Modelling the energy cost of a fully operational wireless sensor network

Transcription

1 Telecommun Sys DOI /s z Modelling he energy cos of a fully operaional wireless sensor nework Walenegus Dargie Xiaojuan Chao Mieso K. Denko Springer Science+Business Media, LLC 2009 Absrac Several applicaions have been proposed for wireless sensor neworks, including habia monioring, srucural healh monioring, pipeline monioring, precision agriculure, acive volcano monioring, and many more. The energy consumpion of hese applicaions is a criical feasibiliy meric ha defines he scope and usefulness of wireless sensor neworks. This paper provides a comprehensive energy model for a fully funcional wireless sensor nework. While he model uses oxic gas deecion in oil refineries as an example applicaion, i can easily be generalized. The model provides a sufficien insigh abou he energy demand of he exising or proposed communicaion proocols. Keywords Wireless sensor neworks Energy-model Energy-efficien proocols Lifeime of a wireless sensor nework 1 Inroducion Several applicaions have been proposed for wireless sensor neworks. The applicaion of Mainwaring e al. [12] gahers W. Dargie ( ) Chair of Compuer Neworks, Technical Universiy of Dresden, Dresden, Germany walenegus.dargie@u-dresden.de X. Chao 9h Floor Tower B, CEC Plaza, NO. 3 Dan Ling Sree, Hai Dian Disric, Beijing , China chaoxj@gmail.com M.K. Denko Deparmen of Compuing and Informaion Science, Universiy of Guelph, Guelph, Onario, Canada, N1G 2W1 denko@cis.uoguelph.ca daa from humidiy, emperaure, baromeric pressure, and ligh sensors for monioring he aciviies of seabirds. Kim e al. [10] use wireless sensor neworks for srucural healh monioring, in which he srucural inegriy of bridges and buildings is inspeced using acceleromeer sensors. The neworks are asked wih measuring he response of a srucure o an ambien exciaion (heavy wind or passing vehicles) or a forced shake (using shakers or impac hammers). The applicaion of Werner-Allan e al. [17] moniors acive volcano using seismic and infrasonic sensors. The underlying nework was able o capure 230 volcano evens jus over hree weeks. The applicaion of Soianov e al. [15]useshydraulic and acousic/vibraion sensors for monioring large diameer, bulk-waer ransmission pipelines. The mos prevalen concern in wireless sensor neworks is he limied lifeime. The nodes operae wih exhausible baeries; and recharging or replacing hese baeries, given he sheer size of he nework and he deploymen seings, is a significan hurdle. For example, because of he energy consrain, Kim e al. [10] sugges ha wireless sensor neworks can only be used during occasional inspecion of bridges and buildings, hereby limiing heir scope as well as usefulness. Subsequenly, almos all ypes of communicaion proocols and daa processing algorihms arge efficien use of energy and opimizaion of nework lifeime as heir design goal. In his paper, we carefully analyse he energy cos of a fully operaional wireless sensor nework. The applicaion we use for our analysis will be oxic gas deecion in oil refineries. We will consider highly referenced, energy-aware proocols for esablishing and running he nework. We shall give paricular consideraion o he link and nework layer as well as o he self-organizaion (neighbor discovery and ineres disseminaion) aspecs, as hese claim a significan porion of he energy budge. Finally, we shall provide comprehensive analyic and simulaion models based on which

2 WDargieeal. he lifeime of he nework can be esimaed. The models ake ino accoun node densiy, disribued sleeping schedules, muli-hop communicaion and ime synchronizaion. The res of his paper is organized as follows: In Sec. 2, we discuss relaed work; in Sec. 3 we will briefly discuss oxic gas deecion in refineries; in Sec. 4, we will esablish basic assumpions for he nework model; in Secs. 5 and 6, we will provide a comprehensive analysis and simulaion of he energy cos. Finally in Sec. 7, we will discuss our experiences and observaions and provide concluding remarks and ouline for fuure work. 2 Relaed work Tseng [16] provide an analyic energy model for esimaing he energy consumpion of a wireless sensor nework ha employs he S-MAC medium access conrol proocol [18]. The model akes he cos of conrol messages (RTS/CTS/ACK/DIFS) and he duy cycle of he sleeping schedule of individual nodes ino accoun. The model aemps o define and esimae he energy consumpion of various operaion modes. In [19], an analyic, inegraed daalink layer model is presened. The model enables o esimae he energy cos of link layer proocols. The srengh of he model is in is capabiliy o give insigh abou he effec of a link layer decision on oher layer concerns, including channel assignmen, rae of ransmission, power and managemen. However, he framework does no offer a comprehensive undersanding of he energy cos of he enire nework. Feeney [6] propose an analyical model for examining he energy cos of rouing in a mobile ad hoc neworks. The work aemps o demonsrae he rade-off beween energy consumpion and reliabiliy. Two popular rouing proocols are chosen for he analysis: Dynamic Source Rouing (DSR) [13] and Ad hoc On-demand Disance Vecor (AODV) [11]. These wo proocols suppor rouing in fla opology neworks, wih all nodes paricipaing equally in he rouing process. Moreover, boh proocols are on-demand proocols, in which nodes discover and mainain roues as needed. DSR heavily depends on he cache of nework wide opology informaion exraced from source rouing headers, while AODV is a desinaion-oriened proocol based on he disribued Bellman-Ford algorihm. Boh proocols are adapive for dynamic opology. Similar o oher energy models, he nework inerface has four possible energy consumpion saes: ransmiing, receiving, idle, and sleeping. The idle mode is he defaul mode for ad hoc environmen. The energy cos is calculaed as a funcion of packe size. The uni energy of a packe is decided by he sender, he inended receiver(s), and he nodes overhearing he message. Chao e al. [4] repor an iniial resul of his work, bu is mahemaical model was no fully developed. 3 Toxic gas deecion The applicaion we use o analyse he energy cos of he communicaion proocols in wireless sensor neworks is a oxic gas deecion applicaion in oil refineries. There are wo reasons for choosing oxic gas deecion: (1) Oil refineries cover exensive areas, requiring large scale sensing o deec oil and gas leakages in pipelines. This fis ino he basic assumpion ha a wireless sensor nework is made up of hundreds and housands of wireless sensing nodes. (2) Presenly, a good porion of he oil indusry is replacing cable based sensing sysems by porable and wireless devices which can easily be deployed and mainained. The nex evoluion in oxic gas deecion will be owards wireless sensor neworks. For he deail descripion of he various oxic gases ha should be sensed, we refer our readers o [4] and [5]. 4 Nework model Our analysis and simulaion of he nework s energy consumpion and lifeime is based on a nework model. The nework model esablishes he basic assumpions concerning he nework s opology, he disribuion and densiy of nodes, and he way he nework is conneced. Moreover, i defines he nework s sensing ask. Deploymen refers o he way wireless sensor nodes are placed in areas where he sensing ask should be carried ou. This decision direcly affecs he qualiy of sensing as well as he overall energy consumpion of he enire nework. While here can be hree basic monioring sraegies spo, area and fence for oxic gas monioring, spo monioring is he mos suiable sraegy [4]. Coverage is anoher significan performance meric. In [2], i indicaes how well a given area can be moniored by he nework. Even hough here are some exising models for esimaing he number of sensors required o cover he enire sensing field wih a probabiliy, p, of deecion an even, coverage is deploymen dependen. For a spo monioring scenario, even hough he whole area is no necessarily covered, all poenial leakage sources are moniored. As shown in Fig. 1, N nodes are disribued randomly on a recangular area A of size A = a b. Wihou loss of generaliy, we assume ha a b. The node disribuion can be modelled as a wo-dimensional Poisson disribuion wih average densiy, λ. The probabiliy of finding k nodes in A is given by: λa (λa)k P(k nodes A) = e (1) k! The conneciviy figure speaks abou he exisence of a communicaion link beween a source anywhere in he nework and a single sink. In muli-hop communicaion, here

3 Modelling he energy cos of a fully operaional wireless sensor nework 5 Energy model Fig. 1 2D Poisson disribued node deploymen is a leas one muli-hop pah beween a node and he sink (base saion). The probabiliy ha a nework is conneced, i.e., all nodes can communicae wih he sink eiher direcly or wih he suppor of inermediae nodes, mainly depends on he node densiy and he ransmission range of individual nodes. If he nodes are assumed o be homogeneous, he relaionship beween conneciviy probabiliy, ransmission range and node densiy is esimaed by 1 [3]: p(conn) = (1 e λπr2 0 ) n where p(conn) is he probabiliy ha he nework is conneced; λ is he densiy of he nework, n/a; r o is he hreshold ransmission rage; and n 1 is he number of deployed nodes. The deploymen scenario for our case is depiced in Fig. 1. The spo monioring sraegy is complemened by addiional randomly deployed nodes for improved conneciviy. Each node has he same radio ransmission range R, and wo nodes can communicae via a wireless link if heir Euclidean disance is less ha he ransmission range, i.e., d R. For simplificaion, fading and pah efficiency are no aken ino accoun; we do no consider also he presence of obsacles in he pah of propagaion. Finally, he sensing ask for which he nework is deployed deermines he daa raffic size in he nework. For oxic gas deecion, here are wo essenial concerns: he long and shor erm impac of oxic gases release. Hence, every sensor node should periodically (a unable parameer) repor he concenraion of H 2 S and NH 3 o a sink. This is define as a normal case wih a normal prioriy. In case of a leakage ha surpasses a hreshold defined by he safey board of he refinery (his is usually a concenraion beween 10 and 15 ppm, an alarm should be fired off wihin 30 seconds. This is characerized as an abnormal condiion wih high prioriy. 1 This is wihou aking he border effec ino accoun. (2) In Sec. 4, we presened a number of facors ha affec he qualiy of sensing and he lifeime of a wireless sensor nework. In his secion, we shall ranslae hose facors ino quanifiable erms so ha we can esimae he energy cos. The model ogeher wih he sensing ask descripion, and he specificaion of he hardware devices and he communicaion proocols will be sufficien o esimae he lifeime. The communicaion proocols we employ o esablish he wireless sensor nework are he S-MAC [18], for medium access conrol, and he Direced Diffusion [8], for supporing self-organizaion and rouing. The jusificaion for hese proocols is given in more deail elsewhere [4]. A more echnical assessmen of hese proocols can be found in [20] and [21]. Hop coun is an essenial performance parameer and indicaes how many hops a packe is relayed in average for a given disance in a nework. For a deerminisic opology, his hop-coun esimaion is a simple geomery problem. For a random nework model, however, a combinaion of saisics and probabiliy heory is required. Forunaely, here are many exising models already. To calculae he minimum hop coun, we deermine he disance S beween wo random nodes and divide i by he ransmission range R. In he lieraure, he random disance formula [1] is widely adoped. I is based on he calculaion of he random disance disribuion wihin a recangular area: E{S}= 1 [ a 3 15 b 2 + b3 ( )] a 2 + a 2 + b 2 3 a2 b 2 b2 a 2 [ ( + 1 b 2 6 a ln a + ) a 2 + b 2 b ( + a2 b ln b + )] a 2 + b 2 a Taking E(S) as he expeced disance beween he source and he desinaion in our random nework, he lower bound of he expeced value of hop coun can be expressed as: H min = E{S}/R (4) To achieve a more realisic analysis, ransmission error due o packe loss and collision should be included in he energy model. Because he lisening ime in S-MAC is fixed, a fixed conenion window is beer for coordinaion and synchronizaion han an exponenial back-off. However, a fixed conenion window can cause significan packe loss. We used Bianchi s model [7] o esimae packe loss due o collision a he link layer. According o he model, he prob- (3)

4 WDargieeal. 5.1 Energy consumpion analyic model Fig. 2 Possible inersecions of wo neighbor nodes abiliy of successful ransmission, p succ, can be calculaed as: (λ 1)τ(1 τ)λ 2 p succ = 1 (1 τ) λ 1 (5) where λ refers o he nework s node densiy and τ = 2 (CW+1) and CW is he carrier sensing conenion window. All daa packes in S-MAC, excep ineres disseminaion, are unicas and will cause RTS/CTS/ACK conrol overhead. To esimae he energy cos of adapive lisening, i is useful o esimae he number of neighbors which poenially overhear he RTS/CTS message, i.e., he average neighbors in enclosure of he sender and he receiver. This can be calculaed by firs geing he overlaps of communicaion coverage beween wo random neighbors. When wo nodes becomes neighbors, heir ransmission circles inersec, in which case Fig. 2 shows he wo exreme scenarios. The inersecion area can be described as [14]: 2R 2 cos 1 ( d 2R ) 12 d 4R 2 d 2 (6) where 0 d R and d is he Euclidean disance beween wo nodes. Taking he assumpion of he random Poisson disribuion of he nodes ino accoun, hen d is bound in (0,R) wih a uniform probabiliy disribuion. Accordingly, d will be: d = R (7) 2 Then he average overlap of wo circles can be described by: A iner sec 2.152R 2 (8) is The enclosure area for neighbors of a sender or a receiver A 1 = 2πR R R 2 (9) wih λ = N πr2 a b And, (10) N neighb = A 1 a b N A 1 λ = 1.314λ (11) πr2 For a horough analysis of he energy model (from (12) o (65)), he variables (parameers) lised in Table 1 and heir corresponding descripions should be referred o. Addiional variables will be explained according o heir conex of use. We propose wo analyic models o esimae he energy consumpion of a oxic gas deecion nework. We call he firs model Pure Synchronizaion Energy Model (PSE) and he oher Full Applicaion Energy Model (FAE). In PSE, here will no be daa ransmission in he nework; nodes communicae wih each oher o perform synchronizaion (i.e., exchanging sleeping schedules). Mos exising S-MAC based energy models assume ha he whole nework is synchronized wihou acually considering he energy consumed by he synchronizaion process. We presen he PSE model o provide a realisic picure of he conribuion of ime synchronizaion on he overall energy consumpion. In he simulaion secion, we shall demonsrae ha synchronizaion and periodical neighbor discovery cos more energy han daa ransmission. FAE models a fully funcional nework in which boh periodical and incidenal daa ransmission and ime synchronizaion are aking place Pure synchronizaion energy model S-MAC carries ou ime synchronizaion in 4 seps: In he firs sep, every node is iniially acive for sync p cycles, waiing for he arrival of SYNC packe from oher nodes. The energy consumpion of his phase is expressed as: E lisen_sync = N sync p T frame P idle (12) In he second sep, nodes periodically resynchronize o avoid clock drif. During his ime,, he number of aemps every node sends SYNC packe is expressed as, N sync_sen_ry = ( / ( ) ) sync p T frame syncp (13) Due o packe collision and loss, only a porion of hese packes will be successfully received: N sync_sen = N sync_sen_ry p succ (14) The energy consumed during sending SYNC packes a his sage is given by: E sync_per_node_sen = E rans + E idle + E sleep (15) where E rans = M sync /R daa_rae P rans (16)

5 Modelling he energy cos of a fully operaional wireless sensor nework Table 1 Variables definiion Variables P rans, P sleep, P recv, P idle M sync, M RT S, M CT S, M ACK, M ineres, M daa sync_cw, daa_cw backoff, DIFS, SIFS idle adap I normal, I abnormal i normal, i abnormal d repor_abnormal R daa_rae duy_cycle T frame p succ R rery f srch_cycle sync p N neigh λ N N leak H min Definiion Energy consumpion per ime uni of four modes SizeofSYNC,RTS,CTS,ACK, Ineres, and daa Message Size of conenion window of SYNC and Daa Message Size of backoff, DCF, Iner Frame Space and Shor Iner Frame Space Idle period of every ransmission/recepion pair of one daa packe Adapaion ime, frame lengh dependen Ineres propagaion frequency for Normal and Abnormal case Normal and Abnormal even repor inerval Repor duraion afer a leak is deeced Daa rae Duy cycle Frame lengh Probabiliy of successful packe ransmission/recepion Max rery imes Frequency of neighbor Discovery The iniial Synchronizaion period Average neighbors in enclosure of sender and receiver Nework densiy Toal number of nodes in an area, A The number of nodes ha deeced leakage Minimum hop coun (Topology dependen) And, E idle = P idle (T frame duy_cycle M sync /R daa_rae ) (17) E sleep = P sleep T frame (1 duy_cycle) (18) E sync_per_node_recv = (1 λ) (E recv + E idle_recv + E sleep_recv ) (19) The energy consumed during receiving he SYNC packes is expressed as, E recv = (M sync /R daa_rae P recv ) (20) When a SYNC packe arrives a a receiving node, i eiher succeeds or fails due o collision or channel error. Since a failure recepion consumes he same amoun of energy as a successfully received packe, we merge boh scenarios ogeher. In oher words, all (λ 1) neighbor nodes will receive he SYNC packe regardless of is usefulness. Then oal amoun of energy consumed during periodical SYNC packe sending and receiving is herefore calculaed as: E period_sync_pure = N sync_sen_ry N E sync_per_node_sen + N sync_sen N E sync_per_node_recv (21) In he hird sep, every node periodically performs neighbor discovery by lisening for he whole sync p cycles as described in he firs sage, i.e., for every sync p f srch_cycle cycles. Noe, however, ha no all node ener ino neighbor discover phase a he same ime since hose nodes ha lose during conenion for channel access will compee only in he nex conenion cycle, afer sending a SYNC packe. Thus he periodical neighbor discovery will be delayed due o collision.

6 WDargieeal. E nb_srch = N sync p p succ T frame P idle T frame sync p f srch_cycle (22) Finally, o calculae he energy consumpion of ransmiing empy frames, 2 firs, we find ou he number of empy frames. N empy = (/T frame sync p ( p succ ) /(T frame f srch_cycle ) N sync_sen_ry + N sync_sen (λ 1)) N (23) Here /T frame gives he oal number of frames per node for he period,. sync p is he probable duraion of he iniial synchronizaion ime in which a node wais for SYNC (T frame f srch_cycle) packe from oher nodes. is he neighbor discovery frames; and N sync_sen λ expresses he number of frames for sending and ransmiing periodical SYNC packes. Subsequenly, he expeced energy consumpion for synchronizaion is expressed as: E empy = N empy T frame (P idle duy_cycle + P sleep (1 duy_cycle)) (24) The energy consumpion for SYNC overhead wihou daa ransmission is given by: E sync_pure = E lisen_sync + E period_sync_pure + E nb_srch + E empy (25) 5.2 Full applicaion energy model In his model, he energy model conains wo pars: he energy consumpion due o synchronizaion and he energy consumpion due o daa ransmission. The four sages of synchronizaion discussed in Sec apply for he Full Applicaion Energy Model as well. The amoun of energy consumed during lisening for Sync packes and neighbor discovery is he same as in he previous case. However, even hough boh SYNC and daa packes can be processed in he same frame, in sage 2 of he synchronizaion sage, we calculaed only he energy for sending/receiving SYNC packes. The energy consumed during he remaining ime can be accouned for daa ransmission or receiving; or for idly lisening. Suppose N sync_sen is he number of imes every node sends SYNC packes successfully and N sync_sen_ry is he number of imes a node broadcass SYNC packes. 2 Here we define empy frames as frames ha conain scheduled idle ime only. In hese frames, we need only calculae he energy consumed during idle ime. The energy consumpion during sending and receiving every SYNC packe is given as follows: E sync_per_node_sen = M sync R daa_rae P rans + P idle ( sync_cw + backoff + DIFS ) (26) E sync_per_node_recv = (λ 1) M sync /R daa_rae P recv (27) Because of he reason saed in sep 2 of he PSE model, we merge boh scenarios ogeher. E period_sync = N sync_sen_ry N E sync_per_node_sen + N sync_sen N E sync_per_node_recv (28) Unlike sage 4 in Pure Synchronizaion Model, he empy frames in his scenario are boh daa and SYNC packes dependen; hus he oal energy consumed during synchronizaion is given as follows: E sync = E lisen_sync + E period_sync + E nb_srch (29) Given he average neighbors in enclosure of wo nodes, he number of neighbors ha overhear an RTS/CTS message can be known. 3 We use he p succ N neigh o denoe he number of nodes ha will join adapive lisening. The energy consumpion due o nodes paricipaing in an Adapive Lisening is given by: E adap = (p succ N neigh adap + idle ) P idle (30) In One-phase pull of he Direced Diffusion rouing proocol, here are no exploraory and reinforcemen overheads. One only needs o calculae he cos of flooding ineres and daa ransmission. In he Ineres propagaion phase, he sink periodically sends ineres o all nodes. The duraion of a period is relaively large. The successful ransmission and reransmission rae are described in Table 2. α = p succ + (1 p succ ) p succ 2 + (1 p succ ) 2 p succ 3 + +(1 p succ ) R rery 1 p succ R rery (31) Based on he back off behavior of S-MAC, for every ransmission/recepion pair of one daa packe, he idle period can be described as follows. idle = daa_cw + backoff + DIFS + 3 SIFS (32) 3 There are also nodes ha may no be able o hear an RTS/CTS message.

7 Modelling he energy cos of a fully operaional wireless sensor nework Table 2 Transmission imes of RTS Number of Send/Resend Send Times of ransmission imes Possibiliy M RT S 1 p succ 1 2 (1 p succ ) p succ 2 3 (1 p succ ) 2 p succ 3 R rery (1 p succ ) (Rrery 1) p succ R rery When a node finishes ransmiing/receiving a packe, he remaining ime may no always fi o he scheduled acive and sleep ime of he node, in which case he node has o keep idle unil he nex acive or sleep ime arrives. Since we already ake he acive period in one frame ino accoun, he exra idle ime can be esimaed by: (1 duy_cycle) T frame 2. Accordingly, he energy consumpion of ineres propagaion can be expressed as: E ineres_per_node = E usef ul + E wase (33) where E usef ul = M ineres /R daa_rae (P rans + p succ And, (λ 1) P recv ) (34) E wase = ( DIFS + daa_cw + backoff ) P idle + (1 + (λ 1) p succ ) (P idle + P sleep ) 1 duy_cycle) T frame (35) 2 Every ineres packe is successfully ransmied wih a probabiliy of p succ. This holds rue for boh normal and abnormal condiions. E normal_se = E abnormal_se = N E ineres_per_node (36) During a reporing phase, we have eiher a normal even or an abnormal even. During a normal repor, he H 2 S concenraion is below 10 ppm. We firs calculae he energy consumpion of a single even delivery pah. Every packe along a single pah will be received H min imes. I will be forwarded o he nex hop if he concenraion is larger han he max value in memory of he curren node. The possibiliy of every inermediae packe being successfully forwarded is assumed o be 0.5. Thus, E normal_repor_one_pah = H min (E OH + E rans + E wase ) (37) where E OH = (M daa + M RT S + M CT S + M ACK ) /R daa_rae P recv (38) And, E ran = 0.5 (M daa + M RT S α + M CT S + M ACK )/R daa_rae P rans (39) E wase = 0.5 E adap α + (P idle + P sleep ) (1 duy_cycle) T frame (40) 2 The energy consumpion during an abnormal case can be calculaed in a similar way. Based on he resul of he wo phases above, we derive he energy consumpion by N nodes during ime,. This includes he energy consumpion of ineres propagaion phase and reporing phase: E rouing_normal = E normal_se + I normal i normal E normal_repor_one_pah N (41) Similarly, he energy consumpion for he abnormal case is expressed as follows: E rouing_abnormal = I abnormal E abnormal_se + d repor_abnormal i abnormal E abnormal_repor_one_pah N leak (42) Here d repor_abnormal i abnormal refers o he number of messages ha a leakage even keeps on reporing Energy for empy frames and missed par As menioned before, we now express he energy consumed in idle ime of empy frames ha are no used during synchronizaion or daa ransmission/recepion during ime. To esimae he number of empy frames, we calculae he number of frames occupied in rouing and synchronizaion based on he analysis above. From he ineres propagaion phase, we ge he number of frames for boh cases: N normal_se = N abnormal_se = N λ (43) The reporing frame is defined as N normal_one_pah = ( α) H min (44)

8 WDargieeal. We divide he inersecion beween daa and synchronizaion ino sub periods as ϕ 1 and ϕ 2 o decrease he uncerainy. By adding frames on boh payload and synchronizaion, we can esimae he oal frames produced by a node. This is expressed as follows: N work = N daa + N sync ϕ 1 ϕ 2 (53) Fig. 3 Raio among number of frames N abnormal_one_pah = (1 + α) H min (45) Now wih he above inermediae calculaion, we derive he number of frames required for daa exchange: N daa = F comb + F normal + F ab (46) where, F comb = And, F normal = I normal N normal_se + I abnormal N abnormal_se (47) i normal (N 1) N normal_one_pah (48) F abnormal = d repor_abnormal i abnormal N leak N abnormal_one_pah (49) Then wih he number of frames for neighbor discovery and SYNC packes exchanged, we compue a he n synchronizaion sage, he number of frames for synchronizaion: N sync_neighbor_discovery = ( sync p + N sync_exchange (T frame f srch_cycle ) p succ ) N (50) = (N sync_sen_ry + N sync_sen (λ 1)) N (51) N sync = N sync_neighbor_discovery + N sync_exchange (52) Figure 3 shows he raio among a number of frames used for synchronizaion, daa, or empy ϕ 1 and ϕ 2 are he number of frames ha handle boh SYNC and daa packes. While ϕ 1 represens he overlap beween frames of daa and neighbor discovery (he whole frame is in idle sae), and ϕ 2 denoes he overlap beween frames of daa and common SYNC packes exchange. I is difficul o precisely deermine how many frames a node uses for boh SYNC and daa ransmiing/receiving. The oal number of frames communicaed during is: N oal = /T frame N (54) So he number of empy frames can be calculaed by subracing N work from N oal. N empy = N oal N daa N sync_neighbor_discovery N sync_exchange + ϕ 1 + ϕ 2 (55) Accordingly,we ge he energy consumed by empy frames: E empy = N empy T frame (duy_cycle P idle + (1 duy_cycle) P sleep ) (56) As we menioned before, we only calculae he energy for SYNC packes exchange ill now, we need o add he missing par here. From he Fig. 3, hen sync_miss can be calculaed as follows: N sync_miss = N sync_exchange ϕ 2 (57) Thus E sync_miss = (N sync_exchange ϕ 2 ) (P idle (T frame duy_cycle M sync /R daa_rae ) + P sleep T frame (1 duy_cycle)) (58) If we add E empy and E sync_miss, we can ge E empy + E sync_miss Wih = N + T frame N sleep_idle (N sync_exchange ϕ 2 ) (P idle M sync /R daa_rae ) (59) N = N oal N daa N sync_neighbor_discovery + ϕ 1 (60) And, N sleepi dle = duy_cycle P idle + (1 duy_cycle) P sleep (61) ϕ 1 [0, min(n daa,n sync_neighbor_discovery )] (62) ϕ 2 [0, min(n daa,n sync_exchange )] (63)

9 Modelling he energy cos of a fully operaional wireless sensor nework Based on ϕ 1 and ϕ 2 s range, we could derive he upper bound and lower bound of he sum of E e mpy and E sync_miss. The disribuion of ϕ 1 and ϕ 2 can be assumed by a Binomial disribuion wih probabiliy of 0.5, and wih a mean value of: ϕ 1 = 0.5 min(n daa,n sync_neighbor_discovery ) (64) ϕ 2 = 0.5 min(n daa,n sync_exchange ) (65) And finally, aking all inermediae resuls ino consideraion, he overall energy consumpion of he nework can be summed up as follows: E oal = E rouing_normal + E rouing_abnormal + E sync + E empy + E sync_miss (66) 6 Energy analysis The simulaion environmen we use is he NS-2 simulaor, version2.31[9]. Our simulaion model combines S-MAC and he one-phase-pull algorihm in Direced Diffusion. In he S-MAC proocol, we enable he adapive lisening and global schedule funcionaliies. The defaul duy cycle is se a 10 percen, and he daa rae is 2 Mbps for he message sizes we proposed in Sec. 5, he S-MAC frame lengh will be 1.31 seconds wih 10% duy cycle. Error encoding raio is se a 2, as specified by he defaul seing in S-MAC. The daa message size is 136 byes and ineres size is 96 byes. We se he ineres refresh ime as 300 seconds and changed he ping applicaion o repor normal daa once in 600 seconds, he even generaion ime is randomly seleced. For every abnormal even, i generaes 6 abnormal messages repeaedly wihin 10 s. We use he opology of randomly disribued nodes in an area of 100 m 70 m. One of hese nodes is specified as he sink node. The simulaion duraion is 600 seconds. All he oher parameer values are described in Table 3. We change he nework densiy and compare he energy consumpion for boh he PSE and FAE models. There is a linear relaionship beween he densiy and energy consumpion (Fig. 4). The analyic resul for boh PSE and FAE models is remarkably similar o he simulaion resuls, for densiy below 45. The small deviaion in he energy consumpion of he wo scenarios illusraes ha he synchronizaion cos is high when S-MAC is used. There are wo reasons for his: (1) S-MAC repeaedly uses SYNC packes o synchronize he local imer and discover new neighbors during he enire lifeime; and (2) A node relenlessly aemps o send ou a broadcas SYNC packe even if i loses a conenion. For a high densiy neworks, efficien packe ransmission can be achieved by uning parameers such as he even generaion inerval and he ineres propagaion duraion. Fig. 4 Energy consumpion increases when nework densiy becomes higher Fig. 5 Energy consumpion as duy cycle changes 6.1 Model validaion and duy cycle Figure 5 shows how energy consumpion can be affeced by he duy cycle of he MAC proocol. We varied he duy cycle of wo differen nework densiies: 14 and 35. The analyic resuls of he FAE model are similar o he simulaion resuls wih he deviaion of less han 10% for boh densiies. The energy consumpion increases due o he addiional acive ime as well as collision and synchronizaion overhead. Because in S-MAC he lisen ime is fixed, when duy cycle

10 Table 3 Simulaion parameer lis Basic parameer Defaul value WDargieeal. Conrol message RTS/CTS/ACK 10 byes SYNC message 9 byes Ineres message 96 byes Daa message 136 byes Ineres propagaion frequency 300 seconds Normal even repor inerval 300 seconds Abnormal even repor inerval 10 seconds Abnormal even repor period 60 seconds Abnormal even occurrence raio 1% Duy cycle 10% Bandwidh 2 Mbps Nework densiy λ Minimum hop couns Topology dependen S-MAC Frame lengh Message size, duy cycle and Backoff Window Adapaion ime Frame lengh dependen Max rery imes 5 Frequency of neighbor Discovery 22 Synchronizaion period 10 Nominal ransmission Range 40 m Sensing field 7000 m 2 (70 m 100 m) Transmission power 31.2 mw Receive/idle power 22.2 mw Radio@sleep saus 3 µw Fig. 6 Energy consumpions varies along wih he leakage sources Fig. 7 Collision varies as number of leakage sources increases

11 Modelling he energy cos of a fully operaional wireless sensor nework bu i reduces he raffic in he enire nework significanly. Figure 8 depics he considerable energy saving under all nework densiies. 7 Conclusions Fig. 8 Daa aggregaion impac on energy consumpion varies, he frame lengh will vary adversely. Therefore when he duy cycle increases, he whole ime will be divided ino more frames, which will resul in SYNC packe overhead increase. This in urn affecs SYNC packes broadcasing inerval and he neighbor discovery, boh of which are frame size dependen. Figure 6 denoes he relaionship beween energy consumpion and he number of leakage sources. We simulaed wih hree differen densiies: 14, 29, 43. When he leakage source increases from 1 o 15 wih an increasing sep of 5, he energy consumpion rises in seps, bu here is anomalous reducion in he simulaion curves. The anomalous reducion becomes more obvious when nework densiy increases. When abnormal evens dominae daa ransmission for a cerain period of ime, he synchronizaion as well as neighbor discovery will be delayed, and SYNC packe collisions will be reduced emporarily and evenually resuls in a ransien energy decrease. The relaionship beween collision and he number of leakage sources is shown in Fig. 7. In Fig. 6 and Fig. 7, hese curves reveal similar behavior. In Fig. 6, hough our analyical resul approaches he simulaion resul, he analyical energy consumpion raises only slighly in a liner fashion, wihou any anomalous poin. This is because energy consumpion in he analyical model is more ideally calculaed. Though i considers he collision possibiliy in a saisical way, he collisions wih oher nework behaviors such as synchronizaion and message queuing were difficul combine. One way of reducing he daa raffic in he nework is by forwarding a repor from a node only if he maximum H 2 S and NH 3 concenraions i repors is greaer han all he oher nodes in is neighborhood. This requires daa aggregaion, Boh in he analysis and simulaion case, as he densiy of he nework increases, he energy uilizaion of he nework increases also. One reason for his is ha in a large densiy neworks, he power consumpion of each node a he link layer is significanly high due o collision. S-MAC begins applying he sleep schedule for each node only once he nodes have exchanged heir schedule. Synchronizaion claims a significan amoun of energy. The disproporional energy disribuion even during normal sensing makes S- MAC unsuiable for oxic gas deecion. Moreover, during simulaion, we have observed ha S-MAC s performance deerioraes considerably when he number of nodes in he sensing field exceeded 40. The Bianchi model for compuing he energy cos during conenion assumes sauraion raffic, in which all he nodes have daa o send a all imes. While his is plausible for normal, periodic repors, i is unsuiable for irregular and bursy raffics. The energy cos of normal and abnormal evens propagaion decreases exponenially as he ineres propagaion inerval increases. Ineres has o be disseminaed in he nework o updae rouing pahs and o define a new sensing ask. Ineres disseminaion promps gradien compuaion and reinforcemen. The longer he inerval, he lower he energy cos. On he oher hand, choosing a long ineres propagaion inerval implies a poenial increase in laency of even propagaion, since old pahs migh be broken for a number of reasons, as such is he case when some nodes exhaus heir energy more quickly han ohers. There is a rade-off beween laency and energy cos. In our energy model, we have no considered he energy required for local signal processing, such as he energy consumed by he analog-o-digial (ADC) converer o produce a high resoluion senor daa. In realiy, however, he ADC consumes a significan amoun of power. In he fuure, we will accommodae his fac o assess he feasibiliy of using exising off-he-shelf hardware for building wireless sensor neworks. References 1. Ghosh, B. (1951). Random disances wihin a recangle and beween wo recangles. Bullein of he Calcua Mahemaical Sociey, Boukerche, A., Fei, X., & Araujo, R. B. (2006). An energyefficien sensing coverage proocol for surveillance and monioring applicaions using wireless sensors. In Performance, compuing, and communicaions conference, IPCCC h IEEE inernaional (pp ). April 2006.

12 WDargieeal. 3. Beseer, C. (2002). On he conneciviy of wireless mulihop neworks wih homogeneous and inhomogeneous range assignmen. In IEEE vehicular echnology conference, VTC 2002 (pp ). 4. Chao, X., Dargie, W., & Lin, G. (2008). Energy model for h2s monioring wireless sensor nework. In CSE 08: proceedings of he h IEEE inernaional conference on compuaional science and engineering (pp ). Washingon: IEEE Compuer Sociey. 5. Dargie, W., Schill, A., Mochaourab, R., & Guan, L. (2009). A opology conrol proocol for 2d Poisson disribued wireless sensor neworks. In The hird inernaional workshop on elecommunicaion neworking, applicaions and sysems. 6. Feeney, L. M. (2001). An energy consumpion model for performance analysis of rouing proocols for mobile ad hoc neworks. Mobile Neworks and Applicaions, 6(3), Bianchi, G. (2000). Performance analysis of he IEEE disribued coordinaion funcion. IEEE Seleced Areas in Communicaions, 18, Inanagonwiwa, C., Govindan, R., Esrin, D., Heidemann, J., & Silva, F. (2003). Direced diffusion for wireless sensor neworking. IEEE/ACM Transacions on Neworking, 11(1), Issariyakul, T., & Hossain, E. (2008). Signal & communicaion. In Inroducion o nework simulaor NS2. Berlin: Springer. 10. Kim, S., Pakzad, S., Culler, D., Demmel, J., Fenves, G., Glaser, S., & Turon, M. (2007). Healh monioring of civil infrasrucures using wireless sensor neworks. In IPSN 07: proceedings of he 6h inernaional conference on informaion processing in sensor neworks (pp ). New York: ACM. 11. Lee, S.-J., Belding-Royer, E. M., & Perkins, C. E. (2003). Scalabiliy sudy of he ad hoc on-demand disance vecor rouing proocol. Inernaional Journal of Nework Managemen, 13(2), Mainwaring, A., Culler, D., Polasre, J., Szewczyk, R., & Anderson, J. (2002). Wireless sensor neworks for habia monioring. In ACM inernaional workshop on wireless sensor neworks and applicaions (WSNA 2002) (pp ). 13. Nasipuri, A., Casa, N. R., & Das, S. R. (2001). Performance of mulipah rouing for on-demand proocols in mobile ad hoc neworks. Mobile Neworks and Applicaions, 6(4), Spivak, M. (2006). Calculus (3rd ed.). Cambridge: Cambridge Universiy Press. 15. Soianov, I., Nachman, L., Madden, S., & Tokmouline, T. (2007). Pipene: a wireless sensor nework for pipeline monioring. In IPSN 07: Proceedings of he 6h inernaional conference on informaion processing in sensor neworks (pp ). New York: ACM. 16. Wei Tseng, H., Yang, S.-H., Chuang, P.-Y., Wu, H.-K., & Chen, G.-H. (2004). An energy consumpion analyic model for a wireless sensor mac proocol. In Vehicular echnology conference (pp ). 17. Werner-Allen, G., Lorincz, K., Welsh, M., Marcillo, O., Johnson, J., Ruiz, M., & Lees, J. (2006). Deploying a wireless sensor nework on an acive volcano. IEEE Inerne Compuing, 10(2), Ye, W., Heidemann, J., & Esrin, D. (2002). An energy-efficien mac proocol for wireless sensor neworks. In Infocom (pp ). 19. Zhong, L. C. (2004). A unified daa-link energy model for wireless sensor neworks. PhD hesis, Chair-Jan M. Rabaey. 20. Zimmerling, M., Dargie, W., & Reason, J. (2007). Energy-efficien rouing in linear wireless sensor neworks. In The fourh IEEE inernaional conference on mobile ad-hoc and sensor sysems. 21. Zimmerling, M., Dargie, W., & Reason, J. M. (2008). Localized power-aware rouing in linear wireless sensor neworks. In CASE- MANS 08: Proceedings of he 2nd ACM inernaional conference on conex-awareness for self-managing sysems (pp ). New York: ACM. Walenegus Dargie obained a Ph.D. in Compuer Engineering from he Technical Universiy of Dresden, Germany (2006), a M.Sc. degree in Elecrical Engineering from he Technical Universiy of Kaiserslauern, Germany (2002) and a B.Sc. in Elecrical and Elecronics Technology from he Nazareh Technical College, Ehiopia (1997). Prior o his curren posiion, he has been working as a researcher a he Universiy of Kassel, Germany ( ) and a he Fraunhofer Insiue of Experimenal Sofware Engineering, Germany ( ). His research ineress include digial signal processing, wireless and mobile neworks, wireless sensor neworks, and pervasive compuing. Presenly, Dr. Dargie servers as a Gues Edior o he Inernaional Journal of Auonomous and Adapive Communicaion Sysems (IJAACS) and o he Journal of Compuer and Sysem Science (JCSS). He is also a chair or co-chair of a number of IEEE and ACM workshops, including he CASEMANS 2009 (ACM) and PMECT 2009 (IEEE). Dr. Dargie is he member of IEEE. Xiaojuan Chao Xiaojuan Chao is a graduae of he Technical Universiy of Dresden, from which she obained a M.Sc. degree in Compuaional Engineering in Her research ineress include disribued sysems, web sofware archiecure, wireless communicaions and wireless sensor neworks. She is now focusing on Inerne echnologies, Projec Managemen and Archiecure. Chao has more han 9 years of experience in sofware design and sysem archiecure. Mieso K. Denko received his M.Sc. degree from he Universiy of Wales, UK, and his Ph.D. degree from he Universiy of Naal, Souh Africa, boh in Compuer Science. Currenly, he is wih he Deparmen of Compuing and Informaion Science, Universiy of Guelph, Guelph, Onario, Canada. His curren research ineress include wireless neworks, mobile and pervasive compuing, wireless mesh neworks, body sensor neworks and nework securiy. Dr. Denko is a founder/cofounder of a number of ongoing inernaional workshops and served as program chair/co-chair of a number of IEEE/ACM inernaional conferences. Currenly he is serving as gues co-edior of Special Issues for a number of journals including he ACM/Springer Mobile Neworks and Applicaions (MONET) and IEEE Sysems Journal. Dr. Denko has co-edied wo books in he areas of pervasive compuing and wireless neworking, and currenly coediing wo forhcoming books, auonomic compuing and neworking

13 Modelling he energy cos of a fully operaional wireless sensor nework wih Springer and Pervasive Compuing and Neworking wih Wiley. He is ediorial board member of inernaional journals including, he Inernaional Journal of Smar Homes (IJSH), he Journal of Ubiquious Compuing and Communicaions, (UBICC), and Associae Edior of he Inernaional Journal of Communicaion Sysems (IJCS), Wiley, Securiy & Communicaions Nework (SCN), Wiley and he Journal of Ambien Inelligence and Humanized Compuing, Springer. He is a senior member of he ACM and IEEE.