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PeRF-Mesh:APerformance AnalysisToolforLarge
ScaleRF-mesh-basedSmartMeterNetworkswith
FHSS
Filippo Malandra
DepartmentofElectricalEngineering
EcolePolytechniquedeMontreal
Montreal,Qu´ebec
Email: filippo.malandra@polymtl.ca
BrunildeSans`o
DepartmentofElectricalEngineering
EcolePolytechniquedeMontreal
Montreal,Qu´ebec
Email: brunilde.sanso@polymtl.ca
Abstract—Thiswork dealswiththeperformance analysisof
aparticulartypeofAMI: theRF-mesh basedsmartmeter
network.ThesystemimplementsaMAC access withatime-
slottedALOHA withtheFrequencyHoppingSpread Spectrum
(FHSS) toreduce co-channel interference by other users.We
developedthePeRF-meshanalytictooltostudytheperformance
ofsuchsystems,takinginto account the combinedeffectsof
ALOHAaccess and ofFHSS ontheperformance.Thetoolallows
the evaluationofcurrentlydeployedsystemsand canalsohelp
inthedesign phaseofnewones.
I.INTRODUCTION
Inmany countriesaround theworld,powerutilitieshave
already equippedalargepercentageofhouseholdswithsmart
meters;othersareplanning on a comprehensiveinstallation
process intheforthcoming future.Smartmetersassume a
keyroleinmany smartgridapplicationsbecauseoftheir
doublenatureofsensing and communicating devices.In order
toaccomplishtheir functions,smartmetersneedto have a
two-waycommunication link withthepowerutilitymanage-
mentsystem: thisisthemainreason why thepenetration of
AdvancedMetering Infrastructure(AMI) isvery deepwithin
smartgridsystems.
AMIsarelargescalesystemsinwhichthousandsof
nodesareinvolved(e.g.sensors,smartmeters,routers,data
collectors)and many applicationsare enabled(e.g.remote
reading,loadmanagementand Vehicle-to-Grid).Theyare
usually proprietarysystems,owned by powerutilitiesand
installed by third partycompanies.Several technologieshave
beenadoptedand installedforAMIsofar:some arebased
on theuseoftheInternet,employing different typesofaccess
(mainlycellularorWiFi),whileothersexploit thepresence of
electricwiresby using PowerLineCommunication (PLC).
Furthersolutionsconsidertheuseof radiofrequenciesin
free and unlicensed bands:forexample,forRF-mesh,the
Industrial,Scientific and Medicalbandwidthfrom902 to 928
MHzisused.
RF-meshisconsidered oneofthemostpopulartech-
nologieswithinAMIsystemsand it will bepresentedwith
furtherdetailsinSection III.It ischaracterized by asim-
ple architecture composed ofsmartmeters,routersand data
collectors;RFantennasare cheapand theinfrastructureis
proprietary,featureresearched by thepowerutilitiesthatdo not
want torely on telecommunication providers,mainly because
ofcostand data confidentialityreasons.Nevertheless,some
ofthe advantagesofthistechnology canalso beseenas
shortcomings: the absence ofarecognizedstandardwithinthe
plurality ofvendorsjeopardizestheinteraction ofonesystem
withanother;also,it isdifficult to definetheperformance
ofproprietarysystemsbecausemany featuresofthedevices
are covered by confidentialityagreements.Moreover,avery
lowdata-rateisachievablewiththistechnology: thenominal
throughput isintheorderoftensofkilo-bits,anumberthat
soundsanachronisticbutwhichcanstill enablemany smart
gridapplications.Themultitude and vicinity ofnodes,which
especiallycharacterize urbanenvironments,canleadtosevere
interference problems.Theissueistackled by employing
FrequencyHopping SpreadSpectrum(FHSS)protocol.Tothe
bestofourknowledge,noneofthe existing comprehensive an-
alyticstudieson theperformance oflargescalemeshsystems
considersthe effectofFHSS protocol.However,as showed
inSection V,wherewe comparenumericalresultswithand
withoutFHSS,thisprotocolhasafundamental importance in
largescaleRF-meshsystems.
RF-meshsystemsareusuallysoldasblack boxesto power
utilitiesand many questionsarisewhenit comestothe analysis
oftheperformance:what isthe averagedelay?Howmany
routersarenecessarytocoveragivenarea? Howmany packets
can bereceived on time,coping with peculiarapplications
requirements?Theobjectiveofourworkisto provide answers
tothe aforementioned questionsby meansofPeRF-mesh,the
analytictoolweimplemented,helpful in defining measuresand
indexesofperformance forlargescaleRF-mesh basedsmart
metercommunication systems.
Thedocumentathand is structuredasfollows:Section II
containsashort literaturereviewcentered on theperformance
analysisinwireless mesh networks,withaparticular focuson
smartgridsystems;Section III presentsthemodeling ofthe
systemunderconsideration;Section IVdescribesPeRF-Mesh,
the analytictoolforperformance evaluation; inSection Vsome
numericalresultsareshownand inSection VIthe conclusions
ofthepresentworkaresummarized.
II.STATE OFTHEART
Agreatdealof researcheffort iscurrently being expended
on theperformance study ofRF-mesh networks.Theimpor-
tance ofthisthemeisderivedfromtheincreasing interest
in newsmartgridapplications.Themainapproachesthat
havebeenfollowedinliterature can begroupedintwosub-
categories:stochasticsimulations[1],[2],[3],[4]and real-field
measurements[5],[6].
Bothapproacheshavesomestrong pointsaswell as some
shortcomings.Asamatterof fact,awell configuredsimulator
can performsignificantperformance studieswith greatsavings,
and can behelpful in designing and testing newand not
yet implementedfeaturesand solutionsforexisting systems.
Ontheotherhand,real-fieldmeasurementspermit analyses
ofactualsystemsand notofamodeled version ofthese.
Also,testing systemsinarealenvironmentcan givedeeper
insightson theircharacteristics:somefeatures(e.g.realistic
propagating conditions)arevery difficult to predictand model,
and realfieldtestscancast lighton inconsistenciesofthe
model,whichasimulatorcould hardly discoverbecauseof
theidealenvironment it workswithin.
Athirdapproach,whichwedecidedtofollow,istotally
analytic:known propertiesofwireless networksareusedto
find mathematicalequationsthatallowtoanalyze thesys-
tem’sperformance.The analyticmethodology canreduce the
computationalburdentypicalofsimulationsand can be easily
extendedto differentscenariosand technologies.
Thewireless interference problemiswell explainedin[7],
whereseveralprotocolstomodel interference arepresented.
Oneofthemostused,whichwe chosetoadopt,istheprotocol-
interference model.Inthismodel,firstpresentedin[8],all
thenodesata certain distance fromanodejare considered
possibleinterferersina communication directedto nodej.
Inalargescalenetworkwiththousandsofusersthatshare
thesamebandwidth,theperformance isclearlyaffected by the
choice oftheMAClayerprotocol: oneofthemostwidespread
inRF-meshsystemsistheslottedALOHA.Anextensive
researchfocusing on ALOHA performance hasbeencarried
outsince itsfirstpresentation in1971 by NormanAbramson
[9].Thepioneerworksof [10],[11],[12]laidthefoundations
ofthe analyticperformance study ofslottedALOHA systems,
focusing on single-hop systemsonly.[13]triedtoanalyze
multi-hop systemswithsimple and regulartopology (e.g.
loop and bus).Wetook inspiration fromthe extensivework
on ALOHA performance analysismodelsin ordertofind a
mathematicalequation forthe collision probabilityinaRF-
meshsystem.Tothebestofourknowledge,a comprehensive
analyticstudy ofthe combinedeffectofALOHA and FHSS
protocolson network performance isnotavailableinliterature.
III.RF-MESHSYSTE MARC HITE CTUREAND MAIN
FEATURES
Oneofthemain difficultiesinmodeling AMIsisthefact
that these areproprietarysystemsand many oftheir features
areundisclosed.Forthiswork,featuresoftheRF-mesh
smartmetercommunication networkarederivedfrompublicly
availabledata aboutaRF-meshsystemalready installedin
Qu´ebec [14].
Collector
Router
Smart Meter
Zigbee
RF Mesh
HAN NAN WAN
Satellite
Cellular
Metering Data
Management
System (MDMS)
Fig.1:Architectureofthewhole communication system.
hop
#11
hop
#6
hop
#14
hop
#2
hop
#21
f(MHz)
{
Ch. 1
{
Ch. i-1
{
Ch. i
{
Ch. i+1
{
Ch. n
Fig.2:Exampleof frequency hopping sequence.
Thesystemunderstudy hasathree-layersarchitecture,
as showninFigure1: thefirst istheHomeArea Network
(HAN),thatconsistsofsensors,smartmeters,appliancesand
all theotherdeviceswithinthedomestic area; thesecond is
theNeighborhood Area Network(NAN),whosemainscope
istoconnectsmartmeters(and consequentlytheHAN)to
data collectorsinameshtopology thatalsoincludesrouters;
data collectorsareusedasgatewaytothethirdlayerof
the architecture,theWideArea Network,anIPbackbone
connectedtothepowerutilityMetering DataManagement
System(MDMS).
Thefirstand thethirdlayersofthe architectureimplement
well-knowntechnologiesand protocols: theHAN adoptsZig-
bee shortrangelinks,whiletheWAN usesIPoversatellite
orcellularconnections.Ontheotherhand,theNAN is
characterized by wireless linksintheISMband of902 −928
MHz: thistechnology iscalledRF-mesh.Theperformance of
theHAN and theWAN arewell definedand agood branch
of researchinvolvesanalysisofZigbee,satelliteorcellular
networks.Thus,intherestofthiswork,wewill focuson
analyzing theperformance oftheRF-meshNAN,notyetwell
definedand standardized.
Inthe currently deployedmulti-hop wireless NANs,there
isonedata collectorperseveral thousandsofsmartmeters.
Thenumberof routersdependson thescenario: it ishigherin
ruralnetworkswithrespect to urbanenvironments,in orderto
ensurethe connectivityinamore extendedarea.
TheRF-meshsystemadoptstheFHSS protocol,which
isatechniquehelpful inreducing co-channel interference,
generated by thetransmission ofmultipledevicesusing the
samefrequency band,eitherwithinthesameNAN orin
differentnetworks1.
1TheISMband areused,among theothers,by somemicrowaveovens,car
keyremote controllers,ZigBee and RFID
ThefrequencyspectrumoftheRF-meshsystemunder
study is subdividedinn=80 channelsof300 kHzbandwidth
each[15].Apredeterminedsequence ofhops,schematized
inFigure2,isknowntoall thenodesinthenetwork.Each
device usesthesamesequence to determinethefrequency
channelwhichitsreceiving antennamustbetunedto: the
sequence isconvenientlyshiftedintimein ordertoavoid
thatall thedevicesusethesame channels simultaneously.Any
nodeisableto determinethereceiving frequencychannelofits
neighborsatany time; therefore,beforetransmitting apacket to
aneighbornodej,nodeicantuneitsantennatothefrequency
channelofnodej.
The access tothemediumiscontrolled by meansofthe
synchronousALOHA protocolwithtimeslotsofduration
τ=0.7s.Devices synchronization isachievedthrough the
NetworkTimeProtocol(NTP):collectorsare equippedwith
high precision clocks(e.g.iridium)and provide a reference
timefortheothernodes.NTPcanideally yield good results
intermsofsynchronization ofextended networks:unavoidable
errorsinsynchronization aretackled by restricting theportion
oftimeinwhichit ispossibletotransmit to only400 msout
ofthe available700 ms,thusleaving theremaining 300 ms
intentionallyidle asasafetymargin[14].
A.Interference and probabilityofcollision
Interference isoneofthemainlimitsofwireless commu-
nications: theradiochannel is sharedamong multipleusers
thatcaninterferewitheach other.Therefore,any wireless
technology hastoconsiderinterference and reduce itseffect
on performance.
InRF-meshsystems,the access tothemediumisregulated
by ALOHA,asimplerandomaccess protocolconceived
fornetworkswith verylowdata-rates.Whentwo ormore
interfering usersattempt totransmit apacket,a collision is
experiencedand theinvolved packetsareto bere-transmitted.
Ananalytic expression tocalculatetheprobability ofcollision
inamulti-hop system,validwhenaPoisson distribution of
trafficgeneration isassumed,waspresentedin[16]:
pi=P(XIi>0)=1−P(XIi=0)=1−e
−τP
j∈Ii
λj
1−pj
(1)
whereIiisthelistofinterferersofnodei,XIisthenum-
beroftransmitting nodesinsetI,λithemeantransmission
rateofnodeiand τthetimeslotduration.
Thenumericalresultsin[16]wereobtained using equation
(1),withoutconsidering FHSS.Asdiscussedinthatpaper,
theresultshighlightedthenecessity ofintegrating theFHSS
protocol intheperformance analysisoflargescaleRF-mesh
systems.
Afirststepintheintegration ofFHSS wastakenin[16]
withthe analyticformula:
Fig.3:Block diagramofPeRF-meshanalytictool.
pi=
+∞
X
g=1
P(XIi=g)p(g)=
=
+∞
P
g=11−1−1
Qg τP
j∈Ii
λj
1−pj!g
g!e
−τP
j∈Ii
λj
1−pj
(2)
Inequation (2),Qisthenumberofnon-overlapping
channelsused by FHSS and p(k)istheprobability ofhaving
at least two nodesoutofkusing thesamefrequencychannel
among theQavailable:
p(k)=1−1−1
Qk
(3)
Equation (2)isusedinPeRF-meshtool tocalculatethe
delayand defineotherimportantperformance indexes,as
explainedinSection IV.
IV.PERF-MESH
A.Inputs
PeRF-meshisthe analytictoolwedevelopedtoanalyze
theperformance ofalargescaleRF-meshsystemwithFHSS.
Its structureisdisplayedinFigure3.Thetoolneedsthe
preliminary definition ofsomeinputs: topology,routing and
traffic.
The characterization ofthetopology consistsoftwo phases:
nodesplacementand linksdefinition.Wedecidedtocreate
ourtopology starting frompubliclyavailabledata abouta
pilot installation ofsmartmetersinQu´ebec.Data about the
position of routersand collectorswere extracted by meansof
GoogleEarth,starting fromamap publishedinareport tothe
R´
egiedel’´
energie2ofQu´ebec [14].Since thenumberofsmart
metersinthereference topology isgreaterthan3000,it wasnot
possibletoacquireinformation about theirpositionsfromthe
mapincludedinthereport.Therefore,in ordertofind their
position,wedevelopedaPython script to obtainfromBing
MapstheGPS coordinatesof residentialbuildingspresent in
thepilotprojectareas.The assumption ofonesmartmeterper
building wasused: thisassumption workswell inruralareas
2Aneconomicregulation agency ofthe energy market.
wherethereisamajority ofone-family buildings; in urban
areas,the assumption needsto bemodifiedin ordertoaccount
forbuildingswithmany apartments.Thelinksweredefinedin
astaticway: two nodesare assumedtocommunicatewitheach
otherifand onlyiftheirdistance islowerthanafixedcovering
ray.Thevariablepropagating conditionsof radiosignalsare
takenintoaccountby employing differentcovering raysin
differentscenarios.Forexample,propagating conditionstend
to bemore convenient inruralareaswithrespect to urban
environments,becauseless obstaclesarepresenton average;
whenstudying aruralarea scenario,largercovering rayswill
beused.
Therouting mechanismadoptedinthetool isbased on
shortestpaths,using distance asmetrics.Nevertheless,this
static assumption mightneglectsomeimportantdynamic as-
pectsofRF-meshsystems:other routing mechanisms(e.g.
layer-based,AODV,geographical)are currently being inves-
tigatedand will beintegratedintothetool inthenear future.
Thetraffic characterization istakenfrom[14].We consider
two different trafficstreams:uplink,fromsmartmetersto
thedata collector,and downlink,intheoppositedirection.
Routersdo notgenerate any packet,theysimplyforward
packetstransmitted by otherdevices.Thepacketgeneration
rateisassumedto bePoisson-distributedin both directions
withmean parametersλupand λdownforuplink and downlink
respectively.
λiistherateofpacket transmission ofnodei: it includes
packetsgenerated by nodeiand also packetsforwhichiis
anintermediatenodebetweensource and destination.In[16]
ananalytic expression forλiwasfound:
λi=
ξi(λup+λdown)+λup,ifiisasmartmeter
ξi(λup+λdown),ifiisarouter
|M|λdown,ifiisa collector
(4)
whereξiisthenumberofshortestpathsthatcontain node
iand |M|isthetotalnumberofsmartmeters.
B.Mathematicalmodeling
Once all inputsaredefined,theprobability ofcollision
needsto be calculated.
Forevery nodeofthe communication system,anequation
(2)that linksitscollision probabilitytothe collision probability
ofitsneighborscan bewritten.The|V|equations,Vbeing
thesetofnodesinthenetwork,formafixed-pointsystemof
equations.
Thefollowing least-squaresoptimization model([16]) is
usedtofind numericalvaluesofpi(fori=1...|V|):
min
p
kf(p)k2
2(5)
s.t.:pi≥0∀pi∈p
pi<1∀pi∈p
(6)
where:
p=
p1
.
.
.
p|V|
f(p)=
f1(p)
.
.
.
f|V|(p)
fi(p)=
+∞
P
g=11−1−1
Qg τP
j∈Ii
λj
1−pj!g
g!e
−τP
j∈Ii
λj
1−pj
−pi
It isimportant toremarkthatequations(1)and (2)are
consistentwitheach other: infact,(2)isequivalent to(1)
whenthenumberofavailable channelsisone3.
C.Delay
Thedelayisoneofthemost importantparametersina
communication system.Several typesofdelayarepresent ina
communication network,buta common practice intime-slotted
systemswithsmall size packetsistoconsiderthetimeslot
duration to prevail overpropagation,processing and queuing
delay.Thesedelaycomponentsareneglectedinthe current
modelbutwe are evaluating thepossibilitytoincludesome
ofthem,namelythequeuing delay,inaMarkov-modulated
model,incourseofdevelopmentat thetimeofwriting.
Inanidealsystemwith no interference,only onetransmis-
sion would berequiredforasinglehop inapath; inreality,the
presence ofinterference entailscollisions,and eachcollision
impliesare-transmission ofthepacket.Therefore,the average
numberoftimeslotsnecessarytotransmit apacket inasingle
hop is:
Nij=1
1−pi
Asaresult,theoverall delayinasinglehop corresponds
tothetimeslotduration τ,multiplied by the averagenumber
of re-transmissions:
dij=τX
(uw)∈ρij
Nuw(7)
whereρijisthesetoflinksforming theshortestpathfrom
itoj.Inthiswork,we considerthedelayinamulti-hop path
fromnodeito nodejto bethesumofthedelaysineach hop.
Two delay quantities,du
iand dd
i,aredefined,relatedto uplink
and downlink streamsofcommunications,respectively.
D.Otheroutputs
As showninFigure3,PeRF-mesh providestwoadditional
performance indexes,previouslyintroducedin[16]: the critical
nodesinthesystemand theso-calledsurvival function.
Anodeisconsideredcritical ifand onlyifitscollision
probabilityisabove a certainthreshold.Suchananalysisis
very useful to discovereventualbottlenecksofthesystem.
3Thisisduetothefact that
+∞
P
n=1
an
n!=ea−1
Thesurvivalfunction isamathematicalfunction thatrep-
resentstheprobabilitythatarandomvariableisgreaterthana
certain value.If appliedto delaystatistics,thesurvivalfunction
can provideinteresting insight inthefeasibility ofgeneric
smartgridapplications,whoserequirementsarelimitedtoa
certain portion ofnodes.Anexampleof feasibilityassessment
using thesurvivalfunction wasprovidedin[16].
V.NUMERICALRESULTS
Inthis section,somenumericalresultsobtainedwithPeRF-
meshanalytictoolarepresented.
We chosetotestourmethodology using datarelatedto
Mansonville,aruralarea inQu´ebec and oneofthree zones
involvedinthe aforementioned pilot installation ofsmart
meters[14],in 2011.The area isextended over240 km2and
includes3415 devices(1data collector,114 routersand 3300
smartmeters).
We assumedthesamepacketgeneration ratein uplink
(λup) forall thesmartmetersand alsothesamepacket
generation rate(λdown) fromthe collectortoeverysmart
meter.Inmultipleruns,welet themean packetgeneration
times(1/λupand 1/λdown)varyintheintervalbetween0.5
and 4hoursin orderto highlight theperformance ofthesystem
atdifferent trafficloads,representativeofdifferentsmartgrid
applications.
Thesystemofequations(5)-(6)was solved by using
MATLABon aIntel(R)QuadCore(TM)i7−3770 CPU
@3.40GHzprocessor.The average computational timewas
below15 minutes.
A.Collision probability
InFigure4wereportedthevariation ofthemaxima
(dashedline)and the averages(continuousline)ofcollision
probabilitieswithrespect to packetgeneration ratesin uplink
and downlink.In particular,weusedfixed valuesofthemean
generation timein downlink (1/λdown=1,2,3,4hours)
and drewthevariation ofcollision probabilityaccording to
λup.Thisfigureshowsthat the collision probabilitiesdo
notundergo largevariationsasthetrafficgeneration rate
changes.Forinstance,wefound that themean ofthe collision
probabilitywhen1/λdown=1houris0.22%at1/λup=4
hourand 0.52%at1/λup=30 minutes.
B.ImpactofFHSS
Numericalresultson the collision probabilityin different
trafficscenarios(reportedinTableI) werepresentedin[16].
Inthatpaperit was shownthat,forhigh trafficscenarios,the
collision probabilitiesreached valuescloseto one.
In orderto highlight theimpactofFHSS protocolon the
performance analysisresults,Figure5reportsa comparison of
the collision probabilitiesfound withFHSS (in gray)against
thosepresentedin[16],withoutFHSS (in black).Forthesake
ofclarityinthe comparison,trafficscenariosIDsareusedin
thisfigure.Areduction ofcollision probability greaterthanan
orderofmagnitude asfound inall thescenarios; thereforewe
cansafelystatethatFHSS hasakeyimpacton theperformance
oflargescaleRF-meshsystem.
0.5 11.5 22.5 33.5 4
10−3
10−2
1/λup [h]
Collision probability
average
maximum
2h
3h
4h
1h
2h
3h
4h
1h
1/λdown
Fig.4:Analysisofthe collision probabilitywithFHSS accord-
ing toλupwithfixed valuesofλdown.
510 15 20 25 30
10−3
10−2
10−1
100
Scenario ID
Collision probability
maximum with FHSS
average with FHSS
maximum without FHSS
average without FHSS
Fig.5:Comparison ofcollision probabilitieswithand without
FHSS.
C.Delay
InSubsection IV-C,we explained howthedelayiscalcu-
latedfromtheprobability ofcollision inPeRF-mesh.
InFigure6,thevariation ofthedelayin uplink isreported
according to differentvaluesoftrafficgeneration rate.In
particular,wefixedthedownlink mean generation timeto1
hourand let the1/λupvaryfrom5minutesto4hours.
Ontheleftsideofthe curve,forlowermean generation
times(and consequently highertrafficgeneration rates)there
isaslightvariation inthedelay:weobserve a mean value
of12.27 secondswithλup=5minutesand of11.84 swith
λup=10 minutes,whichresultsinavariation of−3.5%.On
theotherhand,thelast twomean valuesofthedelayare11.5
and 11.49 seconds,withavariation ofonly−0.087%.
TABLE I:TrafficscenarioIDaccording toλupand λdown,
takenfrom[16].
1
λdown[h]
1
λup[h]
0.5 1 1.522.5 3 3.5 4
11 5 9 13 17 21 25 29
22 6 10 14 18 22 26 30
33 7 11 15 19 23 27 31
44 8 12 16 20 24 28 32
510 20 30 40 50 60 90 120 150 180 210 240
12
14
16
18
20
22
1/λup [min]
Collision probability
1/λdown=1h
maximum
average
Fig.6:Variation ofthedelayaccording toλupwithafixed
valueofλdown=1h.
Theflattening ofthe curvedependson thelowerimpact
ofcollision probability on thedelayasthetrafficdecreases.
Asthemean packetgeneration timeincreases,thevalueof
theprobability ofcollision is solowthat it doesnothave an
impacton thedelay.Insuchcases,thedelay ofapacketfrom
nodeito nodej,as showedin(7),tendstoτ|ρij|where|ρij|
isthenumberofhopsfromnodeito nodej.
VI.CON CLUSIONSAND FUTURESTE PS
InthisworkwepresentedPeRF-mesh,ananalytictool to
study theperformance oflarge-scaleRF-meshsystemswith
FHSS.To ourknowledge,thisisthefirstanalytictool totake
intoaccount theinteraction ofFHSS and ALOHA MACaccess
inaperformance analysis study.
Performance analysisiskeytoassess thefeasibility of real
smartgridapplicationsand it has some advantageswithrespect
tostochasticsimulationsand real-fieldmeasurements.
PeRF-meshallowsthorough analysisoflarge-scaleRF-
meshsystemswithashortcomputational time.Analysisof
collision probability,delayand criticalnodescanalsoallow
toidentify possiblebottlenecksofthesysteminthedesign
phase,resulting in high economicaland resources savings.
TheimpactoftheFHSS protocolwashighlighted by
a comparison ofthenumericalresultsobtainedwithPeRF-
meshagainst thoseobtainedwithamodelwithoutFHSS and
availablein[16].Asubstantial improvementwasobserved,
intermsofareduction inthe collision probabilityand the
consequentdecreaseinthedelay.
Oneofthefuturestepsconsistsintherefinementofthe an-
alyticmodel,investigating thepossibleuseofaMarkov modu-
latedsystem; inspiteofincreasing themodel’scomplexity,this
canrepresentadditionalfeaturesof realRF-meshsystems,not
consideredsofar (e.g.probability of re-transmission).Other
pathstoexplore aretheintegration ofmore complex propaga-
tion modelsand ofmoredynamicrouting protocols.Finally,a
combination ofoptimization and performance analysisisinthe
agenda:we are currentlyconceiving amodelfortheoptimal
placementof routersand data collectors.
ACKNOWLEDGMENT
Thisworkwaspartiallyfunded by anECOEnergy Inno-
vation InitiativegrantfromNaturalResourcesCanada.
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