Journal of Network and Computer Applications 38 (2014) 106–124

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Journal of Network and Computer Applications

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Enhancement of wireless sensor network lifetime by deployingheterogeneous nodes

Subir Halder a,n, Sipra Das Bit b

a Department of Computer Science and Engineering, Dr. B. C. Roy Engineering College, Durgapur, Indiab Department of Computer Science and Technology, Bengal Engineering and Science University, Shibpur, India

a r t i c l e i n f o

Article history:Received 14 October 2012Received in revised form7 March 2013Accepted 12 March 2013Available online 22 March 2013

Keywords:Wireless sensor networkConnectivityCoverageNode deploymentEnergy balanceNetwork lifetime

45/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.jnca.2013.03.008

esponding author. Tel.: þ91 943 3438861; fax3 2503424.ail address: subir_ece@rediffmail.com (S. Hald

a b s t r a c t

Energy is one of the scarcest resources in wireless sensor network (WSN). One fundamental way ofconserving energy is judicious deployment of sensor nodes within the network area so that energy flowremains balanced throughout the network. This avoids the problem of occurrence of ‘energy holes’ andensures prolonged network lifetime. We have first investigated the problem for enhancing networklifetime using homogeneous sensor nodes. From our observation it is revealed that energy imbalance inWSN occurs due to relaying of data from different parts of the network towards sink. So for improvedenergy balance instead of using only sensor nodes it is desirable to deploy relay nodes in addition tosensor nodes to manage such imbalance. We have also developed a location-wise pre-determinedheterogeneous node deployment strategy based on the principle of energy balancing derived from thisanalysis, leading to an enhancement of network lifetime. Exhaustive simulation is performed primarily tomeasure the extent of achieving our design goal of enhancing network lifetime while attaining energybalancing and maintaining coverage. The simulation results also show that our scheme does notcompromise with other network performance metrics such as end-to-end delay, packet loss, throughputwhile achieving the design goal. Finally all the results are compared with two competing schemes andthe results confirm our scheme's supremacy in terms of both design performance metrics as well asnetwork performance metrics.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Recent advances in wireless communications, low power sen-sors and microcontrollers enable a new wide area monitoringparadigm commonly known as wireless sensor networking (Yicket al., 2008; DasBit and Ragupathy, 2008). Wireless sensor net-works (WSNs) allow inexpensive, high-quality monitoring of largegeographical areas. WSNs are usually implemented as havingpotentially large number of wireless sensor nodes that commu-nicate over multiple hops (Ghosal et al., 2011, 2010) with one ormore sink or base station. The task of the sink is processing thedata for the final user. Although in most existing WSNs, nodes arestatic, some modern applications involve nodes that are mobile.The sensor nodes possess several scarce resources, with batterypower (or energy) being the most critical one. The rate of energydepletion in the network primarily depends on the deploymentnature of the nodes. The nature of deployment, on the other hand,mainly depends on the application environment.

ll rights reserved.

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er).

In WSNs, nodes can be deployed either randomly or in a pre-determined manner. In random deployment, nodes are deployedrandomly generally in an inaccessible terrain. For example, in theapplication domain of disaster recovery or in forest fire detection,nodes are dropped from helicopters in random manner (Younisand Akkaya, 2008). On the contrary, in pre-determined deploy-ment, the locations of the nodes are specified. This type ofdeployment is used in applications when sensors are expensiveor when their operation is significantly affected by their positions.The applications include placing imaging and video sensors,populating an area with highly precise seismic nodes, underwaterWSN applications, monitoring manufacturing plants etc.

One important way of energy conservation is through uniformdistribution of energy, i.e., through uniform load distribution in allparts of the network. Non-uniform dissipation of energy in anypart of the network may stop functioning of that part of thenetwork leading to a phenomenon known as energy hole problem.Therefore, if any part of the network is affected by the energy holeproblem, the whole network gets affected badly as uneven con-sumption of energy in the network leads to premature decrease ofthe network lifetime. Sometimes even after the network lifetimegets over, a substantial amount of energy still remains in the nodesleading to a significant wastage of energy (Lian et al., 2006).

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124 107

The energy hole problem arises when more data are trans-mitted by certain nodes of the network than the other nodesresulting in extra energy dissipation of those nodes (Li andMohapatra, 2007). For example, nodes which are located closerto the sink transmit more data than the other nodes located faraway from the sink and so their energy gets exhausted faster. Toavoid this, care should be taken that nodes are deployed in such amanner that the energy dissipation of all nodes takes placeuniformly ensuring load balancing throughout the network.

Many works have been reported so far that deal with the issue ofbalancing the load throughout the network with a goal to reduceenergy hole problem for prolonging network lifetime. All these workshave been conducted using different approaches for achieving thisgoal. In (Song et al., 2009; Azad and Kamruzzaman, 2011; Shi et al.,2011) solutions based on regulation of transmission distance has beenreported for enhancing network lifetime. In (Efthymiou et al., 2006;Lin and Chen, 2010; Jarry et al., 2011; Boukerche et al., 2012) theauthors have proposed data propagation or routing path basedstrategies where routing path is chosen based on certain computedprobability value for balanced energy depletion in the network. Theprobability values are computed differently in each of these works. In(Olariu and Stojmenovic, 2006; Wu et al., 2008; Chang and Chang,2008; Cardei and Cardei, 2006;Wang et al., 2011; Yang et al., 2012) theauthors have proposed various node deployment strategies for solvingenergy hole problem. Out of these works, in (Cardei and Cardei, 2006;Wang et al., 2011; Yang et al., 2012) the authors have consideredheterogeneous node deployment for improving the network lifetime.In (Ammari and Das, 2008; Luo and Hubaux, 2010; Bartolini et al.,2011; Lin et al., 2012) schemes are proposed for mitigating energy holeproblem and enhancing network lifetime by considering mobility ofnodes including sink. Each type of the above schemes has their ownstrengths and limitations.

In most of these works, the proposed deployment strategiesand data routing algorithms have guaranteed the increase innetwork lifetime by balancing the energy while maintainingcoverage and connectivity of the network. However, most of thesedeployment strategies do not belong to the class of location-wisepre-determined deployment strategy in its truest sense. Here, bylocation-wise pre-determined strategy we mean not only thenumber of nodes in an area is determined a priori but also theexact locations within the area are also pre-determined. Most ofthe existing works are silent about the exact locations of placingthe nodes, which is an important criterion for some applications.Our work describes a deployment strategy where the locations ofthe nodes are pre-determined. The proposed work is related to theexisting schemes (Wu et al., 2008; Halder et al., 2011). However, inthe present work there are significant differences with the existingschemes in many ways. The main contributions of this paper arelisted below:

–

We have analyzed the conditions responsible for achievingenhancement of network lifetime. From the analysis, it isrevealed that the target can be achieved by keeping the energyconsumption balanced throughout the network. It is alsoobserved that complete energy balancing is not achievableusing homogeneous nodes.

–

Based on the analysis, energy balancing principle is derived andthat in turn is used for deciding the number of sensor nodeswhich are heterogeneous in terms of performing tasks (sensingand relaying) to be deployed along with their deploymentlocations so that network lifetime is maximized.

–

Unlike existing schemes (Wu et al., 2008; Halder et al., 2011),the proposed node deployment scheme uses heterogeneousnodes and achieves energy balancing to a greater extent.

–

Performance of the scheme is evaluated both through qualita-tive and quantitative analyses and all the claims made through

qualitative analysis are justified by quantitative analysis i.e.simulation. Quantitative analysis under more realistic scenariois also provided for showing the impacts of routing andmedium access control (MAC) protocols on the performanceof the scheme.

The rest of the paper is organized as follows. In Section 2,literature review is elaborated. The network model considered forthe present work is presented in Section 3. Analysis on networklifetime is done in Section 4. Section 5 presents essentiality ofenergy balancing in achieving prolonged network lifetime andderives a principle for maintaining such a balance. A nodedeployment scheme exploiting the derived principle of energybalancing is proposed in Section 6. In Section 7, the performanceof the scheme is evaluated based on both qualitative and quanti-tative analyses. Finally the paper is concluded with some mentionabout the future scope of the work in Section 8.

2. Related works

The works addressing the solutions of energy hole problem andsubsequent enhancement of network lifetime, mentioned in theprevious section has been elaborated in this section. We havecategorized the existing works based on their commonality inapproaches which are presented below.

2.1. Transmission range regulation based strategies

In these types of strategies, transmission range is chosen by anode considering data traffic and either Euclidean distancebetween the node and the sink or between the node andneighboring nodes towards sink, with a target for prolongingnetwork lifetime.

Song et al. (2009) have presented two algorithms—centralizedand distributed with an objective of maximizing the networklifetime in corona-based network architecture. Network lifetimehas been optimized using a proposed decision factor computed byselecting right transmission range of nodes in each corona. Thecentralized algorithm is proposed for deterministic node deploy-ment. The transmission range list of each corona is prepared basedon parameters such as the radius of the whole area, density etc.Nodes in each corona transmit data according to the transmissionrange list for maximizing network lifetime. For non-deterministicnode deployment, the distributed algorithm is proposed, where,initially the transmission list is taken as prepared by the centra-lized algorithm. Now based on the values in the transmissionrange list, nodes in each corona compute their energy consump-tion rate. This is done through consultation with the nodes of theadjacent coronas by adjusting transmission range for gettingmaximal network lifetime.

Azad and Kamruzzaman (2011) have proposed energy-balanced transmission range regulation policies for maximizingnetwork lifetime in WSNs. Authors have considered the concentricring based network architecture where the sink is located atcenter. Firstly they have analyzed the traffic and energy usagedistribution among nodes and found two parameters—ring thick-ness and hop size responsible for energy balancing. Based on theanalysis, they have proposed a transmission range regulationscheme of each node and determined the optimal ring thicknessand hop size for maximizing network lifetime. Further, energyusage distribution and critical energy changes with hop sizevariation are analyzed by the authors based on which they haveproposed three transmission range regulation policies. Each ofthese transmission range regulation policies is different in terms oftheir degree of flexibility in using variable transmission ranges and

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124108

their associated duty cycles among nodes. Simulation results showsubstantial improvements in terms of network lifetime and energyusage distribution over existing policies. However, before imple-mentation of the proposed transmission policies it requires sig-nificant computation to determine the optimal ring thickness andhop size where computational complexity increases with increasein network size. Also the scheme requires the minimum nodedensity for its implementation.

Shi et al. (2011) have proposed a topology control algorithm fordata collection in sensor network towards achieving prolongednetwork lifetime by adjusting transmission range of each sensornode. They have considered collaborative multi-path data deliveryand formulated the lifetime maximization problem as a max-fair-flow problem. A modified Push–Relabel algorithm for solving max-fair-flow problem is proposed by constructing an auxiliary graph.Prior to the application of modified Push–Relabel algorithm eachsensor node is initialized by both the upper bound of max-fair-flow and the upper bound of max flow. Now using modified Push–Relabel algorithm on created auxiliary graph each node calculatemax flow of the network using link capacity. If calculated max flowis less than the upper bound of max flow each node adjust itstransmission range to attain the upper bound of max flow andnetwork lifetime is maximized. Otherwise the network lifetime iscalculated from the equation provided for the upper bound ofmax-fair-flow. Simulation results show that the proposed algo-rithm ensures prolonged network lifetime compared with existingpower assignment schemes.

The works (Song et al., 2009; Azad and Kamruzzaman, 2011;Shi et al., 2011) provide solution for energy balancing byregulating the transmission range of each node assuming standarddeployment whereas our scheme provides energy balancing byproposing a location-wise pre-determined deployment schemeconsidering an existing routing algorithm.

2.2. Routing path based strategies

In these types of strategies, nodes judiciously choose datapropagation or routing path for transmitting data destined forthe sink. The nodes choose either single hop or multiple hoprouting path to reach the sink. When a node chooses routing pathit is chosen differently in each of the works described below:

Efthymiou et al. (2006) have proposed a probability basedbalanced data propagation algorithm where a node decideswhether to propagate data in multi-hop towards the sink ordirectly send data to the sink. The choice between the twoforwarding methods is based on a proposed probability value.Two important parameters i.e., network size and the distance ofthe node from the sink, are used to evaluate the probability. Theprobability value is chosen in such a manner that the averageenergy consumption per unit area remains same for the wholenetwork ensuring energy balance. One major drawback of theproposed algorithm is that it does not support network scalability.

Lin and Chen (2010) have formulated the energy equilibriumproblem as an optimal corona division in a corona-based WSNwith data fusion in place. The authors have proved that the energyequilibrium of intra-corona can be realized no matter whetherdata fusion or data slice is adopted with uniform node distribu-tion, while energy equilibrium of inter-coronas in the wholenetwork cannot be realized. They have also shown that maximumenergy equilibrium for a given circular area can be achieved only ifthe area increases in geometric progression from the outer coronato the neighbor inner corona except for the outermost one.Further, they have provided suitable range of values for increasingratio of corona area from outside to inside. Based on the analysis,finally the authors have proposed a routing strategy exploiting

corona structure for achieving energy equilibrium and prolongednetwork lifetime.

Jarry et al. (2011) have analyzed data gathering and networklifetime maximization problem where they have proved thatbalanced energy consumption among the nodes ensures maximi-zation of both network lifetime and flow of data towards the sink.Based on the analytical results authors have designed probabilisticonline distributed routing strategies for different network struc-tures. In one such proposed probabilistic online distributed routingstrategy, a node computes the probability of choosing a neighbornode for forwarding its data as follows: if the energy consumptionby the neighbor node is larger than the average energy consump-tion of the other neighbor nodes including it then the probabilitydecreases. Accordingly if the node realizes that its own probabilityvalue is larger than its neighbor nodes, the node sends its datadirectly to the sink otherwise it chooses the neighbor node withlower probability value for forwarding the data.

Boukerche et al. (2012) have initially studied the problem ofenergy-balanced data propagation in corona-based wireless sen-sor networks both for uniform and non-uniform deployments. Theauthors have proposed a density-based data propagation protocoltowards balancing the energy consumption and thus increasingthe lifespan of the network. The basic idea of the proposedprotocol is that in each step the node in a corona that holds dataon-line calculates the probability of data delivery either by hop-by-hop or direct to the final destination (the sink) based on thedensity information of the neighboring coronas. Finally authorshave shown that the proposed density-based data propagationprotocol works well for both uniform and non-uniform networkdeployments compared to other well-known energy balance datapropagation algorithms. In particular, performance of the pro-posed density-based data propagation protocol is near-optimal foruniform node deployment.

The works in (Efthymiou et al., 2006; Lin and Chen, 2010; Jarryet al., 2011; Boukerche et al., 2012) provide solution for energybalancing by choosing data propagation or routing path assumingstandard deployment whereas our scheme provides energy bal-ancing by proposing a deployment scheme considering an existingrouting algorithm.

2.3. Deployment based strategies

The following works are based on judicious node deploymentso that the network lifetime is enhanced.

2.3.1. Homogeneous node deployment based strategiesThese types of strategies ensure uniform energy consumption

in the network by deploying homogeneous nodes so that networklifetime is prolonged.

Olariu and Stojmenovic (2006) have explored network designguideline for maximizing lifetime while avoiding energy holeconsidering uniform node deployment strategy. They show thatuneven energy depletion due to energy hole is unavoidable forfree-space model, but can be prevented in two-ray model. Theyhave also provided the design guideline for multi-path model withcorona architecture. However, they have not explored the poten-tial of non-uniform node deployment.

Wu et al. (2008) have explored the theoretical aspects ofenergy hole problem in sensor networks with non-uniform nodedistribution where the ratio between the node densities ofadjacent layers varies by geometric proportion that ensures max-imum energy efficiency in the network. Here, number of nodes tobe distributed in a layer is determined based on the minimumnumber of nodes required in the upper adjacent layer. Finally theauthors have proposed a distributed shortest path routing

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124 109

algorithm (q-switch) which increases energy efficiency further.However, the authors have not mentioned the minimum numberof nodes required to be placed in the farthest layer from the sink tomaintain connectivity and coverage.

Chang and Chang (2008) have proposed two node deploymentstrategies that are distance-based and density-based strategies,with an objective for balanced energy consumption among thenodes. In distance-based strategy, deployment positions of nodesare selected such that the nodes' neighbors towards sink arelocated relatively closer compared to other neighboring nodes.The density-based strategy partitions the network into a numberof equal-sized zones, adjusts the density of nodes in each zone bycontrolling the switching mode as on/off and balances the load ofeach zone. Finally, authors have proposed a collision-free MACscheduling protocol for preventing energy wastage resulting out ofdata collision and subsequent retransmission of data. However, thescheme requires various control mechanisms that are difficult toimplement in resource-constrained WSN.

In (Olariu and Stojmenovic, 2006; Wu et al., 2008; Chang andChang, 2008) authors have provided the guideline about sensor nodedeployment to balanced the energy consumption. On the contrary,our scheme gives solution of both the sensor and relay nodedeployment for a given network area. However, both the schemesattempt to achieve energy balancing and lifetime maximization.

2.3.2. Heterogeneous node deployment based strategiesThese types of strategies deployed heterogeneous nodes to

ensure balanced energy consumption in the network so thatnetwork lifetime is elongated.

Cardei and Cardei (2006) have also proposed heterogeneousnode deployment strategy for improving sensor network lifetime.By heterogeneous nodes the authors mean two types of nodes—one is resource-constrained nodes and the other is resource-richsuper-nodes. They have proposed two algorithms, one is integerprogramming based heterogeneous connected set covers (IP-HCSC) and the other is distributed heterogeneous connected setcovers (Distr-HCSC), with an objective of prolonging networklifetime. The IP-HCSC algorithm constructs the connected setcovers so that within each set at a time, randomly one sensornode and one relay node are kept active while the other nodespresent in the set are kept in sleep mode. Next the authors haveimproved the algorithm and developed Distr-HCSC algorithmwhere the nodes are not chosen randomly for keeping them inactive mode. Here in each set, sensor node having maximumresidual energy is selected for keeping it in active mode whereasthe relay node nearest to the active sensor node is chosen as theactive relay node. Distr-HCSC is more scalable and adapts better todynamic and large topologies.

Wang et al. (2011) have presented an in-depth analysis on thetraffic-aware relay node deployment problem considering locationsof sensor node and sink that are known before hand. Based on theanalysis they have developed optimal solution for relay nodedeployment with single sensor node, both with single and multipletraffic flows. The authors have transformed the general relay nodedeployment problem into a generalized Euclidian Steiner Mini-mum Tree problem (ESMT) and developed a hybrid algorithm thatsuccessfully returns optimal number of relay nodes and theirrespective locations. As the ESMT based solution works in contin-uous domain resulting in fractional number of relay nodes andsimple rounding of the numbers cause severe performance degra-dation, the authors have finally developed an algorithm for discreterelay node assignment. The results show that network lifetimeachieved by the algorithm is very close to the upper bound of theoptimal solution and it achieves up to 6 to 14 times improvementover the existing traffic-aware relay node deployment strategies.

Yang et al. (2012) have studied two-tiered constrained relaynode placement problems, where the relay nodes are placed atpre-determined locations. In two-tiered relay node placement, thesensor nodes transmit their sensory data to a relay node or a sink,but do not forward packets of other sensor nodes. Authors haveproposed two algorithms for formulating the minimum number ofrelay nodes placement problem—one for 1-connected single coverand another for 2-connected double cover. The 1-connected singlecover algorithm is used for fulfilling connectivity requirementwhereas 2-connected double cover algorithm ensures enhance-ment of network lifetime. The objective of the 1-connected singlecover algorithm is placing an optimal number of relay nodes suchthat each sensor node is covered by at least one sink or relay nodeand the relay nodes form a connected network with the sink(s) whereas the objective of the 2-connected double coveralgorithm is placing an optimal number of relay nodes such thateach sensor node is covered by at least two sinks or relay nodesand the relay nodes form a 2-connected network with the sink(s).The scheme has provided lower bounds for optimal solutionsusing linear programming. Simulation results show that the upperbound for number of relay nodes needed as per the proposedalgorithms is always within twice that of the optimal solution.

In (Cardei and Cardei, 2006; Wang et al., 2011; Yang et al., 2012)authors have provided the guideline about deployment of relaynodes only, considering locations of sensor nodes and basestations are given according to application requirements. On thecontrary, our scheme gives solution of both the sensor and relaynode deployment for a given network area. However, all theschemes including ours attempt to achieve energy balancing andlifetime maximization.

2.4. Mobility based strategies

In these types of strategies, load among all the nodes aredistributed in a balanced manner by changing the position ofnodes including sink so that network lifetime is enhanced.

Ammari and Das (2008) have provided three different solutionsfor eliminating energy hole problem. In one of the three solutions,the authors have proposed a localized energy aware Voronoidiagram based data forwarding protocol considering homoge-neous nodes and mobile sink. A node selects an appropriateforwarder node based on the forwarder node’s proximity to thesink and its residual energy thereby ensuring energy balancing.

Luo and Hubaux (2010) have investigated the problem of moredata pressure on nodes closer to the sink than the nodes at adistance resulting in increased energy consumption of nearbynodes. The authors have proposed to solve the uneven energyconsumption by considering mobile sink. If mobile sink is used,then the nodes lying nearer to the sink keep on changing resultingin even distribution of load among the nodes. Therefore, the taskof forwarding data is evenly distributed among the nodes. Theauthors have further extended their work by introducing a routingprotocol which supports sink mobility as well as minimizes packetloss during sink movement.

Bartolini et al. (2011) have proposed an algorithm for mobilesensors that facilitate self deployment of the sensor nodes.The nodes coordinate their movements autonomously for achiev-ing complete coverage. The deployment approach considers pla-cing sensor nodes at variable densities for ensuring uniformenergy depletion and mitigating sink–hole problem. They haveidentified different models for representing load imbalance causedby centralized communication towards the sink. Also a densityfunction is proposed that maps the varying density requirementsfor unbalanced communication. The function of the proposedalgorithm ensures that the deployment process continues till thenetwork is fully covered. Moreover, if any portion of the network

Fig. 1. Regular hexagonal cell architecture.

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124110

becomes uncovered due to node failure in that region, the mobilenodes can move and occupy that area so as to avoid incompletecoverage.

Lin et al. (2012) have developed an energy balancing schemefor cellular-topology based clustered WSN using mobile agents.They have designed an energy prediction strategy by means ofwhich mobile agents know about the remaining energy of allsensor nodes and accordingly the mobility of agents is controlledso that the nodes with less remaining energy can communicatethrough mobile agent and avoid long-distance communicationthereby evading uneven energy consumption. The authors havealso proposed a cluster routing for achieving both inter and intra-cluster energy balancing. The mobile agent is responsible formanagement of all sensor nodes and remains active, while theordinary sensor nodes go to the sleep state when they have notasks to perform. The major drawback of this work is that highenergy consumption is incurred as two kinds of transmissionpower are adopted—one is the higher transmission power forensuring inter-cluster communication among mobile agents andthe other is the lower transmission power used for intra-clustercommunication.

As all these schemes (Ammari and Das, 2008; Luo and Hubaux,2010; Bartolini et al., 2011; Lin et al., 2012) are based on mobility ofnodes including sink, it incurs significant amount of cost for theapplications. Another major drawback of sink mobility basedstrategies is that it incurs additional energy consumption of thenodes for keeping track of the sink.

3. Network model

In this section, we describe the network architecture alongwith the assumptions. This section also presents communicationand sensing model, energy model and the concept of networklifetime considered for this work.

3.1. Architecture

We consider regular hexagonal cell (RHC) architecture (Halderet al., 2011) where the network coverage area is divided into layerscontaining regular hexagonal cells as shown in Fig. 1. In an N-layered RHC, the number of cells in each layer is 6i, where i¼1,2,…,N. Here i¼1 indicates the layer nearest to the sink and i¼Nindicates the layer farthest from the sink. The center cell wherethe sink is located is considered as layer 0 having one cell called assink cell. A cell is identified by Cj

i where for a given i, j¼1,2,…,(6i)and radius of each cell is r. For example, the cell C9

2 identifies the9th cell in layer-2.

The sensor nodes in the RHC-based network architecture isdeployed in such a way that it creates a hexagonal grid topology(Iyengar et al., 2009). Further the sensor nodes in the RHC-basednetwork architecture is deployed either in the center of a RHC oron the boundary between two consecutive layers. We define Bi asthe boundary between two consecutive layers i and (iþ1). So thecells at layers i and (iþ1) share a common boundary Bi wherei¼1,2,…,(N−1). Each boundary has a number of vertices and for aboundary Bi there are [6(2iþ1)] such vertices. For example B3(Fig. 1) is the boundary between layer-3 and layer-4. Sensor nodesare placed in cells of different layers surrounding the center cell.The cells of all the layers, except layer-0 are further categorizedinto two groups—primary and secondary. Primary cells (Cp) in alayer are those cells where the layer takes a turn of 601 and share acommon boundary with more number of cells of the upperadjacent layer. Primary cells in the architecture (Fig. 1) are shownas shaded hexagonal cells. Secondary cells (Cs) are those whichshare a common boundary with relatively lesser number of cells of

the upper adjacent layer. Secondary cells are shown as non-shadedhexagonal cells.

We classify the vertices located on a boundary based on theirresponsibility of sharing the load for forwarding data of theneighbor nodes located at the upper adjacent cells and theirdistances from the sink. Priorities are assigned to the locationsbased on the load shared by the nodes placed at these locations. Ifthere is any dearth of nodes, deployment may be completed fillingonly the locations with higher priorities ensuring a certain level ofperformance. The minimum-distant vertices associated with theCp cells on the boundary Bi are categorized as heavily loadedvertices (Vh). For example, on the boundary B2, there are twominimum-distant vertices associated with a Cp cell ðC5

2Þ. These twovertices are heavily loaded vertices. Similarly the minimum-distant vertices associated with a Cs cell on the boundary Bi areclassified as moderately loaded vertices (Vm). There is only oneminimum-distant vertex moderately loaded associated with a Cscell ðC2

2Þ on the boundary B2. The rest of the vertices (if any) on theboundary are lightly loaded (Vl). There are two lightly loadedvertices associated with cell C4

3 on the same boundary B3 whichare not minimum distant vertices.

3.2. Assumptions

We assume all the sensor nodes have same initial energy ε0 andsame energy requirement for sensing, processing, transmittingand receiving sensory data. A node is considered as dead if itsresidual energy crosses a threshold energy level. Here by deadnode we mean the node which exhausts its energy below thethreshold level and is unable to participate in any activity such assensing, transmitting etc. The nodes are static and uniformlydistributed within the network with a given node density. Thenode density is defined (Li and Mohapatra, 2007; Wu et al., 2008)as the ratio of the number of nodes in a layer and area of the layer.We consider periodic data gathering applications in which eachsensor node uniformly generates n bits of data and sends the datato the sink at fixed time-interval q(t). The nodes of a layer sense,process and transmit their own processed data as well as transmitprocessed data received from the nodes of the farther layers. Thenodes of the farthest layer from the sink sense and transmit theirown data only. For theoretical analysis, an ideal MAC layer with nocollisions and retransmissions is assumed. However, for simulationa realistic MAC is assumed. This is elaborated in Section 7.2.1. Inrealistic MAC we have considered the nodes located within a fewhops from the sink uses TDMA (schedule-based) access methodwhereas CSMA/CA (contention-based) is used in nodes located faraway from the sink.

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124 111

3.3. Sensing and communication model

3.3.1. Communication modelThe network is considered as connected, if any active node can

communicate with any other active node either in single hop or inmultiple hops (Halder et al., 2011). We assume two nodes candirectly exchange messages if their Euclidean distance is not largerthan the communication range Rc. The relationship between r andRc must satisfy the condition r≤Rc=

ffiffiffi7

pfor ensuring connectivity in

the network area (Fig. 1).We assume that a node communicates with another node for

transmitting data to the sink via the shortest path i.e. a node inlayer-i (Section 3.1) requires i hops to transmit data to the sink.However, in a practical scenario the number of hops may begreater than ihops to reach the sink. We have considered theq-switch routing protocol (Wu et al., 2008) where a node choosesa node as a forwardee (among the one-hop communication range)which is towards the sink and has the highest residual energy forsending its data. Next, the forwardee node employs same proce-dure to choose the next forwardee node for sending its data. Thisprocess repeats till the data arrives at the sink.

Lemma 1. For a given network area M�M, in order to maintainconnectivity of the network, the number of layers (N) shouldfollow the relationship N≥

ffiffiffiffiffiffiffiffi7=6

pðM=RcÞ−1=2.

Proof. If the radius of each cell of the multi-layered architecture isr, then the distance between the center of the sink cell and thefarthest edge of a cell of any other layer is given by

ffiffiffi3

priþð

ffiffiffi3

p=2Þr,

where i is the layer number.

Similarly, the distance between the center of sink cell to thefarthest point in the network area is M=

ffiffiffi2

p, then replacing i by N,

we getffiffiffi3

prNþð

ffiffiffi3

p=2Þr≥M=

ffiffiffi2

por, N≥

ffiffiffiffiffiffiffiffi7=6

pðM=RcÞ−1=2 [replacing

r≤Rc=ffiffiffi7

p].

3.3.2. Sensing modelA unit area is said to be covered (Halder et al., 2011), if every

point in that area is within the sensing range of at least one activenode. The nodes perform observation at an angle of 3601. Themaximal circular area centered around a node v that can becovered by it is defined as its sensing area S(v). The radius of S(v) is called the v's sensing range Rs. We assume that the relation-ship between r and Rs must satisfy the condition r≤Rs=

ffiffiffi3

p(Cardei

and Cardei, 2006) for covering the network area (Fig. 1) underconsideration. Also, the coverage area C(X) of a set of nodes X is theunion of the sensing areas covered by each node in X i.e. C(X)¼∪∀v∈XS(v) (Tian and Georganas, 2005).

Corollary 1. For a given network areaM�M, the number of layers(N) must follow the relationship N≥ðM=

ffiffiffi2

pRsÞ−1=2, in order to

preserve network coverage.

Proof. From Lemma 1, the relationship between M and N isevaluated as,

ffiffiffi3

prNþð

ffiffiffi3

p=2Þr≥M=

ffiffiffi2

por, N≥M=

ffiffiffi2

pRs−1=2 [repla-

cing r≤Rs=ffiffiffi3

p].

3.4. Energy model

A sensor node consists of sensing unit, processing unit andtransceivers. We have considered energy consumption for fourdifferent tasks—transmission, reception, sensing and processing inour model. The energy consumption formula (Heinzelman, 2000)used for our analysis throughout the paper is as follows:

Energy consumption for transmitting (etx) n-bits data over adistance Rc

etxðn,RcÞ ¼ ðβ1þβ2 Rαc Þn¼ et n ð1aÞ

where et ¼ ðβ1þβ2 Rαc Þ, α (2≤α≤4) is the propagation loss exponent,

β1 and β2 are both system parameters.Here et is the energy required to transmit one bit of data. Based

on the communication distance between transmitter and receiverthere are two channel propagation models. If the distancebetween transmitter and receiver is less than a certain cross-over distance, free-space model is used where energy consump-tion for transmission is directly proportional to R2

c (α¼2). If thedistance between transmitter and receiver is greater than thecross-over distance, two-ray model is used where energy con-sumption for transmission is directly proportional to R4

c (α¼4)(Heinzelman, 2000).

Energy consumption for receiving (erx) n-bits data from adistance Rc is

erxðnÞ ¼ er n ð1bÞwhere er is energy required to receive one bit of data.

Energy consumption for sensing (esx) n-bits data around adistance Rc is

esxðnÞ ¼ es n ð1cÞWhere es is energy required to sense one bit of data.

Energy consumption for processing (epx) n-bits data in each is

epxðnÞ ¼ ep n ð1dÞwhere ep is energy required to process one bit of data.

3.5. Network lifetime

In presence of several existing state-of-the-art definitions ofnetwork lifetime (Dietrich and Dressler, 2009) we have consideredlifetime of a network in terms of coverage of the network. It isdefined as the time till the proportion of dead nodes exceeds acertain threshold, which may result in loss of coverage of a certainregion, and/or network partitioning (Li and Mohapatra, 2007). Inour network model, as the nodes are deployed within differentlayers so, loss of coverage of a certain region, and/or networkpartition occurs when the nodes of a layer is dead. We consider anode as dead when the amount of energy of the node is less than apre-determined threshold value so that it is neither able to senseany event nor able to transmit any data. Therefore, in our casenetwork lifetime is same with the lifetime of a layer.

Our design goal is to find howmany numbers of nodes are to bedeployed and their deployment location so that network lifetimeis maximized in many-to-one wireless sensor network.

4. Analysis of network lifetime

In this section analysis on network lifetime is done to establishthe fact that judicious deployment of nodes can ensure properutilization of node's energy that in turn enhances lifetime of thenetwork. Here by judicious node deployment we mean nodedeployment which ensures uniform energy consumption through-out the network. The principle of node distribution to achievemaximum network lifetime is explored at the end of this section.

Now, except the nodes which belong to the farthest layer fromthe sink, nodes of all the other layers spend their energy bysensing events within their sensing range, transmitting their ownsensed data, receiving data from the nodes of farther adjacentlayers and forwarding the received data. Nodes of the farthestlayer from the sink spend their energy only for transmitting theirown data and sensing events within their sensing range.

From the geometry of RHC, area of ith layer Ai ¼ ½6 ið3ffiffiffi3

pr2=2Þ�

where cell radius is r and total area of the networkAnet ¼ ½6NðNþ1Þ=2� 3

ffiffiffi3

pr2=2�. Assuming node density as λ, total

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124112

number of nodes in the N-layered network Tnet¼λAnet (excludinglayer-0 or sink cell) and number of nodes in layer-i, Ti¼λAi. As eachnode uniformly generates and transmits data packet of size n bitsat fixed time-interval q(t), energy consumption per q(t) time-interval for transmission in the entire network is

Tnet n et ¼ λ Anet n et ¼ λ 6NðNþ1Þ2 � 3

ffiffi3

pr2

2

h in et ð2Þ

Now the energy consumption per q(t) time-interval for layer-i(i¼1,2,…,N) for transmission is as follows:

For transmitting their own data:

λ 6 i3ffiffi3

pr2

2

� �n

h iet ¼ Ti n et ð3aÞ

For transmitting the relay data received from the fartheradjacent layers:

∑Nh ¼ iþ1λ 6 h3

ffiffi3

pr2

2

� �n

h iet ¼ ∑N

h ¼ iþ1Th� �

n et ð3bÞ

So the total energy consumption per q(t) time-interval forlayer-i due to transmission ðTECTx

i Þ is computed from Eqs. (3a)and (3b). It is given as

TECTxi ¼ ½Tiþ∑N

h ¼ iþ1Th� n et for i¼ 1,2,…,ðN−1ÞTN n et for i¼N

(ð3cÞ

In the same way we can calculate the total energy consumptionper q(t) time-interval by the nodes of layer-i (where i¼1,2,…,(N−1)) for receiving ðTECRx

i Þ data from farther layers that is givenbelow:

TECRxi ¼ ∑N

h ¼ iþ1λ 6h3ffiffi3

pr2

2

� �h in er ¼ ∑N

h ¼ iþ1Th� �

n er ð3dÞ

The total energy consumption per q(t) time-interval by thenodes of layer-i (where i¼1,2,…,N) for sensing ðTECSx

i Þ events is

TECSxi ¼ λ 6 i3

ffiffi3

pr2

2

� �h in es ¼ Ti n es ð3eÞ

Finally the total energy consumption for processing the dataðTECPu

i Þ by the nodes in layer-i (where i¼1,2,…,N) in each time-interval q(t) is

TECPui ¼ Ti n ep ð3fÞHence the total energy consumption per q(t) time-interval by

the nodes of a layer i is

TECi ¼ TECSxi þTECPu

i þTECTxi þTECRx

i :

The total energy consumption rate by the nodes of layer-i is

TECi ¼

TECSxi þTECPu

i þTECTxi þTECRx

i

qðtÞ for i¼ 1,2,…ðN−1Þ

TECSxN þTECPu

N þTECTxN

qðtÞ for i¼N

8>>>><>>>>:

ð3gÞ

Let us consider that εi is the total initial energy content in layer-i and its value is given as εi¼ε0Ti where ε0 is initial energy of anode and Ti is number of nodes in layer-i. As mentioned in Section3.5, network lifetime (LT) is synonymous with lifetime of a layer.So the network lifetime or lifetime of a layer-i (LTi) is derived asfollows:

LTi ¼εi

TECi:

Ideally at the end of network lifetime all the nodes shouldexhaust energy completely. But in practice significant amount ofenergy still remains within the nodes of a layer at the end ofnetwork lifetime. Let EUi is the unused energy that remains withinthe nodes in the layer-i at the end of network lifetime. Therefore,generalized formula for network lifetime is evaluated by applying

Eq. (3g) as

LTi ¼

½εi−EUi�qðtÞTECSx

i þTECPui þTECTx

i þTECRxi

for i¼ 1,2,…,ðN−1Þ

½εi−EUN�qðtÞTECSx

N þTECPuN þTECTx

N

for i¼N

8>>>><>>>>:

ð3hÞ

From Eq. (3h), it can be concluded that to maximize networklifetime, unused energy which remains after the network lifetimeends must approach towards zero i.e., EUi¼0 (Lian et al., 2006;Efthymiou et al., 2006). So, the expression for maximum networklifetime ðLTmax

i Þ is as

LTmaxi ¼

εi qðtÞTECSx

i þTECPui þTECTx

i þTECRxi

for i¼ 1,2,…,ðN−1Þ

εi qðtÞTECSx

N þTECPuN þTECTx

N

for i¼N

8>>>><>>>>:

ð4Þ

In order to maximize network lifetime, all the layers must bealive for maximum time as well as the unused energy in themmust be zero. Here we argue that EUi is zero for i¼1,2,…,N, only ifbalanced energy consumption takes place amongst all layers in thenetwork. One possible way of balanced energy consumption ateach layer is energy-balanced node deployment (Lian et al., 2006;Wu et al., 2008) where each node irrespective of their layernumber consumes energy uniformly over the time period.

5. Energy balancing mechanism

In this section, the criterion for balancing energy consumptionamong all the layers is explored.

5.1. Analysis of energy balancing

This section explores the principle of energy-balanced nodedistribution. Energy depletion across the network is balancedwhen all the nodes of the network exhaust their energy at thesame time (Wu et al., 2008). To be more specific, if balancedenergy depletion is attained in the network then the nodes locatedin any layer will have the same lifetime. So for energy balancing,the following condition must be satisfied

ε0 T1

TEC1¼ ε0 T2

TEC2¼⋯¼ ε0 Ti

TECi,

where ε0 is initial energy of each sensor node and i¼1,2,…,N. Now:

ε0 Ti

TECi¼ ε0 Tiþ1

TECiþ1

Applying Eq. (3g), we have TECSxi þTECPu

i þTECTxi þTECRx

i

� �=

qðtÞ Ti ¼ TECSxiþ1þTECPu

iþ1þTECTxiþ1þTECRx

iþ1

� �=qðtÞ Tiþ1

Dropping q(t) from both sides and replacing the values given inEqs. (3c)–(3e) in the above equation, we have

nTi

Ti esþ Tiþ∑Nh ¼ iþ1Th

� �etþ ∑N

h ¼ iþ1Th� �

er� �þTECPu

iTi

¼ nTiþ 1

Tiþ1 es�

þ Tiþ1þ∑Nh ¼ iþ2Th

� �etþ ∑N

h ¼ iþ2Th� �

er�þTECPu

iþ 1Tiþ 1

ð5Þ

Energy requirement per node for processing is same for layer-iand layer-(iþ1), i.e., TECPu

i =Ti ¼ TECPuiþ1=Tiþ1 ¼ n ep (Eq. (3f)).

Therefore, after simplifying Eq. (5) we obtain

Ti n ðes þ et ÞTi|fflfflfflfflfflffl{zfflfflfflfflfflffl}

LHS−1

þ ∑Nh ¼ iþ1Th

� �n ðes þ et ÞTi

h i|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

LHS−2

¼ Tiþ 1 n ðes þ et ÞTiþ 1|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}RHS−1

þ ∑Nh ¼ iþ2Th

� �n ðes þ et ÞTiþ 1

h i|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

RHS−2

:

In the above relation LHS-1 and RHS-1 are equal and the termsrepresent energy consumption for sensing and transmitting databy each node of layer-i and layer-(iþ1) respectively. The

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124 113

significance of equality of these two terms is that each node oflayer-i and layer-(iþ1) consume energy n(esþet) per q(t) time-interval. So it can be concluded that irrespective of layer number,each node consumes equal energy for sensing and transmitting itsown sensory data. Hence as far as sensory data is concerned it issufficient to deploy nodes uniformly in all the layers.

Further, in the relation LHS-2 represents relaying load wheredata is generated by ∑N

h ¼ iþ1Th nodes and the load for relayingdata is shared among Ti nodes of layer-i. On the other hand, RHS-2represents relaying load where data is generated by ∑N

h ¼ iþ2Th

nodes and the load for relaying data is shared among Tiþ1 nodes oflayer-(iþ1). Also the relay load per node in layer-i is greater thanthe relay load per node in layer-(iþ1) i.e.

∑Nh ¼ iþ1Th

� �n ðerþetÞTi

� 4 ∑N

h ¼ iþ2Th� �n ðerþetÞ

Tiþ1

� :

So there is an imbalance in sharing of relay load, whichaccording to us is the primary reason for uneven energy con-sumption among the nodes of different layers. Now for balancingthe energy consumption amongst the layers, LHS-2 and RHS-2should be made equal i.e.,

∑Nh ¼ iþ1Th

� �n ðesþetÞTi

� |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

LHS−2

¼ ∑Nh ¼ iþ2Th

� �n ðesþetÞTiþ1

� |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

RHS−2

:

To make the two terms equal, Ti has to be equal to ∑Nh ¼ iþ1Th

i.e., number of nodes to be deployed in layer-i can share the relayload generated by ∑N

h ¼ iþ1Th number of nodes. Similarly Tiþ1 hasto be equal to ∑N

h ¼ iþ2Th. So we have to distribute ∑Nh ¼ iþ1Th

number of nodes in layer-i and ∑Nh ¼ iþ2Th number of nodes in

layer-(iþ1) to share the relay load equally among the nodes in alllayers.

From the above analysis we conclude that to handle the relayload in layer-i, ∑N

h ¼ iþ1Th nodes needed for deployment. Wefurther observe that at the farthest layer i.e. i¼N the term becomeszero which signifies that there is no relay load in this layer.

5.2. Energy balancing using heterogeneous sensor nodes

From the above analysis it can be inferred that energy imbal-ance due to relay load can be balanced by deploying a number ofrelay nodes in addition to sensor nodes which are essential formaintaining coverage. Therefore, heterogeneous node deploymentis considered in the proposed scheme. Here by heterogeneousnodes we mean two types of nodes where one type is sensor node(SN) and another is relay node (RN). The SN senses the environ-ment, generates data, and periodically transmits the sensory datato neighboring RN. A RN forwards the data received from both theneighboring sensor nodes (SNs) and neighboring relay nodes

0

20

40

60

80

100

120

140

50Initial energy of a RN (J)

Initi

al e

nerg

y of

a S

N (

J)

75 100 125 150 175 200

α = 2

Fig. 2. Varying initial energies of SN and RN. (a)

(RNs) which are farther away from the sink. In this way sensorydata from a SN reaches the sink through intermediate RNs. Thistype of RNs is now-a-days commercially available (CrossbowMica2 motes and Stargate-Xscale). In Section 3.2, we haveassumed that all nodes have same initial energy and same energyrequirement for sensing, processing and transmitting sensorydata. Here we further assume that all RNs have same initial energywhere energy is consumed for receiving, processing and transmit-ting relay data. Our objective is to deploy nodes in the sensor fieldin such a way that all kinds of nodes completely deplete theirenergy at the same time.

Let us consider that TSNi number of SNs and TRN

i number of RNsare deployed in layer-i. Also assume that e0 is the initial energy ofeach SN and E0 is the initial energy of each RN. Total energyconsumption by the SNs of layer-i per q(t) time-interval is given as

TECSNi ¼ TSN

i n ðesþepþetÞ for i¼ 1,2,…,N: ð6aÞTotal energy consumption by the RNs of layer-i per q(t) time-

interval is given as

TECRNi ¼ ∑N

h ¼ iþ1Th� �

n ðerþepþetÞ

TECRNi ¼ TRN

i n ðerþepþetÞ for i¼ 1,2,…,ðN−1Þ: ð6bÞ

Theorem 1. In RHC architecture, uniform energy depletion of SNand RN is guaranteed if the initial energy e0 of a SN and the initialenergy E0 of a RN stand in relation as follows-e0 ¼ ðesþepþetÞ=ðerþepþetÞE0.

Proof. For balancing the energy consumption or uniform energydepletion in the entire network each SN and RN must deplete theirenergy at the same time or the lifetime of a SN is equal to thelifetime of a RN. So, for uniform energy depletion in the entirenetwork the condition is given by

TSNi e0

TECSNi

¼ TRNi E0

TECRNi

TSNi e0=T

SNi nðesþepþetÞ ¼ TRN

i E0=TRNi n ðerþepþetÞ [Using Eqs.

(6a) and (6b)]

e0 ¼ðesþepþetÞðerþepþetÞ

E0:

Thus, for uniform energy depletion the initial energy of SN andRN are to be set according to the above relation. The analyticalresult from Theorem 1 is illustrated in Fig. 2. Here the values of es,et and er are taken from (Li and Mohapatra, 2007) and the value ofep is taken from (Heinzelman, 2000). As the path loss parameter(α) affects et, the results are plotted for α¼2 and α¼4 in Fig. 2

0

20

40

60

80

100

120

140

Initi

al e

nerg

y of

a S

N (

J)

50Initial energy of a RN (J)

75 100 125 150 175 200

α = 4

E0 vs. e0 for a.¼2 and (b) E0 vs. e0 for a¼4.

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124114

(a) and (b) respectively. For example in Fig. 2(a) we observe that ifinitial energy of a RN is 50 J, then for balancing the energyconsumption, initial energy of a SN would be 32.5 J. Similarly fromFig. 2(b) it is observed that if initial energy of a RN is 50 J then forbalancing the energy consumption, initial energy of a SN would be30.5 J. This variation is due to the fact that the value of et for α¼2 isgreater than that of α¼4.

6. Heterogeneous node deployment scheme (HNDS)

In the first phase, SNs are deployed at the center of each cellensuring coverage of the network. In the second phase RNs areplaced throughout the network area with a target to ensureconnectivity. The main objective of the present node deploymentscheme including first and second phases is to balance the energyconsumption among the layers so that network lifetime can beprolonged while maintaining connectivity and coverage.

6.1. Location of node deployment

The deployment scheme is pre-determined in nature and thelocation (x, y) where the nodes are to be placed can be computedas follows:

X ¼ffiffiffi3

pr a cosðmðπ=3ÞÞþ

ffiffiffi3

pr ði−aÞ cosððmþ1Þπ=3Þ

þS cosðð2m73Þπ=6Þþ Q cosðð2pþ1Þπ=6Þ ð7aÞ

Y ¼ffiffiffi3

pr a sinðmðπ=3ÞÞþ

ffiffiffi3

pr ði−aÞ sinððmþ1Þπ=3Þ

þS sinðð2m73Þπ=6Þþ Q sinðð2pþ1Þπ=6Þ ð7bÞwhere the variables used in the above expressions are as follows:

The network area is divided into six equilateral triangularregions. The value of m identifies each of the six regions. Onevalue of m is required to find out the center location of a set ofcells as given below:

m¼

0 for C1i , C

2i ,⋯, Ci

i

1 for Ciþ1i , Ciþ2

i ,⋯, C2ii

2 for C2iþ1i , C2iþ2

i ,⋯, C3ii

3 for C3iþ1i , C3iþ2

i ,⋯, C4ii

4 for C4iþ1i , C4iþ2

i ,⋯, C5ii

5 for C5iþ1i , C5iþ2

i , ⋯, C6ii

8>>>>>>>>>>><>>>>>>>>>>>:

ð8aÞ

where i¼1, 2,…,N.For example, the value of ‘m’ can be found out for determining

the center location of the cell C52: as i¼2, the cell can be mapped

with C2iþ1i ; so m¼2.

a¼i for Vh of C

i ðk−1Þþ1i cell

1, 2,…,i for Vm, Vl and centre location of cell Cka,C

kþ1 ðmþ1Þaþ1 , Ckþ2 ðmþ1Þ

aþ2 , …, CkþðN−aÞ ðmþ1ÞN

8<: ð8bÞ

where k¼(m� a)þ1.For example, the value of ‘a’ can be found out for determining

the center location of the cell C52: as i¼2 and m¼2 (as shown

earlier), the cell can be mapped with Cka where k¼(m� a)þ1¼

(2� a)þ1¼5; so a¼2.

S¼0 for Vm, Vl and centre location of each cellr for Vh

(

Q ¼0 for Vh and centre location of each cellr for Vm and Vl

(

p¼

do not care for Vh and centre location of each cell0 for m¼ 1, 3, 5 for Vm

0 for m¼ 0,2, 4 for Vl

1 for m¼ 0,2,4 for Vm

1 for m¼ 1,3, 5 for Vl

8>>>>>><>>>>>>:

ð8cÞ

For example, the value of ‘p’ for determining the moderatelyloaded vertex (Vm) associated with the cell C19

4 is computed asfollows: i¼4, m¼4, a¼1 and p¼1, we get the coordinates of a Vm

vertex belonging to the boundary B3 (Fig. 1). In another example,the value of ‘p’ for determining the lightly loaded vertex associatedwith the cell C18

4 is computed: i¼4, m¼4, a¼1 and p¼0, we getthe coordinates of a lightly loaded vertex (Vl) belonging to theboundary B3.

6.2. Quantification of nodes to be deployed

The present scheme is an improvement over our earlierscheme (Halder et al., 2011). The previous node distributionscheme dealt with prolonging network lifetime deploying homo-geneous nodes only whereas the present scheme deals withdeployment of heterogeneous nodes. As discussed in Section 4,the target of maximizing network lifetime is achieved by main-taining balanced energy consumption throughout the network.Further, according to the discussion in Section 5, for balancingenergy consumption in the network, heterogeneous nodes are tobe deployed in the network.

In the first phase of deployment, SNs are deployed at the centerof each cell for ensuring coverage. In the second phase, RNs areplaced at locations according to their priorities which are set asper the locations' amount of work pressure in terms of energyconsumption for relaying data of their neighboring nodes. In casethere is no dearth of nodes' availability, all the prioritized locationsare to be filled with nodes; otherwise according to the availability,nodes are to be placed at heavily loaded vertex first, then atmoderately loaded and finally at lightly loaded vertex. In this waya certain level of performance is maintained even in presence oflimited number of nodes. However, if there is any dearth of SNnodes the deployment scheme is not implementable.

Theorem 2. For a given N-layered RHC network, the deploymentscheme HNDS requires total 3[N(Nþ1)] number of SNs and total3½∑N

i ¼ 2ðNþ iÞðN−iþ1Þ� number of RNs in the entire network forbalancing energy consumption while maintaining connectivityand coverage.

Proof. Let us consider the number of SNs and RNs in a layer i isTSNi and TRN

i respectively where i¼1,2,…,N. If the total number of

nodes present in the layer i is denoted by Ti, then

Ti ¼ TSNi þTRN

i : ð9aÞ

It is mentioned in Section 5.1 that the nodes need to bedeployed uniformly for getting sensory data. So we consider,similar to our previous work (Halder et al., 2011), of deploying 6inumber of SNs in layer-i for ensuring coverage. In addition to this,for energy balancing at each layer i, number of RNs to be deployedis ∑N

h ¼ iþ1Th. When i¼N, the number of SNs required for ensuring

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124 115

coverage is TSNN ¼ 6N and no RNs are required. For i¼N−1, the

number of SNs required is TSNN−1 ¼ 6ðN−1Þ and number of RNs

required is TRNN−1 ¼ 6N. Similarly for i¼N−2, the number of SNs

required is TSNN−2 ¼ 6ðN−2Þ and TRN

N−2 ¼ 6½ðN−1ÞþN� number of RNsis required. For layer-i, the number of SNs required is

TSNi ¼ 6 i ð9bÞ

and number of RNs required is TRNi ¼ TSN

iþ1þTRNiþ1

TRNi ¼ 6ðiþ1Þþ∑N

h ¼ iþ26 h

TRNi ¼ 6½ðiþ1Þþðiþ2Þþ⋯þN�

TRNi ¼ 3½ðN−iÞðNþ iþ1Þ�: ð9cÞNow using Eqs. (9b) and (9c) we have

Ti ¼ 6 iþ∑Nh ¼ iþ16 h

Ti ¼ 6 iþ3½ðN−iÞðNþ iþ1Þ�: ð9dÞEq. (9d) represents the total number of nodes (SNs and RNs)

required in layer-i.So total number of SNs ðTSN

netÞ to be deployed in the network isas follows:

TSNnet ¼∑N

i ¼ 16 i¼ 3½NðNþ1Þ�: ð9eÞSimilarly the total number of RNs ðTRN

netÞ required is as follows:

TRNnet ¼∑N

i ¼ 26 iþ∑Ni ¼ 36 iþ⋯þ6 N

TRNnet ¼ 6 ðNþ2ÞðN−1Þ

2 þðNþ3ÞðN−2Þ2 þ⋯þN

h iTRNnet ¼ 3½∑N

i ¼ 2ðNþ iÞðN−iþ1Þ�: ð9fÞFor example, consider a 4-layer architecture (see Fig. 3). In

layer-4, there are 6�4 cells and the number of SNs required is6�4¼24 and number of RNs required is 3[(4−4)� (4þ4þ1)]¼0 i.e., no RNs are needed. For layer-3, the number of SNs required is6�3¼18 and number of RNs required is 3[(4−3)� (4þ3þ1)]¼24(number of SNs required for layer-4). Similarly, the number of SNsrequired for layer-2 is 6�2¼12 and number of RNs required is3[(4−2)� (4þ2þ1)]¼42. For layer-1, the number of SNs is6�1¼6 and number of RNs required is 3[(4−1)� (4þ1þ1)]¼54(number of SNs required for layer—4, 3 and 2).

The total number of SNs required in 4-layered architecture is[6þ12þ18þ24]¼60 and it tallies with Eq. (9e). Similarly the totalnumber of RNs required is [54þ42þ24þ0]¼120 and it also tallieswith Eq. (9f).

Fig. 3. Distribution of nodes.

6.3. Sensor node deployment

In the first phase, the scheme requires ∑Ni ¼ 16 i number of SNs.

The deployment scheme is pre-determined in nature and thelocation (x, y) where the SNs are to be placed can be computedusing Eqs. (7a) and (7b).

During node deployment in the first phase, an SN is placed atthe center of each cell. This ensures that network coverage ismaintained. Let us consider a 4-layer architecture (see Fig. 3)where the radius of each cell is 4 (r¼4). As an example, forcomputing the center location of cell C5

2, putting i¼2, r¼4, m¼2,a¼2, S¼0, Q¼0 and p¼do not care in Eq. (7a) we get the value ofx-coordinate as −4

ffiffiffi3

p. For y-coordinate, putting the same values in

Eq. (7b) we get the value of y-coordinate as 12. So, (x, y) coordinateof the center of C5

2 cell is ð−4ffiffiffi3

p, 12Þ. Similarly the coordinates of

the center of other cells can be obtained using the above equation.As far as quantification of nodes is concerned, for the example

network, layer-1 needs 6 SNs one at the center of each of its 6 cells,whereas layer-2 needs 12 SNs, one at the center of its 12 cells.Similarly layer-3 and layer-4 require 18 and 24 SNs at the centersof 18 and 24 cells respectively.

6.4. Relay node deployment

In the second phase of distribution, RNs are distributed ensur-ing network connectivity. The number of RNs is3½∑N

i ¼ 2ðNþ iÞðN−iþ1Þ�. These RNs are now deployed at verticeslocated at the boundary of each layer starting from heavily loadedvertices, then moderately loaded vertices and at last lightly loadedvertices. As discussed in Section 5.1, the layer N i.e. the farthestlayer has no relaying node, and therefore, in this phase there is noneed to deploy nodes in this layer.

Let us consider the 4-layer architecture (see Fig. 3) once againwhere the radius of each cell is 4 (r¼4). In layer-1, all cells areprimary and the vertices on boundary B1 are either heavily loadedor moderately loaded. The RNs are deployed first at heavily loadedvertices and then at moderately loaded vertices. On this boundarythere are 6 heavily loaded vertices Vh and 12 moderately loadedvertices Vm. As computed in Section 6.2, the number of RNsrequired is 54. So these 54 RNs are at first distributed in thevertices located on this boundary (B1). After deploying 6 and 12relay nodes at Vh and Vm respectively, remaining 36 (54−18) RNsare distributed equally within each cell area in random manner.The locations for random deployment are found by using Eqs.(10a) and (10b) as follows

X ¼ Xcþffiffi3

p2 r rand ð0, 1Þ � cosð2π rand ð0, 1ÞÞ ð10aÞ

Y ¼ Ycþffiffi3

p2 r rand ð0, 1Þ � sinð2π rand ð0, 1ÞÞ ð10bÞ

where Xc and Yc are the x and y coordinates of the center of a cellwithin which the nodes are randomly deployed.

Here the predetermined places or vertices are located on theboundary between the adjacent layers. Now the coordinate of eachvertex can be computed by putting appropriate values of differentparameters (i, r, m, a, S, Q, and p) of a particular cell adjacent tothat vertex. For example in Fig. 3, the (x, y) coordinate of one Vh

located on the boundary B1 and associated with C11, C

21, and C2

2 cellsis computed as ð4

ffiffiffi3

p, 4Þ by putting the parameter values as i¼1,

r¼4, m¼0, a¼1, S¼4, Q¼0 and p¼do not care in Eqs. (7a) and(7b). The co-ordinate of one Vm associated with C1

1, C21, and C2

2 cellslocated on the same boundary are computed as ð6

ffiffiffi3

p, 2Þ by putting

appropriate values of i, r, m, a, S, Q and p in Eqs. (7a) and (7b).The vertices on the boundary B2 and onwards are any one of

the three (Vh, Vm, Vl) types of vertices. After placing RNs at thevertices in the order of their priorities, if excess RNs remain, they

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124116

are distributed within the cell area randomly. On the boundary B2,there are 12 Vh vertices, 6 Vm and remaining 12 vertices are with Vl.In this case, out of the total 42 RNs, 12 nodes are placed at heavilyloaded vertices, 6 are placed at moderately loaded vertices and 12are placed at lightly loaded vertices. The remaining 12 (42−12−6–12) RNs are distributed equally within each cell area in randommanner. The vertex associated with C6

3, C73, and C5

2 cells that ismoderately loaded, also lie on this boundary. As an example, thelocation can be found out as ð−4

ffiffiffi3

p, 16Þ by putting i¼2, r¼4,

m¼2, a¼2, S¼0, Q¼4, and p¼1 in Eqs. (7a) and (7b). The locationð−4

ffiffiffi3

p, −16Þ of another vertex associated with C9

2, C133 and C14

3 cellson the same boundary is lightly loaded and the location is obtainedby putting parameter values i¼3, r¼4, m¼4, a¼1, S¼0, Q¼4 andp¼0 in Eqs. (7a) and (7b).

The vertices on the boundary B3 are any one of the three typesof vertices. In this boundary, there are 12 Vh vertices, 6 Vm verticesand remaining 24 vertices are Vl. In this case, out of the total 24RNs, 12 nodes are placed at Vh, 6 are placed at Vm and remaining6 are placed at Vl vertices. For example, the location of one Vm

vertex associated with C173 , C18

3 and C234 cells can be found out as

ð10ffiffiffi3

p, −10Þ by putting i¼3, r¼4, m¼5, a¼2, S¼0, Q¼4, and

p¼0 in Eqs. (7a) and (7b). The location ð−6ffiffiffi3

p, −22Þ of another

vertex which is lightly loaded (Vl) and associated with C173 , C18

3 andC133 cells on the same boundary is obtained by putting parameter

values i¼4, r¼4, m¼4, a¼1, S¼0, Q¼4 and p¼0 in Eqs. (7a)and (7b).

7. Performance evaluation

The effectiveness of the proposed node deployment schemereported in the earlier section is evaluated by both qualitative andquantitative analyses.

7.1. Qualitative analysis

In this section, parameters involved in achieving the target ofenhancing network lifetime by employing energy-balancing whilemaintaining coverage and connectivity are described.

7.1.1. Coverage densityTo measure coverage, the concept of coverage density (ki) (Tian

and Georganas, 2005) has been used. Consider a layer i with area Aiwhere TSN

i number of nodes is deployed. If the sensing area S(v)(Section 3.3) of each node is mutually exclusive, the coverage densityki of layer-i is defined as ki ¼ TSN

i � SðvÞ=Ai. If ki¼1, we say that Ai iscovered by minimum number of nodes and coverage area of eachnode is mutually exclusive. If ki41, we say that Ai is covered bymore than the minimum number of nodes and therefore, coveragearea of a node overlaps with the coverage area of the other nodes inthe area. The coverage density ki is also called degree of overlapping.The higher degree of coverage overlapping results in higher sensingaccuracy and more robust performance against sensing failures.

Lemma 2. For a given network area, the proposed node deploy-ment scheme gives the coverage density of layer-i as ki ¼ 2π=

ffiffiffi3

p.

Proof. Consider Ti numbers of nodes are deployed in layer-i. The S(v) of each sensor is calculated as πR2

s where Rs is sensing range.

From the definition of ki we haveki ¼ TSN

i � SðvÞ=Ai ¼ 6 i� πR2s =½6 ið3

ffiffiffi3

pr2=2Þ�:

Replacing r by Rs=ffiffiffi3

p(Section 3.3), we have

ki ¼ 6 i� πR2s =½ð6 iÞ � 3

ffiffiffi3

p=2� R2

s =3� ¼ 2π=ffiffiffi3

p:

From the above equation, we can conclude that in our schemecoverage density is uniform throughout the network and it isindependent of layer number and network size.

7.1.2. Network lifetimeIn this section we have formulated the network lifetime for our

proposed heterogeneous node deployment strategy. As we haveconsidered two types of nodes are deployed, energy consumptionof the network depends on both types of nodes. Let us considerthat the number of SNs and RNs in a layer-i are TSN

i and TRNi

respectively where i¼1,2,…,N. Now as mentioned in Section 5.2,both the SN and RN contribute towards energy consumption fortransmission. So Eq. (3c) can be rewritten as follows:

TECTxi ¼

TSNi n etþTRN

i n et for i¼ 1,2,…,ðN−1ÞTSNN n et for i¼N

(ð11aÞ

where TSNi n et is energy consumption for transmitting sensory

data by TSNi number of SNs and TRN

i n et is energy consumption fortransmitting the relay data by TRN

i number of RNs.Similarly energy consumption for receiving data by the RNs of

layer-i is calculated by modifying Eq. (3d) and it is given as

TECRxi ¼ TRN

i n er for i¼ 1,2,…,ðN−1Þ ð11bÞwhere TRN

i n er is the required energy for receiving the relay databy TRN

i number of RNs of layer-i.Energy consumption for sensing event by the SNs of layer-i is

calculated by modifying Eq. (3e) and it is given as

TECSxi ¼ TSN

i n es for i¼ 1,2,…,N: ð11cÞEnergy consumption for processing data by the SNs and RNs of

layer-i is

TECPui ¼ ðTSN

i þTRNi Þn ep for i¼ 1,2,…,N: ð11dÞ

Therefore, the energy consumption rate by the nodes of layer-igiven in Eq. (3g) is modified as follows:

TECi ¼TECSx

i þTECPui þTECTx

i þTECRxi

qðtÞ :

By replacing the value given in Eqs. (11a)–(11d))

TECi ¼

TSNi n ðesþepþetÞþTRN

i n ðerþepþetÞqðtÞ for i¼ 1,2,…ðN−1Þ

TSNN n ðesþepþetÞ

qðtÞ for i¼N:

8>>>><>>>>:

ð11eÞSo, the expression for maximum network lifetime given in

Eq. (4) is now modified as LTmaxi ¼ εi=TECi, where

εi ¼ TSNi e0þTRN

i E0 is the total initial energy content in layer-i.Now replacing the value of TECi given in Eq. (11e) and εi in theabove equation the maximum network lifetime is given as follows:

LTmaxi ¼

TSNi e0þTRN

i E0h i

qðtÞTSNi n ðesþepþetÞþTRN

i n ðerþepþetÞfor i¼ 1,2,…,ðN−1Þ

ð11fÞSimilarly for i¼N using Eq. (11e), maximum network lifetime is

given as

LTmaxN ¼ e0 qðtÞ

n ðesþepþetÞð11gÞ

Generalized formula for network lifetime is evaluated byapplying Eqs. (11f) and (11g) as

LTmaxi ¼

½TSNi e0þTRN

i E0�qðtÞTSNi n ðesþepþetÞþTRN

i n ðerþepþetÞfor i¼ 1,2,…,ðN−1Þ

e0 qðtÞn ðesþepþetÞ

for i¼N

8>>>><>>>>:

ð11hÞLet us now study the parameters, which affect the network

lifetime. It is seen from the above discussions that the parameters

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124 117

of concern are e0, E0, TSNi , TRN

i , q(t), n, es, ep and et. As the values ofes, ep, et, er and n are constant, we should concentrate on rest of thefive parameters e0, E0, T

SNi , TRN

i and q(t). We have already given thetrade-off between the initial energy of a SN (e0) and a RN (E0) aswell as that between the number of SN ðTSN

i Þ and RN ðTRNi Þ to be

deployed in layer i for balancing the energy consumption which inturn maximizes the network lifetime. The interval of periodic datageneration q(t) is another deciding parameter for network lifetime.From Eq. (11h) it is inferred that as the interval of periodic datacollection rate increases, the lifetime of the network also increaseskeeping the other parameters unchanged. Increase in interval ofperiodic data collection refers to less data collection, therebyresulting in reduced energy consumption.

7.2. Quantitative analysis

The effectiveness of the proposed node deployment scheme isevaluated through simulation.

7.2.1. Simulation environmentThe simulation is performed using MATLAB (version 7.1).

Simulation results of HNDS are compared with two existingschemes, non-uniform node distribution strategy (NNDS) (Wuet al., 2008) and energy-balanced node deploymentscheme (EBNDS) (Halder et al., 2011). Extensive simulations havebeen performed and average results of 100 independent runs hasbeen taken while plotting the simulation graphs.

In NNDS, to balance the energy consumption, sensor nodes aredeployed among layers in such a way that the ratio between thenode densities of adjacent layers varies by geometric proportion.The number of nodes to be distributed in a layer is determinedbased on the minimum number of nodes required in the upperadjacent layer. In EBNDS, to balance the energy consumption thenodes are deployed among layers in accordance with the relationof being inversely proportional with the area of each layer. In bothworks, it has been considered that all sensor nodes generate andsend data to the sink at constant time-interval. In NNDS, authorshave also proposed q-switch routing algorithm where data istransmitted from farthest layers towards the sink following themaximum remaining energy policy, where a node in a layerchooses a neighbor as next-hop when that neighbor has themaximum residual energy compared to the other neighbors.Random selection is done if there is more than one node withthe same maximum remaining energy.

We consider both ideal MAC and realistic MAC layer issueswhile implementing all the three works. The realistic MAC hasbeen implemented by funneling-MAC (Ahn et al., 2006). Thefunneling-MAC is a hybrid MAC protocol where TDMA (sche-dule-based) is used in nodes located within a few hops from thesink whereas CSMA/CA (contention-based) is used in nodeslocated far away from the sink. The sink broadcasts a beacon fornodes located within a smaller number of hops by controlling thetransmission power of the beacon. The nodes which receive thebeacon are considered as f-nodes and perform TDMA while thenodes that do not receive the beacon perform CSMA/CA. Duringsimulation we have considered the nodes located within layer-2use TDMA schedule whereas nodes beyond layer-2 use CSMA/CA.Further, we have considered energy consumption rate as 20%, 5%,and 2.5% (Ferng et al., 2011) of the energy consumption rate ofreception for sensing, remaining idle and remaining in the sleepmode respectively.

During implementation of all the three schemes, we havedeployed equal number of SNs in addition to that in HNDS wehave deployed additional RNs. The number of SNs deployed in allthree schemes is varied from 36 to 168 and in top of that the

number of RNs deployed in HNDS is varied from 48 to 672 forvarious network sizes. For all the schemes, in order to have aninteger number of nodes for each layer the upper ceil function ⌈:⌉ð Þis employed. Further we have considered both node multiplyingfactor (EBNDS) and the ratio between nodes of adjacent layer-i andlayer-(iþ1) (NNDS) as 1.3. As mentioned in communication model(Section 3.3.1), we have used the q-switch routing algorithm (Wuet al., 2008) for implementation of all the three schemes. We havevaried the time-interval (q(t)) between two successive data packetgenerations from 0.1 s to 1 s. Each sensor node generates packet ofsize 1000 bits. Therefore, packet generation rate varies from1 packet/s to 10 packets/s.

7.2.2. Simulation metricsEvaluation of the performance of HNDS is divided into two

stages: measuring extent of achieving major design considerationand evaluation of network performance. By design parameters wemean coverage density, energy balancing and network lifetimewhereas network performance metrics are end-to-end delay,packet loss and throughput.

Two of the design parameters – coverage density and networklifetime are already used in qualitative analysis and defined inSections 7.1.1 and 3.5 respectively. We define two more parametersfor evaluating the extent of energy balance which is the otherdesign parameter. One parameter is average energy consumptionrate per node and the other parameter is average residual energyper node. Though the concept of the parameter energy consump-tion rate per node is used in Section 4, the same is formallydefined here.

–

Average energy consumption rate per node (SN/RN) in a layer (AvgECR per Node) is defined as energy consumption by a node ineach q(t) time-interval. It is evaluated as

Avg ECR per Node

¼ Energy consumption by a layer in qðtÞ time-intervalNumber of nodes in the layer

As we have deployed two types of node i.e., SN and RN, avg ECRper node represents combined contribution of both the nodes.

–

Average residual energy per node in a layer (Avg RE per Node) isdefined as the residual energy or unused energy of a node in alayer after network lifetime ends. It is evaluated as

Avg RE per Node¼ Sum of residual energy of nodes in a layerNumber of nodes in the layer

Further, we define three network performance parametersmentioned above as follows:

–

End-to-end delay is defined as the difference in time betweenthe time when one data packet is generated at the source nodeand the time when this packet is received at the sink (Wanget al., 2012).

–

Packet loss is represented by measuring overall packet loss ratein the network. Packet loss rate is defined as the number ofpackets lost in the network divided by the number of packetstransmitted in the network (Ahn et al.., 2006).

–

Throughput is defined as the amount of data (in terms of bits)received at the sink (Ahn et al., 2006).

Here packet loss rate and throughput are measured over aperiod of 1 s. During evaluation of network performance we have

0

1

2

3

4

5

6

7

1Layer Number

Cov

erag

e D

ensi

ty

3-layer

5-layer

7-layer

2 3 4 5 6 7

Fig. 4. Coverage density for various network sizes.

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124118

used two-ray model (Section 3.4) and multi-hop benchmark (Ahnet al., 2006) setup in our simulation.

We compare our scheme’s performance with the two compet-ing schemes considering both ideal MAC and realistic MAC. Weconsider funneling-MAC protocol, described in Section 7.2.1, in oursimulation for investigating the impact of MAC protocol to makethe assumption more realistic. In simulation plots schemes namedwith ‘(R)’ signify performances under realistic MAC (realisticscenario) and the schemes without ‘(R)’ denotes performancesunder ideal MAC (ideal scenario). The parameters and theircorresponding values used for simulation are listed in Table 1.Unless specified otherwise, we use the same parameters withsame values of funneling-MAC as described in (Ahn et al., 2006)during implementation of funneling-MAC e.g., slot size, super-frame size, moving average factor. Experiments are conducted forthree different network sizes viz. network with 3, 5, and 7 layers.Table 2 provides the necessary number of SNs and RNs that aredeployed for each of the three different network sizes and for allthe three competing schemes.

7.2.3. Achieving design goalThree sets of experiments are conducted for evaluating the

performance of the present scheme by measuring the extent ofattaining design objective in terms of coverage density, energybalancing and network lifetime. One set of experiment measurescoverage density, the second one measures energy balancing inthe network and the last one measures the enhancement ofnetwork lifetime.

7.2.3.1. Coverage density. In Fig. 4, we plot coverage density in allthe layers for networks with three different sizes where each barrepresents degree of overlapping (Section 7.1.1). As per Table 2, forsimulation of HNDS we have deployed 36, 90 and 168 number ofsensor nodes in 3-layer, 5-layer and 7-layer networks respectively.Our primary observation is irrespective of network sizes HNDS

Table 1Parameters and their corresponding values used in simulation.

Parameters Value

Initial energy of a RN 100 J for both α¼2 and α¼4Initial energy of a SN 65 J for α¼2 and 61 J for α¼4β1 45�10−9 J/bitβ2 for α¼2 10�10−12 J/bit/m2

β2 for α¼4 0.001�10−12 J/bit/m4

er 135�10−9 J/bites 60�10−9 J/bitep 5 nJ/bit/reportThreshold energy for dead node 5 nJCommunication range of a node (Rc) 61 mSensing range of a node (Rs) 40 mPacket size (n) 1000 bitsNetwork area 200 m�200 m to 425 m�425 m

Table 2Node required for various network sizes.

Deployment scheme Network size Sensor node Relay node

HNDS 3-layer 36 485-layer 90 2407-layer 168 672

EBNDS 3-layer 36 Nil5-layer 907-layer 168

NNDS 3-layer 365-layer 907-layer 168

gives uniform coverage density and its value is 3.62. The resultsconform to the analysis (Section 7.1.1) which states that coveragedensity of our proposed deployment strategy is independent ofnetwork size and it gives us uniform coverage.

7.2.3.2. Energy balancing. As mentioned earlier, in these sets ofexperiments energy balancing is measured based on twoparameters avg ECR per node and avg RE per node in a layer atthe end of network lifetime under ideal and realistic scenarios. Wehave conducted two sets of experiments for measuring the avgECR per node. In the first set, we have measured the individualaverage energy consumption rate of SN and RN. While in thesecond set we have measured combined contribution of SN andRN in average energy consumption rate. Furthermore we havecompared the performance of our scheme with two competingschemes EBNDS and NNDS considering avg RE per node in a layeras parameter. During simulation we have considered q(t) as 1 s forboth energy model.

7.2.3.2.1. Average energy consumption rate per node (avg ECR pernode). Average energy consumption rate per node in a layer iscalculated using Eq. (11a) for our proposed scheme. Fig. 5 showsaverage ECR in different layers. To be more specific, while Fig. 5(a) and (b) show individual average energy consumption rate of SNand RN i.e., avg ECR per SN and RN respectively for 7-layernetwork, Fig. 5(c) and (d) show avg ECR per node which iscombined contribution of SNs and RNs. All the plots consider bothfree-space (α¼2) model and two-ray (α¼4) model. Also all theresults are plotted both for ideal and real MAC scenarios.

It is observed from Fig. 5(a) that avg ECR per SN is fairly constantfor all the layers. Similarly avg ECR per RN (Fig. 5(b)) is also fairlyconstant irrespective of layer numbers. It is also observed that thevalue of avg ECR per RN is greater than the avg ECR per SN. This is dueto the fact that the RNs handle more data pressure than the SNs andtherefore, on an average, one RN has greater energy consumption ratethan one SN. Similar to the plots of Fig. 5(a) and (b), in Fig. 5(c) and(d) we observe that the avg. ECR per node for a particular networksize is almost constant for all the layers and this rate varies withnetwork sizes. For example in ideal MAC, in Fig. 5(c), when α¼2, fornetwork with 3, 5 and 7 layers, the avg ECR per node is 0.359 mJ,0.353 mJ and 0.348mJ respectively. In Fig. 5(d) when α¼4, fornetwork with 3, 5 and 7 layers, the avg. ECR per node is 0.335 mJ,0.333 mJ and 0.331 mJ respectively. The results imply that the avg.ECR per node increases with increase in network size. The value ofavg. ECR per node remains constant for all the layers, and therefore,these results also conform to the analysis (Section 5.2).

0.13

0.132

0.134

0.136

0.138

0.14

0.142

1Layer Number

Avg

EC

R p

er S

N (

mJ/

s)

α=2 α=2 (R)

α=4 α=4 (R)

0.2

0.202

0.204

0.206

0.208

0.21

0.212

0.214

0.216

0.218

Avg

EC

R p

er R

N (

mJ/

s)

α=2 α=2 (R)

α=4 α=4 (R)

0.33

0.335

0.34

0.345

0.35

0.355

0.36

0.365

0.37

0.375

0.38

Avg

EC

R p

er N

ode

(mJ/

s)

3-layer 3-layer (R)

5-layer 5-layer (R)

7-layer 7-layer (R)0.32

0.323

0.326

0.329

0.332

0.335

0.338

0.341

0.344

0.347

0.35

Avg

EC

R p

er N

ode

(mJ/

s)

3-layer 3-layer (R)5-layer 5-layer (R)7-layer 7-layer (R)

2 3 4 5 6 7 1Layer Number

2 3 4 5 6 7

1Layer Number

2 3 4 5 6 7 1Layer Number

2 3 4 5 6 7

Fig. 5. Energy consumption rate per node under ideal and realistic scenarios for various network sizes. (a) Avg ECR per SN, (b) Avg ECR per RN, (c) Avg ECR per Node for free-space model (α¼2) and (d) Avg ECR per Node for two-ray model (α¼4).

S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124 119

We also compare the results of ideal MAC and realistic MAC forall network sizes and the results are plotted in Fig. 5(c) and (d). Itis observed that in all the cases avg ECR per node in realistic MACis higher compared to avg ECR per node in ideal MAC. Theadditional energy usage for realistic MAC is due to the implemen-tation of MAC protocol. Another important observation is inrealistic MAC, ECR slightly varies in different layers for a givennetwork size. As CSMA/CA is used in nodes away from the sink,unlike TDMA, it causes variation in energy consumption rate ofnodes in different layers and this justifies the above result.

7.2.3.2.2. Average residual energy per node (avg RE per node). Inthis set of experiment the performance of our scheme HNDS iscompared in terms of average residual energy per node both for idealMAC and realistic MAC. Here also the competing schemes are EBNDSand NNDS and measurements are taken at the end of networklifetime. The entire result set is plotted in Fig. 6 where Fig. 6(a) and(b) illustrate the results for free-space model, Fig. 6(c) and (d) presentthe results for two-ray model. We observe by comparing the resultsof Fig. 6(a) and (b) that the nature of the plot in HNDS is flat while inEBNDS it is steep and in NNDS it is steeper. To be more specific, inHNDS the nodes in all the layers have same and very small amount ofunused energy at the end of network lifetime whereas in EBNDS theunused energy steadily decreases as the layers approach the sink andin NNDS it decreases abruptly. We also observe that in NNDS, energyof nodes in layer-1 has drained out completely, though the nodes ofother layers in the network have sufficient energy for carrying outnormal network operation, causing the phenomenon known as

energy hole. In EBNDS, the plots up to certain layers starting fromthe nearest layer from the sink are relatively flat compared to theresults in rest of the layers thereby implying energy wastage causedby imbalance in energy consumption among the layers. Therefore,EBNDS also suffers from energy imbalance problem affecting networklifetime. However, HNDS plot is almost a straight line indicating thatall the nodes in each layer exhaust energy when network operation isterminated. For example, in case of ideal MAC it leaves less than3.5 nJ energy for 3-layer network and for 7-layer network it is 3.1 nJ.Similarly, in case of realistic MAC, it leaves less than 2.5 nJ energy for3-layer network and for 7-layer network it is 2.25 nJ. Furthermore, forEBNDS and NNDS in case of ideal MAC it leaves more than 3.3 μJ and3.5 μJ energy for 3-layer network whereas for 7-layre network it ismore than 3.8 μJ and 3.54 μJ. The values of residual energy clearlyindicate that in HNDS residual energy is in the range of nano joulewhereas in the other two schemes it is in the range of micro joule.Therefore, we can say that HNDS is energy-balanced and utilizeenergy, the scarcest resource, more efficiently than other deploymentschemes.

Similar to Fig. 6(a) and (b), we observe from Fig. 6(c) and(d) average residual energy per node is same in all the layers inHNDS whereas in the other two schemes it varies in all layersirrespective of network sizes. For example, in EBNDS, energy ofnodes in layer-1 (Fig. 6(c)) and nodes in each of layer-1 and layer-2(Fig. 6(d)) is drained out completely, though the nodes of otherlayers in the network retain sufficient energy for carrying outnormal network operation thereby resulting in the phenomenon

0

5

10

15

20

25

30

123Layer Number

Avg

RE

per

Nod

e (μ

J)HNDS HNDS (R)

EBNDS EBNDS (R)NNDS NNDS (R)

0

10

20

30

40

50

60

1234567Layer Number

Avg

RE

per

Nod

e (μ

J)

HNDS HNDS (R)

EBNDS EBNDS (R)NNDS NNDS (R)

0

5

10

15

20

25

30

123Layer Number

Avg

Re

per

Nod

e (μ

J)

HNDS HNDS (R)

EBNDS EBNDS (R)NNDS NNDS (R)

0

10

20

30

40

50

60

1234567Layer Number

Avg

RE

per

Nod

e (μ

J)

HNDS HNDS (R)

EBNDS EBNDS (R)

NNDS NNDS (R)

Fig. 6. Average residual energy per node under ideal and realistic scenarios for various network sizes. (a) 3-layer network (α¼2), (b) 7-layer network (α¼2), (c) 3-layernetwork (α¼4) and (d) 7-layer network (α¼4).

Fig. 7. Network lifetime for 7-layer network under ideal scenario. (a) free-space model and (b) two-ray model.

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of energy hole. Similarly in NNDS, energy of nodes in layer-1 (Fig. 6(c)) and nodes in each of layer-1 and layer-2 (Fig. 6(d)) is drainedout completely, though the nodes of other layers in the networkhave adequate energy for normal network operation. So NNDS alsosuffers from energy hole problem.

7.2.3.3. Network lifetime. In this section network lifetime isevaluated for various network sizes. As mentioned in Section 3.5,

the network lifetime is computed as the time interval from thevery beginning of the network operation until the proportion ofdead nodes exceeds a certain threshold, which may result in lossof coverage of a certain region, and/or network partition.

In this set of experiment, firstly network lifetime is observed interms of coverage density. We see in Fig. 7 that the coverage densityfor seven different layers of a 7-layer network becomes zero at thesame time for both the free-space and two-ray models. The resultssignify that the network lifetime also ends at the same time for all the

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seven layers. For example, in case of free-space model the networklifetime ends after 131.32 h (Fig. 7(a)) and it ends after 138.01 h (Fig. 7(b)) in two-ray model. Alternatively the SNs in all the layers depletetheir initial energy at the same timewhich has become possible due tothe scheme’s energy balancing nature.

Secondly, for the same network size network lifetime ismeasured (Fig. 8) with varying data collection period. FromFig. 8(a) and (b) it is inferred that as the interval of periodic data

collection rate increases, the lifetime of the network also increaseskeeping the other parameters unchanged. Increase of interval ofperiodic data collection refers to less data collection, therebyresulting in reduced energy consumption rate which conforms toour theoretical analysis that we have made in Section 7.1.2. It isalso observed that by increasing the interval of periodic datacollection from 0.5 s to 1 s, network lifetime increases by 50%,while increasing the interval of periodic data collection from 0.1 s

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to 1 s, network lifetime increases by 80% for both free-space andtwo-ray models.

Finally in this set of experiment performance of our schemeHNDS is compared with the two competing schemes consideringnetwork lifetime as a metric. The network lifetime is plotted bothfor free-space and two-ray models in Fig. 9(a), (b) and Fig. 9(c),(d) respectively. In each of the plot we have taken one set of dataassuming ideal MAC and the other set of data assuming real MAC.We observe from Fig. 9(a) and (b) that for ideal MAC the networklifetime of HNDS is 68% and 111% more than that of EBNDS andNNDS respectively for 3-layer network. For 7-layer network thesevalues are 72.36% and 120%. Similarly from Fig. 9(c) and (d), it isobserved that the network lifetime of HNDS is 67.77% and 94.9%more than that of EBNDS and NNDS respectively for 3-layernetwork. For 7-layer network it is 84% and 102.94% more thanthat of EBNDS and NNDS respectively.

Now if we compare the simulation results of network lifetimeboth for ideal MAC and realistic MAC, network lifetime is reduced inrealistic MAC scenario, as there is additional energy consumption dueto implementation of MAC. Further, in realistic scenario, irrespectiveof network sizes, the reduction in network lifetime is less near thesink compared to other parts of the network. To be more specific, inHNDS when reduction is 5% near the sink, it is 6% in rest of thenetwork. Similarly in EBNDS and NNDS these values are 11.75% & 13%and 12.95% & 18% respectively. As CSMA/CA is used in the entirenetwork area except near the sink, due to collision and retransmis-sion, additional energy is consumed compared to near the sinkwhere TDMA is used. From the above observations, it is also revealedthat the impact on network lifetime caused by the inclusion ofrealistic scenario in NNDS is severest whereas HNDS incurs the leastimpact. This ensures that energy in HNDS is balanced to a greaterextent than both the competent schemes.

We further observe that in all the cases of Fig. 9, HNDS's plot isflat in nature compared to EBNDS and NNDS. This ensures that inall the layers, network lifetime of HNDS terminates at the sametime as compared to EBNDS and NNDS. We therefore, infer thatenergy in HNDS is balanced to a greater extent than both thecompetent schemes.

7.2.4. Evaluation of network performanceThis section is dedicated to observe network performance

while achieving the design goal described in Section 7.2.3. Theperformance is measured using standard metrics such as end-to-end delay, packet loss and throughput. During conducting the

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simulation on these three network performance metrics, weconsider 5-layer network where 90 SNs are deployed for all thethree schemes and additional 240 RNs are deployed for HNDS.Needless to mention, during measuring network performancemetric we consider the realistic scenario.

7.2.4.1. End-to-end delay. The end-to-end delay measured in ourscheme along with the competing schemes is plotted in Fig. 10. Itis shown from the figure that the end-to-end delay for HNDS isquite comparable to the other two schemes EBNDS and NNDS. Asexpected, end-to-end delay increases with the increase in distanceof layers from the sink. It is because of packets coming from thenodes located in the layers far away from the sink that requirehigher propagation time than packets coming from near to thesink. The differences between the end-to-end delays amongst theschemes are due to network congestion. In HNDS, SNs generatesensory data packets and these are delivered to the sink throughthe intermediate RNs. On the other hand in EBNDS and NNDSsensor nodes are responsible for generating sensory data packetsand deliver those packets to the sink. As the sensor nodes inEBNDS and NNDS schemes' performs additional task than SNs ofHNDS, therefore, it is the primary reason for occurrence ofnetwork congestion.

7.2.4.2. Packet loss. Fig. 11 shows the packet loss rate across anincreasing layer number from the sink. We observe that gradientof the plot is relatively steep over the first two layers from the sinkcompared to the last three layers. As the transit traffic intensity ismore nearer to the sink it causes significant increase of packetcollision and congestion resulting in occurrence of more packetloss in layers farther from the sink.

We observe that for all the three schemes packet loss rate ishigher in the layers nearer to the sink than the layers far awayfrom the sink. We believe that such reduction in packet loss isachieved by using funneling-MAC protocol which is speciallydesigned to handle higher traffic intensity near the sink. Wefurther observe that though the funneling-MAC has ensuredsignificant reduction of packet loss rate however, complete elim-ination of packet loss is not achieved. The packet loss rate indifferent layers however, is less in HNDS compared to EBNDS andNNDS. For example, at q(t)¼1 HNDS's packet loss rate is 31% atlayer-1, 15% at layer-2 and 5% at layer-3 while for EBNDS and NNDSpacket loss rate is 50%, 55% at layer-1, 26%, 30% at layer-2 and 11%,12% at layer-3 respectively. Furthermore, for all the three schemes,

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S. Halder, S.D. Bit / Journal of Network and Computer Applications 38 (2014) 106–124 123

packet loss rate remains very close to each other for varying q(t)(viz. 0.25 s, 1 s). In EBNDS and NNDS, sensor nodes are responsiblefor generating sensory data as well as delivering the same. On thecontrary, in HNDS the SNs only generate data and relay nodes areresponsible for delivering the data. So, in HNDS SNs carryrelatively less load resulting in less congestion/collision therebyreducing packet loss rate more in HNDS than EBNDS and NNDS.We also believe that this overall reduction of packet loss rate in thefirst few layers impacts the overall throughput performance of thesensor network when nodes are deployed using HNDS scheme.

7.2.4.3. Throughput. Fig. 12 shows data throughput of HNDS, EBNDSand NNDS as measured at the sink under the multi-hop benchmark.We observe from Fig. 12(a) that throughput for EBNDS and NNDSsteadily degrade as time increases. However, in HNDS the plots risesteadily up to a certain point and then degrade slightly over time. InEBNDS and NNDS nodes are deployed in such a way that node densityincreases exponentially from outer layer to the inner layer. As thehighest numbers of nodes are deployed at the nearest layer, therefore,at the beginning we obtain maximum throughput in EBNDS andNNDS. As simulation time progresses, traffic intensity increasescausing collision. Also congestion occurs resulting in packet loss anddegrading the overall throughput. On the contrary, in HNDS, SNs areevenly distributed over the network and significant number of RNsdelivers the data packets to the sink. As a result traffic intensity isjudiciously handled by the RNs which reduce the possibility of packetcollision and congestion. It is shown from Fig. 12(a) that using HNDS,the performance of throughput improves over EBNDS and NNDSschemes' as 36.48% and 39.1% respectively.

It is shown from Fig. 12(b) that the throughput measured at thesink for HNDS rises to a peak of approximately data generationrate of 4 packets/s before the network performance falls into asaturated state. It is also shown that for EBNDS and NNDSthroughput rise to peak when data generation rate is 5 packets/sand 6 packets/s respectively before the network performance fallsinto a saturated state. We obtain 20.46% and 21.53% improvedthroughput in HNDS compared to EBNDS and NNDS respectively.

8. Conclusion and future work

Wireless sensor networks are comprised of resource-constrainedsensor nodes. One of the scarce resources of sensor nodes is energythat needs to be preserved so that network lifetime is prolonged. Inthis paper we have thoroughly analyzed the issue of energy conserva-tion and subsequent enhancement of network lifetime. As a result ofthis analysis it is revealed that energy balancing in all parts of thenetwork is essential to achieve the goal of enhancement of networklifetime. Next we have explored the principle of energy balancing that

shows the need of heterogeneous node deployment instead of onlyhomogeneous nodes. Heterogeneity has been introduced by using twotypes of nodes- sensor nodes and relay nodes. Further, considering theresults of this analysis we have proposed a pre-determined nodedeployment scheme using heterogeneous nodes with a target toenhance network lifetime. Simulation results prove that our schemeachieves design goal by extending network lifetime without compro-mising the other network performance metrics such as end-to-enddelay, packet loss and throughput. The results also show dominance ofour scheme over two other competing schemes (Wu et al., 2008;Halder et al., 2011) in respect to both set of parameters includingparameters for achieving design goal and standard network perfor-mance metrics.

As a future extension of our work, the deployment strategymay be made more realistic by considering 3-D environment.Moreover, the scheme may be analyzed for further improvementconsidering QoS parameters.

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