research article energy-aware hierarchical topology...

Research ArticleEnergy-Aware Hierarchical Topology Control for WirelessSensor Networks with Energy-Harvesting Nodes

Ikjune Yoon1 Dong Kun Noh2 and Heonshik Shin1

1School of Computer Science and Engineering Seoul National University Seoul Republic of Korea2School of Electronic Engineering Soongsil University Seoul Republic of Korea

Correspondence should be addressed to Dong Kun Noh dnohssuackr

Received 30 November 2014 Revised 18 March 2015 Accepted 30 March 2015

Academic Editor Kaibin Huang

Copyright copy 2015 Ikjune Yoon et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The nodes in a wireless sensor network (WSN) are often clustered to improve the efficiency of data transmission but this cancause an imbalance in the energy available at each nodeThis impairs the transmission capability of some nodes and hence reducesnetwork connectivity This imbalance worsens as nodes become defunct We propose a multilayer topology for long-term hybridWSNs which contain both battery-powered and energy-harvesting nodes Each node periodically selects its own layer dependingon the energy it has available in order to balance energy levels and maintain network connectivity Simulations show that thisscheme improves the delivery of data across a WSN

1 Introduction

Wireless sensor networks (WSNs) are now widely used tocollect environmental data AWSN consists of many wirelesssensor nodes which communicate the data they acquire to asink node Because of wireless range limitations this usuallyinvolves multihop transmission passing data from one nodeto the next Nodes also have a limited lifetime because theyrun on batteries and when these are exhausted transmissionscease and other nodes which used the dead node for relayingdata may no longer be able to communicate with the sinkTherefore it is important to prolong lifetime of the sensornodes in a WSN

Controlling the topology of the wireless connectionsbetween nodes can prolong the life of a network by avoidingundue reliance on bottleneck nodes which are likely to faileasily due to the volume of traffic that they handle bringingout large parts of the network However networks with nohierarchy have their own problems Early WSNs had a flattopology and transferred data using a flooding scheme Thiscan cause a broadcast storm and the redundant transmissionsthat result quickly exhaust the nodesrsquo batteries This problemis exacerbated because the nodes closest to the sink use more

energy than the others and when they fail the rest of thenetwork becomes isolated and thus useless

A popular way to create a hierarchical topology is clus-tering Nodes can organize themselves into clusters each ofwhich has a head which aggregates data from the nodes in thecluster and forwards it to the sink nodeThis scheme is betterthan the flat topology but the cluster heads are its weak linksthese nodes consume more energy than the other nodes anddie early isolating the cluster from the sink

This drawback is commonly ameliorated by periodicallychanging the head node within a cluster Even so dead nodesfail early and have to be replaced to achieve a satisfactorynetwork lifetime as a whole We have proposed a multilayertopology control scheme as an alternative way of addressingthe problem In our scheme [1] nodes are allocated toseveral layers depending on the amount of energy they haveavailable with the aim of balancing usage against remainingenergy Nodes with plenty of energy are placed in an upperlayer and these nodes aggregate data received from lowerlayers This has been shown to maintain good connectivityfor far longer than other topology control schemes Howeverour scheme requires to estimate lifetime of the entire networkand the average amount of data relayed by each layer in orderto determine its own layer Unfortunately this information

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 617383 12 pageshttpdxdoiorg1011552015617383

2 International Journal of Distributed Sensor Networks

is not readily available at every node because the accuracywith which it can be estimated depends on the location of thenode Moreover since all nodes are periodically able to moveto other layers estimates soon become inaccurate and thusmany nodes fail to locate themselves in the best layer

The life of a network can also be prolonged if energy isharvested from the environment an energy-harvesting nodecan potentially operate forever by recharging its battery withenvironmental energy Even so a node will eventually ceaseto operate if it consumes more energy than it is able toharvestMany researchers [2] have designed topology controlschemes to maximize the lifetime of a network of energy-harvesting nodes However many practical WSNs contain amixed population of nodes some of which can and some ofwhich cannot harvest energy and prolonging the lifetime ofthis class of WSN has received much less attention

In this paper we propose a topology control schemefor preserving connectivity between nodes in long-termWSNs in which defunct nodes are manually replaced andwhich contains both energy-harvesting nodes and battery-powered nodes In such a WSN the battery-powered nodescan be expected to have diverse amounts of residual energywhich decline with length of deployment As in our previousscheme the nodes arrange themselves into layers and thenodes on the upper layer are given the job of aggregating datareceived from the nodes on the lower layers and sending it to asink node Like previous layering schemes this arrangementimproves energy efficiency and connectivity but this newscheme increases the lifetime of battery-powered nodes bypreferentially locating energy-harvesting nodes on higherlayers

The rest of the paper is organized as follows In Section 2we describe the background to this research and reviewrelated work In Section 3 we introduce our scheme for layer-based topology control and describe how nodes choose theirlayer and establish connectivity with neighboring nodes InSection 4 we present experimental results and assess theperformance of our scheme In Section 5 we introduce aproposal for further research Section 6 concludes the paper

2 Background and Related Work

21 Energy-Harvesting Wireless Sensor Networks WSNs con-sisting solely of battery-powered nodes naturally have alimited lifetime and there have been many proposals [2] touse energy-harvesting nodes to extend the lifetime of WSNs[2] The environmental sources from which it is practical fornodes to harvest energy are the sun [3ndash8] and the wind [8 9]Solar-powered wireless sensor nodes are usually preferred[10] because of the high areal density of solar power (about15mWcm2)

Many schemes have been proposed to maximize thecontribution of solar energy to extending the life of a WSNKansal et al [11] proposed an energymodel for solar-powerednodes which estimates the levels of energy consumption andharvesting which will allow a node to survive indefinitelyNoh and Kang [12] designed an energy allocation schemewhich estimates the energy that will be harvested by a solar

cell every hour and determines future consumption levelswhich will allow the node to survive a complementaryrouting algorithm has also been presented [13]

The efficient use of solar energy requires accurate pre-diction which is relatively easy because of its obviousrelation to the diurnal cycle Nevertheless the availabilityof sunlight is of course affected by weather Kansal et al[3] Piorno et al [14] Moser et al [15] and Cammarano etal [16] have all proposed models for estimating the avail-ability of solar energy using respectively an exponentiallyweighted moving-average (EWMA) the so-called weather-conditioned moving average (WCMA) a weighted sum ofhistorical data and the Pro-Energy model

22 Hierarchical Topology Control for WSNs with Energy-Harvesting Nodes Topology control which determines hownodes connect to each other is an important issue whichaffectsWSN performance Only relatively recently has it beenapplied to WSNs which use energy-harvesting nodes

Voigt et al [17] introduced the solar-aware LEACHalgorithm (sLEACH) which applies LEACH [18] to WSNsconsisting of both solar-powered and battery-powered nodesThe sLEACH algorithm strongly favors the use of solar-powered nodes as cluster heads which have to do more workthan other nodes LEACH is effective in equalizing energyusage across (battery-powered) nodes but sLEACH cannotbe applied to large WSNs because all the cluster heads mustconnect directly to the sink In addition sLEACH tends toallow the harvested energy to be under-utilized or to runout because sLEACHdoes not consider energy stored at eachnode and the rate at which each node acquires energy

Zhang et al [19 20] proposed a scheme which overcomesthe need for each cluster head to connect directly to thesink by using further energy-harvesting nodes to relaytransmissions from the cluster head to the sinkThis can alsosave energy by reducing the range over which cluster headsare required to transmit Gou et al [21] also addressed thedrawbacks of sLEACH by partitioning aWSN and taking theenergy remaining in each node into account

Jakobsen et al [22] and Meng et al [23] also haveproposed hierarchical topology control schemes for energy-harvesting nodes

3 Layer-Based Topology Control with Energy-Harvesting Sensor Nodes

We will now introduce a new layer-based topology controlscheme and explain how to allocate nodes to layers hownodes operate within the layers and how the scheme appliesto energy-harvesting nodes We will assume that a WSNcontains both battery-powered and energy-harvesting nodeswhich periodically forward the data that they have gatheredto the sink node We are also assuming that defunct nodeswill be replaced because this is a long-termWSN

31 Review of Layer-Based Topology Control for Long-TermWSNs with Battery-Powered Nodes In our previous layer-based topology control scheme [1] all the nodes gather data

International Journal of Distributed Sensor Networks 3

s

n1

n2

n3

n4

n5

n6

n7

n8

n9

n10

Layer 0

Layer 1

Layer 2

WSN

Figure 1 Overview of layer-based topology control

and periodically forward it to a sink nodeNodes are arrangedin layers and data travels hierarchicallyThis scheme has beenshown to reduce the imbalance in available energy across thenodes

Each node is periodically allocated to a layer on the basisof its estimated lifetime The nodes in each layer affectivelyconsider all higher-layer nodes as local sink nodes relative totheir own layer and data is routed by the multi-sink-awareminimum-depth tree (m-MDT) algorithm [24] Nodes inthe upper layers forward the data received from lower-layernodes as well as the data they themselves have acquired tonodes in yet higher layers By repetition of these processes allthe data arrives at the actual sink node In order to preventdata being sent on void [25] or cyclic routes nodes are notpermitted to send data to nodes in lower layers Figure 1shows a topology with three layers

Naturally nodes in higher layers will have to transitmore data requiring more energy This is why energy-richnodes are placed in higher layers Each node determines itsown layer on the basis of the amount of energy that it hasremaining the amount of data which it is likely to have totransmit and its estimated lifetime

As we already mentioned a drawback with this scheme isthat the nodesrsquo estimation of the amount of data which theywill have to transmit during a subsequent data transmissionphase is not accurate because it is an average of the amount ofdata transmitted by all the nodes whereas the actual amountdepends on the location of a particular node In additionthis scheme potentially allows all nodes to change their layersvery frequently making it difficult to determine which layeris actually the best because the amount of energy that a nodeforecasts it will consume in a layer is likely to be very differentfrom its actual consumption when it moves itself to thatlayer Furthermore our scheme does not consider energy-harvesting nodes which is the rationale of this present paperWe address all these deficiencies in the new scheme which wewill now describe

32 The Layer Determination Algorithm We will now intro-duce our improved layer-based topology control scheme andexplain how each node determines its layer Unfortunatelythis requires a lot of notation and so we summarize fre-quently used notation in Notation Summary

Table 1 Global TCI message

Notation Description119886 Index of this TCI message119894 Index of the sender node119895 The layer to which the sender belongs (for routing)

321 Operation of a Node When a node 119899119894is deployed in a

network for the first time it joins the lowest layer and selectsa target node among neighboring nodes in response to Localtopology control information (TCI) messages from neighbor-ing nodes Node 119899

119894then begins to gather information from

the environment and sends it to the sink node via its targetnode during every gathering period 119901gather At the beginningof each round the sink node sends a Global topology controlinformation (TCI) message to the entire network using aflooding process This occupies a setup period 119901setup Eachnode then begins its Layer determination process at thebeginning of the subsequent layer determination period119901layer

119894

or earlier if it has received the Global TCI messagefrom the sink node This process determines a nodesrsquo newlayer If a node 119899

119894is moving to another layer then it sends

a Layer notification message to its neighbors and they mayhave to select new target nodes as a result The logic ofnode operation is shown in Figure 2 and Figure 3 shows anexample timeline

322 Topology Control Information for Layer and TargetDetermination To determine the layer in which it shouldreside a node needs information about its 1- and 2-hopneighbor nodes in the networkThis information is deliveredto nodes by topology control information (TCI) messageswhich can be local or global depending on their content andthe range over which they are delivered

Global TCI At the beginning of each setup period 119901setupa Global TCI message containing information relating totopology control and routing is transmitted by the sinknode to the entire network using a flooding process Whena node which receives a Global TCI message it executesthe Synchronous layer determination process presented asAlgorithm 2 and may then change its layer The sink nodeselects setup period 119901setup A longer setup period makestopology control more accurate but the allowable topologycontrol overhead is limited Table 1 shows the contents of aGlobal TCI message

Local TCI A Local TCI message contains information abouta nodersquos 2-hop neighbors the shortest hop-count from thesending node to a higher-layer node and the nodesrsquo expectedlifetime together with general neighborhood informationcommonly exchanged by nodeswithinWSNsAnode 119899119895

119894peri-

odically broadcasts to its 1-hop neighbors following a genericWSN protocol at the beginning of its layer determinationperiod 119901layer119894 Tables 2 and 3 show the contents of a Local TCImessage


Changing layer

Receiving a Layer notification message

Layer andtarget node

determination

Sensing and data transmission

Sending a Layernotification message to

neighbor nodes

Every

Every period pgather

period player119894 or psetup

If layer l ne lprev

If layer l = lprev

Figure 2 Node operation

Synchronous layer determinationAsynchronous layer determinationSensing and gathering data

Time

The sink sends a Global TCI message

player119894

psetup

pgather

Figure 3 Example of node operation The shaded box indicates asingle round

Table 2 Local TCI message

Notation Description119894 Node index119895 The senderrsquos layer119873 Set of neighbor nodes 119899119897

119896isin 119873

ℎ119894

Hop-count to the closest known node on a higher layer119871119894

Expected lifetime of the sender (in rounds)

In our previous system [1] the average expected lifetimeof all nodes was delivered to all the nodes in the WSN bymeans of a Global TCI message and this information was

Table 3 Information about each neighbor node in119873

Notation Description

119904119896

Amount of data which this neighbor node transmittedduring the previous gathering period 119901gather

119905119896 Neighborrsquos target node119897 Neighborrsquos layer

ℎ119896

Shortest hop-count from this neighbor to a node on ahigher layer

119871119896 Expected lifetime of this neighbor (in rounds)

used in determining each nodersquos layer but this procedure isnot appropriate for WSNs in which nodes closer to a sinkuse more energy In our new scheme therefore each nodecalculates a local average expected lifetime from informationsupplied by its 1- and 2-hop neighborsThis average is derivedfrom the expected lifetime 119871

119894of a node 119894 which is determined

as follows

119871119894=

119864remain119894119864round119894

(1)

where 119864remain119894 is the remaining energy in node 119894rsquos batteryand 119864round119894 is the energy that node 119894 consumed during theprevious round


Reuire 119901layer119894 of node 119899119895

119894expires

Ensure Determine whether node 119899119895119894moves to layer 119895 + 1

(1) procedure layer determination(2) Calculate 119871119895+1

119894using (9)

(3) if 119871119895+1119894

gt 119871 and exist119899119897

119896(119897 gt 119895) isin 119873

119894then

(4) 119895 larr 119895 + 1

(5) target determination(119895119873119894)

(6) Broadcast Layer notificationmessage(7) end if(8) end procedure(9) procedure target determination(119895119873

119894)

(10) if 119878 = 119899119897119896| 119897 gt 119895 and 119899

119897

119896isin 119873119894 = 0 then

(11) 119905119894larr 119899119897

119896(has minimum ℎ

119896) isin 119878

(12) else(13) 119905

119894larr 119899119897


119896) isin 119899

119897

119896| 119897 = 119895 119899

119897

119896isin 119873

(14) end if(15) end procedure

Algorithm 1 Asynchronous layer determination

323 Layer Determination Each node 119899119894determines its layer

by executing a Layer determination process at the beginningof its layer determination period 119901layer119894 or when it receives aGlobal TCImessage or a Layer notificationmessageThere aretwo kinds of Layer determination process as follows

Asynchronous Layer Determination Node 119899119895119894performs this

process at the start of every layer determination period 119901layer119894It determines whether tomove up one layer by computing

119871119895+1

119894 which is the estimated lifetime of node 119894 if it moves up

to layer 119895+1The expression for 119871119895+1119894follows later as (9) Node

119899119895

119894compares 119871119895+1

119894with 119871

119894 the average local expected lifetime

of its 1- and 2-hop neighbors If 119871119895+1119894is greater than 119871

119894 then 119899119895

119894

ascends to the next higher layer provided that it will have atleast one node in its set of neighbor nodes119873

119894at the new level

Otherwise 119899119895119894does not change layers to avoid becoming a

void nodeIf node 119899119895

119894moves from layer 119895 to layer 119895 + 1 as a result

of running the Asynchronous layer determination processit broadcasts a Layer notification message to inform itsneighbors of the change A node which receives such amessage redetermines its target node by running the Tar-get determination process This selects the nodersquos neighbor119899119897

119896(119897 gt 119895) which has the minimum hop-count to an upper-

layer node to be its new target node The Asynchronouslayer determination and Target determination processes arepresented as Algorithm 1

Synchronous Layer Determination This process determineswhether a node will descend to the layer below its currentlayer The sink node broadcasts a Global TCI message of theform described in Table 1 and every node which receives itruns the Synchronous layer determination process

If node 119899119895119894receives a Global TCI message from node 119899119897

119896

it calculates its expected lifetime 119871119894using (1) If 119871

119894is less

Require Node 119899119895119894receives Global TCI message from 119899

119897

119896

Ensure Determine whether node 119899119895119894moves to layer 119895 minus 1

(1) Calculate 119871119894using (1)

(2) if 119899119895119894has already received a TCI from another node then

(3) if 119895next gt 119895 and 119897 gt 119895 then(4) 119895 larr MIN (119895next 119897)

(5) 119905119894larr 119899119897

119896

(6) Broadcast Global TCI message(7) end if(8) else(9) if 119871

119894lt 119871 then

(10) 119895next larr 119895 minus 1

(11) else(12) 119895next larr 119895

(13) end if(14) 119895 larr MIN(119895next 119897)(15) 119905

119894larr 119899119897

119896

(16) Broadcast Global TCI message(17) end if

Algorithm 2 Synchronous layer determination

than the local expected lifetime 119871119894 it moves to the next lower

layer 119895 minus 1 Then it selects 119899119897119896as its target node and sends

a Global TCI message to its neighbors However if node 119899119895119894

subsequently receives a duplicate Global TCI message fromanother node 119899119901

119900 it runs the Layer determination process

again If this changes its choice of layer it selects 119899119901119900as

its target node 119905119894and broadcasts its Global TCI message

again Each node repeats this process until all the nodeshave determined their layers and target nodes This processis presented as Algorithm 2

We will now explain why there are two Layer determina-tion processes If all the nodes were to change their layersat the same time their estimates of their own lifetimes 119871would be less accurate because the method of determining119871119894assumes that neighbor nodes will not change their layers

until 119871119894is calculated again Therefore the Asynchronous layer

determination process is used to determine whether a nodeshould move up to the next layer However when a node 119899119895

119894

moves down a layer it is not certain that the nodes whichhave 119899119895

119894as their target node will be able to find a new

route to a higher-layer node This is why the process whichdetermines whether a node moves up a layer is executed byasynchronously at the beginning of each layer determinationperiod 119901layer119894 whereas all the nodes run the process whichdetermines whether they will move down at the same time

324 Estimated Lifetime of a Battery-Powered Node Ourscheme requires each node to calculate its expected lifetimeand then to determine its layer by comparing its ownexpectation with the local expected lifetime 119871

119894 The expected

lifetime of a node can be obtained by applying (1) to theamount of energy which that node consumed during the pre-vious round However the Synchronous layer determination


process presented as Algorithm 1 requires a node to estimateits lifetime on the assumption that it is elevated to layer 119895 + 1We will explain this move complicated process in due course

Estimation of Energy ConsumptionAn estimate of the energyconsumed by a node can be made as follows [26]

119864consume = 119864trans + 119864receive + 119864elec (2)

where 119864trans and 119864receive are respectively the amount ofenergy consumed by the nodersquos radio transceiver duringthe transmission and receipt of data and 119864elec is the energyconsumed by the nodersquos electric circuits The energy which anode 119899119895

119894consumes during the setup period 119901setup starting at

time 119905 is

119864round119895

119894(119905) = int

119905+119901setup

119905

119864consume119895

119894(120591) 119889120591 (3)

119864round119895

119894(119905)

= int

119905+119901setup

119905

(119864trans119895

119894(120591) + 119864receive

119895

119894(120591) + 119864elec119894 (120591)) 119889120591

(4)

where 119864trans119895

119894is the energy required by node 119899119895

119894during period

119901setup which can be determined as follows

int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = 119904120573119889

120572 (5)

int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = lfloor

119901setup

119901gatherrfloor 119904trans

119895

119894120573119889120572

119894 (6)

In this expression 119904 is the amount of data to be transmitted119904trans119895

119894is the amount of data which 119899

119895

119894transmits during

gathering period 119901gather 120572 is the path loss (2 ge 120572 ge 5) 120573is the energy used by the power amplifier in transmitting 1 bitover a distance of 1 meter 119889 is the distance between the nodes[m] By substituting (6) into (4) 119864round

119895

119894(119905) can be expressed

as follows

119864round119895

119894(119905) = lfloor

119901119904

119901119892

rfloor 119904trans119895

119894120573119889120572

119894

+ int

119905+119901setup

119905

(119864receive119895

119894(120591) + 119864elec

119895

119894(120591)) 119889120591

(7)

Let us assume that the data from lower-layer nodes isaggregated into a single packet which is sent immediatelyThe amount of data to be transmitted 119904trans

119895

119894 which varies

from layer to layer can be expressed as follows

119904trans119895

119894= 119904head + 119904sensor + 119904lower

119895

119894+ 119904relay

119895

119894 (8)

where 119904head is the amount of data in a packet header 119904sensor isthe amount of data gathered by the sensor in node 119899119895

119894 119904lower

119895

119894is

the amount of data received by node 119899119895119894from nodes on lower

layers excluding packet headers and 119904relay119895

119894is the amount of

data received from nodes on the same layer

Estimating the Amount of Data That a Node Must Transmit IfIt Moves to a Higher Layer The amount of data which node

Sink node

n

(a) Network topology before Asynchronous layer determination

Sink node

n

Case 1

Case 2

Case 2 Case 1

Layer 3 nodes Layer 2 nodes

Layer 1 nodes

(b) Network topology after Asynchronous layer determination

Figure 4 Estimating the amount of data to be transmitted as partof Asynchronous layer determination

119899119895

119894will have to transmit if it is elevated to layer 119895 + 1 can be

determined by considering three cases shown in Figure 4 Indescribing these cases we will write the set of neighbor nodesof 119899119895119894119873119894 and the target node of 119899

119896as forall119899119897119896isin 119873119894 as 119905119896

Case 1 (target node 119905119896= 119899119895

119898) The highest layer of any of

the neighbor nodes 119899119897119896is 119895 because a node sends data to its

highest-layer neighbors However if 119899119895119894is elevated to become

119899119895+1

119894 it will be the highest-layer node among neighbors of 119899119897

119896


Therefore 119899119895+1119894

becomes the new target node 119899119896 and the 119904data119896

bits which node 119899119896transferred during the previous round

must be added to 119904lower119895+1

119894

Case 2 (119905119896= 119899119895+1

119898and the hop-count of 119899119895+1

119898 ℎ119898gt ℎ119894) The

target node 119905119896will become 119899119895+1

119894 However if 119897 = 119895 + 1 then

119904data119896 + 119904head should be added to 119904relay119895+1

119894 because 119899119897

119896will use

119899119895+1

119894as a relay node but if 119897 lt 119895+1 then 119904data119896 should be added

to 119904lower119895+1

119894 because 119899119895+1

119894will be used as an aggregation node

Case 3 (otherwise) Other nodes already have better targetnodes than 119899119895+1

119894 and so they do not send it any data

All the information which a node requires in order toestimate the amount of data that it will have to relay canbe obtained by exchanging Local TCI messages with itsneighbors

The estimated lifetime 119871119895+1119894 which is the number of

rounds that node 119899119895+1119894

can be expected to survive can nowbe calculated from 119864round

119895+1

119894(119905) as follows

119871119895+1

119894= lfloor

119864remain119894

119864round119895+1

119894(119905)

rfloor (9)

119871119895+1

119894is used in Algorithm 1 to determine whether 119899119895

119894moves

up a layer

33 Introducing Energy-Harvesting Nodes to a Layered Topol-ogy In a WSN that has both energy-harvesting and battery-powered nodes the network lifetime can be extended bypreferential deployment of energy-harvesting nodes onupperlayers as aggregation nodes However a node will eventuallydie if it uses more energy than it harvests and this is a greaterthreat to upper-layer nodes because they have to transmita lot of data It is better to deploy energy-harvesting nodeson layers with workloads that allow them to them to surviveindefinitely

In the previous section we showed how to determine thelayer of a battery-powered node on the basis of a comparisonbetween its estimated lifetime and the average expectedlifetime of neighboring nodes However energy-harvestingnodes do not have well-defined lifetimes and so they mustbe allocated to layers in a different way

331 Energy Model for Energy-Harvesting Nodes Althoughits long-term survival cannot be predicted an energy-harvesting node 119899119895

119894 for the case that it can determine its

layer needs to know whether its lifetime extends beyondthe current round Kansal et al [11] introduced a modelof energy harvesting and consumption and proposed abound on the residual energy which should allow a node tosurvive indefinitely Based on this model the residual energy

available to node 119899119895119894 after a setup period 119901setup beginning at

time 119905 can be expressed as follows

119864remain119895

119894(119905 + 119901setup) = 119864remain119894 (119905) minus 119864round

119895

119894(119905)

+ 119864charge119894 (119905 119901setup)

0 lt 119864remain119894 (119909) lt 119864max119894

(10)

where 119864remain119895

119894(119905) is the residual energy available to node 119899119895

119894

at time 119905 119864round119895

119894(119905) is the energy consumed during 119901setup

119864charge119894(119905 119901setup) is the energy harvested during 119901setup and119864max is the capacity of the nodersquos battery

The expected energy harvest 119864charge119894(119905 119901setup) can bedetermined as follows

119864charge119894 (119905 119901setup) = int119905+119901setup

119905

120582119894(120591) 119889120591 (11)

where 120582119894(120591) is the charging rate of 119899

119894at time 120591 Some

researchers have suggestedways of estimating120582 For instanceKansal et al [3] use an exponentially weighted moving-average (EWMA) algorithm to estimate the charging rate ofa solar cell

The expected energy consumption 119864round119895

119894(119905) can be

calculated using (1) or (7)

332 Determining the Layer of an Energy-Harvesting NodeBecause of the impracticality of estimating the lifetime of anenergy-harvesting node we settle for estimating whether anenergy-harvesting node 119899119895

119894is likely to be alive after 119901setup if it

is allocated to a certain layer If it is expected to survive ona higher layer then it moves up to that layer conversely if itis not expected to survive on its current layer it moves to alower layer

Determining Whether a Node Should Move to a Higher LayerIf the estimated energy conserved stored in the battery of anenergy-harvesting node 119899119895

119894 which is 119864remain

119895+1

119894(119905 + 119901setup) and

can be found using (10) satisfies the following condition thenthe node can move to the next higher layer 119895 + 1

119864remain119895+1

119894(119905 + 119901setup) gt 119864min119894 + 120598119894 (12)

where 119864min119894 is the minimum energy required to operatenode 119899

119894properly which depends on the specification of each

sensor node and 120598119894is the estimation error of119864charge119894(119905 119901setup)

which can be estimated using a charging energy estimationalgorithm [3] If (12) is satisfied node 119899

119894will not become

defunct until next round at the earliest We can now modifythe Asynchronous layer determination process to apply toenergy-harvesting nodes by modifying line 3 of Algorithm 1to reflect (12)

Determining Whether a Node Should Move to a Lower LayerIf the expected energy remaining in energy-harvesting node119899119895


119895

119894(119905 + 119901setup) and can be found using (10)


Table 4 Important parameters used in our simulation

Parameter ValueNumber of nodes 500Node density 003sim007 nodesm2

Node placement RandomAmount of data in a packet 60 bytesAmount of a packet header 40 bytesTransmission range 10sim20mMaximum number of layers 1sim4120572 and 120573 in (6) 4 and 100 pJbitm2

119864elec and 119864receive in (4) 0000048 J and 0048 J119901layer119894 and 119901setup 6 hours119901gather 60 s

satisfies the following condition then that node should moveto a lower layer because it will die in its current layer

119864remain119895

119894(119905 + 119901setup) lt 119864min119894 + 120598119894 (13)

However 119864remain119895

119894(119905 + 119901setup) must be computed using

119864consume119895

119894(119905 minus 119901setup 119905) which is the energy consumed during

the previous round in (7) instead of 119864round119895

119894(119905) We can

modify the Synchronous layer determination process to applyto energy-harvesting nodes by modifying Algorithm 2 toreflect (13)

4 Experimental Results

41 Simulation Environment We wrote a simulation in C++to evaluate the performance of the proposed scheme In thissimulation we measured the average amount of dead nodesand the average number of data arriving at the sink nodewith a network topology consisting of up to four layersrespectively a single layer is a flat topology We deployed500 nodes and each test set was run 20 times for 5000rounds to obtain the average values For topologies withmore than one layer all nodes were assigned to layers at thebeginning of each round using the proposed scheme Eachnode transfers the data that it obtains from its sensor to oneof the nodes in the layer above by running the minimum-depth tree algorithm at intervals of 119901gather The nodes inthe upper layers aggregate their own data with that receivedfrom the nodes below and forward it all to their target nodeTable 4 summarizes the important parameters used in thissimulation

42 Simulation Results Figures 5 and 6 show the cumulativenumber of defunct nodes and the amount of data whichthe sink node received successfully In this experiment allnodes are battery-powered and dead nodes are not replacedWe did not use any data aggregation scheme to excludeits influence on the results Figure 5 shows that the layeredtopology reduces the number of defunct nodes especiallyat the beginning of the simulation compared to the flattopology This demonstrates how the nodes in a layered

0

5

10

15

20

25

30

35

40

45

Num

ber o

f dea

d no

des

Flat2 layers

3 layers4 layers

0 100 200 300 400 500 600 700 800Rounds

Figure 5 Change in the number of dead nodes without replace-ment

450

455

460

465

470

475

480

485

490

495

500

0 100 200 300 400 500 600 700 800

Am

ount

of d

ata d

eliv

ered

Rounds

Flat2 layers

3 layers4 layers

Figure 6 Change in the amount of data gathered at the sink nodewithout replacement

topology prolong their lifetimes by changing layer to managetheir energy usage By round 800 the number of dead nodesin a 4-layer network is reduced by 15 compared to a flatnetwork and the difference increases in subsequent roundsFigure 6 shows that this reduction in the number of deadnodes increases the amount of data reaching the sink

Figure 7 traces the number of defunct nodes over time inthe network in a scenario in which dead nodes are replacedwith new nodes at every 200 rounds This resulting sawtoothcurve results in the pattern of Figure 5 as the network isrefreshed by new nodes with fully changed batteries Figures8 and 9 respectively show the number of dead nodes andthe amount of data that arrived at the sink node as the


0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000

Num

ber o

f dea

d no

des

Rounds

Flat topology2 layers

3 layers4 layers

Figure 7 Variation in the number of dead nodes with periodicreplacement

390

395

400

405

410

415

420

100 150 200 250 300

Num

ber o

f dea

d no

des

Replacement period


3 layers4 layers

Figure 8 Variation in the number of dead nodes with the replace-ment period

replacement period was varied from 100 to 300 The flattopology causes more nodes to die and data transmissionis less effective than it is with the layered topology Theeffectiveness of transmission declines as the redeploymentperiod increases as we would expect because dead nodes arewaiting longer for replacement

Figures 10 and 11 respectively show the number of deadnodes and the amount of data delivered to the sink In thissimulation we assume that the network consists of onlybattery-powered nodes and each node was a naive dataaggregation scheme Nodes aggregate the data received fromthe nodes in lower layers with their own data before sending

Num

ber o

f del

iver

ed d

ata

144e + 07

1445e + 07

145e + 07

1455e + 07

146e + 07

1465e + 07

147e + 07

1475e + 07

148e + 07

1485e + 07

100 150 200 250 300Replacement period


3 layers4 layers

Figure 9 Variation in the amount of data arriving at the sink nodewith the replacement period

300

320

340

360

380

400

420

440

460

480

Num

ber o

f dea

d no

des

0 1 1 5 1 4 1 3 1 2 1 1Head size data size


3 layers4 layers

Figure 10 Number of dead nodes with data aggregation

it to their target node The size of the resulting packet can bereduced omitting the headers of the packets received fromlower-layer nodes and the effectiveness of data aggregationis proportional to the size of a packet header As shown inFigures 10 and 11 our scheme shown reduces the number ofdead nodes by about 10 and delivers slightly more data thanthe flat topology

In order to analyze the effectiveness of our scheme innetworks with energy-harvesting nodes we measured thenumber of dead nodes and the amount of transmitted datain a network consisting of 90 battery-powered nodes and10 of energy-harvesting nodes As shown in Figure 12 the

10 International Journal of Distributed Sensor NetworksA

mou

nt o

f dat

a del

iver

ed

1476e + 07

1478e + 07

148e + 07

1482e + 07

1484e + 07



3 layers4 layers

Figure 11 Amount of data arriving at the sink node with the dataaggregation

number of dead nodes is reduced by about 10 by ourscheme which is very similar to the result for the networkwith only battery-powered nodes Figure 13 shows that ourscheme also delivers more data However it also shows thatthe effectiveness of transmission is sometimes reduced by thepresence of energy-harvesting nodes We suggest that this isbecause the energy-harvesting nodes are not replaced evenwhen they have little energy instead they wait for energyto arrive and charge their batteries Meanwhile transmissionsare failingWe also found that using energy-harvesting nodesas cluster nodes produces the least effective transmissionof data Again we attribute this to the amount of energyacquired by these nodes which is inadequate to transmit lotsof dataThis problemmay be addressed by increasing the sizeof solar panels fitted to energy-harvesting nodes or reducingthe proportion of these nodes that are deployed

5 Future Work

The routing algorithm adopted in this paper causes a nodeto choose the route that reaches a higher-layer node with theminimum hop-count only the length of routes is considerednot the residual energy in the nodes on those routes or theircontribution to overall network connectivity Therefore itdoes not explicitly contribute to the lifetime or connectivityof a network We believe that it should be possible to designa routing scheme for layer-based topology control whichmakes a greater contribution to overall network efficiency

The aggregation scheme reported in this paper is naivein that it only aggregates data delivered from lower layersMore efficient data aggregation or fusion schemes have beendescribed [27ndash30] and we intend to adopt one of themto reduce the volume of data to be transmitted and henceincrease the lifetime of a WSN

100

150

200

250

300

350

003 004 005 006 007

Num

ber o

f dea

d no

des

Density

Flat topologyCluster2 layers

3 layers4 layers

Figure 12 Variation in the number of dead nodes as the proportionof energy-harvesting nodes is increased

003 004 005 006 007

Am

ount

of d

ata d

eliv

ered

Density

6e + 06

65e + 06

7e + 06

75e + 06

8e + 06

85e + 06

9e + 06

95e + 06

1e + 07

105e + 07


3 layers4 layers

Figure 13 Variation in the amount of data arriving at the sink nodeas the proportion of energy-harvesting nodes is increased

6 Conclusions

Since the nodes in a WSN are connected to the sink node bymultihop routes the demise of intermediate nodes reducesthe amount of data that reaches the sink A lot of workby many researches has been put into topology controltechniques to address this problem

In this paper we have proposed a layer-based topologycontrol scheme for WSNs consisting of many nodes someof which are battery-powered and some energy harvestingThese nodes are arranged in layers on the basis of theirresidual energy The nodes in the higher layers aggregate


data received from lower-layer nodes and send it to the sinknode togetherwith data obtained from their own sensorThispreserves the connectivity of the WSN because the expectedlifetimes of nodes are balanced by moving them betweenlayers

Notation Summary

119899119895

119894 Node 119894 in layer 119895

119873119894 Set of neighbors of node 119899

119894

119905119894 Target node of node 119899

119894

120572 Path loss (2 ge 120572 ge 5)120573 Energy consumed by the power

amplifier in transmitting 1 bit over adistance of 1 meter

119901gather Gathering period119901setup Setup period119901layer119894 Layer determination period of 119899

119894

119864remain119894(119905) Energy remaining in the battery of 119899119894

at time 119905119864round

119895

119894(119905) Energy consumed by 119899

119894during 119901setup

starting at 119905119864consume119894(119905) Energy consumed by 119899

119894at 119905

119864trans119894(119905) Energy consumed by the 119899119894rsquos

transceiver at 119905 in transmission119864receive119894(119905) Energy consumed by the transceiver of

119899119894at 119905 in reception

119864elec119894(119905) Energy consumed by the circuits of 119899119894

at 1199051198641015840

charge119894(119905 119901) Expected energy harvest of node 119899

119894

from time 119905 during period119864max119894(119905) Maximum energy capacity of node 119899

119894

119864min119894(119905) Minimum energy to operate node 119899119894

119889119894 Transmission range of node 119899

119894

119904sensor Amount of data gathered by a node119904head Size of a packet header119904trans119895

119894 Amount of data which node 119899119895

119894

transmits during gathering period119901gather

119904lower119895


119894

received from nodes on lower layersexcluding packet headers

119904relay119895

119894 Amount of data which 119899119895

119894receives

from nodes on the same layer119871119895

119894 Expected lifetime of node 119899

119894in layer 119895

(in rounds)119871 Average expected lifetime of the entire

network119871119894 Average local expected lifetime of the

1- and 2-hop neighbors of node 119899119894

120582119894(119905) Charging rate of node 119899

119894at time 119905

ℎ119894 Shortest hop-count from 119899

119894to a node

in a higher layer

Conflict of Interests

The authors declare no conflict of interests

Acknowledgments

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korean government(MEST) (NRF-2012R1A1A2044653 no 2011-0000228) andby Next-Generation Information Computing DevelopmentProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Education Science andTechnology (no 2012M3C4A7032182)

References

[1] I Yoon D K Noh and H Shin ldquoMulti-layer topology controlfor long-term wireless sensor networksrdquo EURASIP Journal onWireless Communications and Networking vol 2012 no 1article 164 9 pages 2012

[2] S Sudevalayam and P Kulkarni ldquoEnergy harvesting sensornodes survey and implicationsrdquo IEEE Communications Surveysamp Tutorials vol 13 no 3 pp 443ndash461 2011

[3] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007

[4] X Jiang J Polastre and D Culler ldquoPerpetual environmentallypowered sensor networksrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 463ndash468 IEEE April 2005

[5] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 IEEE Press April 2005

[6] J Hsu S Zahedi A Kansal M Srivastava andV RaghunathanldquoAdaptive duty cycling for energy harvesting systemsrdquo in Pro-ceedings of the 2006 International Symposium on Low PowerElectronics and Design pp 180ndash185 ACM October 2006

[7] F Simjee and P H Chou ldquoEverlast long-life supercapacitor-operated wireless sensor noderdquo in Proceedings of the Interna-tional Symposium on LowPower Electronics andDesign (ISLPEDrsquo06) pp 197ndash202 IEEE October 2006

[8] C Park and P H Chou ldquoAmbiMax autonomous energyharvesting platform for multi-supply wireless sensor nodesrdquo inProceedings of the 3rd Annual IEEE Communications Societyon Sensor and Ad Hoc Communications and Networks (SECONrsquo06) vol 1 pp 168ndash177 IEEE Reston Va USA September 2006

[9] M A Weimer T S Paing and R A Zane ldquoRemote areawind energy harvesting for low-power autonomous sensorsrdquoin Proceedings of the 37th IEEE Power Electronics SpecialistsConference (PESC rsquo06) pp 1ndash5 IEEE June 2006

[10] S Roundy D Steingart L Frechette P Wright and J RabaeyldquoPower sources for wireless sensor networksrdquo inWireless SensorNetworks vol 2920 of Lecture Notes in Computer Science pp 1ndash17 Springer Berlin Germany 2004

[11] A Kansal D Potter and M B Srivastava ldquoPerformance awaretasking for environmentally powered sensor networksrdquo ACMSIGMETRICS Performance Evaluation Review vol 32 no 1 pp223ndash234 2004

[12] D K Noh and K Kang ldquoBalanced energy allocation scheme fora solar-powered sensor system and its effects on network-wideperformancerdquo Journal of Computer and System Sciences vol 77no 5 pp 917ndash932 2011


[13] D Noh J Kim J Lee D Lee H Kwon and H Shin ldquoPriority-based routing for solar-powered wireless sensor networksrdquo inProceedings of the 2nd International Symposium on WirelessPervasive Computing (ISWPC rsquo07) pp 53ndash58 IEEE February2007

[14] J R Piorno C Bergonzini D Atienza and T S RosingldquoPrediction and management in energy harvested wirelesssensor nodesrdquo in Proceedings of the 1st International Conferenceon Wireless Communication Vehicular Technology InformationTheory and Aerospace amp Electronic Systems Technology (WirelessVITAE rsquo09) pp 6ndash10 IEEE May 2009

[15] C Moser L Thiele D Brunelli and L Benini ldquoAdaptive powermanagement in energy harvesting systemsrdquo inProceedings of theConference on Design Automation and Test in Europe pp 773ndash778 EDA Consortium April 2007

[16] A Cammarano C Petrioli and D Spenza ldquoPro-energy anovel energy prediction model for solar and wind energy-harvesting wireless sensor networksrdquo in Proceedings of the 9thIEEE International Conference on Mobile Ad-Hoc and SensorSystems (MASS rsquo12) pp 75ndash83 IEEE October 2012

[17] T Voigt A Dunkels J Alonso H Ritter and J Schiller ldquoSolar-aware clustering in wireless sensor networksrdquo in Proceedings ofthe 9th International Symposium on Computers and Communi-cations (ISCC rsquo04) vol 1 pp 238ndash243 IEEE July 2004

[18] W R Heinzelman A Chandrakasan and H Balakrish-nan ldquoEnergy-efficient communication protocol for wirelessmicrosensor networksrdquo in Proceedings of the 33rd AnnualHawaii International Conference on System Sciences (HICSS 33)p 10 IEEE January 2000

[19] P Zhang G Xiao and H-P Tan ldquoA preliminary study onlifetime maximization in clustered wireless sensor networkswith energy harvesting nodesrdquo in Proceedings of the 8th Interna-tional Conference on Information Communications and SignalProcessing (ICICS rsquo11) pp 1ndash5 IEEE December 2011

[20] P Zhang G Xiao and H-P Tan ldquoClustering algorithmsfor maximizing the lifetime of wireless sensor networks withenergy-harvesting sensorsrdquo Computer Networks vol 57 no 14pp 2689ndash2704 2013

[21] H Gou G Li and Y Yoo ldquoA partition-based centralizedLEACH algorithm for wireless sensor networks using solarenergyrdquo in Proceedings of the International Conference on Con-vergence and Hybrid Information Technology (ICHIT rsquo09) pp60ndash66 ACM August 2009

[22] M K Jakobsen J Madsen and M R Hansen ldquoDehar adistributed energy harvesting aware routing algorithm for ad-hoc multi-hop wireless sensor networksrdquo in Proceedings of theIEEE International Symposium on a World of Wireless Mobileand Multimedia Networks (WoWMoM rsquo10) pp 1ndash9 IEEE June2010

[23] J Meng X Zhang Y Dong and X Lin ldquoAdaptive energy-harvesting aware clustering routing protocol for wireless sensornetworksrdquo in Proceedings of the 7th International ICST Confer-ence on Communications and Networking in China (CHINA-COM rsquo12) pp 742ndash747 August 2012

[24] H Kim Y Seok N Choi Y Choi and T Kwon ldquoOptimalmulti-sink positioning and energy-efficient routing in wirelesssensor networksrdquo in Information Networking Convergence inBroadband and Mobile Networking vol 3391 of Lecture Notesin Computer Science pp 264ndash274 Springer Berlin Germany2005

[25] B Karp ldquoChallenges in geographic routing sparse networksobstacles and traffic provisioningrdquo in Proceedings of theDIMACS Workshop on Pervasive Networking 2001

[26] T Melodia D Pompili and I F Akyildiz ldquoOptimal localtopology knowledge for energy efficient geographical routingin sensor networksrdquo in Proceedings of the 23rd Annual JointConference of the IEEE Computer and Communications Societies(INFOCOM rsquo04) vol 3 pp 1705ndash1716 IEEE March 2004

[27] B Krishnamachari D Estrin and S Wicker ldquoModelling data-centric routing in wireless sensor networksrdquo in Proceedings ofthe 21st Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM rsquo02) vol 2 pp 39ndash442002

[28] Y Yao and J Gehrke ldquoThe cougar approach to in-network queryprocessing in sensor networksrdquo ACM SIGMOD Record vol 31no 3 pp 9ndash18 2002

[29] S Lindsey and C S Raghavendra ldquoPEGASIS power-efficientgathering in sensor information systemsrdquo in Proceedings ofthe IEEE Aerospace Conference vol 3 pp 3-1125ndash3-1130 IEEEMarch 2002

[30] D Braginsky and D Estrin ldquoRumor routing algorithm forsensor networksrdquo in Proceedings of the 1st ACM InternationalWorkshop onWireless Sensor Networks and Applications pp 22ndash31 ACM September 2002

International Journal of

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RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



is not readily available at every node because the accuracywith which it can be estimated depends on the location of thenode Moreover since all nodes are periodically able to moveto other layers estimates soon become inaccurate and thusmany nodes fail to locate themselves in the best layer

The life of a network can also be prolonged if energy isharvested from the environment an energy-harvesting nodecan potentially operate forever by recharging its battery withenvironmental energy Even so a node will eventually ceaseto operate if it consumes more energy than it is able toharvestMany researchers [2] have designed topology controlschemes to maximize the lifetime of a network of energy-harvesting nodes However many practical WSNs contain amixed population of nodes some of which can and some ofwhich cannot harvest energy and prolonging the lifetime ofthis class of WSN has received much less attention

In this paper we propose a topology control schemefor preserving connectivity between nodes in long-termWSNs in which defunct nodes are manually replaced andwhich contains both energy-harvesting nodes and battery-powered nodes In such a WSN the battery-powered nodescan be expected to have diverse amounts of residual energywhich decline with length of deployment As in our previousscheme the nodes arrange themselves into layers and thenodes on the upper layer are given the job of aggregating datareceived from the nodes on the lower layers and sending it to asink node Like previous layering schemes this arrangementimproves energy efficiency and connectivity but this newscheme increases the lifetime of battery-powered nodes bypreferentially locating energy-harvesting nodes on higherlayers

The rest of the paper is organized as follows In Section 2we describe the background to this research and reviewrelated work In Section 3 we introduce our scheme for layer-based topology control and describe how nodes choose theirlayer and establish connectivity with neighboring nodes InSection 4 we present experimental results and assess theperformance of our scheme In Section 5 we introduce aproposal for further research Section 6 concludes the paper

2 Background and Related Work

21 Energy-Harvesting Wireless Sensor Networks WSNs con-sisting solely of battery-powered nodes naturally have alimited lifetime and there have been many proposals [2] touse energy-harvesting nodes to extend the lifetime of WSNs[2] The environmental sources from which it is practical fornodes to harvest energy are the sun [3ndash8] and the wind [8 9]Solar-powered wireless sensor nodes are usually preferred[10] because of the high areal density of solar power (about15mWcm2)

Many schemes have been proposed to maximize thecontribution of solar energy to extending the life of a WSNKansal et al [11] proposed an energymodel for solar-powerednodes which estimates the levels of energy consumption andharvesting which will allow a node to survive indefinitelyNoh and Kang [12] designed an energy allocation schemewhich estimates the energy that will be harvested by a solar

cell every hour and determines future consumption levelswhich will allow the node to survive a complementaryrouting algorithm has also been presented [13]

The efficient use of solar energy requires accurate pre-diction which is relatively easy because of its obviousrelation to the diurnal cycle Nevertheless the availabilityof sunlight is of course affected by weather Kansal et al[3] Piorno et al [14] Moser et al [15] and Cammarano etal [16] have all proposed models for estimating the avail-ability of solar energy using respectively an exponentiallyweighted moving-average (EWMA) the so-called weather-conditioned moving average (WCMA) a weighted sum ofhistorical data and the Pro-Energy model

22 Hierarchical Topology Control for WSNs with Energy-Harvesting Nodes Topology control which determines hownodes connect to each other is an important issue whichaffectsWSN performance Only relatively recently has it beenapplied to WSNs which use energy-harvesting nodes

Voigt et al [17] introduced the solar-aware LEACHalgorithm (sLEACH) which applies LEACH [18] to WSNsconsisting of both solar-powered and battery-powered nodesThe sLEACH algorithm strongly favors the use of solar-powered nodes as cluster heads which have to do more workthan other nodes LEACH is effective in equalizing energyusage across (battery-powered) nodes but sLEACH cannotbe applied to large WSNs because all the cluster heads mustconnect directly to the sink In addition sLEACH tends toallow the harvested energy to be under-utilized or to runout because sLEACHdoes not consider energy stored at eachnode and the rate at which each node acquires energy

Zhang et al [19 20] proposed a scheme which overcomesthe need for each cluster head to connect directly to thesink by using further energy-harvesting nodes to relaytransmissions from the cluster head to the sinkThis can alsosave energy by reducing the range over which cluster headsare required to transmit Gou et al [21] also addressed thedrawbacks of sLEACH by partitioning aWSN and taking theenergy remaining in each node into account

Jakobsen et al [22] and Meng et al [23] also haveproposed hierarchical topology control schemes for energy-harvesting nodes

3 Layer-Based Topology Control with Energy-Harvesting Sensor Nodes

We will now introduce a new layer-based topology controlscheme and explain how to allocate nodes to layers hownodes operate within the layers and how the scheme appliesto energy-harvesting nodes We will assume that a WSNcontains both battery-powered and energy-harvesting nodeswhich periodically forward the data that they have gatheredto the sink node We are also assuming that defunct nodeswill be replaced because this is a long-termWSN

31 Review of Layer-Based Topology Control for Long-TermWSNs with Battery-Powered Nodes In our previous layer-based topology control scheme [1] all the nodes gather data


s

n1

n2

n3

n4

n5

n6

n7

n8

n9

n10

Layer 0

Layer 1

Layer 2

WSN













119894







119894peri-



Changing layer



determination



neighbor nodes

Every



If layer l ne lprev

If layer l = lprev



Time


player119894

psetup

pgather




119896isin 119873

ℎ119894






119904119896



ℎ119896





as follows

119871119894=

119864remain119894119864round119894

(1)




119894expires



119894using (9)

(3) if 119871119895+1119894

gt 119871 and exist119899119897

119896(119897 gt 119895) isin 119873

119894then

(4) 119895 larr 119895 + 1



119894)

(10) if 119878 = 119899119897119896| 119897 gt 119895 and 119899

119897

119896isin 119873119894 = 0 then

(11) 119905119894larr 119899119897


119896) isin 119878

(12) else(13) 119905

119894larr 119899119897


119896) isin 119899

119897

119896| 119897 = 119895 119899

119897

119896isin 119873







119871119895+1



119899119895

119894compares 119871119895+1

119894with 119871



119894 then 119899119895

119894











119896


119894is less


119897

119896





(5) 119905119894larr 119899119897

119896


119894lt 119871 then

(10) 119895next larr 119895 minus 1

(11) else(12) 119895next larr 119895


119894larr 119899119897

119896














119894





119894 The expected








time 119905 is

119864round119895

119894(119905) = int

119905+119901setup

119905

119864consume119895

119894(120591) 119889120591 (3)

119864round119895

119894(119905)

= int

119905+119901setup

119905

(119864trans119895

119894(120591) + 119864receive

119895

119894(120591) + 119864elec119894 (120591)) 119889120591

(4)



119894during period


int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = 119904120573119889

120572 (5)

int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = lfloor

119901setup


119895

119894120573119889120572

119894 (6)



119895



119895


as follows

119864round119895

119894(119905) = lfloor

119901119904

119901119892


119894120573119889120572

119894

+ int

119905+119901setup

119905

(119864receive119895

119894(120591) + 119864elec

119895

119894(120591)) 119889120591

(7)


119895

119894 which varies


119904trans119895


119895

119894+ 119904relay

119895

119894 (8)


119894 119904lower

119895

119894is






Sink node

n


Sink node

n

Case 1

Case 2

Case 2 Case 1


Layer 1 nodes



119899119895



119896as forall119899119897119896isin 119873119894 as 119905119896

Case 1 (target node 119905119896= 119899119895




119899119895+1


119896


Therefore 119899119895+1119894




119894

Case 2 (119905119896= 119899119895+1


119898 ℎ119898gt ℎ119894) The


119894 However if 119897 = 119895 + 1 then


119894 because 119899119897

119896will use

119899119895+1


to 119904lower119895+1

119894 because 119899119895+1






rounds that node 119899119895+1119894


119895+1

119894(119905) as follows

119871119895+1

119894= lfloor

119864remain119894

119864round119895+1

119894(119905)

rfloor (9)

119871119895+1


119894moves

up a layer








119864remain119895


119895

119894(119905)

+ 119864charge119894 (119905 119901setup)

0 lt 119864remain119894 (119909) lt 119864max119894

(10)



119894

at time 119905 119864round119895





119905

120582119894(120591) 119889120591 (11)





119894(119905) can be







119895+1

119894(119905 + 119901setup) and


119864remain119895+1

119894(119905 + 119901setup) gt 119864min119894 + 120598119894 (12)









119895








119864remain119895

119894(119905 + 119901setup) lt 119864min119894 + 120598119894 (13)



119864consume119895



119894(119905) We can





0

5

10

15

20

25

30

35

40

45

Num

ber o

f dea

d no

des

Flat2 layers

3 layers4 layers

0 100 200 300 400 500 600 700 800Rounds


450

455

460

465

470

475

480

485

490

495

500

0 100 200 300 400 500 600 700 800

Am

ount

of d

ata d

eliv

ered

Rounds

Flat2 layers

3 layers4 layers





0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000

Num

ber o

f dea

d no

des

Rounds


3 layers4 layers


390

395

400

405

410

415

420

100 150 200 250 300

Num

ber o

f dea

d no

des

Replacement period


3 layers4 layers




Num

ber o

f del

iver

ed d

ata

144e + 07

1445e + 07

145e + 07

1455e + 07

146e + 07

1465e + 07

147e + 07

1475e + 07

148e + 07

1485e + 07



3 layers4 layers


300

320

340

360

380

400

420

440

460

480

Num

ber o

f dea

d no

des



3 layers4 layers





mou

nt o

f dat

a del

iver

ed

1476e + 07

1478e + 07

148e + 07

1482e + 07

1484e + 07



3 layers4 layers



5 Future Work



100

150

200

250

300

350

003 004 005 006 007

Num

ber o

f dea

d no

des

Density


3 layers4 layers


003 004 005 006 007

Am

ount

of d

ata d

eliv

ered

Density

6e + 06

65e + 06

7e + 06

75e + 06

8e + 06

85e + 06

9e + 06

95e + 06

1e + 07

105e + 07


3 layers4 layers


6 Conclusions





Notation Summary

119899119895

119894 Node 119894 in layer 119895


119894


119894




119894



119895




119894at 119905



119899119894at 119905 in reception


at 1199051198641015840


119894


119894



119894



119894


119904lower119895


119894


119904relay119895


119894receives



119894in layer 119895





119894at time 119905


119894to a node

in a higher layer



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










s

n1

n2

n3

n4

n5

n6

n7

n8

n9

n10

Layer 0

Layer 1

Layer 2

WSN













119894







119894peri-



Changing layer



determination



neighbor nodes

Every



If layer l ne lprev

If layer l = lprev



Time


player119894

psetup

pgather




119896isin 119873

ℎ119894






119904119896



ℎ119896





as follows

119871119894=

119864remain119894119864round119894

(1)




119894expires



119894using (9)

(3) if 119871119895+1119894

gt 119871 and exist119899119897

119896(119897 gt 119895) isin 119873

119894then

(4) 119895 larr 119895 + 1



119894)

(10) if 119878 = 119899119897119896| 119897 gt 119895 and 119899

119897

119896isin 119873119894 = 0 then

(11) 119905119894larr 119899119897


119896) isin 119878

(12) else(13) 119905

119894larr 119899119897


119896) isin 119899

119897

119896| 119897 = 119895 119899

119897

119896isin 119873







119871119895+1



119899119895

119894compares 119871119895+1

119894with 119871



119894 then 119899119895

119894











119896


119894is less


119897

119896





(5) 119905119894larr 119899119897

119896


119894lt 119871 then

(10) 119895next larr 119895 minus 1

(11) else(12) 119895next larr 119895


119894larr 119899119897

119896














119894





119894 The expected








time 119905 is

119864round119895

119894(119905) = int

119905+119901setup

119905

119864consume119895

119894(120591) 119889120591 (3)

119864round119895

119894(119905)

= int

119905+119901setup

119905

(119864trans119895

119894(120591) + 119864receive

119895

119894(120591) + 119864elec119894 (120591)) 119889120591

(4)



119894during period


int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = 119904120573119889

120572 (5)

int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = lfloor

119901setup


119895

119894120573119889120572

119894 (6)



119895



119895


as follows

119864round119895

119894(119905) = lfloor

119901119904

119901119892


119894120573119889120572

119894

+ int

119905+119901setup

119905

(119864receive119895

119894(120591) + 119864elec

119895

119894(120591)) 119889120591

(7)


119895

119894 which varies


119904trans119895


119895

119894+ 119904relay

119895

119894 (8)


119894 119904lower

119895

119894is






Sink node

n


Sink node

n

Case 1

Case 2

Case 2 Case 1


Layer 1 nodes



119899119895



119896as forall119899119897119896isin 119873119894 as 119905119896

Case 1 (target node 119905119896= 119899119895




119899119895+1


119896


Therefore 119899119895+1119894




119894

Case 2 (119905119896= 119899119895+1


119898 ℎ119898gt ℎ119894) The


119894 However if 119897 = 119895 + 1 then


119894 because 119899119897

119896will use

119899119895+1


to 119904lower119895+1

119894 because 119899119895+1






rounds that node 119899119895+1119894


119895+1

119894(119905) as follows

119871119895+1

119894= lfloor

119864remain119894

119864round119895+1

119894(119905)

rfloor (9)

119871119895+1


119894moves

up a layer








119864remain119895


119895

119894(119905)

+ 119864charge119894 (119905 119901setup)

0 lt 119864remain119894 (119909) lt 119864max119894

(10)



119894

at time 119905 119864round119895





119905

120582119894(120591) 119889120591 (11)





119894(119905) can be







119895+1

119894(119905 + 119901setup) and


119864remain119895+1

119894(119905 + 119901setup) gt 119864min119894 + 120598119894 (12)









119895








119864remain119895

119894(119905 + 119901setup) lt 119864min119894 + 120598119894 (13)



119864consume119895



119894(119905) We can





0

5

10

15

20

25

30

35

40

45

Num

ber o

f dea

d no

des

Flat2 layers

3 layers4 layers

0 100 200 300 400 500 600 700 800Rounds


450

455

460

465

470

475

480

485

490

495

500

0 100 200 300 400 500 600 700 800

Am

ount

of d

ata d

eliv

ered

Rounds

Flat2 layers

3 layers4 layers





0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000

Num

ber o

f dea

d no

des

Rounds


3 layers4 layers


390

395

400

405

410

415

420

100 150 200 250 300

Num

ber o

f dea

d no

des

Replacement period


3 layers4 layers




Num

ber o

f del

iver

ed d

ata

144e + 07

1445e + 07

145e + 07

1455e + 07

146e + 07

1465e + 07

147e + 07

1475e + 07

148e + 07

1485e + 07



3 layers4 layers


300

320

340

360

380

400

420

440

460

480

Num

ber o

f dea

d no

des



3 layers4 layers





mou

nt o

f dat

a del

iver

ed

1476e + 07

1478e + 07

148e + 07

1482e + 07

1484e + 07



3 layers4 layers



5 Future Work



100

150

200

250

300

350

003 004 005 006 007

Num

ber o

f dea

d no

des

Density


3 layers4 layers


003 004 005 006 007

Am

ount

of d

ata d

eliv

ered

Density

6e + 06

65e + 06

7e + 06

75e + 06

8e + 06

85e + 06

9e + 06

95e + 06

1e + 07

105e + 07


3 layers4 layers


6 Conclusions





Notation Summary

119899119895

119894 Node 119894 in layer 119895


119894


119894




119894



119895




119894at 119905



119899119894at 119905 in reception


at 1199051198641015840


119894


119894



119894



119894


119904lower119895


119894


119904relay119895


119894receives



119894in layer 119895





119894at time 119905


119894to a node

in a higher layer



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Changing layer



determination



neighbor nodes

Every



If layer l ne lprev

If layer l = lprev



Time


player119894

psetup

pgather




119896isin 119873

ℎ119894






119904119896



ℎ119896





as follows

119871119894=

119864remain119894119864round119894

(1)




119894expires



119894using (9)

(3) if 119871119895+1119894

gt 119871 and exist119899119897

119896(119897 gt 119895) isin 119873

119894then

(4) 119895 larr 119895 + 1



119894)

(10) if 119878 = 119899119897119896| 119897 gt 119895 and 119899

119897

119896isin 119873119894 = 0 then

(11) 119905119894larr 119899119897


119896) isin 119878

(12) else(13) 119905

119894larr 119899119897


119896) isin 119899

119897

119896| 119897 = 119895 119899

119897

119896isin 119873







119871119895+1



119899119895

119894compares 119871119895+1

119894with 119871



119894 then 119899119895

119894











119896


119894is less


119897

119896





(5) 119905119894larr 119899119897

119896


119894lt 119871 then

(10) 119895next larr 119895 minus 1

(11) else(12) 119895next larr 119895


119894larr 119899119897

119896














119894





119894 The expected








time 119905 is

119864round119895

119894(119905) = int

119905+119901setup

119905

119864consume119895

119894(120591) 119889120591 (3)

119864round119895

119894(119905)

= int

119905+119901setup

119905

(119864trans119895

119894(120591) + 119864receive

119895

119894(120591) + 119864elec119894 (120591)) 119889120591

(4)



119894during period


int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = 119904120573119889

120572 (5)

int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = lfloor

119901setup


119895

119894120573119889120572

119894 (6)



119895



119895


as follows

119864round119895

119894(119905) = lfloor

119901119904

119901119892


119894120573119889120572

119894

+ int

119905+119901setup

119905

(119864receive119895

119894(120591) + 119864elec

119895

119894(120591)) 119889120591

(7)


119895

119894 which varies


119904trans119895


119895

119894+ 119904relay

119895

119894 (8)


119894 119904lower

119895

119894is






Sink node

n


Sink node

n

Case 1

Case 2

Case 2 Case 1


Layer 1 nodes



119899119895



119896as forall119899119897119896isin 119873119894 as 119905119896

Case 1 (target node 119905119896= 119899119895




119899119895+1


119896


Therefore 119899119895+1119894




119894

Case 2 (119905119896= 119899119895+1


119898 ℎ119898gt ℎ119894) The


119894 However if 119897 = 119895 + 1 then


119894 because 119899119897

119896will use

119899119895+1


to 119904lower119895+1

119894 because 119899119895+1






rounds that node 119899119895+1119894


119895+1

119894(119905) as follows

119871119895+1

119894= lfloor

119864remain119894

119864round119895+1

119894(119905)

rfloor (9)

119871119895+1


119894moves

up a layer








119864remain119895


119895

119894(119905)

+ 119864charge119894 (119905 119901setup)

0 lt 119864remain119894 (119909) lt 119864max119894

(10)



119894

at time 119905 119864round119895





119905

120582119894(120591) 119889120591 (11)





119894(119905) can be







119895+1

119894(119905 + 119901setup) and


119864remain119895+1

119894(119905 + 119901setup) gt 119864min119894 + 120598119894 (12)









119895








119864remain119895

119894(119905 + 119901setup) lt 119864min119894 + 120598119894 (13)



119864consume119895



119894(119905) We can





0

5

10

15

20

25

30

35

40

45

Num

ber o

f dea

d no

des

Flat2 layers

3 layers4 layers

0 100 200 300 400 500 600 700 800Rounds


450

455

460

465

470

475

480

485

490

495

500

0 100 200 300 400 500 600 700 800

Am

ount

of d

ata d

eliv

ered

Rounds

Flat2 layers

3 layers4 layers





0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000

Num

ber o

f dea

d no

des

Rounds


3 layers4 layers


390

395

400

405

410

415

420

100 150 200 250 300

Num

ber o

f dea

d no

des

Replacement period


3 layers4 layers




Num

ber o

f del

iver

ed d

ata

144e + 07

1445e + 07

145e + 07

1455e + 07

146e + 07

1465e + 07

147e + 07

1475e + 07

148e + 07

1485e + 07



3 layers4 layers


300

320

340

360

380

400

420

440

460

480

Num

ber o

f dea

d no

des



3 layers4 layers





mou

nt o

f dat

a del

iver

ed

1476e + 07

1478e + 07

148e + 07

1482e + 07

1484e + 07



3 layers4 layers



5 Future Work



100

150

200

250

300

350

003 004 005 006 007

Num

ber o

f dea

d no

des

Density


3 layers4 layers


003 004 005 006 007

Am

ount

of d

ata d

eliv

ered

Density

6e + 06

65e + 06

7e + 06

75e + 06

8e + 06

85e + 06

9e + 06

95e + 06

1e + 07

105e + 07


3 layers4 layers


6 Conclusions





Notation Summary

119899119895

119894 Node 119894 in layer 119895


119894


119894




119894



119895




119894at 119905



119899119894at 119905 in reception


at 1199051198641015840


119894


119894



119894



119894


119904lower119895


119894


119904relay119895


119894receives



119894in layer 119895





119894at time 119905


119894to a node

in a higher layer



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119894expires



119894using (9)

(3) if 119871119895+1119894

gt 119871 and exist119899119897

119896(119897 gt 119895) isin 119873

119894then

(4) 119895 larr 119895 + 1



119894)

(10) if 119878 = 119899119897119896| 119897 gt 119895 and 119899

119897

119896isin 119873119894 = 0 then

(11) 119905119894larr 119899119897


119896) isin 119878

(12) else(13) 119905

119894larr 119899119897


119896) isin 119899

119897

119896| 119897 = 119895 119899

119897

119896isin 119873







119871119895+1



119899119895

119894compares 119871119895+1

119894with 119871



119894 then 119899119895

119894











119896


119894is less


119897

119896





(5) 119905119894larr 119899119897

119896


119894lt 119871 then

(10) 119895next larr 119895 minus 1

(11) else(12) 119895next larr 119895


119894larr 119899119897

119896














119894





119894 The expected








time 119905 is

119864round119895

119894(119905) = int

119905+119901setup

119905

119864consume119895

119894(120591) 119889120591 (3)

119864round119895

119894(119905)

= int

119905+119901setup

119905

(119864trans119895

119894(120591) + 119864receive

119895

119894(120591) + 119864elec119894 (120591)) 119889120591

(4)



119894during period


int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = 119904120573119889

120572 (5)

int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = lfloor

119901setup


119895

119894120573119889120572

119894 (6)



119895



119895


as follows

119864round119895

119894(119905) = lfloor

119901119904

119901119892


119894120573119889120572

119894

+ int

119905+119901setup

119905

(119864receive119895

119894(120591) + 119864elec

119895

119894(120591)) 119889120591

(7)


119895

119894 which varies


119904trans119895


119895

119894+ 119904relay

119895

119894 (8)


119894 119904lower

119895

119894is






Sink node

n


Sink node

n

Case 1

Case 2

Case 2 Case 1


Layer 1 nodes



119899119895



119896as forall119899119897119896isin 119873119894 as 119905119896

Case 1 (target node 119905119896= 119899119895




119899119895+1


119896


Therefore 119899119895+1119894




119894

Case 2 (119905119896= 119899119895+1


119898 ℎ119898gt ℎ119894) The


119894 However if 119897 = 119895 + 1 then


119894 because 119899119897

119896will use

119899119895+1


to 119904lower119895+1

119894 because 119899119895+1






rounds that node 119899119895+1119894


119895+1

119894(119905) as follows

119871119895+1

119894= lfloor

119864remain119894

119864round119895+1

119894(119905)

rfloor (9)

119871119895+1


119894moves

up a layer








119864remain119895


119895

119894(119905)

+ 119864charge119894 (119905 119901setup)

0 lt 119864remain119894 (119909) lt 119864max119894

(10)



119894

at time 119905 119864round119895





119905

120582119894(120591) 119889120591 (11)





119894(119905) can be







119895+1

119894(119905 + 119901setup) and


119864remain119895+1

119894(119905 + 119901setup) gt 119864min119894 + 120598119894 (12)









119895








119864remain119895

119894(119905 + 119901setup) lt 119864min119894 + 120598119894 (13)



119864consume119895



119894(119905) We can





0

5

10

15

20

25

30

35

40

45

Num

ber o

f dea

d no

des

Flat2 layers

3 layers4 layers

0 100 200 300 400 500 600 700 800Rounds


450

455

460

465

470

475

480

485

490

495

500

0 100 200 300 400 500 600 700 800

Am

ount

of d

ata d

eliv

ered

Rounds

Flat2 layers

3 layers4 layers





0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000

Num

ber o

f dea

d no

des

Rounds


3 layers4 layers


390

395

400

405

410

415

420

100 150 200 250 300

Num

ber o

f dea

d no

des

Replacement period


3 layers4 layers




Num

ber o

f del

iver

ed d

ata

144e + 07

1445e + 07

145e + 07

1455e + 07

146e + 07

1465e + 07

147e + 07

1475e + 07

148e + 07

1485e + 07



3 layers4 layers


300

320

340

360

380

400

420

440

460

480

Num

ber o

f dea

d no

des



3 layers4 layers





mou

nt o

f dat

a del

iver

ed

1476e + 07

1478e + 07

148e + 07

1482e + 07

1484e + 07



3 layers4 layers



5 Future Work



100

150

200

250

300

350

003 004 005 006 007

Num

ber o

f dea

d no

des

Density


3 layers4 layers


003 004 005 006 007

Am

ount

of d

ata d

eliv

ered

Density

6e + 06

65e + 06

7e + 06

75e + 06

8e + 06

85e + 06

9e + 06

95e + 06

1e + 07

105e + 07


3 layers4 layers


6 Conclusions





Notation Summary

119899119895

119894 Node 119894 in layer 119895


119894


119894




119894



119895




119894at 119905



119899119894at 119905 in reception


at 1199051198641015840


119894


119894



119894



119894


119904lower119895


119894


119904relay119895


119894receives



119894in layer 119895





119894at time 119905


119894to a node

in a higher layer



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















time 119905 is

119864round119895

119894(119905) = int

119905+119901setup

119905

119864consume119895

119894(120591) 119889120591 (3)

119864round119895

119894(119905)

= int

119905+119901setup

119905

(119864trans119895

119894(120591) + 119864receive

119895

119894(120591) + 119864elec119894 (120591)) 119889120591

(4)



119894during period


int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = 119904120573119889

120572 (5)

int

119905+119901setup

119905

119864trans119895

119894(120591) 119889120591 = lfloor

119901setup


119895

119894120573119889120572

119894 (6)



119895



119895


as follows

119864round119895

119894(119905) = lfloor

119901119904

119901119892


119894120573119889120572

119894

+ int

119905+119901setup

119905

(119864receive119895

119894(120591) + 119864elec

119895

119894(120591)) 119889120591

(7)


119895

119894 which varies


119904trans119895


119895

119894+ 119904relay

119895

119894 (8)


119894 119904lower

119895

119894is






Sink node

n


Sink node

n

Case 1

Case 2

Case 2 Case 1


Layer 1 nodes



119899119895



119896as forall119899119897119896isin 119873119894 as 119905119896

Case 1 (target node 119905119896= 119899119895




119899119895+1


119896


Therefore 119899119895+1119894




119894

Case 2 (119905119896= 119899119895+1


119898 ℎ119898gt ℎ119894) The


119894 However if 119897 = 119895 + 1 then


119894 because 119899119897

119896will use

119899119895+1


to 119904lower119895+1

119894 because 119899119895+1






rounds that node 119899119895+1119894


119895+1

119894(119905) as follows

119871119895+1

119894= lfloor

119864remain119894

119864round119895+1

119894(119905)

rfloor (9)

119871119895+1


119894moves

up a layer








119864remain119895


119895

119894(119905)

+ 119864charge119894 (119905 119901setup)

0 lt 119864remain119894 (119909) lt 119864max119894

(10)



119894

at time 119905 119864round119895





119905

120582119894(120591) 119889120591 (11)





119894(119905) can be







119895+1

119894(119905 + 119901setup) and


119864remain119895+1

119894(119905 + 119901setup) gt 119864min119894 + 120598119894 (12)









119895








119864remain119895

119894(119905 + 119901setup) lt 119864min119894 + 120598119894 (13)



119864consume119895



119894(119905) We can





0

5

10

15

20

25

30

35

40

45

Num

ber o

f dea

d no

des

Flat2 layers

3 layers4 layers

0 100 200 300 400 500 600 700 800Rounds


450

455

460

465

470

475

480

485

490

495

500

0 100 200 300 400 500 600 700 800

Am

ount

of d

ata d

eliv

ered

Rounds

Flat2 layers

3 layers4 layers





0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000

Num

ber o

f dea

d no

des

Rounds


3 layers4 layers


390

395

400

405

410

415

420

100 150 200 250 300

Num

ber o

f dea

d no

des

Replacement period


3 layers4 layers




Num

ber o

f del

iver

ed d

ata

144e + 07

1445e + 07

145e + 07

1455e + 07

146e + 07

1465e + 07

147e + 07

1475e + 07

148e + 07

1485e + 07



3 layers4 layers


300

320

340

360

380

400

420

440

460

480

Num

ber o

f dea

d no

des



3 layers4 layers





mou

nt o

f dat

a del

iver

ed

1476e + 07

1478e + 07

148e + 07

1482e + 07

1484e + 07



3 layers4 layers



5 Future Work



100

150

200

250

300

350

003 004 005 006 007

Num

ber o

f dea

d no

des

Density


3 layers4 layers


003 004 005 006 007

Am

ount

of d

ata d

eliv

ered

Density

6e + 06

65e + 06

7e + 06

75e + 06

8e + 06

85e + 06

9e + 06

95e + 06

1e + 07

105e + 07


3 layers4 layers


6 Conclusions





Notation Summary

119899119895

119894 Node 119894 in layer 119895


119894


119894




119894



119895




119894at 119905



119899119894at 119905 in reception


at 1199051198641015840


119894


119894



119894



119894


119904lower119895


119894


119904relay119895


119894receives



119894in layer 119895





119894at time 119905


119894to a node

in a higher layer



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Therefore 119899119895+1119894




119894

Case 2 (119905119896= 119899119895+1


119898 ℎ119898gt ℎ119894) The


119894 However if 119897 = 119895 + 1 then


119894 because 119899119897

119896will use

119899119895+1


to 119904lower119895+1

119894 because 119899119895+1






rounds that node 119899119895+1119894


119895+1

119894(119905) as follows

119871119895+1

119894= lfloor

119864remain119894

119864round119895+1

119894(119905)

rfloor (9)

119871119895+1


119894moves

up a layer








119864remain119895


119895

119894(119905)

+ 119864charge119894 (119905 119901setup)

0 lt 119864remain119894 (119909) lt 119864max119894

(10)



119894

at time 119905 119864round119895





119905

120582119894(120591) 119889120591 (11)





119894(119905) can be







119895+1

119894(119905 + 119901setup) and


119864remain119895+1

119894(119905 + 119901setup) gt 119864min119894 + 120598119894 (12)









119895








119864remain119895

119894(119905 + 119901setup) lt 119864min119894 + 120598119894 (13)



119864consume119895



119894(119905) We can





0

5

10

15

20

25

30

35

40

45

Num

ber o

f dea

d no

des

Flat2 layers

3 layers4 layers

0 100 200 300 400 500 600 700 800Rounds


450

455

460

465

470

475

480

485

490

495

500

0 100 200 300 400 500 600 700 800

Am

ount

of d

ata d

eliv

ered

Rounds

Flat2 layers

3 layers4 layers





0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000

Num

ber o

f dea

d no

des

Rounds


3 layers4 layers


390

395

400

405

410

415

420

100 150 200 250 300

Num

ber o

f dea

d no

des

Replacement period


3 layers4 layers




Num

ber o

f del

iver

ed d

ata

144e + 07

1445e + 07

145e + 07

1455e + 07

146e + 07

1465e + 07

147e + 07

1475e + 07

148e + 07

1485e + 07



3 layers4 layers


300

320

340

360

380

400

420

440

460

480

Num

ber o

f dea

d no

des



3 layers4 layers





mou

nt o

f dat

a del

iver

ed

1476e + 07

1478e + 07

148e + 07

1482e + 07

1484e + 07



3 layers4 layers



5 Future Work



100

150

200

250

300

350

003 004 005 006 007

Num

ber o

f dea

d no

des

Density


3 layers4 layers


003 004 005 006 007

Am

ount

of d

ata d

eliv

ered

Density

6e + 06

65e + 06

7e + 06

75e + 06

8e + 06

85e + 06

9e + 06

95e + 06

1e + 07

105e + 07


3 layers4 layers


6 Conclusions





Notation Summary

119899119895

119894 Node 119894 in layer 119895


119894


119894




119894



119895




119894at 119905



119899119894at 119905 in reception


at 1199051198641015840


119894


119894



119894



119894


119904lower119895


119894


119904relay119895


119894receives



119894in layer 119895





119894at time 119905


119894to a node

in a higher layer



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















119864remain119895

119894(119905 + 119901setup) lt 119864min119894 + 120598119894 (13)



119864consume119895



119894(119905) We can





0

5

10

15

20

25

30

35

40

45

Num

ber o

f dea

d no

des

Flat2 layers

3 layers4 layers

0 100 200 300 400 500 600 700 800Rounds


450

455

460

465

470

475

480

485

490

495

500

0 100 200 300 400 500 600 700 800

Am

ount

of d

ata d

eliv

ered

Rounds

Flat2 layers

3 layers4 layers





0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000

Num

ber o

f dea

d no

des

Rounds


3 layers4 layers


390

395

400

405

410

415

420

100 150 200 250 300

Num

ber o

f dea

d no

des

Replacement period


3 layers4 layers




Num

ber o

f del

iver

ed d

ata

144e + 07

1445e + 07

145e + 07

1455e + 07

146e + 07

1465e + 07

147e + 07

1475e + 07

148e + 07

1485e + 07



3 layers4 layers


300

320

340

360

380

400

420

440

460

480

Num

ber o

f dea

d no

des



3 layers4 layers





mou

nt o

f dat

a del

iver

ed

1476e + 07

1478e + 07

148e + 07

1482e + 07

1484e + 07



3 layers4 layers



5 Future Work



100

150

200

250

300

350

003 004 005 006 007

Num

ber o

f dea

d no

des

Density


3 layers4 layers


003 004 005 006 007

Am

ount

of d

ata d

eliv

ered

Density

6e + 06

65e + 06

7e + 06

75e + 06

8e + 06

85e + 06

9e + 06

95e + 06

1e + 07

105e + 07


3 layers4 layers


6 Conclusions





Notation Summary

119899119895

119894 Node 119894 in layer 119895


119894


119894




119894



119895




119894at 119905



119899119894at 119905 in reception


at 1199051198641015840


119894


119894



119894



119894


119904lower119895


119894


119904relay119895


119894receives



119894in layer 119895





119894at time 119905


119894to a node

in a higher layer



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000

Num

ber o

f dea

d no

des

Rounds


3 layers4 layers


390

395

400

405

410

415

420

100 150 200 250 300

Num

ber o

f dea

d no

des

Replacement period


3 layers4 layers




Num

ber o

f del

iver

ed d

ata

144e + 07

1445e + 07

145e + 07

1455e + 07

146e + 07

1465e + 07

147e + 07

1475e + 07

148e + 07

1485e + 07



3 layers4 layers


300

320

340

360

380

400

420

440

460

480

Num

ber o

f dea

d no

des



3 layers4 layers





mou

nt o

f dat

a del

iver

ed

1476e + 07

1478e + 07

148e + 07

1482e + 07

1484e + 07



3 layers4 layers



5 Future Work



100

150

200

250

300

350

003 004 005 006 007

Num

ber o

f dea

d no

des

Density


3 layers4 layers


003 004 005 006 007

Am

ount

of d

ata d

eliv

ered

Density

6e + 06

65e + 06

7e + 06

75e + 06

8e + 06

85e + 06

9e + 06

95e + 06

1e + 07

105e + 07


3 layers4 layers


6 Conclusions





Notation Summary

119899119895

119894 Node 119894 in layer 119895


119894


119894




119894



119895




119894at 119905



119899119894at 119905 in reception


at 1199051198641015840


119894


119894



119894



119894


119904lower119895


119894


119904relay119895


119894receives



119894in layer 119895





119894at time 119905


119894to a node

in a higher layer



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










mou

nt o

f dat

a del

iver

ed

1476e + 07

1478e + 07

148e + 07

1482e + 07

1484e + 07



3 layers4 layers



5 Future Work



100

150

200

250

300

350

003 004 005 006 007

Num

ber o

f dea

d no

des

Density


3 layers4 layers


003 004 005 006 007

Am

ount

of d

ata d

eliv

ered

Density

6e + 06

65e + 06

7e + 06

75e + 06

8e + 06

85e + 06

9e + 06

95e + 06

1e + 07

105e + 07


3 layers4 layers


6 Conclusions





Notation Summary

119899119895

119894 Node 119894 in layer 119895


119894


119894




119894



119895




119894at 119905



119899119894at 119905 in reception


at 1199051198641015840


119894


119894



119894



119894


119904lower119895


119894


119904relay119895


119894receives



119894in layer 119895





119894at time 119905


119894to a node

in a higher layer



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Notation Summary

119899119895

119894 Node 119894 in layer 119895


119894


119894




119894



119895




119894at 119905



119899119894at 119905 in reception


at 1199051198641015840


119894


119894



119894



119894


119904lower119895


119894


119904relay119895


119894receives



119894in layer 119895





119894at time 119905


119894to a node

in a higher layer



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article energy-aware hierarchical topology...

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