An Analysis of Lifetime-extended Algorithm for

Wireless Sensor Networks

Chien-Erh Weng1, Jia-Ming Zhang2 and Ho-Lung Hung

1Department of Electronic Communication Engineering,

National Kaohsiung Marine University, Kaohsiung, Taiwan. ROC

2Institute of Communications Engineering,

National Chung Cheng University, Chia-Yi, Taiwan, ROC

Department of Electrical Engineering, Chienkuo Technology University

e-mail: hlh@ctu.edu.tw * Correspondence addressee

Abstract-Rapid advances in sensor technology and wireless communications have led to the

development of wireless sensor networks (WSNs). However, the sensor nodes in WSNs have

a finite lifetime since it is often impractical, or even impossible, to recharge their batteries

once they have been deployed. When the energy of a sensor node has been fully consumed, it

can play no further role within the WSNs. In an attempt to prolong the lifetime of WSNs,

various schemes have been proposed. This paper proposed a lifetime-extension under

uniform distribution (LEUD) scheme which not only prolongs the lifetime of WSNs, but also

optimizes its performance by maximizing the total number of active regions within the

networks. To evaluate the effectiveness of our scheme, we chose three uniform distribution

algorithms with LEUD to analyze and compared the performance of our scheme. Numerical

simulations are performed which demonstrate that when the deployed sensor nodes have an

equal initial energy and are distributed uniformly within the networks, LEUD provides an

improved networks performance.

Keywords: WSNs, LEUD, lifetime, uniform distribution.

I. Introduction

The rapid growth in digital signal processing techniques and integrated circuits have led

to considerable interest in the development of low-cost, low-power wireless sensor networks

(WSNs). Such networks have the potential for deployment in various applications, including

environmental detection and monitoring, home automation, telemonitoring of human

physiological data, forest fire detection, battlefield surveillance, nuclear, biological and

chemical attack detection and reconnaissance, urban search and rescue operations, and so

forth [1].

A typical WSNs comprises a large number of sensors densely deployed either within the

environment of interest or very close to it and designed to perform continuous sensing, event

detection, event identification, location sensing, or local actuation functions. The deployment

of WSNs in inhospitable or actively hostile fields, in which the networks must function

correctly under limited radio coverage has attracted particular interest. In such environments,

recharging the sensor nodes’ batteries is generally impossible, and hence it is essential to

conserve the sensor nodes’ energy in order to extend the network operation. Various

solutions for energy conservation within WSNs have been proposed, including energy-

efficient routing schemes, efficient medium access control protocols, power-aware

algorithms, and so on [2-6]. However, relatively little attention has been paid to the problem

of optimizing WSNs in terms of their power efficiency, coverage area and deployment costs.

Nevertheless, these are crucial issues when deploying mobile sensor nodes in any region of

interest (ROI) since the optimal deployment of sensors ensures their maximum possible

utilization [7].

In general, sensor networks can be deployed using one of two different strategies, namely

random or controlled. In the latter case, a total of K independent sets of sensor nodes are

deployed to provide a surveillance service in the sensing field, and each set of sensor nodes,

known as a cover, is sufficient to provide complete coverage of the field. In operation, each

cover is activated in turn, while the remaining covers are allowed to sleep, thereby

conserving their energy. Under this deployment strategy, the duty cycle of each sensor node

is reduced to 1/K, and thus its lifetime is effectively prolonged by up to K times [8].

A sensor field can be represented as an array of two-dimensional grid points. The

granularity of the grid points is determined by the positioning resolution required when

monitoring the networks. Figure 1 illustrates a typical network in which the sensing field is

covered with 3 x 5 grid points. As shown, network surveillance is performed using six sensor

nodes, located in grids (1, 2), (2, 1), (2, 2), (4, 2), (4, 3) and (5, 2), respectively. The sensor

nodes are assumed to be homogeneous, i.e. they are identical in terms of their computational

abilities, initial energy, functional capabilities, and so forth. Furthermore, the effective

detection radius of each sensor node is assumed to be 1. In other words, the sensor node

situated in grid (2, 2) covers grid points (1, 2), (2, 1), (2, 2), (2, 3) and (3, 2). Similarly, the

sensor node located in grid (4, 3) covers grid points (4, 3), (3, 3), (5, 3) and (4, 2). If each

grid in the sensor field is covered by at least one sensor node, i.e. as in Figure 1, the field is

said to be completely covered. Figure 2 presents three alternative deployment schemes for

obtaining complete coverage of a 3 x 5 sensing field [7].

Monitoring a wide ROI requires the deployment of a large number of sensor nodes.

However, if all of these sensor nodes are active all of the time, their energy will be rapidly

consumed and the lifetime will be seriously curtailed. However, by specifying an appropriate

deployment of the sensor nodes, a degree of “coverage redundancy” can be introduced into

the networks such that at any point in time, a sub-set of the total sensor population can be

allowed to sleep, thereby conserving their energy. In [8], the authors employed a controlled

deployment strategy to enhance energy conservation within the networks. By contrast, the

present study considers the case where the ROI is monitored using sensor nodes randomly

deployed within the sensing field. In the proposed approach, the ROI is divided into a total of

Z small regions of uniform size. If more than one sensor node is located within the same

small region, one of the sensor nodes is maintained in an active mode, while the remaining

sensor nodes are allowed to sleep. However, since the sensor nodes are randomly deployed in

the ROI, it may be that some small regions of the ROI have no sensor nodes. In other words,

the ROI may not be fully covered. In [9] presented a uniform, energy-efficient deployment

algorithm (UEEDA) to make a random deployment topology achieve a uniform deployment

topology. UEEDA was an efficient sensor deployment algorithm which successfully

optimized the resulting WSNs in terms of its power efficiency, coverage area and deployment

cost. Importantly, it was also shown that a uniform distribution of the sensor nodes within the

ROI minimized the risk of incomplete coverage.

In managing the finite energy of WSNs, the energy conservation strategy can either be

considered during the “sensor deployment phase”, i.e. the period of time between the initial

random distribution of the sensor nodes and their final uniform distribution, or during the

“post-sensor deployment phase”, i.e. the period of time following the point at which the

uniformly-distributed sensor nodes first begin to monitor the sensing field [10]. This paper

uses the UEEDA to conserve energy during the deployment phase and develops a new

scheme named as lifetime-extension under uniform distribution (LEUD) to minimize energy

consumption in the post-deployment phase. The overall objective of LEUD is to prolong the

lifetime of the sensor networks while simultaneously ensuring that each sensor node can

communicate with all of it neighboring sensor nodes within a one-hop distance.

The remainder of this paper is organized as follows. Section II presents the details of the

LEUD scheme, while Section III describes the use of LEUD to optimize the WSNs lifetime.

Section IV performs numerical simulations to demonstrate the validity and effectiveness of

the proposed approach. Finally, Section V provides some brief concluding remarks.

II. Overview of lifetime-extended under uniform distribution (LEUD) algorithm

From a sensor deployment perspective, the energy conservation strategy can be

considered in the "deployment phase" and the "post-deployment phase" [11]. The duration

from the time of the initial random distribution to the time of the uniform distribution is

defined as the deployment phase. The post-deployment phase can be defined as the time

when these sensor nodes begin to monitor the sense fields. The deployment phase uses

UEEDA to conserve energy. The aim of UEEDA is to achieve the configuration of a

uniformly distributed sensor node topology by using a self-deployment algorithm that

reduces the time and conserves energy spent in moving. After uniformly distributed sensor

topology is achieved, the sensor nodes will be used to monitor the sensor fields. If each

sensor node senses targets or events continuously, the battery attached to the sensor nodes

will quickly run out. This will shorten the lifetime of the sensor nodes and the time for

monitoring a sensor field. In the post-deployment phase, we proposed a scheme, called the

Lifetime-Extended under Uniform Distribution (LEUD) to reduce energy consumption. The

design goals are to prolong sensor networks lifetime and each sensor node can communicate

with its neighboring sensor nodes within a one hop distance. The LEUD algorithm contains

the following steps:

Assuming that the sensor nodes are uniformly distributed in the ROI, it is reasonable to

speculate that each small region of the ROI contains at least one sensor node. As a result, the

overall lifetime of the WSNs can be prolonged by activating just one sensor node within each

region. The LEUD scheme contains four basic steps, as described in the following:

(1) Divide the ROI into small regions: To ensure that sensor nodes located within a one-hop

distance of one another can communicate with each other, the maximum one-hop distance

must be less than the sensor nodes’ communication range (cR). Adopting this constraint, the

side length (x) of each small region in the ROI and the total number of small regions in the

ROI (i.e. Z) can be calculated using Eqs. (1) to Eqs. (4). Obviously, the value of Z depends

on cR, as shown in Figure 3. For a fixed number of sensor nodes in the ROI (i.e. N), the

average number of sensor nodes in each small region increases as the value of Z decreases.

As a result, the system lifetime increases since more sensor nodes within each region can be

inactive at any time. Therefore, the lower bound of Z is chosen (i.e. ) in

order to prolong the system lifetime.

, (1)

, (2)

, (3)

, (4)

(2) Categorize the sensor nodes into their own specific small regions: Each small region in

the ROI is distinguished by a unique two-dimensional coordinate (x, y). Each sensor node

within a particular region is assigned the two-dimensional coordinates of that region as its

ID. In other words, all of the sensor nodes within the same region share the same ID.

(3) Select one sensor node in each small region to be active: If the number of sensor nodes

deployed in the ROI is fairly large, it is probable that each small region in the ROI will

contain more than one sensor node. As described above, energy consumption in the network

can be reduced by maintaining just one sensor node in each region in an active mode, while

allowing the remaining sensor nodes to sleep. Each sensor node maintains an energy table

detailing its own energy information and also that of all its neighboring sensor nodes with the

same ID. If a sensor node establishes that its energy are higher than those of any of the other

sensor nodes in the same region of the ROI, it nominates itself as the “major sensor” and sets

itself to the active mode; otherwise it sets itself to the sleep mode.

(4) Determine the WSNs lifetime: Once all of the sensor nodes in the ROI have been to set to

their respective modes, the major sensor nodes in each small region assume responsibility for

sensing targets or events and begin to consume an increased amount of energy. The energy

consumed by a sensor node in each unit of time is defined as the continuous power (CP).

When the remaining energy of a major sensor node falls below CP, the sensor node

broadcasts a packet to its neighboring sensor nodes with the same ID informing them to

choose a new major sensor node (using the process described in Step 3). The time at which

the deployed sensor nodes first begin to monitor the ROI is defined as the system

initialization point, while the time at which more than m % of the small regions are inactive

(i.e. the energies of all of the sensor nodes within these regions are less than CP) is defined as

the system termination point. The interval between the initialization point and termination

point is defined as the system lifetime (SL).

III. Optimization of system lifetime

This section of the paper examines the combined influence of the sensor node topology

distribution and the sensor node energy distribution on the system lifetime. In optimizing the

sensor networks, the objective is to establish the energy and sensor node topology

distributions which maximize the system lifetime. In performing the system lifetime analysis,

some notations are defined as follows:

: Set of sensor indexes.

: Set of small region indexes.

: Number of sensor nodes within ith small region at time t, where t is the

iteration loop number, i.e. 0 1iN t , ,...,N , i V .

: Average energy per sensor node in ith small region at time t , where t is the

iteration loop number, i V .

, where is the average lifetime per sensor node in ith small region

at time t, where t is the iteration loop number, and CP is the continuous power, .

: Total energy of sensor nodes in ROI.

: Lifetime of ith small region at time t, where t is the iteration

loop number. Note that for convenience, is simplified to Li , to Ni , and

to , i V .

: Active sensor node indicator, set to 1 if there are no active sensor nodes in the

ith small region and set to 0 otherwise. Note that t is the iteration loop number, i V .

Note that if is 1, the corresponding region is denoted as “inactive”, else it is

denoted as “active”.

Initially, the lifetime of each small region in the ROI are stored in a lifetime array, i.e.

. The elements of L are then ordered sequentially from the shortest lifetime

to the longest lifetime and the first m % of these elements are transferred to a second array

, where R = and . In other words, stores

the lifetimes of all the small regions which are equal to or less than SL. The elements in ~L

which have the same value are consolidated to form a single group. An assumption is made

that this consolidation process results in the formation of a total of K groups within the array

~L

with lifetime , where K R and . Let be the number of small

regions within the ith group, i.e. , . Thus, SL = . The is given by

. (7)

When K = 2, the upper bound, i.e. , has its maximum value when

and . In other words, the maximum SL is .

The small regions are located sensor nodes and the lifetime for these small

regions is identical. If the initial average energy of each sensor node for these small regions

is identical, the number of sensor nodes for these small regions is also identical as shown in

Figure 4.

Although the sensor node distribution shown in Figure 4 maximizes the system lifetime,

it can be seen that some of the small regions in the ROI are inactive while the remainder of

the system is working. As a result, events which take place within these inactive particular

regions may pass unnoticed. Therefore, to optimize the system operation, it is necessary to

maximize the number of active small regions within the ROI. This paper proposes the use of

a reward / penalty scheme to maximize the number of active small regions at each time unit,

i.e.

Assign each active small region a reward of 1.

Assign each inactive small region a penalty of 1 - p.

As stated previously, in optimizing the operation of the WSNs, the aim is not only to

maximize the number of active small regions in every time unit, but also to increase the

value of SL, i.e. to extend the system life. Therefore, the objective function is defined as

, (8)

where t is the iteration loop number of the algorithm.

From Eq. (8), it is apparent that the optimal value of SL depends on both the sensor node

topology distribution and the sensor node energy distribution. When this objective function

achieves its maximum value, the corresponding value of SL represents the optimal system

lifetime.

Initially, the lifetimes of each small region of the ROI are stored in an array

. The elements in this array are arranged in sequence from the shortest

lifetime to the longest lifetime and the first m % of these elements are then transferred to a

second array. The array stores the lifetimes of the small regions which are equal to or

smaller than SL. The elements in which have the same value are consolidated to form a

single group. It is assumed that the resulting array contains K groups with lifetimes ,

where K R and . Let be the number of small regions in the ith group, i.e.

, . Therefore, the objective function can be written as:

, (9)

If K = 1, then , and array is as

. (10)

As shown, the first R elements of have the same value. Furthermore, the elements in array

are characterized by

, (11)

. (12)

From Eq. (12), the upper bound of is . Since , the maximum

value of the objective function is given by . If K = 2, the parameters ( )

are subject to the following constraints

, (13)

, (14)

. (15)

The objective function can be modified as

, (16)

. (17)

Three specific cases of Eq. (16) can be identified, namely , , and

.

: According to Eq.(15)to Eq. (17), we choose and

is given by

. (18)

From Eq. (13), (14) and (18), , where and

.

: According to Eq.(15)to Eq. (17), we choose , and

has the form shown in Eq. (19), in which the parameters ( ) are

subject to the constraints given in Eq. (20) to Eq. (23). Hence, in Figure 5, the maximum

value of is constrained within the shaded area.

, (19)

(20)

(21)

(22)

(23)

We obtain Eq. (24) to Eq. (29) by using Lagrangian method

, (24)

, (25)

, (26)

, (27)

, (28)

, (29)

where . In Eq. (24) and (25), if , then . To satisfy Eq.

(26), to Eq. (29), . In other words, and

. Therefore, for the objective function to be meaningful, the value

of parameter must be greater than one. If , it can be shown that

and .

: According to Eq. (16), . To maximize ,

we choose and thus .

From the discussions above, it is impossible to determine whether or not the maximum

value of decreases with increasing K. Therefore, Figure 6 plots the relationship between

the maximum value of and K for different values of R, while Figure 7 illustrates the

relationship between the maximum value of and K for different values of p. The two

figures confirm that the maximum value of decreases as the value of K increases. In

other words, has its maximum value when K = 1, i.e. the objective function is

maximized when the lifetimes of the different small regions in the ROI are all identical. If the

average energy of the sensor nodes in each small region is identical, the sensor node topology

must have a uniform distribution. Conversely, if the sensor node topology has a uniform

distribution, the average energy of the sensor nodes in each small region must be identical.

Furthermore, according to the reward / penalty rules, when the value of parameter p

increases, the system becomes more sensitive to the number of inactive small regions within

the network as verified by Figure 7.

IV. Simulation results

The objective function can be regarded as a metric of system performance. If the initial

energies of the sensor nodes are identical, a higher value of implies that the sensor node

topology is more uniformly distributed. Figure 8 illustrates the variation of with the

networks size for the case where the distribution of the sensor network topology is first

rendered uniform by using the UEEDA and LEUD is then applied to prolong the system

lifetime. The corresponding results obtained using the Distributed Self-Spreading Algorithm

(DSSA) and Intelligent Deployment and Clustering Algorithm (IDCA) for sensor node

deployment [10] with LEUD are also shown for comparison purposes. The parameter values

used in the simulations are as follows: p = 2, cR = 5, ROI = 10 x10 (m2) and CP = 0.1. The

results show that the value of for the networks topology smoothed using the UEEDA is

higher than that of the networks smoothed using either DSSA or IDCA. Thus, it can be

inferred that UEEDA yields a more uniformly distributed sensor node topology.

If the sensor networks topology with uniform distribution, a larger value of

implies that the sensor node energy is more uniformly distributed in the networks. Figure 9

illustrates the value of for different energy imbalances in the system (i.e. the difference

between the minimum and maximum sensor node energies in the networks) for the case

where the UEEDA with LEUD scheme is applied. The parameter values used in this

simulation are as follows: p = 2, N = 100, cR = 5, ROI = 10x10 (m2) and CP = 0.5. The

results show that the value of reduces as the magnitude of the energy imbalance

increases. In other words, has its maximum value when the sensor nodes within the

networks have identical energies.

Figure 10 shows the variation of against the networks size for three different sensor

location / sensor energy distributions. The parameter values used in these simulations are as

follows: p = 2, cR = 5, ROI = 10x10 (m2) and CP = 0.1. The results show that when all of the

sensor nodes have the same initial energies and the networks has a uniformly distributed

topology, the value of is maximized. When the sensor node topology is formed by

using UEEDA, the networks in which the sensor nodes with the same initial energies has a

higher value of than that of the system in which the initial energies of the sensor nodes

vary randomly.

Figure 11 shows the variation of the number of residual sensor nodes in the networks

over time. The results show that the number of residual sensor nodes is higher at each time

unit when UEEDA is employed to form the network topology since UEEDA achieves a more

uniform distribution of the sensor nodes than either DSSA or IDCA, and hence prolongs the

system lifetime.

V. Conclusions

This paper has presented a lifetime-extension under uniform distribution (LEUD)

scheme which not only extends the lifetime of WSNs, but also optimizes its performance by

maximizing the total number of active regions within the networks. In general, the

simulations results with the LEUD scheme is applied have shown that when all of the

sensor nodes have identical initial energies, a larger value of the objective function indicates

that the networks has a more uniformly distributed sensor node topology. However, the

lifetime of the networks depends not only on the sensor node topology distribution, but also

on the sensor energy distribution. For the case where the average energy of the sensor nodes

in each region of the ROI is identical, the sensor node topology has a uniform distribution.

Similarly, if the sensor node topology is uniformly distributed, the average energy of the

sensor nodes in each region of the ROI is identical. Finally, the optimal system performance

is obtained when the initial energies of the sensor nodes are identical and the networks has a

uniformly distributed topology.

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Figure 1. Complete coverage of sensor field mapped using 5 x 3 grid. (Note each sensor has detection radius of 1).

Figure 2. Sensor node deployments in 5 x 3 sensing field: (a) Cover 1; (b) Cover 2; (c) Cover 3. (Note each sensor has detection radius of 1).

Figure 3. Division of ROI into Z small regions.

Figure 4. Sensor distribution for maximum SL.

Figure 5. Boundary of g1, g2, g3, g4.

1 2 3 4 5280

282

284

286

288

290

292

294

296

298

300

number of groups

max

Obj

ect

R=20%ZR=80%Z

Figure 6. Variation of maximum with K for different R

1 2 3 4 5250

255

260

265

270

275

280

285

290

295

300

number of groups

max

Obj

ect

p=2p=3p=4p=5

Figure 7. Variation of maximum with K for different p

55 60 65 70 75 80 85 90600

700

800

900

1000

1100

1200

1300

1400

1500

number of sensors

Obj

ect

DSSA and LEUDIDCA and LEUDUEEDA and LEUD

Figure 8. Variation of with number of sensors

for DSSA, IDCA and UEEDA.

0 1 2 3 4 5 6 7 8 9 101000

1200

1400

1600

1800

2000

2200

Energy imbalance

Obj

ect

Figure 9. Variation of with energy imbalance.

55 60 65 70 75 80 85 90200

400

600

800

1000

1200

1400

1600

number of sensors

Obj

ect

Equal Energy UEEDAUEEDA and Equal Energy

Figure 10. Variation of with number of sensors for

different sensor location / sensor energy distributions.

0 10 20 30 40 50 60 70 80 900

10

20

30

40

50

60

70

80

90

100

time

resi

dual

nod

es

DSSA and LEUDIDCA and LEUDUEEDA and LEUD

Figure 11. Variation of residual sensors in WSNs over time.

Ho-Lung Hung received the M.S. degree in electrical engineering from University of Detroit Mercy, Michigan, USA, in 1994 and the Ph. D. degree in electrical engineering from National Chung Cheng University, Chia-Yi, Taiwan, in 2007. From1995 to 2006, he was a lecturer with the Department of Electrical Engineering, Chienkuo Technology University, Taiwan. Since 2007, he was an associate professor with the Department of Electrical Engineering, Chienkuo Technology University, Taiwan.

His major research interests include wireless communications, artificial neural networks, evolutionary optimization, wireless sensor networks, intelligent information processing and intelligent systems.

Dr. Hung has served as reviewer for various IEEE journals and conferences, including the IEEE TRANSACTIONS ON COMMUNICATIONS, IEEE TRANSACTIONS ON WIRELESS

COMMUNICATION, IET COMMUNICATIONS, IEEE SMC, International Journal of Communication Systems, Wireless Communications & Mobile Computing, etc. He has authored or coauthored over 50 journal and conference papers. He is an Associate Editor for the TELECOMMUNICATION SYSTEMS.

Chien-Erh Weng received the M.S. degree in Electrical Engineering from the National Yunlin University of Science & Technology, Yunlin, Taiwan, and the Ph.D. degree in electrical engineering from the National Chung Cheng University, Chiayi, R.O.C., in 2000 and 2007, respectively. Since Sep. 2010, he joined the Department of Electronic Communication Engineering at National Kaohsiung

Marine University, Kaohsiung, Taiwan, R.O.C., as an Assistant Professor. His research interest is in the fields of performance study of UWB communication systems, wireless sensor networks and cooperative radio networks.