Energy-efficient data sensing and routing in unreliable energy-harvesting wireless sensor network

Ting Lu1 • Guohua Liu1 • Shan Chang1

Published online: 31 August 2016

� Springer Science+Business Media New York 2016

Abstract Energy-harvesting wireless sensor network

(WSN) is composed of unreliable wireless channels and

resource-constrained nodes which are powered by solar

panels and solar cells. Energy-harvesting WSNs can

provide perpetual data service by harvesting energy from

surrounding environments. Due to the random character-

istics of harvested energy and unreliability of wireless

channel, energy efficiency is one of the main challenging

issues. In this paper, we are concerned with how to decide

the energy used for data sensing and transmission adap-

tively to maximize network utility, and how to route all

the collected data to the sink along energy-efficient paths

to maximize the residual battery energy of nodes. To

solve this problem, we first formulate a heuristic energy-

efficient data sensing and routing problem. Then, unlike

the most existing work that focuses on energy-efficient

data sensing and energy-efficient routing respectively,

energy-efficient data sensing and routing scheme

(EEDSRS) in unreliable energy-harvesting wireless sen-

sor network is developed. EEDSRS takes account of not

only the energy-efficient data sensing but also the energy-

efficient routing. EEDSRS is divided into three steps: (1)

an adaptive exponentially weighted moving average

algorithm to estimate link quality. (2) an distributed

energetic-sustainable data sensing rate allocation algo-

rithm to allocate the energy for data sensing and routing.

According to the allocated energy, the optimal data

sensing rate to maximize the network utility is obtained.

(3) a geographic routing with unreliable link protocol to

route all the collected data to the sink along energy-effi-

cient paths. Finally, extensive simulations to evaluate the

performance of the proposed EEDSRS are performed. The

experimental results demonstrate that the proposed

EEDSRS is very promising and efficient.

Keywords Energy-harvesting sensor network � Energy �Data sensing � Routing � Unreliable links

1 Introduction

Wireless sensor networks (WSNs) are composed of

unreliable wireless channels and resource-constrained

nodes. Energy constraint is the most important problem in

WSNs, because traditional sensor nodes are powered by

batteries with limited capacity. Limited battery capacity

allows WSNs to work only for a period of time. However,

perpetual data service is expected in WSNs. Therefore,

energy problem has restricted the further development of

WSNs [1]. In order to address this problem, heuristic

sensor nodes that have the ability to harvest energy from

surrounding environment by energy scavengers1 are

developed, and energy harvesting technologies are used in

WSNs [2–4]. Rechargeable sensor nodes harvest energy

from surrounding sources such as solar, thermal energy,

light, vibration, and wind. Harvested energy can be stored

in battery when battery level does not exceed the highest

level. The WSN composed of rechargeable sensor nodes

is called as energy-harvesting wireless sensor network

(EH-WSN).& Ting Lu

luting@dhu.edu.cn

1 Donghua University, 2999 Renmin Road, Songjiang District,

Shanghai, People’s Republic of China 1 Energy scavengers provide unlimited energy to sensor node

123

Wireless Netw (2018) 24:611–625

https://doi.org/10.1007/s11276-016-1360-6

Data gathering in WSNs consumes the major part of

energy [5]. Data gathering is divided into two steps: (1)

data sensing, and (2) data transmission (i.e., receiving and

transmitting packets). In order to improve energy effi-

ciency, researchers took account of residual battery energy

and energy consumption in routing protocol design.

Existing work is mainly categorized into two classes [6–8],

i.e., energy-aware routing and geographic routing.

1. Energy-aware routing Over the past few years, energy-

aware routing in traditional WSNs has received

considerable attention by researchers [9–11]. In all of

these work, routing decisions are mainly based on two

metrics: (a) energy consumption for receiving and

transmitting packets, and (b) residual battery energy of

sensor node. The former metric aims to minimize the

total energy consumption, while the latter one aims to

prolong network lifetime. With the development of

energy harvesting technologies, energy-aware routing

protocols in EH-WSN are proposed [12, 13]. Packets

are routed by rechargeable sensor nodes. Path calcu-

lation is based on the global knowledge of network,

which is not desirable in WSNs. In order to address

this problem, Lin et al. [14] proposed a distributed

algorithm. However, the distributed algorithm must

flood the whole network, which will consume more

network resource and reduce network performance

greatly. Thus, more comprehensive study in EH-WSN

is needed to design energy efficient data sensing and

routing scheme.

2. Geographic routing Geographical routing is also called

as position-based routing. The routing decision in

geographic routing is based on location information

which is obtained by location techniques [15, 16], e.g.,

global positioning system (GPS). Location information

is exchanged by neighbor nodes locally. Each node

determines the next hop for a transmitted packet

locally based on the location information of itself,

destination and its one-hop neighbors. Because most

monitoring applications in WSNs require sensor nodes

to know their location information, geographic routing

is quite applicable to WSNs. In addition, per-destina-

tion state and flooding for route establishment are not

required in geographic routing. Thus, geographic

routing has good scalability, which is promising in

WSNs. The most popular research work of geographic

routing is ‘‘greedy’’ geographic routing. ‘‘greedy’’

geographic routing aims to minimize the total number

of transmission hops by forwarding packets to the node

which is geographically close to the destination

[17, 18]. This is an efficient method if the follow

conditions are satisfied: (a) sufficient network density,

(b) accurate localization information, and (c) reliable

links. However, wireless channels are unreliable in

fact, which is not consistent with the condition (c). In

addition, ‘‘greedy’’ geographic routing does consider

the energy constraint on each node. Without consid-

ering the energy constraint will reduce its efficiency

and effectiveness [19]. Researchers proposed energy-

aware geographic routing which took account of either

residual battery energy of node or energy consumption

for receiving and delivering packets [20–24].

Although the aforementioned work took account of the

energy consumption for data transmission and indicated the

importance of energy consumption for data sensing, it

didn’t consider the energy consumption for data sensing in

protocol design. Research work in WSNs [25, 26] pointed

out that the energy consumed by data sensing must be

considered in protocol design to provide perpetual data

service and improve network performance.

How to allocate energy for data sensing and data

transmission according to the harvested energy is a chal-

lenging issue. Generally speaking, the more the collected

data, the better the network monitoring quality. If less

energy is used for data sensing, less data is collected which

results in poor monitoring quality. Conversely, if more

energy is used for data sensing, more data can be collected

and less energy can be used for data transmission. As a

result, not all the collected data can be transmitted to

destinations. Some important information may be lost.

Thus, the energy used for data sensing and data transmis-

sion must be allocated wisely.

In this paper, our objective is to design an energy-effi-

cient data sensing and routing scheme in unreliable EH-

WSN by jointly considering energy consumption for data

sensing and data transmission. In addition, residual battery

energy, harvested energy, limited battery capacity and link

unreliability are considered in protocol design. A com-

prehensive study on link quality estimation, adaptive data

sensing rate allocation, adaptive energy allocation and

energy-efficient routing are conducted. Our contribution is

summarized as follows. Unlike the most existing work that

focused on energy-efficient data sensing and energy-effi-

cient routing respectively, a novel energy-efficient data

sensing and routing (EEDSR) problem that takes account

of energy-efficient data sensing and routing at the

same time in unreliable EH-WSN is formulated. We

propose an energy-efficient data sensing and routing

scheme (EEDSRS) in unreliable EH-WSN, so that EH-

WSN can use the harvested energy wisely for data sensing

and routing. EEDSRS is divided into three steps: (1) an

adaptive exponentially weighted moving average algorithm

(EWMAA) to estimate link quality. (2) a distributed

energetic-sustainable data sensing rate allocation algorithm

(ESDSRAA) to allocate energy for data sensing and

612 Wireless Netw (2018) 24:611–625

123

routing. According to the allocated energy, the optimal data

sensing rate is obtained. (3) a geographic routing with

unreliable link (GRUL) protocol to route the collected data

to destination along energy-efficient paths. Extensive

simulations based on real experimental data of harvested

energy are conducted to demonstrate the advantages of

ESDSRAA and GRUL protocol.

The remainder of this paper is organized as follows.

First, the related work is introduced in Sect. 2. Then, the

network model and problem formulation are described in

Sect. 3. EEDSRS is designed in Sect. 4 and the perfor-

mance evaluation of EEDSRS is shown in Sect. 5. Finally,

the conclusion is given in Sect. 6.

2 Related work

We divide the existing work into three parts: (1) energy-

aware routing in traditional WSN, (2) routing in EH-WSN,

and (3) geographic routing. In this section, we introduce

them in detail.

2.1 Energy-aware routing in traditional WSN

Due to energy constraint, it is required to design energy-

aware routing protocols in WSNs. During the past few

decades, energy-aware routing has been the focus of

researchers [27–31]. Energy-aware routing in traditional

WSNs can be classified into two categories: (1) reducing

energy consumption; and (2) prolonging network lifetime.

For example, Toh [27] proposed an energy-aware routing

protocol to minimize transmission energy. Their protocol

ensured that the energy consumption rate is evenly dis-

tributed among nodes. Madan and Lall [28] proposed dis-

tributed routing algorithms to maximize network lifetime.

The network lifetime in their work is defined as the time at

which the first node runs out of its battery energy. They

formulated the network lifetime problem as a linear pro-

gramming problem and designed distributed subgradient

algorithms to solve it. Similarly, Gatzianas and Georgiadis

[29] formulated the network lifetime maximization prob-

lem as a linear programming problem. They prolonged

network lifetime by routing packets to mobile sink.

Because a lot of sensor nodes may stop working due to

environmental impact and hardware failure, the definition

of network lifetime in [28] is not consistent with the actual

situation. Therefore, Karkvandi et al. [30] developed a

scheme to maximize the normalized network lifetime. Liu

et al. [31] proposed routing algorithms to balance energy

consumption among sensor nodes. The cost function in the

algorithm not only took account of the end-to-end energy

consumption but also remaining battery energy.

Although these schemes are efficient in terms of

reducing energy consumption and prolonging network

lifetime, they are difficult to be implemented in a local

algorithm. Because these work did not take account of

nodes’ capability of harvesting energy and random char-

acteristics of environmental energy, the routing schemes in

traditional WSNs cannot be used in EH-WSN directly. In

addition, these work only took account of the energy

consumption for data transmission. The energy consumed

by data sensing is not considered in protocol design, which

will result in performance degradation of these routing

schemes.

2.2 Routing in EH-WSN

Due to the random characteristics of environmental

energy, one of the challenging problems is to design

energy-efficient routing protocols according to harvested

energy. Research work [26, 32–35] focuses on routing

schemes with environmental energy supply to provide

perpetual data service. For example, Fan et al. [26]

developed a centralized algorithm and a distributed

algorithm to calculate the optimal lexicographic data

sensing rate. Liu et al. [32] proposed a distributed

algorithm, i.e., QuickFix, to allocate data sensing rate.

However, the proposed algorithm may lead to battery

outage and overflow problems. In order to solve these

problems, QuickFix with SnapIt algorithm is developed.

Chen et al. [33] proposed a distributed scheme, i.e.,

NetOnline, to maximize throughput. After that, they [34]

developed a low-complexity energy allocation and rout-

ing scheme to maximize system utility. Their

scheme doesn’t require prior knowledge of replenishment

profile. Zhang et al. [35] investigated data gathering

problem taking account of energy consumption for data

sensing and data transmission. First, they developed a

balanced energy allocation scheme (BEAS) to allocate

energy. Then, they proposed a distributed sensing rate

and routing control (DS2RC) algorithm to optimize data

gathering.

The aforementioned work considered time-varying

characteristics of environmental energy in protocol design.

In order to optimize data gathering, these work carefully

allocated the available energy for data sensing and trans-

mission according to the amount of harvested energy.

However, these work didn’t investigated how to route the

collected data to the sink. In addition, the unreliability of

wireless channel is not considered, which is not consistent

with the real situation [36, 37]. Without considering link

unreliability will greatly reduce the performance of these

schemes.

Wireless Netw (2018) 24:611–625 613

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2.3 Geographic routing

Geographic routing is a promising routing technique in

WSNs due to its good scalability. In geographic routing,

the establishment and maintenance of information for

routing path is no longer needed. Each node locally makes

routing decision based on the location information of

itself, its one hop neighbors and destination. The most

famous ‘‘greedy’’ geographic routing [38] routes packets

to the one-hop neighbor which provides the largest posi-

tive advancement to destination. Link unreliability was

not considered in ‘‘greedy’’ geographic routing. This is

not consistent with the real world. In [36], Cerpa et al.

investigated the unreliability of wireless channel and built

a model for it by statistic approach. They pointed out that

‘‘greedy’’ geographic routing has ‘‘weakest link prob-

lem’’. The neighbor nodes which are closer to destination

than current node may have ‘‘low-quality’’ links. ‘‘Low-

quality’’ links lead to a lot of packet loss and packet

retransmissions, which will consume a large amount of

energy. Recently, more studies focus on the geographic

routing problem in unreliable WSNs. For example, Seada

et al. [23] investigated the trade-off between distance and

hop count in geographic routing. In general, the longer the

transmission distance of each hop, the greater the proba-

bility that packets are lost. If routing scheme aims to

minimize the total number of hop counts by maximizing

the transmission distance per hop (as done in ‘‘greedy’’

forwarding scheme), it may consume more energy due to

retransmission. If routing scheme aims to forward packets

to close neighbors which have highly reliable links, only a

small transmission distance may be achieved by each hop

and more hop counts are needed to reach the destination,

which may also result in more energy consumption. How

to make the trade-off between hop counts and transmis-

sion distance is

challenging. Seada pointed out that the expected

packet advancement, i.e., packet reception rateðPRRÞ �advancement , is an optimal routing metric for geographic

routing in unreliable WSNs. In order to make trade-off

between distance and hop count, Lee et al. [39] proposed

a new routing metric, i.e., normalized advance (NADV).

Zamalloa et al. [40] investigated the impact of different

network parameters (e.g., channel and deployment

parameters) on the performance of different routing

strategies with respect to PRR� advancement. In order to

improve energy efficiency, Yu et al. [41] proposed a

geographic and energy aware routing (GEAR) algorithm

which routed packets to destination in energy-efficient

paths. However, their work didn’t consider the unrelia-

bility of wireless channel. Zeng et al. [24] proposed two

protocols, i.e., GREES-L and GREES-M, which took

account of not only lossy links but also random

environmental energy supply in protocol design. How-

ever, the limited capacity of rechargeable battery was not

considered. To the best of our knowledge, the aforemen-

tioned work only considered the energy consumption for

data transmission. The energy consumed by data sensing

is not considered in protocol design.

3 System model and problem formulation

3.1 Network model

We consider an EH-WSN G(V, E) with N ¼ jVj sensor

nodes (including a sink) and M ¼ jEj directional links.

Each sensor node has a unique identifier i , 1� i�N. If

sensor node i is within the transmission range of sensor

node j , there is a link ðj; iÞ 2 E, and sensor node i is called

as the neighbor node of sensor node j . Let NnbðiÞ denotethe set of neighbor nodes of sensor node i. The network is

mainly used in environmental monitoring and habitat

monitoring. All sensor nodes are equipped with the same

omni-directional antennas, solar cells and rechargeable

batteries with limited capacity Bmaxi . The harvested energy

can be stored in battery if the battery level doesn’t exceed

the highest level. We assume that the energy of sink node is

sufficient and not considered in this paper. Each sensor

node transmits information to the sink along a single path.

Let NpðiÞ be the set of sensor nodes in the path from sensor

node i to the sink. NrðiÞ denotes the set of sensor nodes

which use sensor node i as relay node. Note that i 62 NpðiÞand i 62 NrðiÞ. We assume that a time circle consists of T

time slots (T [ 0). In this paper, a time circle is 1 day and

T ¼ 24. Let Bi;t and qi;t denote the residual battery energy

and harvested energy of sensor node i at slot t , respec-

tively. Allocated energy Ai;t represents the energy allowed

to be used for sensor node i at slot t to collect and route

data, t ¼ 1; 2; . . .; T . We assume that each sensor node

knows the position of itself, its one-hop neighbors and

destination by GPS. In monitoring applications, the

assumption is reasonable because sensor nodes are required

to know position information. Sensing rate allocation and

routing decision are made slot by slot according to har-

vested energy. Sensing rate allocation starts at the begin-

ning of each slot. The network uses the media access

control (MAC) protocol that allows retransmission, e.g.,

IEEE 802.11. The acknowledgement (ACK) mechanism

retransmits the lost information, making lossy links appear

reliable to network layer. If packets are routed to where no

neighbor node is closer to destination than current node, a

‘‘communication void’’ happens. We assume that there is

no ‘‘communication void’’ which is not considered in this

paper.

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3.2 Energy consumption mode

We assume that sensing, transmitting and receiving one

unit of message by sensor node i consume energy esi , etxi

and erxi , respectively. Then, the total amount of energy

consumed by sensor node i at slot t for data sensing and

data transmission is given by

etotali;t ¼ ðesi þ etxi Þ � ri;t þ ðerxi þ etxi Þ �X

j2NrðiÞrj;t; ð1Þ

where ri;t is the data sensing rate of sensor node i at slot t .

3.3 Energy harvesting model

Sudevalayam et al. [42] pointed out the amount of energy

harvested in the future is uncontrollable, but can be esti-

mated with high accuracy according to the harvesting

history. Their methods are used in this paper to estimate

qi;t. Unlike the work in [24] which uses a random process

to model the mean energy harvesting rate of sensor nodes,

we use the real experimental data obtained from the

baseline measurement system (BMS) at the National

Renewable Energy Laboratory [43]. The harvesting profile

of solar power from July to November is shown in Fig. 1.

In Fig. 1, the experimental data is based on

37 mm 9 33 mm solar cell. The data of the first day, the

second day, the third day, the fourth day and the fifth day

are the average value of July, August, September, October

and November, respectively. The average amount of har-

vested energy for the 5 days are 258.65, 302.15, 291.81,

293.6 and 208.59 mWh, respectively.

3.4 Problem definition

Given an EH-WSN G(V, E) , let UðiÞ ¼ logðri;tÞ be the

utility function of sensor node i , where ri;t is the data

sensing rate of sensor node i at slot t . The EEDSR problem

in G(V, E) is to maximize the total utility of all nodes

during a time cycle, i.e.,PN

i¼1

PTt¼1 logðri;tÞ, and route all

the collected data to the sink in energy-efficient paths.

4 Protocol and algorithm design

We propose EEDSRS to solve EEDSR problem. EEDSRS

is divided into three steps: (1) EWMAA to estimate link

quality; (2) ESDSRAA to allocate energy for data sensing

and data transmission; (3) GRUL protocol to route all the

collected data to the sink along energy-efficient paths.

Now, we introduce them as follows.

4.1 Link quality estimation

In order to estimate link quality and transmission cost,

wireless extension layer (WEL) [39] is used. WEL is a sub-

layer which is located on the top of MAC layer. The

structure of WEL is shown in Fig. 2. Link state is estimated

by WEL and MAC layer. Information for link state and

transmission is encapsulated in simple primitives which are

sent to the upper layer protocol.

In this paper, we are not interested in the deails of MAC

layer. We assume that IEEE 802.11 is used on MAC layer.

Because IEEE 802.11 retransmits the lost frames to ensure

good packet delivery ratio (PDR) on network layer, we use

frame delivery ratio (FDR) instead of PDR in this paper. In

probe engine, each sensor node periodically probes link

quality. Since probe is broadcast message, IEEE 802.11

does not acknowledge and retransmit it. ‘‘hello’’ message

are broadcasted periodically to exchange information of

neighbor node. Let FDRij denote FDR from sensor node i

to sensor node j , i; j 2 V .

Fig. 1 Average solar power

harvesting profile of

37 mm 9 33 mm solar panels

obtained by BMS from July to

November

Wireless Netw (2018) 24:611–625 615

123

Because active probing needs to inject frames into net-

work to estimate FDR, we use the passive probing tech-

nique instead of active probing. The general framework of

passive link estimator is shown in Fig. 3. The passive link

estimator has two inputs: (1) message arrival event denoted

as M , and (2) periodic timer event denoted as T . Message

event provides infrequent input, while timer event provides

synchronous and periodic input. The estimated link quality

based on timer events are more accurate than that based on

message events. According to the minimum data rate

R provided by the protocols on higher layer, link estimator

can infer the minimum number of lost data over a period of

time and compensate accordingly.

Since the exponentially weighted moving average

(EWMA) estimator [44] is passive, simple and memory

efficient, it is used in this paper to estimate the link quality.

There are two events making sensor node j update FDRij.

One is the periodical time event T set by sensor node j , i.e.,

sensor node j updates FDRij every t seconds. The other one

is the message arrival event M that sensor node j receives a

probe message (‘‘hello’’ message) from sensor node i .

The psesudocode of the proposed EWMAA is as follows:

where dFDRij is current estimated value for FDRij, R is the

minimum data rate, numlostestimated is the estimated number of

lost frames, numlostactual is the actual number of lost frames,

MAC Layer

Wireless Extension Layer

Probe Engine Routing Protocl

MAC-specific infomation

Information from probes

Link cost query

/responseProbe

messages

Datapackets

Fig. 2 Wireless extension layer

Estimator

MessageArrival Event (M)

Timer Event (T)

Minimum Data RateConstant R

Estimation

Fig. 3 General framework of passive link estimator

Exponentially Weighted Moving Area Algorithm (EWMAA)

Description: algorithm is executed on sensor node jInput: inputting event I

Output: FDRij

FDRij = 1;numlost

estimated = [(current time − tMlast) × R];if (I is M event){

tMlast = tMcurrent;numlost

actual = seqcurrent − seqlast − 1;seqlast = seqcurrent;l = max(numlost

actual − numlostestimated, 0);

numlostestimated = 0;

FDRij = FDRij × αl+1 + (1 − α);}else if (I is T event){

l = numlostestimated;

FDRij = FDRij × αl;}

616 Wireless Netw (2018) 24:611–625

123

seqcurrent is the sequence number of current frame which is

received successfully, seqlast is the sequence number of last

frame which is received successfully, l is the number of

lost frames compensated into estimator, tMlast is the time

stamp of last M event, tMcurrent is the time stamp of the

current M event, ½�� is an integral function (i.e., ½x� � x. For

example, ½2:3� ¼ 2, ½�2:3� ¼ �3Þ, and a (0\a\1) is a

tuning parameter. If the input event isM event, the message

must be received successfully, and EWMAA sets

tMlast ¼ tMcurrent.

Each sensor node i estimates FDRji by EWMAA. The

measured FDRs of node i are included in probes. Each

neighbor node j of sensor node i obtains the FDRji from

probes sent by sensor node i .

4.2 ESDSRAA

We formulate the ESDSRA problem as a combinatorial

optimization problem which aims to minimize the objec-

tive function shown in Eq. (2).

maxri;t

XN

i¼1

XT

t¼1

UðiÞ: ð2Þ

subject to

Ai;t �Bi;t þ qi;t; 8i; 8t; ð3Þ

Ai;t � etotali;t ; 8i; 8t; ð4Þ

XT

t¼1

Ai;t �Bi;1 þXT

t¼1

qi;t; 8i; ð5Þ

Bi;t þ qi;t � Ai;t �Bmaxi ; 8i; 8t: ð6Þ

Equations (3) and (4) ensure that the allocated energy for

sensor node i at slot t cannot be greater than current

available energy and smaller than the total amount of

energy consumed by node i at slot t . Equation (5) ensures

that the total amount of allocated energy at all slots of

sensor node i cannot be greater than the total amount of

available energy. Bi;1 in Eq. (5) represents the initial bat-

tery energy of sensor node i . Equations (3), (4) and (5)

guarantee the energy sustainability of the network, i.e.,

each sensor node cannot run out its energy and stop

working. Equation (6) ensures that the battery level of

sensor node i will not exceed the highest level, i.e., all the

harvested energy can be stored in battery and sensor node i

will not miss the opportunity to recharge. Because the

objective function ( i.e.,PN

i¼1

PTt¼1 UðiÞ ¼

PNi¼1PT

t¼1 logðri;tÞ ) is strictly concave, it can achieve the pro-

portional fairness of sensing rate [45]. If sensing rate is

determined, the energy used for data sensing and trans-

mission can be determined.

In order to solve ESDSRA problem, ESDSRAA is pro-

posed. First, ESDSRAA allocates the energy allowed to be

used by sensor node i at slot t , i.e., Ai;t. Then, ESDSRAA

decides the optimal sensing rate ri;t according to Ai;t. Some

research work [32] demonstrated that the optimal energy

allocation scheme is qi;t ¼ 1T

PTt¼1 qi;t, if the battery capacity

of sensor node i is large enough to store all the harvested

energy at time slot t . However, qi;t is not the optimal allo-

cation scheme since battery capacity is limited. Let

Ai;t ¼ ð1� biÞ � qi;t þ bi � qi;t; ð7Þ

where 0� bi � 1 is a tuning parameter. The proposed

ESDSRAA is as follows:

Energetic-Sustainable Data Sensing Rate Allocation Algorithm(ESDSRAA)

Step 1. Compute the average energy harvesting rate ρi,t of sensor node i,i = 1, 2, . . . , N, t = 1, 2, . . . , T .

Step 2. Compute βi using tuning parameter allocation algorithm (TPAA),i = 1, 2, . . . , N .

Step 3. Compute Ai,t using Eq.(7), i = 1, 2, . . . , N, t = 1, 2, . . . , T .Step 4. Compute ri,t based on Ai,t using sensing rate allocation algorithm (SRAA).

Wireless Netw (2018) 24:611–625 617

123

The TPAA used in ESDSRAA is as follows:

Tuning Parameter Allocation Algorithm (TPAA)

for (each sensor node i, i = 1, 2, . . . , N){

ρi,t = 1T

Tt=1 ρi,t;

βi = 0.5;}for (each sensor node i, i = 1, 2, . . . , N){

for (each slot t, t = 1, 2, . . . , T ){

Ai,t = max(0, min(Bi,t + ρi,t, (1 − βi)ρi,t + βiρi,t));oi,t = Bi,t + ρi,t − Ai,t − Bmax

i ;Bi,t+1 = min(Bi,t + ρi,t − Ai,t, B

maxi );

compute βi = max(0,min(1, βi +max{ oi,t

ρi,t, t = 1, 2, . . . , T}));

until one of the two conditions stated as follows is satisfied:(1) max{oi,t, t = 1, 2, . . . , T} = 0;(2) max{oi,t, t = 1, 2, . . . , T} < 0 while βi = 0;end compute

}}return βi, i = 1, 2, . . . , N

In TPAA, if the battery level of sensor node i at slot t

doesn’t exceed the highest level, oi;t � 0 (8i, 8t). Thus,maxfoi;tqi;t

; t ¼ 1; . . .; Tg� 0.

1. If oi;t\0 (8i), we know that maxfoi;tqi;t; t ¼ 1; . . .; Tg

\0. The negative value of maxfoi;tqi;t; t ¼ 1; . . .; Tg will

lead to bi ¼ 0 eventually. Therefore, when bi ¼ 0,

TPAA stops running and finds the desirable bi.2. If oi;t ¼ 0 (8i), we know that maxfoi;tqi;t

; t ¼ 1; . . .; Tg¼ 0. There is no change on bi for each iteration. TPAA

stops running and finds the desirable bi.3. If there are some oi;t ¼ 0 and some oi;t\0 (8i), we

know that maxfoi;tqi;t; t ¼ 1; . . .; Tg ¼ 0. This situation is

similar to situation (2).

From above analysis, it is obvious that the two termination

conditions in TPAA ensure Eq. (6). In TPAA, Ai;t ¼maxð0; minðBi;t þ qi;t; ð1� biÞ � qi;t þ bi � qi;tÞÞ ensures

Eq. (3), i.e., Ai;t �Bi;t þ qi;t. From Eq. (3), we can deduce

that

XT

t¼1

Ai;t �XT

t¼1

ðBi;t þ qi;tÞ; 8i 2 N: ð8Þ

Since

XT

t¼1

ðBi;t þ qi;tÞ ¼XT

t¼1

Bi;t þXT

t¼1

qi;t �Bi;1 þXT

t¼1

qi;t: ð9Þ

We can get thatPT

t¼1 Ai;t �Bi;1 þPT

t¼1 qi;t; 8i. Therefore,Eq. (5) is satisfied.

When the allocated energy for each sensor node at each

slot is obtained by TPAA, the ESDSRA problem can be

simplified as follows:

maxri;t

XN

i¼1

XT

t¼1

logðri;tÞ; ð10Þ

subject to

Ai;t � etotali;t ; 8i; 8t: ð11Þ

In order to design a distributed algorithm, the theory of

dual decomposition [46] is used. The Lagrangian of the

problem described in Eq. (10) is defined as

Lðai;tÞ ¼maxri;t

XN

i¼1

XT

t¼1

logðri;tÞ�

þ ai;tðAi;t � ðesi þ etxi Þ � ri;t

� ðetxi þ erxi Þ �X

j2NrðiÞrj;tÞ

):

ð12Þ

where ai;t � 0 is the Lagrangian multiplier of sensor node i

at slot t with respect to the constraint shown in Eq. (11).

The dual problem shown in Eq. (10) can be written as

follows:

minai;t

Lðai;tÞ: ð13Þ

618 Wireless Netw (2018) 24:611–625

123

Then, sub-gradient method updates Lagrangian multiplier

ai;t iteratively as follows:

ai;tðmþ 1Þ ¼maxð0; ai;tðmÞ � cðAi;t � ðeri þ etxi Þ � ri;t� ðerxi þ etxi Þ

X

j2NrðiÞrj;tÞÞ;

ð14Þ

where m is the iteration number, and c[ 0 is a constant step

size. For a given sensor node i , Eq. (12) can be written as

Lðai;tÞ ¼maxri;t

XN

i¼1

ðlogðri;tÞ þ ai;t � Ai;t � ai;t � ri;t � ðesi þ etxi Þ

� ri;tX

j2NrðiÞaj;t � ðetxi þ erxi ÞÞg:

ð15Þ

Because logðri;tÞ is a strictly concave function, there is a

unique maximizer ri;tðaÞ for all a . When ai;t(i ¼ 1; 2; . . .;N) are scalars, the maximum sensing data rate

can be obtained by Kuhn–Tucker theorem [47] as follows:

r�i;t ¼ maxri;t

X

i

flogðri;tÞ þ ai;t � Ai;t � ai;t � ri;t � ðesi þ etxi Þ

� ri;t �X

j2NrðiÞaj;t � ðerxj þ etxj Þg

¼ maxð0;minðU0�1 � ðvni;t þ vmi;tÞÞÞ;ð16Þ

where

vni;t ¼ai;tðesi þ etxi Þ; ð17Þ

vmi;t ¼X

j2NrðiÞai;tðerxi þ etxi Þ: ð18Þ

Note that U0�1 is the inverse of U0.The distributed SRAA used in ESDSRAA to allocate

optimal sensing rate is as follows:

4.3 GRUL protocol

In GRUL, each sensor node maintains the information of

its one-hop neighbor nodes, e.g., residual battery energy,

sensing rate, energy harvesting rate, location, and link

quality (e.g., FDR). If sensor node i wants to transmit a

message to the sink D , GRUL tries to balance the geo-

graphical advancement per hop and the available energy on

the neighbor nodes of sensor node i .

Because wireless channel is unreliable, the actual

advancing distance (AAD) of a packet transmission at slot t

from sensor node i to sensor node j should consider

FDRijðtÞ and FDRjiðtÞ [48]. Thus, we define the

AAD(i, j, D, t) from sensor node i to sensor node j towards

the direction of destination D as follows:

AADði; j;D; tÞ ¼ progressði; j;D; tÞ � FDRijðtÞ � FDRjiðtÞ;ð19Þ

where D is the destination node, progress(i, j, D, t) is the

progress distance at slot t from sensor node i to sensor node

j towards the direction of destination node D . FDRijðtÞ �FDRjiðtÞ is the inverse of the expected transmission count

(ETC) defined in [49]. The physical meaning of

AAD(i, j, D, t) is the expected progress distance at slot t

towards the destination D per frame transmission. To

illustrate Eq. (19), an example is given in Fig. 4. The

progress(1, 2, 3, 9) is the distance between sensor node 1

and the projection 20 of sensor node 2 . The projection 20 ison the line connecting nodes 1 and 3. progressð1; 2; 3; 9Þ¼ distð1; 20Þ ¼ 5. Thus, AADð1; 2; 3; 9Þ ¼ progressð1; 2;3; 9Þ � FDR12ð9Þ � FDR21ð9Þ ¼ 5� 0:7� 0:3 ¼ 1:05:

Obviously, the total amount of available energy AE(j, t)

on sensor node j at slot t which is allowed to be used for

delivering messages can be computed by

AEðj; tÞ ¼ Bj;t þ qj;t � esj � rj;t; ð20Þ

Sensing Rate Allocation Algorithm (SRAA)

Input: Ai,t, i = 1, 2, . . . , N, t = 1, 2, . . . , TOutput: ri,t, i = 1, 2, . . . , N, t = 1, 2, . . . , T

for (each sensor node i, i = 1, 2, . . . , N){

for (each slot t, t = 1, 2, . . . , T ){

Step 1. sensor node i updates Lagrangian multiplier ai,t locally by Eq. (14).Step 2. sensor node i sends its ai,t to sensor node j, j ∈ Nr(i), collects

and forwards aj,t, j ∈ Np(i).Step 3. sensor node i computes its vn

i,t and vmi,t by Eqs. (17) and (18).

Step 4. sensor node i computes its sensing data rate ri,t by Eq. (16).}

}return ri,t, i = 1, 2, . . . , N, t = 1, 2, . . . , T

Wireless Netw (2018) 24:611–625 619

123

where esj � rj;t is the amount of energy on node j used for

data sensing.

In GRUL protocol, in order to route a packet to desti-

nation D , routing decision on node i at slot t is based on the

transmission cost cost(i, j, D, t) of link (i, j) ,

costði; j;D; tÞ ¼ 1

l �NAADði; j;D; tÞ þ ð1� lÞ �NAEði; j; tÞ ;

j 2 NnbðiÞ;ð21Þ

where 0�l�1 is a regulate weight. NAAD(i, j, D, t) is the

normalized advancing distance from sensor node i to its

one-hop neighbor node j towards the direction of destina-

tion D ,

NAADði; j;D; tÞ ¼ AADði; j;D; tÞmaxfAADði; k;D; tÞ; k 2 NnbðiÞg

:

ð22Þ

NAE(i, j, t) is the normalized available energy,

NAEðj; tÞ ¼ AEðj; tÞmaxfAEðk; tÞ; k 2 NnbðiÞg

: ð23Þ

Minimizing the cost shown in Eq. (21) is equivalent to

maximizing the denominator, which is a linear combina-

tion of two parts. The first part is NAAD(i, j, D, t) .

NAAD(i, j, D, t) represents how much the normalized

progress a packet can make on unreliable link (i, j) at

slot t towards the destination D . Maximizing

NAAD(i, j, D, t) can reduce the number of hop counts from

source to destination, which reduces the energy consump-

tion (when the transmission power is fixed). The second

part NAE(i, j, t) describes the normalized available energy

of sensor node j at slot t which is allowed to be used for

delivering packets. From Eqs. (20) and (23), we can see

that NAE(i, j, t) is a combination of harvested energy,

residual battery energy and energy consumption for sensing

data. Minimizing Eq. (21) can balance the importance of

progress per packet transmission (related to energy con-

sumption and delay) and residual energy (related to load

balancing and network lifetime).

In Eq. (21), if l ¼ 1, GRUL is equivalent to geographic

routing as in [39], which only took account of unreliability

of wireless channel. If l ¼ 0, GRUL is equivalent to

traditional energy aware routing based on residual energy

and energy consumption (as in [31]).

We assume that there is no communication voids. Thus,

there is at least one neighbor node j of sensor node i sat-

isfying AADði; j;D; tÞ[ 0. In this paper, we follows [24],

i.e., we only consider the neighbor node j 2 NnbðiÞ with

FDRijðtÞ[ 0:2 and FDRjiðtÞ[ 0:2 as the candidate next

hop of sensor node i . Small FDR will make a large number

of retransmissions, which will increase not only the energy

consumption but also the inference to other nodes.

5 Performance evaluation

In this section, simulation results are provided to demon-

strate the performance of the proposed ESDSRAA and

GRUL over existing algorithms, the corresponding residual

energy based protocol and ‘‘greedy’’ routing protocol of

GRUL. All the results are obtained by Matlab and Glo-

MoSim library [50]. GloMoSim library is a scalable sim-

ulation environment for wireless networks.

5.1 Simulation setting

The simulation studies involve random networks with 196

stationary nodes which are uniformly distributed in

250 9 250 m2 square region. All sensor nodes have the

same transmission power. Ground reflection (Two-Ray)

path loss model and Ricean fading model [51] for signal

propagation are used to simulate the unrealiable wireless

channel. The reception decision of a packet is based on the

signal-to-noise ratio (SNR) threshold. If the SNR at the

receiver is larger than the pre-defined constant, the packet

is received successfully. Otherwise, the packet is lost or

received with error. The maximum transmission range is

35 m. a in EWMAA is set to 0.9 . IEEE 802.11 is used as

the protocol on MAC layer. The battery capacity Bmaxi of all

nodes are 304 mWh. The initial battery energy Bi;1 of all

nodes are 150 mWh. We adopt the energy consumption

parameters where etxi ¼ 63mW, erxi ¼ 69mW and esi ¼5:4mW (when transmission power is 0 dBm , transmit data

rate is 250 kbps ). We set l in Eq. (21) to 0.5. In our

protocol, ‘‘hello’’ message broadcasts periodically every

50s to exchange neighbor nodes’ information and probe

link quality.

5.2 Results for ESDSRAA

Figure 5 shows the results of energy allocation for a ran-

domly selected sensor node using ESDSRAA, QuickFix

and QuickFix with SnapIt. From Fig. 5, we can see that the

Fig. 4 Example of AAD(i, j, D)

620 Wireless Netw (2018) 24:611–625

123

values of allocated energy computed by QuickFix and

QuickFix with SnapIt are 0 at some time slots, which

means that the sensor node runs out its energy at these time

slots. However, energy allocation computed by ESDSRAA

does not have this problem. Furthermore, the minimal

values of allocated energy computed by ESDSRAA are

very stable, while the values of allocated energy computed

by the other two algorithms are changed with energy har-

vesting rate. This demontrates the advantage of ESDSRAA

in terms of energy allocation.

Figure 6 shows the battery level of the selected sensor

node. If the sensor node uses QuickFix or QuickFix with

SnapIt, the battery level of the sensor node can reach the

highest battery level or the lowest battery level at some

time slots, which means that the sensor node will miss the

opportunity to recharge its battery or run out of energy. If

the sensor node uses ESDSRAA, the battery level of the

sensor node cannot reach the highest battery level and

lowest battery level, which demonstrates that ESDSRAA

can take full advantage of the opportunity to recharge and

avoid running out of battery energy.

Figure 7 shows the total sensing rates of all nodes for

each day. From Fig. 7, we can see that the total sensing rate

of ESDSRAA is the largest one expect for the first day.

This is because sensor nodes use the initial battery energy

irrespective of the harvested energy in the first day.

Obviously, the larger the total amount of sensing rate, the

better the network monitoring quality. Figure 7 demon-

strates that ESDSRAA achieves the best network moni-

toring quality among the three algorithms.

The network utility of each day is shown in Table 1. It

can be seen that ESDSRAA has the largest network utility

expect for the first day. This is because sensor nodes can

use the initial battery energy irrespective of the harvested

energy in the first day. The network utility of QuickFix and

QuickFix with SnapIt is negative infinity in the third, fourth

and fifth days, because the sensing rate of some sensor

nodes is 0 in these days.

Fig. 5 Energy allocation of a

sensor node

Fig. 6 Battery level states

Wireless Netw (2018) 24:611–625 621

123

5.3 Results for GRUL

In order to evaluate the energy efficiency of GRUL pro-

tocol, two metrics are defined as follows:

• Average residual energy This metric calculates the

average residual battery energy of all sensor nodes at

each time slot. It represents the energy efficiency of

routing protocol, when the same number of packets are

transmitted in the network. The more the average

residual battery energy is, the better the energy

efficiency of the protocol is. A better routing protocol

in EH-WSN should provide more residual energy when

the same amount of packets are transmitted in the

network.

• Standard deviation of residual energy This metric

evaluates the standard deviation of residual energy.

This metric indicates how the energy consumption is

distributed among sensor nodes. The small the value of

this metric is, the better the performance of the routing

protocol is in balancing energy consumption.

Figures 8 and 9 show the simulation results. In the two

figures, ‘‘Greedy’’ denotes the geographic routing without

Fig. 7 Total sensing rate of all

nodes for each day

Table 1 Network utility of

each dayAlgorithm Network utility

First day Second day Third day Fourth day Fifth day

QuickFix 3769 4386 �1 �1 �1QuickFix with SnapIt 3886 3985 �1 �1 �1ESDSRAA 3849 4567 4041 4130 3762

Fig. 8 Average residual energy

of all sensor nodes

622 Wireless Netw (2018) 24:611–625

123

energy awareness. ‘‘Greedy’’ protocol only takes account

of the unreliability of wireless channel, which is the

extreme situation of ESDSRAA by setting l ¼ 1 in

Eq. (21). ‘‘Energy aware’’ denotes the energy aware routing

protocol which considers energy consumption and residual

energy of each node. ‘‘energy aware’’ is the extreme situ-

ation of ESDSRAA by setting l ¼ 0 in Eq. (21).

From Figs. 8 and 9, we can see that ESDSRAA is more

energy efficient than ‘‘energy aware’’ routing and

‘‘Greedy’’ routing in terms of having more average residual

energy and smaller standard deviation of residual energy.

This is because ESDSRAA routing takes into account not

only the harvested energy but also the nodes’ residual

energy. In addition, the unreliability of wireless channel is

considered in ESDSRAA, which reduces energy con-

sumption. From Figs. 7 and 8, we can see that ‘‘Greedy’’

routing has the lowest average residual energy and the

largest standard deviation of residual energy. ‘‘Greedy’’

routing has the worst performance on energy efficiency,

because it considers neither the harvested environmental

energy nor residual battery energy in routing decision.

6 Conclusion and future work

In this paper, we have studied the energy-efficient data

sensing and routing problem in unreliable energy-harvest-

ing wireless sensor network (EH-WSN). We proposed an

energy-efficient data sensing and routing

scheme (EEDSRS), so that EH-WSN can use the harvested

energy wisely for data sensing and transmission according

to current available energy to maximize network utility and

route all the collected data to the sink along energy-effi-

cient paths. EEDSRS is divided into three steps: (1)

adaptive exponentially weighted moving average algorithm

(EWMAA) to estimate link quality. (2) distributed ener-

getic-sustainable data sensing rate allocation algorithm

(ESDSRAA) to allocate energy for data sensing and

transmission. According to the allocated energy, the opti-

mal data sensing rate is obtained. (3) geographic routing

with unreliable link (GRUL) protocol to route all the col-

lected data to the destination along energy-efficient paths.

We performed extensive simulations to demonstrate the

efficiency of our protocol by comparing with existing

work, the corresponding energy aware routing protocol and

‘‘Greedy’’ routing protocol of GRUL. Our future work will

focus on investigating the theoretical analysis of our pro-

tocol and the impact of inaccurate solar power harvesting

profile on data sensing and routing in EH-WSN.

Acknowledgments The authors would like to thank the reviewers

and the editors for their valuable suggestions and comments that

helped improve the paper.

References

1. Yao, Y., Cao, Q., & Vasilakos, A. V. (2015). EDAL: An energy-

efficient, delay-aware, and lifetime-balancing data collection

protocol for heterogeneous wireless sensor networks. IEEE/ACM

Transactions on Networking, 23(3), 810–823.

2. He, S., Chen, J., Jiang, F., Yau, D. K. Y., Xing, G., & Sun, Y.

(2013). Energy provisioning in wireless rechargeable sensor

networks. IEEE Transactions on Mobile Computing, 12(10),

1931–1942.

3. Guo, S., Wang, C., & Yang, Y. (2014). Joint mobile data gath-

ering and energy provisioning in wireless rechargeable sensor

networks. IEEE Transactions on Moble Computing, 13(12),

2836–2852.

4. Zhao, M., Li, J., & Yang, Y. (2014). A framework of joint mobile

energy replenishment and data gathering in wireless rechargeable

sensor networks. IEEE Transactions on Mobile Computing,

13(12), 2689–2705.

5. Akyildiz, I. F., Su, W., Sankarasubramaniam, Y., & Cayirci, E.

(2002). A survey on sensor networks. IEEE Communications

Magazine, 40(8), 102–114.

6. Pantazis, N. A., Nikolidakis, S. A., & Vergados, D. D. (2012).

Energy-efficient routing protocols in wireless sensor networks: A

survey. IEEE Communications Surveys, 15(2), 551–591.

Fig. 9 Standard deviation of

residual energy

Wireless Netw (2018) 24:611–625 623

123

7. Li, F., & Wang, Y. (2008). Routing in vehicular ad hoc networks:

A survey. IEEE Vehicuar Technology Magazine, 2(2), 12–22.

8. Prathap, U., Shenoy, P. D., Venugopal, K. R., & Patnaik, L. M.

(2012). Wireless sensor networks applications and routing pro-

tocols: Survey and research challenges. In Proceedings of inter-

national symposium on ISCOS.

9. Muruganathan, S. D., Ma, D. C. F., Bhasin, R. I., & Fapojuwo, A.

O. (2005). A centralized energy-efficient routing protocol for

wireless sensor networks. IEEE Communications Magazine,

43(3), 8–13.

10. Ergen, S. C., & Varaiya, P. (2007). Energy efficient routing with

delay guarantee for sensor notworks. Wireless Networks, 13(5),

679–690.

11. Zhu, J., & Wang, X. (2011). Model and protocol for energy-

efficient routing over mobile ad hoc networks. IEEE Transactions

on Mobile Computing, 10(11), 1546–1557.

12. Voigt, T., Ritter, H., & Schiller, J. (2003). Utilizing solar power

in wireless sensor networks. In 28th Annual IEEE international

conference on LCN’03.

13. Eu, Z. A., Tan, H. P., & Seah, W. K. G. (2009). Routing and relay

node placement in wireless sensor networks powered by ambient

energy harvesting. In Proceedings of IEEE wireless communi-

cations and networking conference.

14. Lin, L., Shroff, N. B., & Srikant, R. (2007). Asymptotically

optimal power aware routing for multihop wireless networks with

renewable energy sources. IEEE/ACM Transactions on Net-

working, 15(5), 1021–1034.

15. Ou, C. H., & Ssu, K. F. (2008). Flying anchors in three-dimen-

sional wireless sensor networks. IEEE Transactions on Mobile

Computing, 7(9), 1084–1097.

16. Wang, J., Ghost, R. K., & Das, S. K. (2010). A survey on sensor

localization. Journal of Control Theory and Applications, 8(1),

2–11.

17. Frey, H. (2004). Scalable geographic routing algorithms for

wireless ad hoc networks. IEEE Network, 18(4), 18–22.

18. Xing, G., Lu, C., Pless, R., & Huang, Q. (2004). On greedy

geographic routing algorithms in sensing-covered networks. In

Proceedings of MobiHoc’04.

19. Zhang, H., & Shen, H. (2010). Energy-efficient beaconless geo-

graphic routing in wireless sensor networks. IEEE Transactions

on Parallel and Distributed Systems, 21(6), 881–896.

20. Lim, T. L., & Mohan, G. (2005). Energy aware geographical

routing and topology control to improve network lifetime in

wireless sensor networks. In Proceedings of 2nd international

conference on broadband networks.

21. Haider, R., Javed, M. Y., & Khattak, N. S. (2007). EAGR: Energy

aware greedy routing in sensor networks. In: Proceedings of

FGCN.

22. Huang, H., Hu, G., & Yu, F. (2013). Energy-aware geographic

routing in wireless sensor networks with anchor nodes. Interna-

tional Journal of Communication Systems, 26(1), 100–113.

23. Seada, K., Zuniga, M., Helmy, A., & Krishnamachari, B. (2004).

Energy-efficient forwarding strategies for geographic routing in

lossy wireless sensor networks. In Proceedings of ACM

SenSys’04.

24. Zeng, K., Ren, K., Lou, W., & Moran, P. J. (2009). Energy aware

efficient geographic routing in lossy wireless sensor networks

with environment energy supply. Wireless Networks, 15(1),

39–51.

25. Hou, Y. T., Shi, Y., & Sherali, H. D. (2004). Rate allocation in

wireless sensor networks with network lifetime requirement. In

Proceedings of MobiHoc’04.

26. Fan, K. W., Zheng, Z., & Sinha, P. (2008). Steady and fair rate

allocation for rechareable sensors in perpetual sensor networks.

In Proceedings of SenSys’08.

27. Toh, C. (2002). Maximum battery life routing to support ubiq-

uitous mobile compting in wireless ad hoc networks. IEEE

Communications Magazine, 39(6), 138–147.

28. Madan, R., & Lall, S. (2006). Distributed algorithms for maxi-

mum lifetime routing in wireless sensor networks. IEEE Trans-

actions on Wireless Communications, 5(8), 2185–2193.

29. Gatzianas, M., & Georgiadis, L. (2008). A distributed algorithm

for maximum lifetime routing in sensor networks with mobile

sink. IEEE Transactions on Wireless Communications, 7(3),

984–994.

30. Karkvandi, H. R., Pecht, E., & Yadid-Pecht, O. (2011). Effective

lifetime-aware routing in wireless sensor networks. IEEE Sensors

Journal, 11(12), 3359–3367.

31. Liu, A., Ren, J., Li, X., Chen, Z., & Shen, X. (2012). Design

principles and improvement of cost function based energy aware

routing algorithms for wireless sensor networks. Computer Net-

works, 56(7), 1951–1967.

32. Liu, R. S., Sinha, P., & Koksal, C. E. (2010). Joint energy

management and resource allocation in rechargeable sensor net-

works. In Proceedings of IEEE INFOCOM.

33. Chen, S., Sinha, P., Shroff, N. B., & Joo, C. (2011). Finite-

horizon energy allocation and routing scheme in rechargeable

sensor network. In Proceedings of IEEE INFOCOM.

34. Chen, S., Sinha, P., Shroff, N. B., & Joo, C. (2012). A simple

asymptotically optimal energy allocation and routing scheme in

rechargeable sensor networks. In Proceedings of IEEE

INFOCOM.

35. Zhang, Y., He, S., & Chen, J. (2013). Data gathering optimization

by dynamic sensing and routing in rechargeable sensor networks.

In Proceedings of IEEE international conference on SECON.

36. Cerpa, A., Wong, J. L., Kuang, L., Potkonjak, M., & Estrin, D.

(2005). Statistical model of lossy links in wireless sensor net-

works. In Proceedings of IPSN.

37. Guo, S., He, L., Gu, Y., Jiang, B., & He, T. (2014). Opportunistic

flooding in low-duty-cycle wireless sensor networks with unre-

liable links. IEEE Transactions on Computers, 63(11),

2787–2802.

38. Na, J., Soroker, D., & Kim, C. K. (2007). Greedy geographic

routing using dynamic potential field for wireless ad hoc net-

works. IEEE Communications Letters, 11(3), 243–245.

39. Lee, S., Bhattacharjee, B., & Banerjee, S. (2005). Efficient geo-

graphic routing in multihop wireless networks. In Proceedings of

the 6th ACM international symposium on MobiHoc’05.

40. Zamalloa, M. Z., Seada, K., Krishnamachari, B., & Helmy, A.

(2008). Efficient geographic routing over lossy links in wireless

sensor networks. ACM Transactions on Sensor Networks 4(3).

41. Yu, Y., Govindan, R., & Estrin, D. Geographical and energy

aware routing: A recursive data dissemination protocol for

wireless sensor networks. http://www.citeulike.org/group/1388/

article/700446.

42. Sudevalayam, S., & Kulkarni, P. (2011). Energy harvesting

sensor nodes: Survey and implications. IEEE Communications

Surveys and Turorials, 13(3), 443–461.

43. National Renewable Energy Laboratory. (2013). http://www.nrel.

gov.

44. Woo, A., & Culler, D. Evaluation of efficient link reliability

estimators for low-power wireless networks. http://vm133.lib.

berkeley.edu:90/reports/TRWebData/accessPages/CSD-03-1270.

html.

45. Low, S. H., & Lapsley, D. E. (1999). Optimization flow control-I:

Basic algorithm and convergence. IEEE/ACM Transactions on

Networking, 7(6), 861–874.

46. Xiao, L., Johansson, M., & Boyd, S. P. (2004). Simultaneous

routing and resource allocation via dual decomposition. IEEE

Transactions on Communications, 52(7), 1136–1144.

624 Wireless Netw (2018) 24:611–625

123

47. Shi, C., Lu, J., & Zhang, G. (2005). An extended Kuhn–Tucker

approach for linear bilevel programming. Applied Mathematics

and Computation, 162(4), 51–63.

48. Zeng, K., Lou, W., Ren, K., & Moran, P. J. (2006). Energy-

efficient geographic routing in environmentally powered wireless

sensor networks. In Proceedings of IEEE MILCOM.

49. Couto, D., Aguayo, D., Bicket, J., & Morris, R. (2003). A high-

throughput path metric for multi-hop wireless routing. In Pro-

ceedings of ACM MobiCom’03.

50. Zeng, X., Bagrodia, R., & Gerla, M. (1998). GloMoSim: A

library for parallel simulation of large-scale wireless networks. In

Proceedings of PADS’98.

51. Punnoose, R. J., Nikitin, P. V., & Stancil, D. D. (2000). Efficient

simulation of Ricean fading within a packet simulator. In Pro-

ceedings of IEEE-VTS Fall VTC.

Ting Lu Received the Ph.D.

degree in School of Electronic

Information and Electrical

Engineering, Shanghai Jiaotong

University, China in 2013. Her

research interests includes

resource management, cross-

layer optimization, and dis-

tributed algorithm design in

wireless networks.

Guohua Liu has been a full

professor at Donghua Univer-

sity. His current interests

include wireless networks and

internet of things.

Shan Chang Received the

Ph.D. degree in School of

Electronic Information and

Electrical Engineering, Xian

Jiaotong University, China in

2012. Her research interests

includes participatory sensing,

privacy preservation, data trust-

worthiness and data accuracy in

wireless networks.

Wireless Netw (2018) 24:611–625 625

123

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