can set a higher frequency of updating the routing information

for an improved performance by using PEER.

46

Routing updating interval (sec.)0 10 20 30 40 50 60

Pe

rce

nta

ge

of

co

ns

um

ed

en

erg

y

0

20

40

60

80

100without predictionPEER

Figure 3.11: Harvested energy by different updating intervals

47

00.510

0.51

Routing updating interval (sec.)0 10 20 30 40 50 60 70

Lif

eti

me

(s

ec

.)

1000

1500

2000

2500

3000

3500without predictionPEERMaximum Lifetime

Maximum Lifetime

Figure 3.12: Network lifetime by different updating interval

48

Routing updating interval (sec.)0 10 20 30 40 50 60

Am

ou

nt

of

da

ta r

ec

eiv

ed

(kb

)

×104

1

1.5

2

2.5

3

3.5without predictionPEER

Maximum Throughput

Maximum Throughput

Figure 3.13: Network throughput by different updating interval

49

CHAPTER 4

CONCLUSION AND FUTURE WORK

4.1 Conclusion

In this work, we aim at improving the energy-efficiency in both the conventional WSN and

EHWSN. For each part of the work, we propose a new model for the network optimization problem

with theoretical analysis. We validate the proposed energy-efficient routing schemes by simula-

tions. The results show that the proposed routing schemes increase the networks energy-efficiency

significantly.

In the first part, we propose a new algorithm to maximize the network lifetime in WSN. The

concept of flow lifetime has been illustrated. Extensive examples are presented to demonstrate our

method. We formulate the optimization problem as a max-min fairness problem, and proved the

problem to be NP-hard for unspllitable flows. We emphasize the flow lifetime for routing metrics

rather than nodes’ lifetime. By implementing the flow lifetime method, we propose a new routing

algorithm to improve the network lifetime. Our simulation results have shown that the lifetime of

application flows can be prolonged for about 10%. Also, for different update intervals, our method

has almost a stable lifetime within a certain range.

In the second part, we propose an optimization problem to maximize the network throughput

and design a new routing scheme to maximize both the network throughput and lifetime in EHWSN.

The emerging of the energy harvesting in WSN motivates our idea that we can predict the future

condition of energy harvesting to optimize the energy-efficiency of the EHWSN. We propose a

new optimization model for the problem and analyze the optimization solution in terms of various

prediction models. We propose a new routing scheme to improve the network throughput and

lifetime by considering the prediction of energy harvesting as a weighting factor to adjust the

routing algorithm. The proposed PEER algorithm increases the data received and prolongs the

lifetime significantly. The average amount of data received increases by 31.6%. The average network

lifetime increases by 29.8%. The average percentage of consumed energy increases 5.42% and the

harvested energy increases by 8.57%. Also, the network overhead are considerably reduced. The

50

energy-efficiency is a crucial factor to evaluate the performance of both conventional WSN and

EHWSN. Even minor progresses made on the energy-efficiency can contribute tremendous benefits

to many other research areas. In summary, both optimization models and routing algorithms are

proved and validated by extensive simulation results. The energy-efficiency of the conventional

WSN and EHWSN are improved significantly in terms of network lifetime and throughput.

4.2 Future work

However, we acknowledge that there are some deficiencies in the current optimization problems.

More work needs to be done to develop our proposed routing methods.

First, for the comprehensive model of the EHWSN, it’s difficult to find the theoretical optimal

solution of the optimization problem. The choice of the prediction model and its parameters can

influence the solution to a large extent. Also, the data profile of the energy harvesting could be

very different. Moreover, the value of the proposed three weighting factors can largely impact the

optimal solution of the optimization problem. For our future work, we have to find the optimal

solution for different models under different settings separately by applying the tested configurations

and models into the optimization problem. Then we can compare the performance between the

heuristic algorithm and optimal solution in various configurations.

Second, the routing algorithms can be optimized by considering more factors depending on

specific applications. Currently, our proposed the route selection mainly depends on the available

energy and harvesting condition. For specific applications and scenarios, we can improve our

modeling and algorithm to meet the new requirement of the applications for a better performance.

In the future, we have to design and implement a distributed version of the PEER algorithm with

a relatively good performance.

Third, theoretically, how much can the proposed three weighting factors constrain the opti-

mization boundaries remains an issue. We have showed the results with a better performance by

implementing the PEER algorithm. How to prove the effectiveness of the factors in finding the

optimal solution is still a task. Practically, we also have to find the energy-efficient functions to

assign the values of the proposed weighting factors in the simulations.

51

In summary, there are still many issues for the improvement in the research of energy-efficiency

routing in wireless sensor networks. More challenges and opportunities will be discovered in the

future research of wireless sensor networks.

52

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59

BIOGRAPHICAL SKETCH

Yizhou Dong received his B.S. in Electronics and Information Engineering from Huazhong Univer-

sity of Science and Technology (HUST), Wuhan, China, in 2010. He was a research assistant for

project TD-LTE Wireless Communication Terminals Test Set, in Wuhan National Laboratory for

Optoelectronics (WNLO), HUST, from Sep. 2009 to Jul. 2010.

He joined graduate program of the Dept. of Electrical and Computer Engineering of Florida

State University, Tallahassee FL, USA in 2010 as a Master student. He joined the Dr. Ming Yu’s

networking research lab as a research assistant and started the Ph.D program in summer 2011.

During 2010 and 2012, he worked as a research assistant for project The Future Renewable Electric

Energy Delivery and Management (FREEDM), in Center for Advanced Power Systems (CAPS),

FSU. During 2012 and 2015, he was a research associate for project Development of Automated

Testing for Traffic Control Signals Devices and the Security of Traffic Control System in Traffic

Engineering Research Lab, FDOT. He was also a teaching assistant in Dept. of Electrical Computer

Engineering, FSU.

His research interests include the modeling and optimization of the routing algorithms in WSN

and EHWSN, MAC algorithm design in MANET, cross-layer optimization and cooperative com-

munications, MAC and routing algorithms in VANET.

60