exploiting limited density information towards near-optimal energy balanced data propagation

Computer Communications 35 (2012) 2187–2200

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Computer Communications

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Exploiting limited density information towards near-optimal energy balanceddata propagation

Azzedine Boukerche a, Dionysios Efstathiou b,⇑, Sotiris Nikoletseas c,d, Christoforos Raptopoulos c,d

a University of Ottawa, School of Information Technology and Engineering (SITE), 800 King Edward Avenue, Ottawa, Ontario, Canada K1N 6N5b Department of Informatics, King’s College London, The Strand, London, WC2R 2LS, UKc Computer Technology Institute and Press ‘‘Diophantus’’, N. Kazantzaki Str 1, Patras University Campus, Patras 26504, Greeced University of Patras, University campus, Rio 26504, Greece

a r t i c l e i n f o

Article history:Received 12 January 2012Received in revised form 22 July 2012Accepted 23 July 2012Available online 17 August 2012

Keywords:Wireless Sensor NetworksEnergy balanceRouting

0140-3664/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.comcom.2012.07.022

⇑ Corresponding author. Tel.: +44 7706500927.E-mail addresses: [email protected] (A.

upatras.gr (D. Efstathiou), [email protected] (S. Nikoletsea(C. Raptopoulos).

a b s t r a c t

In this work, we investigate the problem of achieving energy-balanced data propagation in a distributedwireless sensor network. The energy balance property is essential for prolonging the network lifetime bymaximizing the functional lifetime of a large portion of sensors. We propose a distributed, adaptive datapropagation algorithm that exploits limited, local density information for achieving energy-balancedpropagation while at the same time keeping energy dissipation at low levels.

Apart from traditional studies considering uniform sensor distribution, we investigate heterogeneoussensor placement distributions. We conduct a detailed experimental evaluation and comparison withstate-of-the-art energy-balanced protocols in order to demonstrate that our density-based protocolimproves energy efficiency significantly while also having better energy balance properties.

To illustrate that our protocol has near-optimal performance, we compare our protocol with a central-ized, off-line optimum solution derived by a linear program which maximizes the network lifetime andshow that it achieves near-optimal performance for uniform sensor deployments.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

We study Wireless Sensor Networks (WSNs) envisioned as verylarge collections of autonomous smart sensor nodes, which distrib-utively form an ad hoc wireless communication network. Thenodes are deployed in a region of interest in order to monitor cru-cial events and propagate sensed data to a base station usuallycalled the Sink. WSNs enable important applications ranging fromsmart/green building automation to environmental monitoring,see [1].

1.1. Motivation and related work

In WSNs it is crucial to design protocols that are energy efficientand maximize the network lifetime. Towards this goal, diverse ap-proaches including hop-by-hop transmission techniques [7], aswell as clustering algorithms [3] and power-saving modes [8] havebeen proposed.

All the above techniques do not explicitly take care of possibleoveruse of certain sensors in the network. For example, in a hop-

ll rights reserved.

Boukerche), [email protected]), [email protected]

by-hop propagation protocol where data must be forwarded tothe Sink, the sensors in the area around the Sink tend to be overusedcreating a bottleneck area, since these nodes have to relay the datafor other nodes, resulting in an unequal energy consumption. Thus,these nodes may die out very early resulting to network disconnec-tion, although there may be still significant amounts of energy inthe other sensors of the network. Also, distant transmissions incluster head schemes, in example by cluster heads [3], tend to over-use the cluster heads as the cost of a transmission is roughly somepower of the distance between the communicating. The rotation ofcluster heads may not be enough (especially in large networks withhigh event generation rate) to avoid their energy depletion.

Lifespan maximization can be achieved by keeping energy bal-ance [6]. To overcome the unbalanced energy consumption, theauthors in [2] proposed a mixed routing strategy where in each stepthe algorithm decides probabilistically and locally whether to prop-agate data one-hop towards the Sink, or to send it directly to theSink. In [2], it was shown that such a randomized mixed strategycan be used to balance the energy consumption among nodes andincrease the lifespan of the network. However, only homogenoustopologies and uniform data generation rates are studied, whilethe energy efficiency itself is not explicitly addressed.

In [5] the authors propose an on-line distributed algorithm forlifespan maximization where in each step the algorithm decidesto propagate data one-hop towards the Sink or to send it directly

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Fig. 1. The sectorized network model.

2188 A. Boukerche et al. / Computer Communications 35 (2012) 2187–2200

to the Sink based however on explicit information about the energyspent by the current node and the energy spent by the nodes thatare one-hop closer to the Sink. No topology heterogeneity is as-sumed and energy efficiency is only indirectly taken into account.

A nice, related but different, approach for achieving load balanc-ing is proposed in [10], where the authors propose a non-uniformnode distribution deployment to achieve energy-balanced con-sumption in the network. More precisely, in the (off-line) networkdeployment phase, they regulate the number of nodes in each sec-tor in order to tune the ratio between the node densities in theadjacent (i+1)th and ith sectors. For this deployment, they alsopresent an efficient routing scheme (q-switch) that achieves en-ergy balance using single hop transmissions. Our protocol can beused for a broad class of network deployments and achieves energybalance in a different way, by using a combination of short, longand ‘‘bypass’’ transmissions.

In [4] the authors suggest exploiting mobility to lower trans-mission power thus indirectly leading to a more uniform energydissipation.

1.2. The problem

We study the problem of how to achieve energy-balanced datapropagation in distributed WSNs for both uniform and heteroge-neous sensor deployments. The energy balance property guaran-tees that the average energy spent per sensor is the same for allsensors in the network at any time during the network operation.This property is crucial for prolonging the network lifetime byavoiding early energy depletion of sensors and the non-utilizationof available energy on sensors. Together with energy balance wealso want (in contrast to Previous work) to optimize the energyefficiency of data propagation.

1.3. Our contribution

Our study was originally motivated by Singh and Prasanna [9]where the authors define the energy balance property and proposean energy-optimal and energy balanced algorithm for the particu-lar problem of sorting in WSNs. In particular, they consider a sin-gle-hop sensor network. Thus, our work extends their approachto the general case of a multi-hop network of either uniform ornon-uniform sensor deployments and for the problem of propagat-ing data to the Sink.

We propose an on-line, distributed algorithm which takes intoaccount limited, local density information towards balancing the en-ergy consumption and thus increasing the lifespan of the network.Apart from the usual well-studied random uniform sensor deploy-ments, we also study, for the first time in the context of the energybalance property, the more realistic case of a heterogeneous sensorplacement by introducing a general model of non-uniform deploy-ment. In the relevant state of the art, energy-balancing protocolshave not been studied in heterogeneous node placement settings.

The experimental results show that our density-based heuristicactually works well for both uniform and non-uniform networkdeployments and has much better performance compared to otherwell-known energy balance data propagation algorithms for bothsensor placement distributions and various node densities. In par-ticular, its performance for uniform sensor deployment (as shownvia comparing to an off-line optimum evaluated by a linear pro-gram) is near-optimal.

2. Model

We consider a plane sensor network, in which the sensors andthe single Sink node are static. We abstract the network by a graph

G(V,E), where V denotes the set of nodes (sensors), while E # V2

represents the set of edges (wireless links). An edge between twonodes in the graph exists iff the distance between the correspond-ing sensors in the network is below the transmission range R. Thedistance between nodes is Euclidean, and the path length is thesum of the hops of the intermediate pairs of subsequent nodes.

Without loss of generality, we assume that network deploy-ment area is a circle of radius D. We virtually slice the network intoM ¼ D

R co-centric Rings and N ¼ 2p/ Slices, where / ¼ p

6. A sector is de-fined as the intersection of a specific ring and slice. For example, inFig. 1 the network is divided into 12 Slices where each Slice con-tains 20 Sectors, resulting in a total of 240 sectors in the network.

Each node knowns its location, has a unique ID and belongs toexactly one Sector of a Slice. Using this information, each nodecan identify in which Slice and Sector it belongs to. Nodes areaware of which nodes belong to neighboring Sectors and the posi-tion of the static Sink. This information can be disseminatedthrough a set-up phase initiated by the Sink during which the po-sition of the Sink and the IDs of the nodes in neighboring Sectorsare diffused.

Uniform deployment. In this case, we deploy the n nodes of thenetwork uniformly at random in the network deployment area,see Fig. 2 (left). Notice that the expected density is the same forall sectors in the network.

Non-uniform deployment. Our experiments are also performed inrandom instances of the following general model of non-uniformdeployment: Denote by Si;j the sector corresponding to the inter-section of slice i and ring j. Let c > 1 be an arbitrary constant. Eachsector Si;j chooses independently a number di;j 2 ½1; c� according tothe uniform distribution U½1; c�. We will refer to the number di;j asthe relative density of sector Si;j. Clearly, values of di;j close to oneimply low relative density and values close to c imply high relativedensity. By combining the knowledge about the total number ofsensors in the network n, together with the relative density di;j

and the area Ai;j of every sector, we compute the number of nodesni;j deployed in sector Si;j by the following formula:

ni;j ¼nP

i0 ;j0Ai0 ;j0

Ai;j

di0 ;j0

di;j

;

where n ¼P

i;jni;j. Finally, we scatter ni;j nodes in the area corre-sponding to sector Si;j, see Fig. 2 (right).

Notice that the fraction of the actual densities of two sectors Si;j

and Si0 ;j0 is exactlyAi0 ;j0

Ai;j

di0 ;j0

di;j(which also justifies the name relative

density for di;j). Furthermore, if all sectors have the same relativedensity (i.e. di;j ¼ di0 ;j0 , for all i0; j0), we get the uniform deployment.

Our protocols operate at the network layer, so we are assumingappropriate underlying data-link, MAC and physical layers. Thenodes’ memory is assumed limited e.g. we allow messages to

Fig. 2. Uniform deployment (left) and Non-uniform deployment (right).

A. Boukerche et al. / Computer Communications 35 (2012) 2187–2200 2189

piggy-back a constant number of bits of information only, encodingthe position of the last node visited and the position of the Sink.

We consider two types of data transmission: (a) single-hoptransmission (cheap in terms of energy and slow) between twonodes belonging to neighboring sectors and (b) direct transmission(expensive in terms of energy and fast) where the node that holdsthe data transmits directly to the Sink.

We assume that the energy spent at a sensor when transmittingdata messages is proportional to the square of the transmitting dis-tance. The size of messages is considered to be constant. We onlycount (for simplicity) energy spent during transmissions.

Sensor networks are characterized by high network dynamicssuch as frequent, dense failures. So we investigate the detailed im-pact of failures on protocols’ performance. In particular, for eachunit of time, failures occur at randomly chosen nodes, instantly,and no further computation and/or communication can be per-formed by these failed nodes. We examine a broad set of failureprobabilities, including low, medium and high ones.

3. The off-line optimal solution to the problem

Consider now a specific slice in our sensor network model. Thisslice contains N sectors, which we denote by S1; S2; . . . ; SN , droppingthe slice number of the sectors for the sake of simplicity. Every sec-tor Si contains ni sensors and each sensor has Einitial initial energy atthe beginning of the network operation. Given a specific slice, wemodel the routing of messages with a linear program (LP) (see be-low Definitions 4, and 5.

Definition 1. k is the number of messages produced by eachsensor in the network.

Definition 2. Einitial is the initial energy of each node in thenetwork.

Definition 3. ni is the number of nodes in sector i, where 1 6 i 6 N.

Definition 4. The k maximization problem is on input fEinitial;nig,to find the maximum number of messages that every sensor canproduce with given initial energy and node ni distribution per sec-tor. If we multiply k with the total number of nodes in the network,we get the maximum number of messages throughout the networkthat are routed to the Sink.

Maximize k:

XN

j¼1

fij i� jð Þ2 � R26 ni � Einitial; 1 6 i 6 N; ð1Þ

XN

j¼0

fij ¼XN

j¼1

fji þ k � ni; 1 6 i 6 N; ð2Þ

fij ¼ 0; j R 0; i� 1f g; 1 6 i 6 N; ð3Þ

fij > 0; j 2 0; i� 1f g; 1 6 i 6 N: ð4Þ

In Eq. (1), fij is the number of messages routed from Sector i to Sec-tor j while not spending more energy than available. Eq. (2) guaran-tees flow preservation i.e. all messages generated at or forwarded toa sector are pushed out of it. Eqs. (3) and (4) allow only next-slicetransmissions and direct transmissions to the sink. Eqs. (5)–(8)are similar. Notice that in the above linear program, k is a variableof the LP and Einitial is given as input, while in the following linearprogram Einitial is a variable of the LP and k is predefined.

Definition 5. The Einitial minimization problem is on input fk;nig, tofind the minimum initial energy Einitial which achieves the desired kdata generation rate per node in a given ni node distribution. Thus,by multiplying the output Einitial of the LP with the number of nodeswe get the optimal energy consumption of the whole network.

Minimize Einitial:

XN

j¼1

fij i� jð Þ2 � R26 ni � Einitial; 1 6 i 6 N; ð5Þ

XN

j¼0

fij ¼XN

j¼1

fji þ k � ni; 1 6 i 6 N; ð6Þ

fij ¼ 0; j R 0; i� 1f g; 1 6 i 6 N; ð7Þ

fij > 0; j 2 0; i� 1f g; 1 6 i 6 N: ð8Þ

4. The protocols

4.1. The Pi energy balance protocol

The authors in [2] propose an energy balance algorithm wherein each step the node that holds the data decides whether topropagate data one-hop towards the Sink with probability pi, orto send data directly to the Sink with probability 1� pi, where iis the current sector. The appropriate probability pi is calculatedas follows:

pi ¼ 1� 3xðiþ 1Þði� 1Þ ;


where x is a free (e.g. controlling) parameter and i is related to thesensor’s distance to the Sink. This randomized choice balances the(cheap but slow) one-hop transmissions with the (expensive butfast) direct transmissions to the Sink, which are more expensivebut ‘‘bypass’’ the nodes lying close to the Sink. Note that, in mostdata propagation protocols, the bottleneck area around the Sinktends to be overused and die out early. The lifespan of the networkis maximized by ensuring that the energy consumption in each sliceis the same. Sensors are assumed to be randomly distributed withuniform distribution.

4.2. The Ei energy balance protocol

In [5] the authors propose an on-line distributed algorithm forlifespan maximization (via energy balance) of a WSN in a datapropagation scenario. Let n be a sensor. Vn is the neighborhoodof node n. Node n knows the energy spent by each node in itsneighborhood. Let m be the sensor of neighborhood Vn with thelowest energy spent. When n holds data it makes the followingdecision:

� If node n has spent more energy than m, then n sends the mes-sage to m (spending one energy unit).� Otherwise, n sends the message directly to the Sink spending d2

energy units, where d is the distance from n to the Sink.

4.3. Our density-based protocol

The basic idea of our protocol is to take into account informa-tion about the density of the Previous and the Next Sectors inthe current Slice in order to take a decision to forward data tothe Next Sector or directly to the Sink.

Definition 6. Let di;j be the density of the jth Sector in the ith Slice.

Definition 7. If S is the current Slice and r is the current Sector ofthe node, let F P

Nbe the fraction of the density of the Previous b Sec-

tors over the density of the Next b Sectors, which is calculated asfollows:

F PN¼Prþ1þb

j¼rþ1 dS;jPr�1j¼r�1�bdS;j

:

We provide three options in order to examine the ratio of the den-sities of the Previous Sectors to the densities of the Next Sectors:

(a) Local knowledge (b ¼ 1). Firstly, to take into account the den-sity of the Previous Sector and the Next Sector only. If S is thecurrent Slice and r is the current Sector, we compute thedensity ratio as follows:

F PN¼ dS;rþ1

dS;r�1:

(b) Partial knowledge (b ¼ 3. Secondly, to take into account thedensity of the Previous b Sectors and the Next b Sectors; bis taken three as a good compromise of information and cost.If S is the current Slice and r is the current Sector, we com-pute the density ratio as follows:

F PN¼Prþ1þb

j¼rþ1 dS;jPr�1j¼r�1�bdS;j

:

(c) Global knowledge (b ¼ N). Thirdly, to take into account thedensity of the all Previous Sectors and the all Next Sectors.If S is the current Slice, r is the current Sector and TSectors isthe total number of Sectors, we compute the density ratioas follows:

F PN¼PTSectors

j¼rþ1 dS;jPr�1j¼1 dS;j

:

We characterize the density of the Next or Previous Sectors as‘‘high’’, when the average density of the Next or Previous b Sectorsis M times larger than the global network density DGlobal; in partic-ular we chose M to be equal with 3. Similarly, we characterize thedensity of the Next or Previous Sectors as ‘‘low’’, when the averagedensity of the Next or Previous b Sectors is M times lower than theglobal network density DGlobal.

Definition 8. If S is the current Slice and r is the current Sector ofthe node, let FPrevious be the fraction of the density of the Previous bSectors over the global network density, which is calculated asfollows:

FPrevious ¼Prþ1þb

j¼rþ1 dS;j

DGlobal:

Definition 9. If S is the current Slice and r is the current Sector ofthe node, let FNext be the fraction of the density of the Next b Sec-tors over the global network density, which is calculated asfollows:

FNext ¼Pr�1

j¼r�1�bdS;j

DGlobal:

4.3.1. Our data propagation scheme

The node that holds the data to be delivered to the Sink decidesto act suitably according to the relation of densities in Previous andNext sectors towards the sink.

(a) FPN< ð1� aÞ, where a constant such that 0 < a < 1. The par-

ticular value of constant a can be chosen by the protocoldesigner to fine-tune performance: a large a value wouldlead to less energy consumption but a higher data deliverylatency while a smaller a would incur a smaller data deliverylatency but it would increase a the energy consumption. Theexperimental evaluation suggested that the value a ¼ 0:7leads to an optimized trade-off. If the density of the Next bSectors is much higher than the density of the Previous bSectors, the node forwards data as following:

– If both the Next and the Previous b Sectors have highdensities then the node forwards data hop-by-hop, sincethe forward area can afford the load of the Previous area.

– If both the Next and the Previous b Sectors have low den-sities then the node forwards data using a probability p1.The probability p1 randomizes the propagation of themessage one-hop towards the Sink or directly to the Sinkas follows:

�
Probability ¼
c1; “Jump” to the Sink;1� c1; Hop-by-hop transmission:

In fact, a small, constant probability c1 where c1 > 0 for jumps sig-nificantly improves performance, while larger values are not appro-priate due to the high energy cost of jumps. The value of c1 ¼ 1

30 hasbeen chosen after many simulations tries suggesting that this valueoptimizes performance. Again, the protocol designer can freelychoose c1 achieve particular trade-offs: a large c1 would lead to fas-ter but more expensive data propagation while a small one wouldresult to more conserving energy consumption but slower datapropagation. This selection encourages a lot the hop-by-hop


transmissions. The jump transmissions are expensive for the sendernode but do not overload the front network area.

(b) ð1� aÞ < FPN< ð1þ aÞ, where a a constant as in case (a).

This suggests a threshold behavior for FPN

around the rel-ative density value 1. This means that if the density ofthe Next b Sectors and the Previous b Sectors are approx-imately the same, the node should forward data as fol-lows:

Dat

a D

eliv

ery

Lat

ency

– If the Previous and the Next b Sectors have high den-sities, comparing with the Global density then thenode forwards data using a probability p2 which ran-domizes the propagation of the message one-hoptowards the Sink or by-passing the overloaded frontarea as follows:
�
400

410

420

430

440

450

460

Probability ¼c2; By-pass transmission;1� c2; Hop-by-hop transmission:

As in the case (a) for jumps, a similar behavior applies this case for by-passes: a very small constant bypass probability c2, where c2 > 0 avery small constant suffices to improve performance a lot, with theprotocol implementor being free to select the particular value accord-ingly. In by-pass transmission a node chooses randomly between theleft and the right diagonal sector towards the Sink in order to transmitits data. The value of probability 1� c2 has been chosen to be 29

30 (i.e.c2 ¼ 1

30) after fine-tuning, encouraging a lot the hop-by-hop transmis-sions, as the front area is dense enough to transmit the data from thebackward network area. However, the by-pass transmissions areused in order to avoid the overloaded front network area.

– If the Previous and the Next b Sector have low densi-ties, the node forwards data to the Next Sector,because the front area can relay the load of the back-ward network area.

000

000

000

000

000

000

000

10.000 Nodes 15.000 Nodes 20.000 Nodes 25.000 Nodes

Number of Nodes

Beta = 1

Beta = 3

Global Density Information

0

2000

4000

6000

8000

10000

Ave

rage

Ene

rgy

Con

sum

ptio

n

1e+007

2e+007

3e+007

4e+007

5e+007

6e+007

7e+007

8e+007

9e+007

1e+008

10.000 Nodes 15.000 Nodes 20.0

Var

iatio

n of

Ene

rgy

Con

sum

ptio

n

Number of No

Global

Fig. 3. Experimental comparison of the variations of our protocol for var

(c) FPN> ð1þ aÞ, where 0 < a < 1 a constant as in cases (a)

and (b). If the density of the Next b Sectors is smallerthan the density of the Previous b Sectors, the node for-wards data using a probability p3 which randomizes thepropagation of the message one-hop towards the Sink orby-passing the overloaded front area as follows:

Probability ¼c3; By-pass transmission;1� c3; Hop-by-hop transmission:

�

Similarly to cases (a) and (b), here again a very small, arbitrarilychosen bypass probability c3, where c3 > 0 a small constant is used.The particular value of probability c3 ¼ 19

20 (i.e. c3 ¼ 120) has been cho-

sen after many simulations tries suggesting that this value opti-mizes performance. This value of probability c3 encourages a lotthe hop-by-hop transmissions over the by-pass transmissions. Theby-pass transmissions are used in order to avoid the overloadedsparse front network area.Overall, this algorithmic design is very simple basically suggesting athreshold behavior around the value 1 for the relation of ‘‘forward’’and ‘‘backward’’ network densities. Also, a probabilistic, adaptiveaddition of a small amount of jumps or bypass transmissions (ontop of multi-hop data propagation, which is the prevailing propaga-tion method) is able to incur significant performance gains.

5. Experimental evaluation

Experimental setup. Our simulation environment for making theexperiments is Matlab 7.9.0. We consider two types of nodedeployment: (a) random uniform and (b) heterogenous. Thetransmission range R is taken 10, the initial energy in each sensoris Einitial ¼ 106 and we conducted experiments for various nodedensities (10�103,15�103,20�103 and 25�103 nodes). As depicted inFig. 1, the circle network of radius 200 is divided into 12 Sliceswhere each Slice contains 20 Sectors.


Number of Nodes

Beta = 1

Beta = 3


00 Nodes 25.000 Nodes

des

Beta = 1

Beta = 3

Density Information

ious node densities in uniform network deployment.

0

100000

200000

300000

400000

500000

600000


Dat

a D

eliv

ery

Lat

ency

Number of Nodes

Beta = 1

Beta = 3


0

1000

2000

3000

4000

5000

6000

7000

8000


Ave

rage

Ene

rgy

Con

sum

ptio

n

Number of Nodes

Beta = 1

Beta = 3


0

2e+007

4e+007

6e+007

8e+007

1e+008

1.2e+008


Var

iatio

n of

Ene

rgy

Con

sum

ptio

n

Number of Nodes

Beta = 1

Beta = 3


Fig. 4. Experimental comparison of the variations of our protocol for various node densities in non-uniform network deployment.


In detail, the network area is rectangular, with length and widthequal to 40 units. For statistical smoothness, we apply several timesthe deployment of nodes in the network and repeat eachexperiment 50 times. For each experiment we simulate 30.000 datapropagations and the average value is taken. The statistical analysisof the findings (the median, lower and upper quartiles, outliers ofthe samples) demonstrates very high concentration around themean, so in the following figures we only depict average values.

The Sink is placed at the center ð100;100Þ of the circle deploy-ment area. In simulation experiments, we focus on the followingmetrics: (a) data delivery latency which is the average numberof hops needed to reach the Sink; (b) average energy consumptionis the average energy spent per node during the network opera-tion; (c) variation of energy consumption which is the deviationof the energy consumed by a node from the average energy con-sumption in the network. This metric is useful to determinewhether the energy consumption in a network is energy-balanced,e.g. as it is impossible to achieve a close to zero deviation, the low-er is the deviation the more energy-balanced is the network andvice versa; and (d) success ratio is the ratio of the total numberof packets received by the sink to the number of packets generatedby the whole network.

We assume an energy model, in which the energy consumed bya message transmission between two nodes is considered thesquare of the distance between the nodes. For the above metricsthe average is taken over all sensor deployments and algorithm’srepetitions.

5.1. The impact of b (network information)

In order to choose the ideal b we have conducted a detailedexperimental comparison of our protocol performance for variouschoices of b. As described previously, b is the amount of knowledgerequired by our protocol. More specifically, b is the number of the

Previous b and Next b Sectors of which a node needs to know theirdensity. In Section 4.3.1, we proposed the following basic choicesabout b, (a) local knowledge of the network (b ¼ 1) in which a nodeknows the density of the neighboring Sectors only, (b) partialknowledge (b ¼ 3) where a node knows the densities of the threePrevious and Next Sectors and (c) global density information(b ¼ N) where a node has global information about the densitiesof all the N Sectors in the Slice.

In Figs. 3 and 4, we present a detailed experimental comparisonof our protocol performance for various choices of b. As describedpreviously, b is the amount of knowledge required by our protocol.More specifically, b is the number of the Previous b and Next b Sec-tors of which a node needs to know their density. In Section 4.3.1,we proposed the following basic choices about b, (a) local knowl-edge of the network (b ¼ 1) in which a node knows the density ofthe neighboring Sectors only, (b) partial knowledge (b ¼ 3) wherea node knows the densities of the three Previous and Next Sectorsand (c) global density information (b ¼ N) where a node has globalinformation about the densities of all the N Sectors in the Slice.

For the uniform deployment scenario our protocol has betterperformance when having global knowledge (b ¼ N). In real-worldapplications having global knowledge of the network is not realis-tic and feasible. However, our findings show that even with a smallamount of knowledge (b ¼ 1 or b ¼ 3) our protocol still has satisfy-ing performance for all the studied metrics. These cases requireonly a small amount of local knowledge of the network.

Interestingly, in the case of the non-uniform deployment, ourprotocol has similar performance for all the studied metrics. Thiscan be explained by the fact that in a heterogeneous network,the knowledge of the average density of many Next or PreviousSectors does not give you more information than knowing onlythe density of the neighboring nodes.

We concluded that the best choice of b is 3, as it is feasible to getdistributively Partial knowledge of the neighboring Sectors and has


better performance from the case of local knowledge b ¼ 1 asshown in Figs. 3 and 4.

6. Using proximity information

It may be more efficient to transmit data directly to the Sinkwhen data is very close to the Sink via e relatively cheap jump(high probability of jump transmission when we are close to theSink). On the other hand, when data is far away from the Sink itwould be preferable to transmit data hop-by-hop to the Next sec-tor rather than using an expensive jump (high probability of hop-by-hop transmission when we are far away from the Sink).

In this variation of the density-based protocol, we propose thatthe probability pi where 1 6 i 6 3, of jump transmission will de-pend on the distance Di between the current node i that holds data

and the Sink. pi ¼ nffiffiffiffiffiffiffi

DiDmax

qwhere Dmax is the maximum distance from

the Sink. We usedffiffiffinp

in order to encourage more hop-by-hoptransmissions over jumps when the data is far away from the Sink.The decision to whether the node forwards data using one-hop to-wards Sink or directly to the Sink is done as below:�

Probabilitypi ¼pi; Hop-by-hop transmission1� pi; Jump to the Sink

In Figs. 5 and 6, we observe that for all the studied metrics thedensity-based protocol that uses only density information per-forms better than the variation of the density-based protocolswhich uses additional proximity information. This experimentalresult strengthens the value of the heuristic choices of the proba-bilities p1; p2 and p3 in the data propagation scheme.

6.1. Comparison of protocols

For the uniform deployment scenario, Fig. 7 (top left) shows anegative impact of our density-based protocol on data delivery la-tency and its performance is close to Pi’s results. On the other hand,

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the Ei protocol is the fastest of all as it makes a lot of direct trans-missions. As the density of the network increases, the Ei protocolbecomes faster while the performance of the other two protocolsremains stable.

The energy-latency trade-off is more clear if you observe Fig. 7(top right) that illustrates the average energy consumption pernode. In more detail, the density-based protocol is the most energyconservative. As expected the Ei protocol depletes the energy of thenodes quickly and its energy-efficiency gets worse as the numberof the network nodes increases.

Fig. 7 (bottom) depicts the variation of energy consumptionwhich is a metric of the energy-balance property. Our density-based protocol has at least 4 times lower deviation from theaverage energy consumption than the deviation of the other twoprotocols. Our protocol’s behavior improves remarkably as thenetwork density increases. We can claim that our density-basedprotocol prolongs the lifetime of the network more than the othertwo energy-balance protocols. This result indicated that knowl-edge of the densities of neighboring areas (or more precisely, pre-dicting the traffic forwarded to and received from other networkareas) can lead to energy balance consumption. The Pi protocolhas the worst energy-balance behavior and this can be explainedby the fact that it uses only proximity information in order todecide the next-hop transmission.

For the non-uniform deployment, the protocols have the samebehavior for the data latency metric as shown in Fig. 8 (top left).The results for the average energy consumption metric are shownin Fig. 8 (top right). The Ei Protocol is more expensive in the case ofheterogeneous deployments rather than the uniform and the mostexpensive of all the protocols for both deployments. Also, in theheterogeneous case, the Ei protocol has lower variation of energyconsumption, see Fig. 8 (bottom), and for smaller networkdensities (10⁄103,15⁄103 nodes) has even better energy-balanceperformance than our density-based protocol. However, ourdensity-based protocol’s energy-balance behavior improves asthe network density increases and achieves a more energy-effi-

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Fig. 9. Energy dissipation map in uniform deployment using the density-based (top left), Pi (top right) and Ei Protocol (bottom).

Fig. 10. Energy dissipation map in non-uniform deployment using the density-based (top left), Pi (top right) and Ei protocol (bottom).


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Fig. 11. Experimental comparison for various node failure rates (10%, 25%, and 50%) in uniform network deployment.


cient balanced consumption than the Ei protocol which has similarenergy-balance behavior but in a less efficient way as it spends 3times more energy than the density-based protocol.

6.2. Energy-balance property

In this section we study the energy-balance property of the pro-tocols. In detail, we present graphically the spatial evolution of en-ergy dissipation in a network of 20.000 nodes after 30.000 datapropagations for both random uniform (see Fig. 9) and heteroge-neous (see Fig. 10) sensor deployments. Nodes with high energydissipation are depicted with dark colors. In contrast, nodes withhigh residual energy are depicted with bright colors.

We observe in Fig. 9 (left), that our density-based protocolachieves better energy balancing than the Pi protocol Fig. 9 (center)and the Ei protocol Fig. 9 (right). In detail, Pi protocol tends to over-use the nodes that are in the middle in each sector, which can beexplained by the random choice of the node of the Next Sector asit is more probable to choose a node which is in the middle ofthe Sector area. The Ei protocol exhausts the distant nodes as itmakes many expensive jumps at the start of the network opera-tion. On the other hand, our density-based protocol spends the en-ergy of the sensors in a more balanced way.

Interestingly, in the scenario of heterogeneous node deploy-ment depicted in Fig. 10 our density-based protocol Fig. 10 (left)is again more energy-balanced than the Pi protocol Fig. 10 (center)and the Ei protocol Fig. 10 (right).

6.3. Impact on the network lifetime

To illustrate density-based protocol’s ability to prolong the net-work lifetime, we measure the number of alive nodes over the timeduring the network operation in a network of 30.000 nodes for60.000 data propagations. As shown in Fig. 13 (left) for the uniformdeployment and Fig. 13 (right) for the non-uniform deployment,

our density-based protocol effectively improved the networklifetime, compared to the Pi and Ei protocols. In detail, the numberof alive nodes using the Ei protocol is decreasing rapidly as the net-work continues to operate, because of the costly direct transmis-sions. On the other hand, the nodes of the network using thedensity-based or the Pi protocol are depleted at a more linear rate.

6.4. Impact of failures

We investigate the performance of the protocols in a network of20.000 nodes after 30.000 data propagations in the presence ofpermanent node failures during protocol evolution. We study thecharacteristic cases where 10, 25 and 50% of the network nodes failduring the simulation time. For each unit of time, failures occur atrandomly chosen nodes, instantly, and no further computationand/or communication can be performed by these failed nodes.As can be seen in the experimental evaluation in Figs. 11 and 12,our protocol operates well in the presence of failures.

6.5. Node death rate

To illustrate density-based protocol’s ability to prolong the net-work lifetime, we measure the number of alive nodes over the timeduring the network operation (Fig. 13 (left) in a network of 20.000nodes for 60.000 data propagations. As shown in Fig. 13 (left) ourdensity-based protocol effectively improved the network lifetime,compared to the Pi and Ei protocols. In detail, the number of alivenodes using the Ei protocol is decreasing rapidly as the networkcontinues to operate, because of the costly direct transmissions.On the other hand, the nodes of the network using the density-based or the Pi protocol are depleted at a more linear rate.

6.6. Using various propagation models

In this Previous performance evaluation sections, we used inour assumed propagation model that the path loss exponent n is

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Fig. 13. The number of alive nodes over time in uniform (left), and non-uniform network deployment (right).


equal to 2, which means that the energy consumed by a messagetransmission between two nodes is considered the square of thedistance between the nodes. To extend our simulation comparisonand validate the performance of our proposed protocol, we inves-tigate the performance of the studied protocols in various propaga-tion models where the power fall more rapidly than the square ofthe distance, for n ¼ 3 and n ¼ 4.

Figs. 14 and 15 depict the experimental results for the propaga-tion model where the path loss is n ¼ 3. By comparing the perfor-mance of all protocols in the case of n ¼ 2 (Figs. 7 and 8) and n ¼ 3,we note that all the protocols have similar performance for bothuniform and non-uniform network deployment.

The experimental results for the case of the propagation modelwhere the path loss is n ¼ 4 are shown in Figs. 16 and 17. For both

uniform and non-uniform deployments, the Ei Protocol has worseaverage energy consumption and variation of energy consumptionin the case of n ¼ 4, than in the traditional case of n ¼ 2. The othertwo energy-balance protocols have similar behavior as in the casewhere the path loss is proportional to the square of the distance.

6.7. Comparing with the optimum

In this section, we compare the performance of the three en-ergy-balance protocols (density-based, Pi and Ei protocol) withthe centralized off-line optimal solution as given by the linear pro-gram described in Definition 5.

In the case of uniform deployment, Fig. 18 (left) shows that thesuccess ratio of density-based protocol is consistently higher dur-

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Fig. 14. Experimental comparison of the three protocols for various node densities in uniform network deployment for n ¼ 3.


ing the network operation as the number of messages generatedper node increases. The success ratio of Ei is close to our protocol’sperformance. On the other hand, Pi has the worst performance interms of success ratio because it has the worse energy-balance

behavior, and the nodes close the critical area around the Sinkare depleted very early.

The energy consumption results are shown in Fig. 18 (right). Asexpected, the Ei protocol is the most expensive as it makes a lot of

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Fig. 16. Experimental comparison of the three protocols for various node densities in uniform network deployment for n ¼ 4.

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Fig. 17. Experimental comparison of the three protocols for various node densities in non-uniform network deployment for n ¼ 4.


jumps at the start of the network operation. Our protocol is themost energy efficient of all and has close to optimal performancein terms of energy consumption. The Pi protocol is the secondexpensive and it is more consuming if you take into consideration

that it has very low success ratio as the network continues to oper-ate (for k > 5).

In the case of heterogeneous deployment, we remark that theenergy consumption of the optimum solution is greatly reduced

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Fig. 19. Success rate (left), and energy consumption (right) of the protocols and the optimum in non-uniform network deployment.


(Fig. 19 (right)), whereas the energy dissipation of other protocolsis increased. As noticed in [10], you can achieve the optimum en-ergy-balanced energy consumption in a sensor network by placingthe nodes in a heterogeneous manner. If you place the nodes uni-formly in the area of interest, the nodes nearer to the sink carryheavier traffic loads and they will deplete their energy faster. Forthat reason, the optimum for the non-uniform deployment casehas better performance from the optimum for the uniformdeployment.

7. Conclusions/future work

Our approach is one of the few first that investigate the problemof maximizing the network lifetime (via energy balance) in thecontext of heterogeneous sensor deployment. We propose a newdistributed, local and lightweight protocol that achieves improvedenergy balanced data propagation than other well known energybalance schemes; the main idea of our method is to exploit somelimited knowledge of node density in the neighborhood of thenode currently holding data under propagation. As shown by de-tailed simulation results, in uniform deployment our protocol hasnear-optimal performance (very close to the centralized off-lineoptimum solution by a linear program); in particular, our methodis energy balanced and energy efficient.

In future work, we intend to study the problem of energy bal-anced data propagation in sensor networks with mobile nodes.Also, we plan to implement the above mentioned energy-balancedprotocols in a experimental test-bed consisting of Xbow’s TelosBmotes, and study their performance in real world conditions. We

plan to also study the behavior of our method in the regulateddeployment of [10].

Acknowledgements

This work has been partially supported by the EU Project HOB-NET (ICT/FIRE STREP 257466).

References

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[2] C. Efthymiou, S. Nikoletseas, J. Rolim, Energy balanced data propagation inwireless sensor networks, Wireless Networks 12 (6) (2006) 691–707.

[3] W.R. Heinzelman, A. Chandrakasan, H. Balakrishnan, Energy-efficientcommunication protocol for wireless microsensor networks, in: Proceedingsof the 33rd Hawaii International Conference on System Sciences HICSS, 2000.

[4] F. Pasquale, A. Clementi, R. Silvestri, Manets: high mobility can make up forlow transmission power, ICALP (2009) 387–398.

[5] O. Powell, A. Jarry, P. Leone, J. Rolim, An optimal data propagation algorithm formaximizing the lifespan of sensor networks, DCOSS 4026/2006 (2006) 405–421.

[6] S. Nikoletseas, A. Jarry, P. Leone, J. Rolim, Optimal data gathering paths andenergy balance mechanisms in wireless networks, DCOSS (2010).

[7] R. Govindan, C. Intanagonwiwat, D. Estrin, Directed diffusion: a scalable androbust communication paradigm for sensor networks, in: Proceedings of the6th ACM/IEEE International Conference on Mobile Computing MOBICOM,2000.

[8] S. Ganeriwal, C. Schurgers, V. Tsiatsis, M. Srivastava, Topology management forsensor networks: exploiting latency and density, MOBICOM (2002) 135–145.

[9] M. Singh, V. Prasanna, Energy-optimal and energy-balanced sorting in a single-hop wireless sensor network, in: Proceedings of the First IEEE InternationalConference on Pervasive Computing and Comminications PERCOM, 2003.

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exploiting limited density information towards near-optimal energy balanced data propagation

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