Sho-hops vs. Long-hops - Enegy efficiency analysis in Wieless Senso Newoks. MEKKAOUI Kheieddine D Moulay Taha Univesiy Depamen of Mahemaics and Compue sciences Saida, Algeia mekda@homail.com RAHMOUN Abdellaif Djillali Liabès Univesiy Depamen of Mahemaics and Compue sciences SBA, Algeia ahmoun abd@yahoo.f Absac Senso newoks consis of miniauized wieless senso nodes wih limied capaciy and enegy souce. As sensos may be deployed in a lage aea, adio ansceives ae he mos enegy consume in senso nodes, so hei usage need o be vey efficien in ode o maximize newok s life. A node can oue i s messages owads desinaion eihe by using small o lage hops, so opimizing he hop lengh can exend significanly he lifeime of he newok. This pape povides a simple condiion, o veify, which makes he enegy consumpion minimal by choosing ideal hop s lengh. Keywods-Wieless Senso Newok;Enegy Efficiency;Mulihop Rouing;Hop Lengh; newok s life; I. INTRODUCTION Recen developmen in Mico-Eleco-Mechanical Sysems (MEMS) echnology, wieless communicaions and digial eleconics have allowed he devellopemen of lowcos, low-powe, mulifuncional senso nodes ha ae small in size and communicae uneheed in sho and long disances. These sensos, also known as moes, ae geneally composed of a powe souce (baey), a pocessing uni wih limied capaciy and a communicaion componen (ansceive) [1], [2].The deploymen of senso nodes fo he monioing/deecion of diffeen evens in envionmen is known as Wieless Senso Newok (WSN). in hese las yeas, WSN s have been used in many applicaions like miliay suveillance [3], disase managemen [4], foes fie deecion, seismic deecion [5], habia monioing, biomedical healh monioing [6], invenoy acking, animal acking, hazadous envionmen sensing and sma spaces, geneal engineeing, commecial applicaions, home applicaions, Indeed, Business 2.0 [7] liss sensos as one of six echnologies ha will change he wold, and Technology Review a MIT and Globalfuue [8] idenify WSNs as one of he 10 emeging echnologies ha will change he wold [9]. A senso newoks is composed of hundeds o myiads of senso nodes, which appea o be deployed andomly by a ca o aiplane. Each node has sic limiaion in he usage of i s elecic powe, compuaion and memoy esouces. They ypically uilize inemien wieless communicaion. Theefoe, senso newoks should be well-fomed o achieve is puposes, indeed how well he newok is fomed deemines he life of he whole newok as well as he qualiy of daa ansmission, also o educe channel conenion. Seno nodes ae endowed by a limied baey powe and andom deploymen in difficul eain ; make i almos impossible o echage o o eplace he dead baey. So, baey powe in WSN is consideed as scace esouce and should be used efficienly. Senso node consumes baey in sensing daa, eceiving daa, sending daa and pocessing daa. The mos enegy-consuming componen is he R/F module ha povides wieless communicaions [10]. Consequenly, Ou of all senso node opeaion, sending/eceiving daa consumes moe enegy han any ohe opeaion. The enegy consumpion when ansmiing 1 bi of daa on he wieless channel is simila o enegy equied o execue housands of cycles of CPU insucions [11]. Theefoe, he enegy efficiency of he wieless communicaion poocol lagely affecs he enegy consumpion and newok lifeime of wieless senso newoks. In he mos imes, senso nodes in WSN do no have powe and communicaion ange o diecly send he message o he base saion. So, he muli-hops mode of communicaion is used o fowad daa[10]. Hence, a ypical senso node would no only sense and fowads is own daa bu also have o ac as oue i.e. fowad he daa of is neighbos. As fa as senso node opeaions ae concened sending/eceiving daa consumes moe enegy han any ohe opeaion. I can be infeed ha daa gaheing and ouing is one of he coe aea in WSN, whee good poocols should be developed in ode o achieve maximum enegy efficiency. All moden adio ansceives could adjus hei ansmiing powe [12], so some desinaion could be each wih eihe lage numbe of smalle hops (muli-hop) o small numbe of lage hops (single-hop). Enegy efficiency of hese wo appoaches depends on: pah loss beween ansmie and eceive, powe consumpion of he adio ansceive in vaious opeaing modes. The debae ove he numbe of equied hops comes fom he fac ha each saegy (long-hops and sho-hops ouing) has is own advanages. Rouing ove many sho hops minimizes he ansmission enegy which inceases
wih he communicaion disance. Howeve, sending packes ove long disance elays educes he ecepion cos (as he numbe of nodes involved in daa ouing deceases). II. RELATED WORKS The issue of ouing packes ove long-hops o sho-hops has been eaed by many auhos in ecen yeas and hei conclusions ae vaied depending on he cieia consideed and he appoach aken [13]. Some heoeical woks [14], [13] shows ha muli-hop ouing is moe efficien han single-hop ouing. This is in an opposie o obsevaions in some eal wold WSN, which shows ha single-hop ouing, can be much moe enegy efficien han muli-hop ouing [15], [16]. Besides enegy efficiency, single-hop ouing can also have advanages fo ohe newok paamees, such as end-o-end delay, lowe packe loss, ec [12]. Yin e al. [17] pesened wo saegy of conol, one of he mehods consiss of deceasing he ansmission ange of each node. Accoding o he auhos, his scheme will educe he oveall powe consumpion of he newok, as a oue wih many sho hops is geneally moe enegy-efficien han one wih a few long hops. Haengi specified many easons why long-hop ouing is moe advanageous [16]. One of hem is he powe efficiency. The auho claimed ha alhough he ansmied enegy dops significanly wih disance, he educion of adiaed powe does no yield a decease in he oal enegy consumpion. In his pape, we povide he opimal lengh fo hops ha make enegy consumpion opimal. Fo his we need o use he model, of he enegy consumpion, defined fo he wieless senso newoks. III. PROPAGATION MODEL Radio channel beween ansmie and eceive can be esablished only when sengh of he eceived adio signal is geae han eceive s sensiiviy heshold [12]. The educion in signal powe densiy, on he pah beween ansmie and eceive, is called pah loss. In ou sudy we use he log-disance pah loss model, so he powe eceived by a node disan of d mees fom he sende can be expessed as follows [12], [13], [18]: ( ) α d0 P (d) = P 0 (1) d whee P 0 epesens he powe of he signal eceived a disance d 0 fom a ansmie and α is he pah loss exponen, which is empiically measued unde diffeen popagaion scenaios [18], [13]. Typical values of pah loss exponen in such scenaios ae pesened in Table I. We use eq.1 o expess he minimum powe equied o communicae ove a given disance and we compae he wo ouing saegies (long-hop and sho-hop ouing). Evey Envionmen α Fee-space 2 Uban aea LOS 2,7 o 3,5 Uban aea no LOS 3 o 5 Indoo LOS 1,6 o 1,8 Facoies no LOS 2 o 3 Buildings no LOS 4 o 6 Table I TYPICAL VALUES OF PATH LOSS EXPONENT node is ansmiing wih he minimum powe, equied o guaanee he signal a he eceive, is equal o he sensiiviy heshold P of he eceive [14], [13]. Accoding o he figue 1 we can heefoe wie: ( ) α d0 P = P x (2) x Fom which, we can ge he enegy equied o each he desinaion : ( ) α x P x = P (3) d 0 Figue 1. Tansmission disance fo one hop In some pue heoeical model of wieless ansmission, auhos assume ha all consumed enegy is adiaed ino he ai by a ansmie, and a eceive doesn spend any enegy duing a ecepion [12]. Accoding o hem, if we conside only he oal powe ansmied ove he pah, hen he sho-hop saegy would be he mos enegy efficien, bu since he ecepion cos should no be negleced [14], [10], [19], we will show in his pape ha he use of longhop saegy beween wo nodes (souce and desinaion)is an opimal alenaive. This is due o he fac ha he savings in ansmission powe by he muli-hop scheme does no compensae fo he esuling addiional ecepion enegy cos. The enegy cos of he ecepion P can be equivalen o ansmiing ove a disan [14]. Thus he fomula: ( ) α P = P (4) IV. SHORT-HOPS VS. LONG-HOPS ANALYSIS Figue 2 epesens wo opologies of muli-hop ouing beween wo disan nodes, a souce A and a desinaion B, wih a disance d. The fis opology uses n hops o ansmi daa fom A o B (using sho-hops of disance x); while he d 0
second uses m hops (using long-hops of disance y); wih n = 2 m (y = 2x), so wa can wie : ( ) α ( ) α d0 d0 P = P x = (5) x y Since y = 2x, eq.5 becomes : Figue 2. = P x 2 α (6) Tansmission disance fo : (1) n hops - (2) m hops Using eq.3 and eq.4, we can now compue he enegy equied o ansmi a message beween A and B. Fo he fis opology, we have a pah wih n hops. Thus we can expess he powe equied o ansmi daa fom A o B, usnig n hops, P nh, as: And i can be expessed, also, as : Wich can be wien as : P nh = np x + np (7) P nh = 2m P x + 2m P (8) We know fom eq.6, ha P x = 2, heefoe eq.8 becomes α : P nh = m 2 α 1 + 2 P ] (9) Wih he same way, we can ge he powe equied o ansmi daa fom A o B, usnig m hops, P mh = m + mp (10) V. SHORT-HOPS VS. LONG-HOPS COMPARISON In his secion we pesen ou main esul. Les compue, now, P nh P mh : P nh P mh = m 2 α 1 + 2 P ] [ m 1 + P ] Which is equal o : P nh P mh = m 2 α 1 1 + P ] P nh P mh > 0 if and only if : Theefoe : Which means : A (n 1) nodes B {}}{{}}{{}}{ P nh = (0P + P x ) + (P + P x )... + (P + P x ) + (P + 0P x ) ineval: (12) 1 2 α 1 1 + P > 0 (13) And since y = 2x, eq.15 becomes : P > 1 1 2 α 1 (14) y < (15) α 1 1 2 α 1 x < 2 α 1 1 2 α 1 (16) And since y > x, inequaliies 15 and 16 means ha opimal enegy consumpion can be achieved when he ] lengh of he hops [ ae included in he 2 α 1 1, 2 α 1 α 1 1 2 α 1 VI. SIMULATION AND RESULTS VALIDATION In his secion, we pefom he expeimens wih wo senso newoks o veify he condiion deduced fom he heoeical analysis, one of hese newoks is composed of Mica2 sensos and anohe composed of Mica2do sensos. In ou simulaion, we will use he expeimenal chaaceisics of hese wo sensos, so in ode o evaluae he powe consumed by Mica2 and Mica2do o ansmi daa fom a node o an ohe, we will use he chaaceisics pesened in [20] and descibed in able II: Mica2 Mica2do Recepion 16 ma 12mA Tansmission 18 ma 14mA Tansmission ange 55 m 135m wih maximum x powe 70m 230 m Which equal o : [ P mh = m 1 + P ] (11) Table II EXPERIMENTAL CHARACTERISTIC OF MICA AND MICA2DOT MOTES
A. Fis case sudy : To simulae he behavio of Mica2 sensos, we assume ha he newoks ae composed Mica2 nodes which ae aligned (Tansmie-Relays-Sink) wih a lengh of 760 mees (disance beween Tansmie and Sink), and we compue he enegy consumed by hese newoks wih diffeen numbe of hops, which means diffeen hop lenghs, which means also, diffeen numbe of elays, see figue 3. Toal enegy consumpion 700 650 600 550 Enegy consumpion of Mica2 moes 500 450 20 40 60 80 100 120 140 Hops Lengh Figue 4. Mica2: Enegy consumpion Vs hops lengh aligned newoks, wih diffeen hops lengh. we go he esuls in able IV Figue 3. Newoks of aligned sensos wih diffeen hops compuing he consumed powe fo hese diffeen aligned newoks, wih diffeen hops lengh, gives he following esuls in able III : Hops numbe Hop lengh m Toal powe consumed ma 6 126.6666 662.7732 8 95.0 557.59 10 76.0 503.672 11 69.0909 488.4290 12 63.3333 475.3866 14 54.2857 466.9028 16 47.5 466.2968 18 42.2222 476.9244 20 38.0 491.836 21 36.1904 499.6533 22 34.5454 503.3204 24 31.6666 521.2308 26 29.2307 546.1027 28 27.1428 569.4514 30 25.3333 591.5625 Table III POWER CONSUMPTION VS HOPS LENGTH We conclude fom he able III, ha he opimal numbe of hops ha povide he minimum enegy consumpion is 16 hops (i.e hop lengh is 47.5 mee), which is veified by ou condiion ha limis he lengh of hops ha offe minimum enegy consumpion in : ]36.6678, 73.3357[. Fo easie eading, we pesen he esuls in he figue 4: B. Second case sudy : Wih he same way, we simulae he behavio of Mica2do sensos, we compue he consumed powe fo diffeen Hops numbe Hop lengh m Toal powe consumed ma 2 380.0 245.7984 4 190.0 158.8992 5 152.0 148.7193 6 126.6666 145.1566 8 95.0 151.4496 10 76.0 164.3596 11 69.0909 172.3269 12 63.3333 180.5783 14 54.2857 199.3528 16 47.5 219.1441 18 42.2222 240.3855 20 38.0 262.1798 22 34.5454 283.5317 24 31.6666 305.7131 26 29.2307 328.7930 28 27.1428 351.6764 30 25.3333 374.4000 Table IV POWER CONSUMPTION VS HOPS LENGTH Fom able IV we can ge he numbe of hops, 6 hops (i.e lengh hop = 126.6666), which makes he enegy consumpion minimum. This esul is veified, also, by ou condiion ha limi he lengh of hops ha ensue he minimum enegy consumpion in ]88.3883, 176.7766[. Fo easie eading, we pesen he esuls in he figue 5: VII. CONCLUSION We have analyzed he poblem of hopping disance saegy in WSN and simulaion esuls shows he impac of he choice of he lengh of hops. We showed, also, ha he condiion expessed in his pape, guaanee moe enegy efficiency, and help us o exend he newok s life. Moeove, using he minimum hop lengh can be moe efficien in he case of ansmission failues ha equies eansmission. In fuues wok we will focus on he poblem of ouing daa by
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