Geographic Random Forwarding (GeRaF) for ad hoc and sensor networks: energy and latency performance

Geographic Random Forwarding (GeRaF) for ad hoc and sensor neworks: energy and laency performance Michele Zorzi, Senior Member, IEEE, and Ramesh R. Rao, Senior Member, IEEE o appear in he IEEE Transacions on Mobile Compuing, vol., n. 4, Oc.-Dec. 3 Absrac In his paper, we sudy a novel forwarding echnique based on geographical locaion of he nodes involved and random selecion of he relaying node via conenion among receivers. We provide a deailed descripion of a MAC scheme based on hese conceps and on collision avoidance, and repor on is energy and laency performance. A simplified analysis is given firs, some relevan radeoffs are highlighed and parameer opimizaion is pursued. Furher, a semi-markov model is developed which provides a more accurae performance evaluaion. Simulaion resuls supporing he validiy of our analyical approach are also provided. I. INTRODUCTION Energy conservaion is one of he key echnical challeges in sensor neworks and ad hoc neworks. I is necessary o devise communicaions and neworking schemes which make judicious use of he limied energy resources wihou compromising he nework conneciviy and he abiliy o deliver daa o he inended desinaion. In addiion, sensor nodes are ofen subjec o furher consrains in erms of CPU power, memory space, ec., which call for simple algorihms and schemes whose memory needs are modes. One of he main mechanisms o save energy is he use of sleep modes a he MAC layer, by which nodes are pu o sleep as ofen as possible. This mus be done in such a way ha conneciviy is preserved, since if oo many nodes are sleeping a he same ime, he nework may end up being disconneced. In he recen lieraure, several schemes have been proposed which address his problem. For example, SPAN [] ries o coordinae he sleeping aciviy of he nodes so ha a connecing backbone is always presen. GAF [] idenifies groups of nodes which are equivalen from a rouing poin of view, i.e., in each group i is sufficien ha a single node is awake a any given ime. STEM [3], on he oher hand, provides a means o communicae wih a node currenly asleep, by implemening a rendez-vous mechanism based on beacon ransmissions. As o he MAC iself, mos papers in he lieraure assume eiher TDMA-based schemes [4], or muli-channel seups in which parallel ransmissions can be performed wihou inerference [5], [6], or varians of classic conenion-based schemes, usually based on RTS/CTS This work has been parially suppored by he European Commission under he EES projec (conrac IST--34734) and by he Ialian governmen under he FIRB VICOM projec. Pars of his work have been presened a IEEE WCNC 3 and IEEE VTC 3 Spring. Corresponding auhor: CNIT and Diparimeno di Ingegneria, Universià di Ferrara via Saraga, 44 Ferrara, Ialy; ph.: +39-53-97484 fax: +39-53-97487 e-mail: zorzi@ing.unife.i Deparmen of Elecrical and Compuer Engineering, Universiy of California a San Diego, La Jolla, CA 993-47, USA; ph.: + 858 8 457 fax: + 858 8 597 e-mail: rrao@ucsd.edu handshake in order o miigae he hidden erminal problem [7], [8]. A common characerisic of he above schemes is ha, a he MAC layer and ofen also a he rouing layer, when a node decides o ransmi a packe (as he originaor or a relay) i specifies he MAC address of he neighbor o which he packe is being sen. Knowledge of he nework opology (hough in many cases only local in exen) is required since a node needs o know is neighbors and possibly some more informaion relaed o he availabiliy of roues o he inended desinaion. This opological informaion can be acquired a he price of some signaling raffic, and becomes more and more difficul o mainain in he presence of nework dynamics (e.g., nodes which move or urn off wihou coordinaion). In addiion, he proposed schemes do have some performance problems, e.g., he radio range is significanly underuilized in GAF (which means ha more hops are needed o cover a given disance) and poenially large delays may be inroduced in STEM (in order o wai for a given node o wake up). We propose here an alernaive soluion, called Geographic Random Forwarding (GeRaF, pronounced as giraffe ), which is based on he assumpion ha sensor nodes have a means o deermine heir locaion, and ha he posiions of he final desinaion and of he ransmiing node are explicily included in each message. In his scheme, a node which hears a message is able (based on is posiion owards he final desinaion) o assess is own prioriy in acing as a relay for ha message. All nodes who received a message may voluneer o ac as relays, and do so according o heir own prioriy. This mechanism ries o choose he bes posiioned nodes as relays. In addiion, since he selecion of he relays is done a poseriori, no opological knowledge nor rouing ables are needed a each node, bu he posiion informaion is enough. Geographic rouing is used here o enable nodes o be pu o sleep and waken up wihou coordinaion, and o inegrae rouing, MAC and opology managemen ino a single layer. This basic idea is described in some more deail in a companion paper [9], where he mulihop performance of he scheme is also sudied. In his paper, a collision avoidance proocol based on his idea is described in deail. We provide a deailed analysis of he energy and laency performance of his proocol. Firs, a simplified analysis is given, which leads o closed-form expressions and, via furher approximaions, o simple parameer opimizaion rules. The energy-laency radeoff is explored, and some performance resuls are presened, showing ha he proposed soluion is a promising alernaive for low-power neworking. As a firs sep, we focus on he fundamenal behavior of GeRaF, and we consider STEM [3] as he mos

appropriae scheme o which we compare, since i is he one which is mos closely relaed o our approach. More exensive comparisons wih oher energy-conserving schemes, including [7], [], are he subjec of fuure work. Furher, a more complee approach is followed in which a semi-markov model for proocol operaion is developed and solved. This second approach is more accurae, especially in neworks which are no very dense. Comparison beween he resuls of he wo approaches shows ha he simplified analysis can accuraely predic he behavior in a large fracion of he range and, more imporanly, i accuraely predics he opimal value of he duy cycle of he sleeping behavior of he nodes. Finally, some preliminary simulaion resuls are shown o confirm he validiy of our analysis. II. COLLISION AVOIDANCE MAC SCHEME We consider a scheme which uses carrier sense before ransmission, which parially avoids collisions bu gives no guaranee agains he hidden erminal problem. Noice ha he fac ha nodes are no always on makes radiional RTS/CTSbased collision avoidance mechanisms ineffecive since a node may wake up afer he CTS was issued. This could be solved by requiring a long idle channel ime o be deeced before a ransmission can sar (essenially enough for he whole packe exchange o complee, which is of course very waseful) or by synchronizing all nodes as in [7], which requires addiional signaling and complexiy. The soluion we adop here is he use of busy ones [], []. I was observed in [3] ha here exis sensor nodes equipped wih wo radios. In [3] he availabiliy of separae channels for he daa raffic and he wakeup signaling is useful o faciliae proocol operaion, in paricular o avoid ha prolonged beacon periods inerfere wih daa raffic. In our case, no prolonged beacon periods are presen, and herefore we could use he second radio o le he receiving node issue a busy one, which is a way o effecively preven collisions a he receiver. More precisely, on he firs frequency ( daa frequency) all message exchanges occur, whereas he second frequency ( busy one frequency) is used for busy ones only. Noice ha we could rade off energy and laency as in [3] by using a pulsed busy one wih some duy cycle, wih he requiremen ha he sensing ime be increased in order o avoid ha silen inervals of he busy one are inerpreed as idle channel. In addiion, hese pulsed busy one messages could ac as parial ACKs hereby allowing recovery of smaller pieces of he message if individual CRCs are available (consideraion of hese variaions as well as heir performance implicaions are lef for fuure sudy). Noe ha his is possible since he ransmier also has wo radios which can be used independenly (in paricular, one o ransmi he daa and he oher o receive he busy one/parial ACK messages). When a node has a packe o send, i lisens o boh frequencies. If eiher is acive, he node backs off. If boh are inacive, he node ransmis. The collision avoidance feaure of his scheme is based on he RTS/CTS message exchange. However, unlike he radiional RTS message which is addressed o a specific node, in his case any node wihin range can respond o i, wih nodes closer o he desinaion doing so wih higher prioriy. Therefore, he CTS message is also subjec o conenion, since muliple nodes may decide o respond o he same RTS a he same ime. The issuance of CTS messages in response o an RTS is done in such a way as o give prioriy o nodes which provide a larger advancemen owards he final desinaion, as deailed below. A. Deailed descripion We now describe in deail he proocol operaion from he ransmier and he receiver side. The curren descripion is for a specific soluion, and many varians are possible which may improve he performance while being more complicaed o explain. In his secion we choose a simple version o highligh he main poins. ) Transmier: When a sleeping node has a packe o send, i eners he acive sae and moniors boh frequencies for fi seconds. If eiher frequency is busy, he node backs off and reschedules an aemp a a laer ime. If on he oher hand boh frequencies are sensed idle during his enire inerval, he node ransmis a broadcas RTS message, which conains he locaion of he inended desinaion as well as is own. Afer sending he RTS, he ransmiing node lisens in he subsequen slos for CTS messages from poenial relays. In each of he CTS slos following he end of he RTS message, he ransmiing node acs as follows: i) if only one CTS message is received, i sars ransmission of he daa packe, whose iniial par acs as a CTS confirmaion for he node which issued he CTS; ii) if i receives no CTSs, i will send a CONTINUE message and lisen again for CTSs, iming ou afer Np empy CTS slos (which forces he node o abor he handshake and o reschedule i a a laer ime); iii) if i hears a signal bu is unable o deec a meaningful message, i will assume ha a CTS collision ook place, and will send a COLLISION message which will rigger he sar of a collision resoluion algorihm (o be described laer) and will lisen again for CTSs. Afer packe ransmission, an immediae ACK is expeced. If i is correcly received, i complees he ransacion and he node can go back o sleep. Noice ha if he receiver is an inermediae node owards he desinaion, in a scheme in which a packe exchange is immediaely iniiaed he RTS message iself could serve as he ACK. Here, on he oher hand, we assume ha an explici ACK is used. If he ransmier does no ge an ACK wihin a given ime, i imes ou and declares he ransacion failed. I will hen reschedule he same packe for fuure ransmission. Afer NMaxA failed aemps for he same packe, he ransmier will give i up and generae an error message for he higher layers. While lisening for CTSs and for he ACK, he node ransmis he busy one o preven inerference from hidden erminals. Noice ha wih he above rules he proocol does no lead o ransmier deadlock, as he sender will never wai indefiniely for CTSs or ACKs. Only in he case of compleed ransacion will he ransmier consider he packe as successfully passed o he nex hop. A remaining problem wih his scheme is

3 ha packe duplicaion may occur. In fac, if he final ACK is los he relay node is now in charge of packe delivery whereas he ransmier will no be aware of his fac and will rery he ransmission of he same packe. This ambiguiy does no compromise he correcness of he scheme and can be solved by inermediae nodes when an addiional copy of he same packe is received and discarded. This requires ha nodes keep memory of recen ransmissions. If his is no possible or desirable, as well as in he case in which muliple copies of he same packe go hrough disjoin ses of nodes, packe duplicaion will be deeced a he desinaion, which leads o some inefficiency ha on he oher hand is miigaed by he fac ha losing an ACK when he packe was successful is a low probabiliy even and he overall performance impac may be expeced o be limied. ) Receiver: Each node will (more or less) periodically wake up and pu iself in he lisening mode. If nohing happens hroughou he lisening ime, whose duraion may be fixed or random, he node goes back o sleep. On he oher hand, if he node deecs he sar of a ransmission, i goes ino he receiving sae. Noe ha he randomness of he evens involved makes he sleep process no exacly periodic. The sleep ime will be considered as a consan in he following, for convenience of explanaion and of analysis. In realiy, more sophisicaed schemes could be envisioned, in which sleep imes could be random or could depend on he baery saus (i.e., nodes wih less charge end o sleep longer). These varians are lef for fuure sudy. Upon deecing he sar of a message, a lisening node sars receiving. A he same ime, i acivaes he busy one on he busy one frequency for a duraion TRT S. If no valid RTS is received, he node goes back o he lisening sae, where i says for he originally scheduled duraion. On he oher hand, if a valid RTS is received, he node reads he informaion in i and deermines is own prioriy as a relay. This prioriy is based on he relaive locaion of he node iself compared o he disance beween he ransmier and he inended final desinaion. Specifically, assume he following: he porion of he coverage area of he ransmier which is closer o he inended desinaion han he ransmier iself is divided in Np regions A ;:::;A Np such ha all poins in A i are closer o he desinaion han all poins in A j for j > i; i =;:::;Np. (Possible choices of hese regions may be o ake all wih he same area or o quanize he advancemen in Np equal levels.) In he firs CTS slo afer he RTS, all nodes in A will send a CTS message, while all ohers will be silen. All nodes will hen lisen for he message from he ransmier in he laer par of he CTS slo. If a packe sar is heard (which conains he idenificaion of he node which sen he CTS), only he designaed node will coninue o receive, whereas all ohers will go back o sleep. Noice ha going back o he lisening sae is no a good sraegy since hese nodes are in he coverage area of he ransmier and herefore will be unable o serve as relays for any oher node. In he ineres of energy saving, he bes hing o do is o go back o sleep Anoher opimizaion, no considered here, would be o le a node sense boh frequency upon wakeup and immediaely go back o sleep if eiher is busy, since in his case i is impossible for i o ac as a relay. regardless of any previous schedule (if he lisening inerval is significanly longer han a complee ransacion, nodes could jus inerrup heir lisening and resume i a he end of he ransmission). If in he second par of he firs CTS slo a CONTINUE message is heard, i means ha here are no nodes in A,and all nodes in A will conend in he second CTS slo. If an ABORT message is received, he ransmier has reached he maximum allowed number of CTS slos and he ransacion is abored. If on he oher hand a COLLISION message is received, his means ha more han one CTS was generaed in he CTS slo. All nodes who did no ransmi will drop ou (hey recognize ha higher prioriy nodes are presen) while hose involved in he collision will sar he collision resoluion algorihm. Each colliding node will decide wih probabiliy.5 wheher or no o coninue. Who decides o coninue will send a CTS in he nex slo. Three evens are possible: i) only one node sends, ransmier sars packe ransmission and all ohers drop; ii) more han one CTSs are sen in he same slo, ransmier sends a COLLISION message, hose who did no send drop ou, hose involved in he collision decide wheher or no o coninue as before, unil he collision is resolved; iii) no CTS is heard, a CONTINUE message is sen by he ransmier, and all nodes who did no selec he curren slo decide again independenly wheher o coninue as before. This procedure will erminae in few slos wih high probabiliy. In order o force i o be limied, he ransmier can send an ABORT message if he collision is no resolved wihin NMaxColl CTS slos. Finally, any node which receives a message i does no undersand will drop ou. Nodes which heard he RTS correcly will follow he sequence of seps above, and hey are guaraneed o eiher become he relay node or o drop ou a some poin. The even ha wo nodes hink hey are he designaed relay can be compleely avoided if he sar of he packe conains he full relay node s address, or made very unlikely in a simplified scheme where a he sar of he packe a random number (included in he CTS as emporary shor address) is ransmied. In order o avoid he hidden erminal problem, each node involved in he above procedure will keep he busy one acive unil i drops ou or, if i is he winner, unil he whole daa packe has been received. We sress he fac ha he above proocol choices (e.g., he deails of he collision resoluion algorihm) are made jus o give an example of how i is possible o provide he relaed funcionaliy. I is no our goal here o opimize hese schemes, bu raher o show ha our proposal is able o achieve saisfacory performance. Even beer performance could be obained if furher opimizaion is pursued, and his is lef as an ineresing opic for furher work. III. APPROXIMATE ANALSIS We firs develop an approximae analysis of he GeRaF collision avoidance scheme described in he previous secion, in order o gain some undersanding of he basic mechanisms and sources of energy consumpion, as well as o compare i o STEM.

4 We assume ha nodes are disribued hroughou he nework according o a Poisson process in wo dimensions, wih inensiy ρ nodes per uni area. A node in he nework, while mosly sleeping, wakes up for wo reasons, namely if i has a packe o ransmi or if i is ime for i o lisen according o he wakeup scheme. Noe ha in he laer case here are hree possibiliies, i.e.: i) nohing is received and he node goes back o sleep afer a specified amoun of ime; ii) aciviy is deeced bu he node is no seleced as a relay; and iii) he node acs as a relay. Clearly hese hree possibiliies correspond o differen amouns of acive ime and energy consumpion. Consider a longime inervalof duraion. The oal average energy consumed during his ime can be expressed as follows: Eo = NT ET + N`E` + TsPs () where NT and N` are he average number of imes (during ) he node ransmis a packe and wakes up o lisen, respecively, while ET ;E` is he average amoun of energy consumed following eiher even. Ts is he oal amoun of ime he node spends in he sleep mode, and Ps is he corresponding power. In he following, he various erms in () are evaluaed. A. Packe ransmission In case of a packe ransmission, he ransmiing node sends an RTS message, of duraion TRT S, and lisens for CTSs unil i hears some signal. If Np CTS slos go by wihou any CTS heard, he sender imes ou and reries. Le N = ρß be he average number of nodes in he coverage area, M = dn he average number of such nodes lisening (d is he duy cycle of he lisening aciviy of each node), and ο he fracion of hose nodes which are considered as relays. The probabiliy ha here are no nodes who can answer he RTS is hen e οm. Each cycle where no nodes respond hen involves, besides he RTS, Np empy CTS slos, i.e., he sender ransmis one RTS, lisens (wihou receiving anyhing) for NpTCTS and ransmis (CONTINUE messages) for NpTCTSr. Onaverage, here are (e οm ) such cycles, followed by a successful handshake, which involves one RTS, x CTSs, and (x ) CTS replies, since he reply o he las (successful) CTS is he sar of he daa packe iself. 3 The average number of CTS slos in a successful handshake, x, can be compued as follows. Le = οm=np be he average number of available relays in each prioriy region. 4 A successful handshake sars wih i empy CTS slos wih probabiliy e i (» i<np), followed by ffk slos wih probabiliy e k =, whereff k is he number of slos needed o resolve a collision in which k nodes are involved. Noe ha, wih he binary spliing sraegy used o resolve collisions, he average number of slos sk = E[ffk], obeys he following recursive relaionship sk = ( P k = + k k i= (k i)s i k> k+ Noe ha nodes who are placed opposie wih respec o he desinaion should no be used as a general rule. 3 For simpliciy, and wih no loss in generaliy, we ignore here he fac ha only a limied number of aemps is allowed, i.e., we ake NMaxA = NMaxColl =. 4 In order o simplify he noaion, here we define he prioriy regions as having he same area. Exension o he general case is sraighforward. () In summary, he join probabiliy of having exacly j empy cycles, followed by a non-empy cycle wih i empy slos (» i<np) plus one non-empy slo in which k CTSs are sen, is given by e Np j e i e k ; j ;» i<np;k (3) Then, for he lengh of he non-empy cycle we have x = E[i + ffk] = = = X X X N p (i + sk) e Np j i e k e j= i= k= e en p e X N p i= ie i + P k= e N pe Np en p + P k= e k sk e e k sk e (4) Finally, he sender ransmis he packe for TD and receives he ACK for TACK. Noe ha hese messages are all ransmied/received on he daa frequency, while ransmission on he busy one frequency is acivaed during CTS slos and he ACK. For laer analyical convenience, we ignore he carrier sense aciviy, which would involve an addiional lisening ime of fi, which is a very reasonable approximaion since fi fi TD. The oal ime he ransmiing node is on (couning wice he imes during which boh radios are acive) is hen given by T = (e οm ) (TRT S + Np(TCTS + TCTSr)) +TRT S +xtct S +(x)tct Sr + TD +TACK (5) If we assume ha he power spen in each of hese funcions (ransmi, receive and lisen) is he same P for all, 5 he oal energy spen every ime a node wans o ransmi a packe is ET = T P, and he conribuion of he energy associaed o packe ransmission o he oal average power consumpion Eo= is NT ET = P T (6) where is he packe arrival rae a each node. B. Lisening/Receiving Each node wakes up periodically wih duy cycle d, and says on for a ime TL. The average rae of packe arrivals in is coverage area is N, and he probabiliy ha no aciviy is deeced is p = e NTL. In his case, he node jus spends he amoun of ime TL lisening and goes back o sleep. On he oher hand, wih probabiliy p, someone in he coverage area will sar an RTS. Before being able o know wheher i can be considered as a relay, he node mus receive his RTS. Since he arrival ime of his RTS is uniformly disribued wihin he lisening inerval, he acions involved are lisening 5 This assumpion is clearly no criical since one can precisely disinguish among he hree funcions, hereby assigning he exac power o each if needed. On he oher hand, even hough possibly no he same, hese power levels have been observed o be comparable, and we expec no addiional insigh from a more accurae definiion of he power levels. The assumpion herefore appears o be reasonable, and is made here o limi he size of he parameer space.

5 o he daa channel for TL= on average, and receiving for TRT S. Noe ha as soon as he node deecs channel aciviy, i urns on is busy one, so ha a ransmi aciviy for TRT S on he busy one frequency mus be accouned for as well. Given ha an RTS is sared, wih probabiliy ο he node will no be in he porion of he coverage area facing he desinaion, and will drop ou immediaely afer receiving he RTS. In his case, here is no addiional aciviy involved. On he oher hand, wih probabiliy ο he node will paricipae in he conenion, along wih oher nodes whose number is a Poisson r.v. wih mean οm. Since all paricipaing nodes have he same probabiliy of being he winner, he probabiliy ha he node wins he conenion is found as X k + k= e οm (οm) k = eοm οm In his case, i.e., he node wins he conenion, i is involved a mos in sending x CTSs (wih x as given in (4)), receiving (x ) CTS replies, receiving he daa packe and finally sending he ACK. When he node is receiving, i.e., for a ime equal o (x )TCTSr + TD, he busy one is on. If on he oher hand he node paricipaes in he conenion bu loses i (wih condiional probabiliy (οm +e οm )=οm), he aciviy involved is upper bounded by receiving (x ) CTS replies and ransmiing coninuously (CTSs or busy one) for (x )(TCTS +TCTSr). Noe in fac ha nodes losing he conenion do no necessarily paricipae unil he end, and wih cerainy do no ransmi in he very las CTS slo (in which somebody else is successful). In summary, he oal average acive ime of he radio (couning wice he imes when boh radios are on) can be found as ` = p TL +(p ) + eοm M» TL +T RT S (xt CTS +(x)tctsr +TD+TACK) + οm ( eοm ) (x )(TCTS +TCTSr) M = TL +(p )[ο(x)(tcts +TCTSr) +TRT S T L + eοm M (T CTS +TD+TACK) : (8) For reasonable scenarios, he probabiliy ha upon wakeup he node ends up being involved in a daa exchange will have o be small (he whole idea being o avoid heavy load of he nodes). In order o have nework sabiliy we mus have N TDAT Aex <, i.e., he average number of users in ransmission sae per coverage area mus be less han uniy (TDAT Aex is he oal ime for a daa ransfer from RTS o ACK). If we assume ha TL fi TDAT Aex, we have ha N TL fi. In his case, we have p =e NTL ' N TL. If once again we assume ha an acive radio consumes a power P regardless of is being in ransmi, receive or lisen mode, he oal average conribuion o he oal average power consumpion Eo= can be found as N`E`=. For an unloaded nework, we would have N`= = d=tl, while in general i is (7) rue ha N`=» d=tl, and he bound is igh for low raffic. In his case, we can wrie N`E` ' = dp + P de` dp ` = TL TL» MT L + οm(x )(TCTS +TCTSr) +MTRT S +(e οm )(TCTS +TD+TACK) where we used he fac ha dp ( p ) TL ' dp N T L TL Λ (9) = P M () C. Sleeping The oal amoun of energy consumed while sleeping is given by TsPs, where Ts is he oal amoun of ime he wo radios are off. Noice ha since in he above analysis we never accouned for sleeping imes in beween acive periods of he radios, Ts mus include hose imes as well. In any even, we can affirm ha he conribuion of sleeping ime o he overall average power consumpion is TsPs» Ps, where Ps is he overall power consumed when boh radios are in sleep mode. In view of he fac ha in he envisioned scenarios he radios mus be sleeping mos of he ime, we have Ts fi, and herefore he above bound is igh and can be used as a reasonable approximaion. D. Toal average energy consumpion We can find he oal normalized average energy consumpion o be ψ = E o P = P NTET + N`E` + T sps () where he expressions for he hree erms are given above. ψ is he oal energy consumed in ime, divided by he energy which would be consumed by a single radio which is always on (ransmiing, receiving or monioring he channel), as is ypical in radiional CSMA-based proocols. In order o simplify he expressions, consider he case in which TRT S = TCT S = TCT Sr = TACK = TSIG. Inhis case, we obain NT ET = P (e οm ) (3Np +)TSIG and N`E` + ' dp + P ψ ' d + P s +(3x +)TSIG + TD] ()» MT L + ( e οm )TD 3οM(x ) + M + ( e οm ) P TsPs TSIGΛ (3) ' Ps (4) +» 3 e οm TD MT L + 3οM(x )+M + ( e οm ) +3x ++(e οm ) (3Np +) TSIGΛ (5)

6 E. Laency We define here laency as he ime i akes from when a node sars he packe ransmission handshake o when he ransmission of he acual daa packe sars, and can be compued similarly o (5) 6 o obain Tla = (e οm ) (TRT S + Np(TCTS + TCTSr)) = (e οm ) (+Np)+x +TRT S + xtcts +(x)tctsr TSIG (6) F. Analysis of STEM A similar analysis can be carried ou for he STEM scheme. We consider here STEM-B [3]. The basic principle of STEM is he following. Nodes are expeced o sleep mos of he ime, and o periodically wake up o lisen. If a node wans o send a packe o one of is neighbors, i sars polling i by sending beacon messages which carry he inended recipien s ideniy. Since he inended recipien is guaraneed o wake up wihin a finie amoun of ime, his polling period ends successfully and resuls in he communicaion link beween he wo nodes involved o be resored. Once his is done, he packe ransfer can occur. The deails of he beacon message as well as a more complee descripion of he scheme can be found in [3]. ) Energy consumpion: The average energy consumpion can sill be divided ino hree erms. In a packe ransmission, he sender sends beacons unil he inended recipien wakes up and receives one. A ha poin, packe exchange akes place via 8.-like MAC. 7 Nodes wake up every T seconds for TL. The average ime he beacon needs o be sen is hen given by (T TB)= +B,where TB is he period wih which beacons are sen and B is he lengh of a beacon [3]. If we assume ha TL = TB + B we obain (T TL)= +:5B, where T = TL=d. The oal average amoun of ime he node is powered on is herefore given by T = T L d T L +:5B +TCTS + TD + TACK = T L( d) + TD +3:5TSIG (7) d where we assumed ha he beacon acs as RTS. The conribuion o he average power consumpion due o packe ransmission is hen given by P T. Afer waking up, a node will be addressed wih probabiliy p,wherep is he probabiliy ha no aciviy is deeced. Noe ha in his case nodes are explicily addressed, and herefore he rae a which messages for a specific node are generaed is lower han before (where on he oher hand all nodes in he coverage area would receive he RTS). However, since a beacon is for a specific node, he inerval of ime during which a new message can be generaed is now T raher han TL. The message arrival rae is hen given by N T N = T L d (8) 6 Specifically, unlike in (5) we do no consider he ime for daa and ACK, and do no coun wice he imes when he busy one is acive. 7 Noe ha STEM could be combined wih various access proocols, such as for example S-MAC [7]. In his seing, we assume a simple conenion-based scheme which enables direc comparison wih GeRaF. Noice ha his is he average fracion of lisening periods in which a node ges a message, and as before in he envisioned scenario we expec his number o be small. Afer waking up, a node will lisen for TL and go back o sleep wih probabiliy p = e TL=d. Wih probabiliy p ' TL=d, he node will be involved in receiving a message. In his case, noe ha in STEM he lisen ime is TL = TB + B. Since he beacon sar ime is uniformly disribued wihin TB, he average ime o receive a beacon is TB= +B = (TL+B )= = (TL+TSIG)=. Afer receiving a beacon, he node s radio is involved in sending a CTS, receiving a daa packe and sending an ACK. The oal aciviy ime for lisening/receiving is herefore ` = p TL +(p )» TL+B +TCTS + TD + TACK» = TL +(p ) T L +T D+:5TSIG» ' TL + T L T L d + T D +:5TSIG (9) Finally, as before, we approximae he conribuion of sleep mode o he overall average power as Ps. The oal normalized average energy consumpion in STEM can herefore be compued as ψs = E o = P +d» T + d` + P s TL P TD +3:5TSIG + T L( d) + d» T L d +T D+:5TSIG TD +6TSIG + T L( d) + P s P = + d + P s () d P Noe ha for a given value of his expression is independen of N. This leads o he conclusion ha STEM as considered here is unable o benefi from an increased node densiy. A somewha more fair comparison would be o consider STEM combined wih GAF as proposed in [3], so ha higher densiies of node deploymen could be exploied o reduce he energy consumpion. This scheme would however have wo significan drawbacks, namely a poorer uilizaion of he coverage radius because of he node organizaion ino grids, and he need for explici signaling among nodes in order o make he GAF mechanism work. As a firs sep, in he following resuls we focus on he original version of STEM. Deailed evaluaion of he combinaion of STEM and GAF, as well as a quaniaive assessmen of he above phenomena, are ou of he scope of he presen paper and are lef for fuure sudy. ) Laency: If we define laency as he ime from when a beacon is iniiaed o he ime an ACK for i is successfully received (and herefore daa exchange can sar), we have as in [3] (we assume here " =, which corresponds o minimum lisening ime TL) Tla = B + + T T B = T L( d) d = T T L +:5B +B +:5TSIG ()

7 IV. PERFORMANCE COMPARISON In his secion, we give some numerical resuls for he schemes considered, and provide a comparison beween hem. Firs of all, noice ha here are hree ypes of parameers in he above formulas: fixed parameers, i.e., parameers which are expeced o be decided once for all and will be considered as consan: in paricular, we choose he number of prioriy classes Np = 4, he relaive size of he relay region ο = :4, he relaive power consumpion in sleep mode, Ps=P = :, and TSIG=TD = : (we assume here for simpliciy ha all signaling packes are of he same lengh TSIG); exernal parameers, i.e., parameers which are common o all schemes and provide he scenario in which hose schemes are compared: in paricular, he node densiy and he nework raffic; here, we use he average number of nodes per coverage area, N, as a measure of he nework densiy, and he average normalized raffic per coverage area, N TD as a measure of he nework load; parameers of he specific schemes, i.e., parameers which play differen roles in differen schemes and can be chosen differenly according o he scheme seleced; for example, he lisening ime or he duy cycle may no be he same in GeRaF and in STEM. In realiy, hese parameers would be he subjec of proocol opimizaion, and a fair comparison should ake ino accoun ha hey can be independenly seleced. As o he parameer opimizaion, noe he following. In STEM, he minimum lisening ime is TB + B = 3TSIG. Since i is obvious ha he bes choice is o selec TL as small as possible, we se TL = 3TSIG here. The only remaining independen parameer is he duy cycle. In GeRaF, if we upper bound he energy consumpion by neglecing he negaive erm MTL=, he lisening ime no longer appears explicily in he expressions, and can herefore be ignored. In his case also, he duy cycle is he only remaining independen parameer. The performance evaluaion can herefore be carried ou in erms of energy consumpion and laency as a funcion of he duy cycle, wih he lisening imes chosen as jus explained. Curves of energy and laency vs. duy cycle, as well as laency vs. energy (while varying he duy cycle), can be provided. As an example, some resuls are shown in Figures hrough 4, in which he performance of GeRaF is compared wih ha of STEM. Figures and show he normalized energy performance, ψ, vs. he duy cycle, d. In boh schemes, for large duy cycle, he energy consumpion is dominaed by he lisening aciviy, as expeced. As he duy cycle is decreased, oher sources of energy consumpion are imporan. In paricular, he fac ha he ransmier mus spend energy o find a neighbor (eiher via he beacon as in STEM or by repeaed aemps as in GeRaF) becomes dominan, and more so as he nework load is higher and he node densiy is smaller. Noe ha GeRaF ouperforms STEM when he node densiy is large. I should be noed ha he choice of he duy cycle does no have o be he same in he wo schemes, as hey may be independenly opimized (noice from Figs. and ha he minimum energy occurs for differen values of d for he wo schemes). However, i is clear from he figures ha for normalized energy, psi_ - - -3 GeRaF, N= STEM, N= GeRaF, N= STEM, N= -3 - - duy cycle, d Fig.. Average normalized energy consumpion, ψ, vs. duy cycle, d. GeRaF and STEM compared. N =;, nework load.. normalized energy, psi_ - - -3-3 - - duy cycle, d GeRaF, N= STEM, N= GeRaF, N= STEM, N= Fig.. Average normalized energy consumpion, ψ, vs. duy cycle, d. GeRaF and STEM compared. N =;, nework load.. dense neworks he minimum energy consumpion achievable by GeRaF may be significanly smaller han ha in STEM. To shed some more ligh on his issue, we plo he rade-off beween energy consumpion and laency (normalized o he duraion of a daa packe, TD) in Figures 3 and 4. The curves are generaed by spanning he range of values of he duy cycle (curves are raveled righ o lef by increasing he duy cycle). For boh schemes, we can observe a region in which here is a real rade-off beween energy and laency, whereas here exiss a sauraion poin beyond which here is no rade-off as boh schemes perform poorly: he laency associaed o long sleep imes is unaccepable, and he persisence in looking for a relay resuls in degraded energy performance as well. In he rade-off region, he relaive performance of GeRaF and STEM depends on he node densiy: GeRaF performs beer han STEM for sufficienly dense neworks, while he opposie is rue when he densiy is small. As shown in he figure, alhough for relaively sparse neworks (N =) GeRaF and STEM perform approximaely he same, for neworks wih

8 normalized energy, psi_ - - -3 GeRaF, N= STEM, N= GeRaF, N= STEM, N= - 3 laency Fig. 3. Average normalized energy consumpion, ψ, vs. laency (in unis of TD). GeRaF and STEM compared. N =;, nework load.. normalized energy, psi_ - - -3 GeRaF, N= STEM, N= GeRaF, N= STEM, N= - 3 laency Fig. 4. Average normalized energy consumpion, ψ, vs. laency (in unis of TD). GeRaF and STEM compared. N =;, nework load.. N = nodes per coverage area GeRaF can gain over STEM almos an order of magniude in laency for comparable energy or in energy for comparable laency. As already menioned, STEM could be improved by coupling i wih GAF, which on he oher hand has significan drawbacks in erms of addiional signaling and increased number of hops. The proposed scheme herefore appears as a promising alernaive for low-power neworking. A. Discussion on he raffic model In he above resuls, we have adoped a raffic model in which, when comparing differen values of N, wehave assumed ha he average nework raffic remains consan. This is jusified by he fac ha in his paper we focus on he use of high node densiies o save energy wihou inroducing oo much laency. In his scenario, deploying more nodes does no lead o more nodes generaing more raffic, bu raher o more nodes sleeping for a larger fracion of he ime, so ha he average aciviy (in erms of boh communicaions aciviy and daa generaion) wihin a given area is unchanged. The oher opion, i.e., using more nodes o enable more daa ransfer, is no he main focus here. In any even, noe ha he curves in Figures hrough 4 can be used in he laer case as well by jus scaling he load by he consan value of N. The comparison beween GeRaF and STEM sill holds, and herefore mos of he above conclusions sill apply. In paricular, GeRaF is beer han STEM for sufficienly dense neworks, while he opposie is rue for small N. Anoher issue relaed o he raffic model is he packe generaion a he sensor nodes. The model considered here assumes ha isolaed packes are generaed, while in he presence of oher models (e.g., burss of packes) he scheme should be changed, e.g., by creaing an associaion beween a node and he relay who wins he conenion in order o avoid muliple conenions for packes in he same burs. V. ENERG OPTIMIZATION From he plos shown, here appears o be a minimum in he energy consumpion, i.e., here exiss an opimal value of he duy cycle which minimizes he energy cos. Here, we invesigae he opimizaion of his parameer. Since he full expression of ψ for GeRaF is oo complex, as a firs sep we look for some accurae approximaion. To his aim, in Figs. 57 we plo he following quaniies: Λ = (e οm ) (3Np +)TSIG + TD () 3 = + = (3x +)TSIG (3)» MT L + ( e οm )TD M + ( e οm ) TSIG Λ (4) 4 =3οM (x )TSIG 5 = d (5) In addiion, we plo he normalized sleep power, Ps=P (sl), he oal normalized raffic (r) esimaed as N TDAT Aex, and he oal consumpion (o) ψ = + + 3 + 4 + 5 + Ps=P (6) The reason we plo he normalized raffic is ha one of he assumpions on which our analysis is based is ha he raffic be low, so ha he approximaions made hold. Ploing he raffic allows us o see in which region he resuls presened are reasonable and where hey may be oo pessimisic. We will elaborae on his issue in Secion 6, where a more deailed model will be developed whose accuracy does no rely on he low raffic assumpion. From he various figures (as well as from he resuls obained in many oher cases, no shown here, which follow he same general rend as in hese examples), i is clear ha for large values of d he conribuion of 5 (energy spen lisening) dominaes, whereas for low duy cycles he dominan erm is, which corresponds o he energy spen looking for a relay. From Fig. 7 we also noe ha for small raffic and dense neworks he effec of he sleep power canno be negleced. 8 8 Noe ha he case N = 5, which may seem exreme, is shown here o demonsrae ha he accuracy of he approximaion is good over a wide range of he parameer values.

9 energy componens Fig. 5. - -4-6 -8-4 -3 - - duy cycle Componens of he normalized average energy consumpion vs. duy cycle. N =5, nework load :. 3 4 5 sl r o minimum energy consumpion - - -3 GeRaF - load=. STEM - load=. GeRaF - load=. STEM - load=. average number of nodes wihin coverage Fig. 8. Opimal normalized average energy consumpion, ψ, vs. average number of nodes wihin coverage, N. Nework load : and.. energy componens - -4-6 -8-4 -3 - - duy cycle 3 4 5 sl r o laency for minimum energy GeRaF - load=. STEM - load=. GeRaF - load=. STEM - load=. Fig. 6. Componens of he normalized average energy consumpion vs. duy cycle. N =5, nework load :. energy componens Fig. 7. - -4-6 -8-4 -3 - - duy cycle Componens of he normalized average energy consumpion vs. duy cycle. N = 5, nework load :. In all cases shown, as well as in all our exensive evaluaions no depiced here, erms ; 3 ; 4 are negligible over he whole range of values considered. Therefore, in order o sudy he behavior of ψ, we can use he approximaion ψ ' + 5 + Ps=P 3 4 5 sl r o average number of nodes wihin coverage Fig. 9. Laency (in unis of TD) corresponding o opimal energy consumpion vs. average number of nodes wihin coverage, N. Nework load : and.. Λ = (e οm ) (3Np +)TSIG + TD + d + Ps=P (7) whose accuracy has been esed wih excellen resuls. Based on his expression, and recalling ha M = dn, we can jus differeniae ψ wih respec o d and se he derivaive o zero, obaining ha he opimal choice of he duy cycle as a funcion of he various parameers involved is given by where dop = log w οn (8) p w = ff ++ ff(ff+4) ; ff=(3np +)οntsig (9) From he expression of he energy consumpion of STEM we obain he equaion @ψs @d = T L d + = =) dop = r TL (3)

A. Resuls Figure 8 shows he opimized performance of GeRaF and of STEM versus he average number of nodes wihin coverage, N. In each curve, he value of he oal average nework load is kep consan, i.e., decreases as we move o he righ. For each value of N, he opimal duy cycle is compued according o he above formulas and used o compue he energy performance. We noe from he above expressions ha for GeRaF dop is approximaely inversely proporional o N, as is for fixed nework load (recall ha he nework load is defined as N TD). Therefore, we expec he minimum energy consumpion o be inversely proporional o N, ashe figure shows. In STEM, on he oher hand, dop is proporional o p, i.e., inversely proporional o p N. Looking a he expression for ψs, he behavior is iself inversely proporional o p N, as he figure shows. Noice ha he slopes of he curves corresponding o he wo schemes are herefore differen, and while STEM shows superior performance for a relaively small number of nodes per coverage area, when he nework is more dense GeRaF ouperforms STEM, as expeced. This is due o he fac ha since any node can ac as a relay, a higher densiy provides a higher probabiliy ha such a node wakes up. We remark here ha he resuls of Figure 8 are energyopimized wihou aking ino accoun laency. A fair comparison should herefore consider laency as well. Figure 9 shows he laency performance which for each N corresponds o choosing dop. The figure clearly shows ha, in he considered case of fixed nework raffic, he laency of GeRaF is consan, since choosing dop (roughly) inversely proporional o N resuls in a consan value of M, he numberof available relays wihin coverage, which is he key facor in deermining laency. On he oher hand, in STEM he opimal choice of d resuls in a value of laency which is proporional o p N, as he figure shows. Clearly, when N is larger han abou 5-, STEM has worse energy and laency performance han GeRaF. For a more complee invesigaion of he rade-off beween energy and laency, refer o he already discussed Figures 3 and 4. Similar resuls for he case in which is kep consan (and herefore he average nework load increases wih N) are shown in Figures and. I can be seen ha in his siuaion STEM chooses a fixed poin in he energy-laency space, whereas GeRaF can sill benefi from increased densiy, as in he previous case. VI. SEMI-MARKOV MODEL In he previous subsecion we have menioned ha he simple analysis presened can be expeced o apply only for low raffic in he nework, as i assumes ha when a packe is ready for ransmission he medium is never busy, and neglecs oher issues which could become relevan if he channel is occupied for a significan fracion of he ime. This is he reason why, for low duy cycles and significan raffic per node, he approximae expression (acually, upper bound) for he energy consumpion may increase beyond he normalized value of wo, which is he maximum possible since he wors possible case is ha boh radios are always on. I is herefore imporan o validae he goodness of he previous analysis and o deermine he range of values of he minimum energy consumpion - - -3 GeRaF - lambda=. STEM - lambda=. GeRaF - lambda=. STEM - lambda=. average number of nodes wihin coverage Fig.. Opimal normalized average energy consumpion, ψ, vs. average number of nodes wihin coverage, N. Traffic per node =: and.. laency for minimum energy Fig.. GeRaF - lambda=. STEM - lambda=. GeRaF - lambda=. STEM - lambda=. average number of nodes wihin coverage Laency (in unis of TD) corresponding o opimal energy consumpion vs. average number of nodes wihin coverage, N. Traffic per node = : and.. parameers in which he above resuls are meaningful. In order o do so, we develop a more complee model in which he effec of muliple aemps is accouned for. More specifically, we rack he evoluion of a node, which can be in one of he following saes: ransmirts : he node has decided o sar a handshake and sends an RTS; ransmipk : a handshake has been successfully compleed and packe ransmission sars; packeready : he node has a packe ready for ransmission; sleep : he node is in sleep mode; lisen : he node is in idle lisening mode; receiverts : an RTS has sared while he node was lisening, and he node sars receiving i; receivepk : he node has won conenion o be a relay and now receives he packe. We build he ransiion srucure among hese saes according o he various evens which can occur. For each ransiion we can deermine he associaed energy consumpion as well as oher relevan merics. The resuling semi-markov model can be solved o obain he performance resuls of ineres.

ransmi RTS no CTS received Fig.. CTS received idle medium packe ready busy medium: backoff correc packe o be relayed TX failure ransmi packe receive packe packe arrival before wakeup corruped packe TX success packe arrival win collision no aciviy deeced no RTS deeced sleep lisen receive RTS no packe arrival before wakeup aciviy deeced Transiion diagram of he semi-markov model for GeRaF. lose collision or drop ou Noice ha even his model is no compleely accurae, as an exac model would require o keep rack of he sae of all nodes joinly, a clearly impossible ask. However, i does capure imporan behaviors, e.g., he fac ha in a loaded nework a node may spend more ime in a given sae han anicipaed. In he sequel, we derive he ransiion srucure for he semi-markov model. The model has seven saes and sixeen ransiions, and is depiced in Figure. ransmirts This sae corresponds o a node which has decided o sar a handshake and sends an RTS, i.e., medium sensing has been successfully performed. The possible ransiions in his case are he following. Wih probabiliy e οm, here is a relay available, he node receives a CTS and eners he ransmipk sae. Given ha here is a leas one acive user in he relay area, he average ime o solve he conenion (in number of CTS slos) is given as x = x + x,where x = e οm NX p i= A e i+ i (3) is he average number of empy CTS slos (no relays in he corresponding area), and x = e οm NX p i= A X e i+ k i+ sk k= (3) is he average number of CTS slos from he one in which a leas one CTS is sen o when he collision is resolved (i.e., a single CTS is sen). 9 The radio on he daa channel is always on, ransmiing one RTS and x CTS replies, receiving x CTSs, and lisening 9 In his secion we specifically use j o denoe he average number of nodes in A j, so ha he analysis applies o he case in which he prioriy regions are generally defined. for x CTSs. On he oher hand, he second radio (only used for busy ones) is acive only when he firs radio does no ransmi, i.e., during he x CTS slos. We arrange he ime spen by each radio in he four modes (ransmi, receive, lisen, sleep) ino a marix, where he wo rows correspond o he wo radios and he columns correspond o he four modes in he given order. Noe ha he sum of he elemens of each row mus be he same and is equal o he oal average ime associaed o he considered ransiion. In his case we have B @ TRT S+ (x )TCTSr x TCTS x TCTS xtcts TRT S+ (x )TCTSr The oher possibile ransiion is o sae packeready,and occurs when no CTS is received, i.e., no relays could be found and he node backs off. This even has probabiliy e οm,and he associaed imes are B @ TRT S + NpTCTSr NpTCTS Tbackoff NpTCTS TRT S + NpTCTSr +Tbackoff ransmipk This sae is enered when a successful handshake has been compleed. A daa packe is hen ransmied and an ACK received. Two evens are possible here, i.e., he packe is successfully received wih probabiliy Psucc, for which TD TACK TACK TD and which leads o he sleep sae; or, he packe is corruped wih probabiliy Psucc, forwhich TD TACK Tbackoff TACK Tbackoff + TD and which leads o packeready since a new aemp needs o be scheduled. packeready This sae corresponds o he node having a packe ready for ransmission. The acion aken is sensing he channel. If he channel is sensed idle for Tsensing, a ransiion occurs o sae ransmirts, oherwise, he node reurns in packeready afer some backoff ime wih average Tbackoff. Le Pidle be he probabiliy ha he channel is sensed idle. Then, wih probabiliy Pidle here is a ransiion o ransmirts wih imes Tsensing Tsensing C A whereas wih probabiliy Pidle here is a ransiion o packeready wih imes Tsensing Tbackoff Tsensing Tbackoff Noe ha he acual number of CTSs which he ransmier receives may be less han x, since some of he CTS slos during he resoluion of a conenion may be empy. Wha we consider here is a conservaive approximaion, which may be expeced o be very igh since he power for receive and lisen is almos he same and, in addiion, as shown in Secion 5, he conribuion of his ransiion is small. C A