Thesis Outline and Contributions

InChapter2,weconsideraWSNinwhichthesensornodesaresourcesofdelaysensitivetrac

thatneedstobetransferredinamulti-hopfashiontoacommonprocessingcenter. Weconsider

the following data sampling scheme: the sensor nodes have a sampling process independent

(layered architecture) of the transmission scheme as shown in Figure 1.3. This system is

like thepacketradio network (PRN)for which exact analysisis not available. We also show

that thestability condition proposedin the PRN literature is not accurate. First, a correct

stability condition for such a system is provided. Then, we proposed a cross-layered data

samplingscheme inwhich, thesensornodessamplenewdataonly whenithasaopportunity

(cross-layeredarchitecture) oftransmittingthedataasshowninFigure1.3. Itisalsoobserved

thatthis scheme gives a better performance in terms of delays and is moreover amenable to

analysis.

Figure1.3: ALayered andCross-LayeredArchitecture

To provide meaningful service such asdisaster and emergency surveillance, meeting

real-time and energy constraintsand the stabilityat mediumaccess control (MAC) layerarethe

basic requirements of communication protocols in such networks. We also propose a

cross-layerarchitecturewithtwotransmitqueuesatMAClayer,i.e.,oneforitsowngenerateddata,

and theother for forwarding trac asshown in Figure1.4. We usea probabilistic queueing

discipline. Our rstmain resultconcerns the stability oftheforwardingqueuesat thenodes.

Itstatesthatwhetherornottheforwardingqueuescanbestabilized, byappropriatechoiceof

weighted fairqueueing (WFQ) weights, dependsonly on routing and channel access rates of

thesensors. Further,theweightsoftheWFQsplayaroleindeterminingthetradeo between

the power allocated for forwarding and the delay ofthe forwarding trac.

We then addressthe problemof optimal routing thataims at minimizing theend-to-end

delays. Since,weallowfortracsplittingatsourcenodes,weproposeanalgorithmthatseeks

theWardropequilibriuminsteadofasingleleastdelaypath. Wardropequilibriarstappeared

inthecontextoftransportationnetworks. Wardrop'srstprinciple states: Thejourneytimes

in all routes actually used are equal and less than those which would be experienced by a

single vehicle on any unused route. Each user non-cooperatively seeks to minimize his cost

of transportation. The trac ows thatsatisfythis principle areusually referred to as"user

equilibrium" (UE) ows, since each user chooses the route that is the best. Specically, a

user-optimized equilibriumisreachedwhennousermaylowerhistransportationcostthrough

Figure1.4: ASystem withTwo-Queues at MAC

unilateral action.

The distributed routing scheme is designed for a broad class of WSNs which converges

(in the Cesaro sense)to theset ofCesaro-Wardrop equilibria. Each linkis assigneda weight

and theobjectiveistoroutethroughminimumweight pathsusingiterative updatingscheme.

Convergence is established using standard results from the related literature and validated

by TinyOS simulation results. Our algorithm can adapt to changes in the network trac

and delays. The scheme is based on the multiple time-scale stochastic approximation

algo-rithms. The algorithm is simulated in TOSSIM and numerical results from the simulations

are provided.

InChapter3,weconsidera two-tier SANETand addresstheminimumdelayproblemfor

data aggregation. We analyzethe average end-to-end delayin thenetwork. The objective is

to minimize the total delay inthe network. We prove that this objective function is strictly

convex for the entire network. We then provide a distributed optimization framework to

achieve the required objective. The approach is based on distributed convex optimization

and deterministic distributed algorithm without feedback control. Only local knowledge is

used to update the algorithmic steps. Specically, we formulate the objective as a network

leveldelayminimizationfunctionwheretheconstraintsarethereception-capacity andservic

e-rate probabilities. Using the Lagrangian dual composition method, we derive a distributed

primal-dual algorithm to minimize thedelay inthenetwork. We furtherdevelopa stochastic

delay-control primal-dual algorithm inthe presence of noisyconditions. We also present its

convergence and rateof convergence properties.

This chapter also investigates a delay-optimal actuator-selection problem for SANETs.

Each sensor must transmit its locally generated data to only one of the actuators. A

poly-nomial timealgorithm is proposedfor delay-optimal actuator-selection. We nally proposea

distributedmechanismforactuation control which covers alltherequirementsforan eective

actuation process.

In Chapter 4, we consider a three-tier SANET and present the design, implementation,

and performance evaluation of a novel low-energy, adaptive and distributed (LEAD)

self-organization framework. Thisframeworkprovidescoordination, routing,andMAClayer

pro-tocols fornetworkorganization andmanagement. Theframework isshowninFigure1.5. We

organizetheheterogeneous SANET into clusters where eachcluster ismanaged byan

actua-tor. To maximize the network lifetime and attain minimum end-to-enddelays,it is essential

tooptimally matcheach sensornode to anactuator and ndan optimal routingscheme. We

provide an actuator discovery protocol (ADP) that nds out a destination actuator for each

sensorinthenetwork basedon the outcome ofa cost function. Further,oncethedestination

actuatorsarexed,weprovideanenergy-optimal routingsolutionwiththeaimofmaximizing

networklifetime. Wethenproposeadelay-energy awareTDMAbasedMACprotocolin

com-pliancewiththeroutingalgorithm. Theactuator-selection,optimalrouting,andTDMAMAC

schemes together guarantees a near-optimal lifetime. The proposal is validated bymeans of

analysisandns-2 simulationresults.

Figure1.5: The LEADFramework

Delay and energy constraints have a signicant impact on the design and operation of

SANETs. Furthermore, preventing sensornodes frombeing inactive/isolated is very critical.

Theproblem of sensorinactivity/isolation arises fromthe pathloss and fading thatdegrades

the quality of the signals transmitted from actuators to sensors, especially in anisotropic

deploymentareas,e.g.,roughandhillyterrains. SensordatatransmissioninSANETs heavily

reliesontheschedulinginformationthateachsensornodereceivesfromitsassociatedactuator.

Therefore, ifthe signalcontainingscheduling information isreceived ata verylowpowerdue

to the impairments introduced by the wireless channel, the sensor node might be unable to

decodeit andconsequently it will remaininactive/isolated.

Sensors transmit their readings to the actuators. All actuators cooperate and jointly

transmit scheduling information to sensors with the useof beamforming. This results in an

important reductionofthe numberofinactivesensorscomparing tosingleactuator

transmis-sion for agivenlevelof transmit power. The reductionisdue to theresultingarray gain and

the exploitation ofmacro-diversity thatis provided bythe actuator cooperation. In order to

maximize network lifetimeandattain minimumend-to-enddelays,itisessential to optimally

match each sensor node to an actuator and nd an optimal routing solution. A distributed

solution for optimal actuator selection subjectto energy-delay constraints isalso provided.

InChapter5, we consideraUASNand rstanalyze amodulation schemeand associated

receiver algorithms. This receiver design take advantage of the time reversal 5

(TR) and

properties of spread spectrum sequences known as Gold sequences. Furthermore, they are

much less complex than receivers using adaptive equalizers. This technique improves the

signal-to-noise ratio (SNR) at the receiver and reduces the bit error rate (BER). We then

applied the phase conjugation to network communication. We show that this approach can

give almost zero BERfor atwo-hop communicationmode compared to thetraditionaldirect

communication. This linklayer information is usedat thenetwork layer to optimize routing

decisions. We showthese improvements by meansof analyticalanalysis andsimulations.

In Chapter 6, we present a general summary of the work achieved and the conclusions

concerning the results obtainedduring this thesis. Some perspectivesand openquestionsare

given for the continuation of this work in the area of cross-layer optimizations in wireless

sensor, sensor-actuator, andunderwater acousticsensornetworks.

5

Itisalsoknownasphaseconjugation(PC)inthefrequencydomain

Cross-Layer Routing in WSNs

Inthis Chapter, we considera WSN inwhich thesensor nodes aresources ofdelaysensitive

trac thatneedstobetransferredinamulti-hopfashiontoacommon processingcenter. We

rst consider the layered architecture. This system is like PRNs for which exact analysis is

not availableinthe literature. Wealso showthatthestabilityconditionproposedinthePRN

literature is not accurate. First, a correct stability condition for such a system is provided.

We thenproposea newdatasampling scheme: thesensornodessample newdataonly when

it hasanopportunity (cross-layered) oftransmitting thedata. It isobservedthatthis scheme

givesa better performanceinterms ofdelays andmoreoveris amenableto analysis.

We also propose a closed (cross-layered) architecture with two transmit queues at each

sensor

i

^{, i.e., one for its own generated data, and the other for forwarding trac. Our rst}

mainresultconcernsthestabilityoftheforwardingqueuesatthenodes. Itstatesthatwhether

ornottheforwardingqueuescanbestabilized(byappropriatechoiceofWFQweights)depends

only on routing and channel access rates of the sensors. Further, the weights of the WFQs

play a role in determining the tradeo between the power allocated for forwarding and the

delay oftheforwardingtrac.

We then addressthe problem ofoptimal routing thataims at minimizing theend-to-end

delays. Since we allow for trac splitting at source nodes, we propose an algorithm that

seeks the Wardrop equilibrium (i.e., the delays on the routes that are actually used by the

packets from a source areall minimumand equal) insteadof a single leastdelay path. Each

link is assigned a weight and the objective is to route through minimum weight paths using

iterative updating scheme. The algorithm is implemented in TinyOS Simulator (TOSSIM)

andnumerical resultsfrom thesimulation areprovided.

2.1 Introduction

WSNs are an emerging technology that has a wide range of potential applications including

environment monitoring, medical systems,robotic exploration, and smart spaces. WSNs are

becomingincreasinglyimportantinrecentyearsduetotheirabilitytodetectandconvey

real-time, in-situ information for many civilian and military applications. Such networks consist

of largenumberofdistributedsensornodesthatorganizethemselvesintoa multihop wireless

network. Eachnodehasoneormoresensors,embeddedprocessors,andlow-powerradios,and

is normallybattery operated. Typically,these nodescoordinateto perform a common task.

We propose a closed (cross-layered) architecture for data sampling (application layer)

in a wireless sensor network. In this architecture, there is a strong coupling between the

sampling process andthechannel accessschemeasshowninFigure1.3. The objective inthe

closed architecture is to provide sucient and necessary conditions for the stability region

and reducing end-to-end delays. With mathematical analysis and simulations, we show that

the closed architecture outperforms the traditional layered scheme, both in terms of stable

operatingregion aswell astheend-to-end delays.

We also propose a closed architecture with two transmit queues for data sampling in a

wirelesssensornetwork. In thisarchitecture, weconsider anewdatasampling scheme: Node

i

^,

1 ≤ i ≤ N,

^{hastwo queuesassociated withit: one queue}

Q _i

^{contains thedatasampled by}

the sensornode itselfand the otherqueue

F _i

^{contains packetsthat node}

i

^{hasreceived from}

any of its neighbors and hasto be transmitted to another neighbor as shown in Figure 1.4.

In this architecture, there is coupling between the sampling process and the channel access

scheme. Theobjectiveintheclosedarchitectureistostudytheimpactofchannelaccessrates,

routing, and weights ofthe WFQson systemperformance.

We thenproposeanadaptive anddistributedrouting schemeforageneral classofWSNs.

TheobjectiveofourschemeistoachieveCesaroWardropequilibrium,anextensionofthe

no-tionofWardropequilibriathatrstappearedin[28 ]inthecontextoftransportationnetworks.

Wardrop's rst principle states: The journey times in all routes actually used areequal and

lessthan thosewhichwouldbeexperiencedbyasinglevehicleonanyunusedroute. Eachuser

non-cooperatively seeks to minimize hiscost of transportation. The trac ows that satisfy

this principleareusuallyreferredtoas"userequilibrium"(UE)ows,sinceeachuserchooses

the routethat isthe best. Specically, a user-optimizedequilibrium isreached when no user

may lower his transportation cost through unilateral action. The notion is dened in (2.1)

later in this chapter. Our algorithm is actually an adaptation of the algorithm proposed in

[29 ]tothecaseofWSNs. Inthealgorithm of[29],eachsourceusesatwotime-scalestochastic

approximation algorithm. Dierences inthe two algorithmsare:

1. In WSNs that we consider, each node has an attribute associated with it namely the

channel access rate. The delay on a route depends on the attributes of the nodes on

the route. However, in orderto maintain some longterm data transferrate, each node

needs to adaptits attributeto routing.

2. The dierence intime scalesthatwe usefor various learning/adaptation schemes helps

us prove convergence of ouralgorithm [C-4](sucha proof isnot present in[29 ]).

In this thesis, we consider a static wireless sensor network with

n

^{sensor nodes. Given is}

an

n × n

neighborhood relation matrix

N

^{that indicates the node pairs for which direct}

communication ispossible. We willassume that

N

^{isa symmetric1 matrix, i.e.,ifnode}

i

^can

transmitto node

j

^,then

j

^{canalso transmit tonode}

i

^{. For suchnode pairs,the}

(i, j) ^th

^entry

of the matrix

N

^{isunity,i.e.,}

N _i,j = 1

^{if node}

i

^and

j

^can communicate witheach other; we willset

N _i,j = 0

^ifnodes

i

^and

j

^{can not} communicate. For anynode

i

^{,we dene}

N _i = { j : N _i,j = 1 } ,

Whichis theset ofneighboring nodesof node

i

^{. Similarly, thetwo hop neighbors ofnode}

i

^{are dened as}

1

Theassumptionofsymmetryistoonlydrivetheanalysis. Weconsiderassymmetriclinksforconducting

simulations.

S _i = { k / ∈ N _i ∪ { i } : N _k,j = 1 f or some j ∈ N _i }

Notethat

S i

^{doesnot include anyof the rst-hopneighborsof node}

i

^.

Eachsensornodeis assumedto be sampling(or, sensing) itsenvironment at a predened

rate; we let

λ i

^{denote this sampling rate for node}

i

^{. The units of}

λ i

^{will be packets per}

second, assuming same packet size for all the nodes in the network. In this work, we will

assume that the readings of each of these sensor nodes are statistically independent of each

other so that distributed compression techniques are not employed (see [30] for an example

wheretheauthorsexploitthecorrelationamongreadingsofdierentsensorstousedistributed

Slepian-Wolf Coding[31] to reducethe overall transmissionrateof thenetwork).

Eachsensornodewantstousethesensornetworktoforwarditssampleddatatoacommon

fusion center (assumed to be a part of the network 2

). Thus, each sensor node acts as a

forwarder ofdatafrom othersensor nodesinthenetwork. We willassume thatthebuering

capacity of each node is innite 3

,sothat there isno data loss inthenetwork. We will allow

for thepossibility thata sensor node discriminates between its own packets and thepackets

to be forwarded(thus allowing forthemodelof[32]whichconsidersanAdHocnetwork. The

nodes in this network probabalistically schedule their transmissions to discriminate between

the fowarding trac and the one generated bynode itself).

Welet

φ

^denotethe

n × n

^{routingmatrix. The}

(i, j) ^th

^{elementofthismatrix,denoted}

φ _i,j

^,

takes valuein the interval

[0, 1].

^{This means a} probabilistic ow splittingas inthe model of [33 ],i.e., afraction

φ i,j

^ofthetrac transmitted fromnode

i

^{isforwardedbynode}

j

^asshown

in Figrue 2.1. Clearly, we need that

φ

^{is a stochastic matrix, i.e., its row elements sum to}

unity. Also notethat

φ _i,j > 0

^{ispossibleonly if}

N _i,j = 1

^.

Figure2.1: FlowSplitting

We assume that the system operates in discrete time, so that the time is divided into

2

Conceptually,wecanassumethat thisfusioncenterisalsoasensornode,whichhas

0

^{samplingrate. A}

negativesamplingratewouldmeanpushingdatafromthenetworktowardsthefusioncenter.

3

We assumeinnitebuersizeonlyto keepthe analysissimple. Later,weconsiderxedbuersizesand

lookatvarioustypesofdatalosses.

(conceptually) xedlength slotsasshown inFigure2.2. Thesystem operateson CSMA/CA

MAC 4

.Assuming that there is no exponential back-o, the channel accessrate of node

i

^(if

ithas a packet to be transmitted) is

0 ≤ α _i ≤ 1

^{. Thus,}

α _i

^{is the}probability that node

i

^,if

it hasa packetto be transmitted, attempts a transmission inanyslot. A node can receive a

transmissionfromits neighbor ifitisnot transmitting andalso no otherneighboring node is

transmitting. Again, this isa fairlystandard assumption for analysispurposes.

Figure2.2: MediumAccessControl

Undertheabovemodeltherewillbeadelay,say

y _j,i

^{ofthepacketfromnode}

j

^tobeserved

atnode

i

^{;thispacketcouldhaveoriginated atnode}

j

^{ormayhavebeenforwardedbynode}

j

^.

Theexpecteddelayofapackettransmittedfromnode

j

^isthus

P

i 6 =j φ _j,i y _j,i

^{. Sincedelaysare}

additive overa path, packets from anynode will have a delay over any possible route to the

fusion center. A route will be denoted byan ordered set of nodes that occur on that route,

i.e., therstelement willbethe sourceoftheroute, thelastelement willbethefusioncenter

and theintermediate elementswill be nodesarranged intheorderthat apackettraverses on

this route. Let the total numberof possible routes (cycle-free) be

R

^{. Let route}

i

^,

1 ≤ i ≤ R

be denoted by the set

R i

^{consisting of}

R _i

^{elements with}

R i,j

^{denoting the}

j ^th

^{entry of this}

route. Then, a trac splitting matrix will correspond to a Wardrop equilibriumi for any

i

(see[29 ] for this denition)

P

1 ≤ j ≤ R: R j,1 =i

Q R j − 1

k=1 φ R j,k , R j,k+1 P R j − 1

k=1 y R j,k , R j,k+1

= P R l −1

k=1 y R l,k R l,k+1 ,

^(2.1)

for any

l

^with

R l,1 = i

^{and such that}

Q R l −1

k=1 φ R l,k , R l,k+1 > 0

^{, i.e., the delays on the}

routesthat areactually usedbypacketsfrom node

i

^{are allequal. Insimple terms, eq. (2.1)}

statesthat, for any given

i

^{, there will be a route that guarantees minimum delay. It is also}

possible thatthere isa setof routes thatguarantee thesame,thendelay shouldbe thesame

on allsuchroutes. Our objective inthis thesisis to come up with analgorithm using which

any node (say

i

^{) isable to converge to the} correspondingrow of thematrix

φ

corresponding totheWardropequilibrium.

Theorganizationofthischapterisasfollows. Section2.2overviewssomeinterestingrelated

work. InSection 2.3,weformulated theproblem. InSection 2.4,we detailthedierent data

4

It isimportanttonotethatweconsiderCSMA/CAinorderto provideanalyticalanalysisofthesystem

under consideration. Further, CSMAis alsobeing used inIEEE 802.15.4 [34 ] (Zigbee). Theendless list of

availableMACs for WSNs,is generally categorized into scheduled MACs (e.g. TSMP [35 ]),protocols with

commonactive period (e.g. SMAC [36]),and preamblesampling basedMACs (e.g. 1-HopMAC [37 ]). We

will consider all these categories inthe chaptersto come. In this section, we focus only onCSMA part of

will consider all these categories inthe chaptersto come. In this section, we focus only onCSMA part of

Dans le document Cross layer optimization of wireless sensor and sensor-actuator networks (Page 29-37)