WIRELESS sensor networks are created by networks

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1 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 8, NO. 7, SEPTEMBER Hressig Bttery Reovery Effet i Wireless Sesor Networks: Experimets d Alysis Chi-Ki Chu, Member, IEEE, Fei Qi, Smir Syed, Muhmmd Husi Whb, Yg Yg, Seior Member, IEEE Abstrt My pplitios of wireless sesor etworks rely o btteries. But most btteries re ot simple eergy reservoirs, d exhibit bttery reovery effet. Tht is, the deliverble eergy i bttery be self-repleished, if left idlig for suffiiet time. As vible pproh for eergy optimistio, we mde severl otributios towrds hressig bttery reovery effet i sesor etworks. ) We empirilly exmie the gi of bttery rutime of sesor devies due to bttery reovery effet, d ffirm its sigifit beefit i sesor etworks. We lso observe sturtio threshold, beyod whih more idle time will otribute oly little to bttery reovery. ) Bsed o our experimets, we propose Mrkov hi model to pture bttery reovery osiderig sturtio threshold d rdom sesig tivities, by whih we study the effetiveess of duty ylig d bufferig. ) We devise simple distributed duty yle sheme to tke dvtge of bttery reovery usig pseudo-rdom sequees, d lyse its trde-off betwee the idued ltey of dt delivery d duty yle rtes. Idex Terms Wireless Sesor Networks, Eergy Optimistio, Bttery Reovery Effet, Duty Cyle. I. INTRODUCTION WIRELESS sesor etworks re reted by etworks of smll devies, itegrted with tiy embedded proessors, rdio trseivers, d MEMS miro-sesors. My pplitios of sesor etworks require btteries s eergy soure for the sesors. However, smll form ftors of devies ofte prohibit the uses of lrger pity btteries. Also, dho deploymet of sesor etworks d the ioveiee of bttery reolletio usully ostri frequet replemets of o-bord btteries. Hee, the desig of eergy-effiiet protools hs beome ruil topi i sesor etworkig. There re my studies o eergy optimiztio tht regrd btteries s idel eergy reservoirs, where eergy is dried t ostt dishrgig voltge, d be hlted d resumed ytime t the sme voltge. However, most ommeril btteries re govered by omplex itrisi hemil retios Musript reeived My 9; revised 6 Februry. C.-K. Chu ws supported by Crouher Foudtio fellowship. Y. Yg ws prtilly supported by CONET uder FP7 with otrt umber FP7-7-- d by the Ntiol Nturl Siee Foudtio of Chi (NSFC) uder the grt 69. C.-K. Chu is with Computer Lbortory, Uiversity of Cmbridge, UK (e-mil: hi-ki.hu@l.m..uk). F. Qi d S. Syed re with Eletroi & Eletril Egieerig Deprtmet, Uiversity College Lodo, UK (e-mil: {f.qi,s.syed}@ee.ul..uk). M. H. Whb is with the Computer Siee Deprtmet, Uiversity College Lodo (e-mil: h.whb@s.ul..uk). Y. Yg is with Shghi Reserh Ceter for Wireless Commuitios (WiCO), SIMIT, Chiese Ademy of Siees, Chi (e-mil: yg.yg@shrw.org). Digitl Objet Idetifier.9/JSAC //$. IEEE to produe eergy. Suh hemil retios re kow by hemil egieers to be depedet o vriety of evirometl ftors d opertiol prmeters (e.g., dishrge durtio, urret d history) [], []. Prtiulrly, there is subtle pheomeo lled bttery reovery effet, whih refers to the proess tht the tive hemil substes i bttery be self-repleished if left idlig for suffiiet period of time. I this pper, we re motivted to exploit bttery reovery effet to optimise the eergy effiiey of wireless sesor etworks. There re severl immedite questios. ) Is bttery reovery effet suffiietly sigifit to exted bttery rutime? ) If so, is there simple but effetive pproh to tke dvtge of bttery reovery effet i sesor etworks? ) Suh pproh my ievitbly ffet the performe of sesor etworks. The how will the idued performe (e.g., ltey of dt delivery) be ffeted? To ddress these questios, i this pper we first empirilly exmie the gi of bttery rutime due to bttery reovery effet, through test-bed experimets o ommeril sesors. Sie rdio trseivers osume sigifit portio of eergy (eve i listeig mode), s ompred to proessig d sesig tivities, we espeilly mesure the bttery rutime i the presee of duty yled rdio opertios uder both determiisti d rdomised shedules. We foud tht there is up to gi of %-% to the ormlised bttery rutime betwee duty yled d otiuous rdio opertios. We the empirilly study the hrteristis of bttery reovery effet, with respet to differet duty yle shedules. We observe tht there exists sturtio threshold, beyod whih more oseutive idle time will otribute oly little to bttery reovery. The rmifitio to sesor etworkig is tht if we refully djust the sleep time period of bttery before rehig the sturtio threshold, we mximise bttery reovery without exerbtig the ltey of dt delivery. Next, we model the proess of bttery reovery osiderig sturtio threshold d rdom sesig tivities. We study oe-hop sesor etworks by Mrkov hi model, d ivestigte the effetiveess of eergy optimistio by duty ylig d bufferig. We obti severl lytil isights for the bttery rutime, orroborted by simultio. We the exted our study to multi-hop sesor etworks, where eh sesor t s rely to forwrd the sesig dt for other sesors to the sik. I suh settig, there Normlised bttery rutime is the mesured bttery rutime multiplied by the duty yle rte.

2 CHAU et l.: HARNESSING BATTERY RECOVERY EFFECT IN WIRELESS SENSOR NETWORKS: EXPERIMENTS AND ANALYSIS requires oorditio sheme mog the duty yled sesors, suh tht eh sesor disover the pproprite timeslot to trsmit dt without wstig eergy to probe the vilbility of their relys. We dpt distributed rdomised oorditio sheme from [], d exted it to tke dvtge of bttery reovery. I our sheme, eh sesor ifers the rdom duty yle shedule of the rely bsed o pseudo-rdom sequee. The rdom duty yle shedule is set to let sesor to sleep for period of time withi the sturtio threshold, whe it hs bee tive for erti period of time. Through simultio, we show tht our bttery-wre duty yle sheme sigifitly exted the bttery rutime. Filly, sie there is ievitble trde-off betwee the ltey of dt delivery d the eergy effiiey i duty yled sesor etworks, to shed light o the performe uder ostried eergy budgets we lyse d boud the ltey of our bttery-wre duty yle sheme i multi-hop sesor etworks (d lso speifilly i lttie etworks). The lysis is bsed o the results i our previous work []. I summry, our otributios re threefold: ) I Se. III, we provide the experimetl evidee o the sigifit gi of bttery rutime by bttery reovery effet, d report tht the gi is hrterised by sturtio threshold. ) I Se. IV, we model bttery reovery d study eergy optimistio by duty ylig d bufferig, i the presee of sturtio threshold d rdom sesig tivities. ) We preset distributed duty yle sheme tht tkes dvtge of bttery reovery usig pseudo-rdom sequee i Se. V, d study the idued ltey of dt delivery i Se. VI. We lso preset the bkgroud d relted work i Se. II, d disuss some issues of our work i Se. VII. Beuse of spe ostrit, the proofs of theorems re deferred to []. II. BACKGROUND AND RELATED WORK A. Bttery Models There re my studies o the performe of btteries i hemil egieerig []. I etworkig, [6] rried out empiril study to mesure the performe of btterypowered sesors, but did ot exmie the sturtio threshold. Although bttery osumptio hs bee modelled extesively i etworkig, my extt models over-simplified the relisti bttery hrteristis (e.g., llowig ulimited bttery reovery). There re two mi models tht osider relisti bttery hrteristis. First, the kieti bttery models [7], [8] ttempt to model the detiled hemil retios d diffusio proess betwee the eletrode d eletrolyte i bttery through set of prtil differetil equtios. These models im to fully pture the o-lier dymis i bttery. However, these models re less trtble, d differet form ftors of btteries sigifitly ffet the ury of the models. Seod, there re stohsti bttery models [9] [] tht pture the bttery dymis usig rdomised Mrkovi models. But most of them did ot osider the effet of idle time period. While [] osiders idle time period i embedded systems, it did ot ddress the performe i sesor etworks. We remrk tht while ll these stohsti bttery models ttempt to imitte the kieti bttery model with less omplexity, the uses of rdomised bttery reovery is differet from the determiisti kieti bttery models. Moreover, these models re lso less trtble, with few lytil isights provided. I this pper, we preset more lysble Mrkov hi model tht simplifies the stohsti bttery models [9], [], []. Prtiulrly, our model uses determiisti bttery reovery, yet is ble to pture relisti bttery hrteristis, suh s limited bttery reovery d the effet of idle time period. More importtly, severl lytil isights for relisti bttery behviour be derived from our model. B. Eergy Mgemet d Optimistio There re my studies o eergy optimiztio i sesor etworks, iludig topology mgemet d etwork lyer optimistio. Prtiulrly relevt to our work re those bsed o MAC lyer, whih im to redue redudt rdio opertios i MAC protools: ) idle listeig (keepig rdio o eve whe o reeptio), ) overherig (reeptio of messge ot iteded for the reeiver), d ) protool overhed (redudt heders or sigllig messges). Exmples ilude S- MAC, SEEDEX, O-MAC, RI-MAC [] [6]. Listeig d reeptio osume sigifit eergy i wireless sesors. This pper redues idle listeig d overherig by duty yle bsed o pseudo-rdom sequee [] d bttery reovery effet. There re other MAC protools tht osider bttery hrteristis. BAMAC d Bel-MAC [7], [8] relied o exhgig dymi bttery stte iformtio to optimise the use of btteries mog sesors. But suh iformtio ot be obtied without relyig o olie mesuremet of bttery. However, our ide of exploitig sturtio threshold does ot rely o olie mesuremet. Also, [9] osidered bttery reovery i shedulig d routig, but did ot iorporte the iformtio of sturtio threshold, ulike our distributed oorditio sheme mog the duty yled sesors. III. EXPERIMENTAL RESULTS I this setio, we preset the experimetl results from our sesor etwork test-bed to show the sigifie of bttery reovery effet. These experimets were rried out o two types of ommeril sesors from Crossbow: TelosB d Imote. Both re populr models for wireless sesor etworkig. TelosB is osisted of MSP s MCU d CC s rdio trseiver. Imote is osisted of PXA7 s CPU d CC s rdio trseiver. TelosB llows more eergy-svig settigs with low eergy osumptio, wheres Imote is equipped with more omputtio bility with high eergy osumptio. Here, we mily study TelosB. I the experimets, we used logue-digitl oversio (ADC) iterfe rd d softwre LbVIEW to mesure d reord the dishrge profiles of ommuitig sesors. Eh sesor ws powered by stdrd AAA NiMH 6 mah btteries (TelosB hs two d Imote hs three). Whe the supply voltge of the bttery is lower th erti threshold (lled stop voltge), the devie o loger operte, whih

3 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 8, NO. 7, SEPTEMBER Voltge V Ative:s,Sleep:s Ative:s,Sleep:s Ative:s,Sleep:s Ative:s,Sleep:8s Ative:s,Sleep:6s Ative:s,Sleep:s. Ative:s,Sleep:s Alwys Ative Normlised Bttery Rutime mi. 6 8 Fig.. The dishrge profiles of TelosB i determiisti duty yle shedules of rdio trseiver w.r.t. differet sleep time periods. Gi Sleep Time Period s 6 8 Fig.. The gi of ormlised bttery rutime of Fig., s ompred to the otiuous (lwys tive) rdio opertio. Voltge V.6.. Ative:9s,Sleep:s. Ative:6s,Sleep:s Ative:s,Sleep:s. Ative:s,Sleep:s Ative:7s,Sleep:s. Ative:6s,Sleep:s. Ative:s,Sleep:s Ative:s,Sleep:s. Ative:s,Sleep:s Alwys Ative Normlised Bttery Rutime mi. Fig.. The dishrge profiles of TelosB i determiisti duty yle shedules of rdio trseiver w.r.t. differet tive time periods. Voltge (V). Gi Ative Time Period s Fig.. The gi of ormlised bttery rutime of Fig., s ompred to the otiuous (lwys tive) rdio opertio. Gi (%).. Ative:mi,Sleep:.67mi Ative:mi,Sleep:.mi Alwys Ative. Normlised Bttery Rutime. Fig.. The dishrge profiles of Imote i determiisti duty yle shedules of rdio trseiver w.r.t. differet sleep time periods. Sleep Time Period (mi) Fig. 6. The gi of ormlised bttery rutime of Fig., s ompred to the otiuous (lwys tive) rdio opertio. is osidered s ompletely dishrged. We set differet duty yle rte o the sesors by puttig the rdio trseiver i tive d sleep modes periodilly, d mesure the idued bttery rutime. The duty yle rte is defied s the frtio of tive time periods, d the ormlised bttery rutime is the mesured bttery rutime multiplied by the duty yle rte. First, we tested o determiisti duty yle shedules. Figs. d show the dishrge profiles of the trsmitter i ormlised bttery rutime for TelosB d Fig. for Imote. Figs.,, show the respetive gi of ormlised bttery rutime, ompred to the otiuous rdio opertio. The key observtios from the experimets re: ) There re ler sigs of bttery reovery effet. With the sme tive time period, loger sleep time period Note tht beuse TelosB hs muh loger bttery rutime, we used lower smplig rte to filitte dt loggig, whih gives ppretly smooth profile urve. However, the dishrge profiles should be s rgged s the oes of Imote i Fig..

4 CHAU et l.: HARNESSING BATTERY RECOVERY EFFECT IN WIRELESS SENSOR NETWORKS: EXPERIMENTS AND ANALYSIS Curret A. Fig. 7. We use the sme pseudo-rdom sequee to geerte the rdom duty yle shedules for both trsmitter d reeiver. This is spshot of the urret profile of pir of trsmitter-reeiver. The higher urret idites the periods of higher eergy osumptio i tive slots. idues loger ormlised bttery rutime, d hee lrger deliverble eergy of bttery. ) The effet of sleep time period is o-lier. It ppers tht sleep time period more th erti threshold will otribute muh less to bttery reovery, whih we ll sturtio threshold. ) The effet of tive time period is lso o-lier. Very smll tive time period ppers to hve lrge gi of ormlised bttery rutime (up to % i TelosB for tive/sleep time s se/ se). ) Eve the sesor is i sleep mode o rdio trseiver, there is still eergy osumptio due to the timer d other proessig tivities. TelosB osumes 6.μA i sleep mode, wheres Imote osumes.8ma. We observe tht bttery reovery tke ple uder low bttery osumptio, d the impt of bkgroud osumptio is ot substtil to bttery reovery. Next, we study the gi of rdomised duty yle shedules. We used the sme pseudo-rdom sequee to geerte the rdom duty yle shedules for both trsmitter d reeiver (see Fig. 7 for spshot). Fig. 8 shows two dishrge profiles of trsmitter d reeiver both with the sme duty yle rte s. (oe sets eh rdom slot s. se, other s se). We observe tht the gis of ormlised bttery rutime betwee the -se d.-se ses re 7% d % for trsmitter d reeiver respetively. Note tht the ormlised bttery rutime of -se rdom slots is omprble to the determiisti duty yle shedule (tive d sleep time period s se) i Fig., while the oe of.-se rdom slots is omprble to the lwys tive shedule. The implitios re ) the gi of bttery rutime is determied by how the tive d sleep time periods lst, rther by the duty yle rte loe, d ) the rdomised duty yle shedules hve omprble gi s the determiisti duty yle shedules. Note tht the tul bttery rutime is muh loger th the ormlised bttery rutime (whih is multiplied by the duty yle rte). Hee, duty yle shedules ot oly prolog the etwork lifetime by spedig time i sleep mode, but lso irese the deliverble eergy by llowig bttery reovery. Although our mesuremet of the gis of bttery reovery my differ i other evirometl settigs (e.g., differet temperture), the isights reveled by our experimets will still be useful to the modellig d optimistio of bttery reovery i sesor etworks. I geerl, uder pulsed (duty yle) dishrge profile, bttery is ble to reover hrge durig idle time periods, whih effetively ireses the deliverble eergy of the bttery. But the effetiveess of bttery reovery is ritilly determied by the tive d sleep time periods. The presee of sturtio threshold ppers uiversl i differet duty yle shedules. We evisio tht oe Voltge V.6... Trsmitter: se Rdom Slots. Reeiver: se Rdom Slots. Trsmitter:.se Rdom Slots. Reeiver:.se Rdom Slots. Normlised Bttery Rutime mi. 6 8 Fig. 8. Two dishrge profiles pir of trsmitter-reeiver of TelosB i pseudo-rdom duty yle shedules of rdio trseiver (duty yle rte s.): oe sets eh rdom slot s. se, while other sets eh rdom slot s se. evlute the sturtio threshold (i some itervls) for erti eviromets i -priori mer through experimets. Next, we desig etwork protools tht exploit bttery reovery by tkig the estimted sturtio threshold s prmeter. IV. MODEL OF BATTERY RECOVERY Our experimets orroborted the presee of bttery reovery effet d sturtio threshold. It is useful to employ simple model to pture these essetil hrteristis qulittively, whih ebles further lysis d lrger sle simultio o vrious bttery osumptio ptters. Hee, we re motivted to preset simplified Mrkov hi model, where time is disretised s slots, to pture the bttery osumptio by trsmittig rdom sesig dt. I this model, we ssume tht the sesig dt rrivig to sesor i the previous slots, will be trsmitted i the urret slot. The stte of bttery is hrterised by tuple,, t, where,, t re o-egtive itegers. is the theoretil pity determied by the mout of hemils i the eletrode d eletrolyte, is the omil pity determied by the mout of vilble tive hemils for hemil retios i the bttery, d t is the umber of idle slots sie lst dishrgig. The use of, follows populr bttery model desribed i [9], []. But we itrodue t i this pper, s relted to the sturtio threshold. I the dishrgig proess, both d re deresig. The mout of vilble tive hemils ostris the eergy of bttery deliver, despite the presee of uused hemils i the bttery. Thus, we require. But whe the bttery stops dishrgig, there is reovery proess, s diffusio proess betwee eletrode d eletrolyte to repleish vilble tive hemils, whih effetively ireses (whih however ot irese theoretil pity ). There is sturtio threshold t st for t, suh tht more oseutive idle slots t > t st will ot otribute more reovery. Here, we ormlise the uit of d, suh tht t eh idle slot, be reovered by oly oe uit. I this setio, we study this bttery model i oe-hop sesor etwork, where the multi-hop study will deferred to the ext setio. Eh sesor is lef ode, whose tsk to trsmit its deteted sesig dt to the sik. We ssume the sik is

5 6 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 8, NO. 7, SEPTEMBER lwys tive, but the sesor my follow duty yle shedule o its rdio opertios. Ad the sesor is simple trsmitter, requirig o feedbk from the sik. For geerlity, we ssume tht sesig dt rrivl proess follows Poisso distributio. The osumptio of bttery is proportiol to the mout of sesig dt for trsmissio to the sik i slot. Next, we study two serios: ) the lwys-tive se where the dt is trsmitted i the followig slot, d ) the duty ylig se where the dt is buffered for erti period before trsmissio. A. Alwys-tive Cse without Duty Cylig We model the serio without duty yle s Mrkov hi M bt with the set of sttes s: { },, t :,, t re o-egtive itegers, d,,t is bsorptio stte tht will ot trsit to other sttes, orrespodig to omplete dishrged bttery. Due to Poisso rrivl of dt, the trsitio probbilities from sttes of re obtied s: ) Dishrgig:,, t -k, -k, for k d -k, d the trsitio probbility is p λ po(k) λk e -λ k!,whereλis the verge Poisso rrivl rte of dt i slot. b) Completely Dishrged: b,, t,-, d the trsitio probbility is p λ po (k) = k= k= λ k e -λ k!. Tht is, whe osumptio exeeds omil pity, the bttery will be ompletely dishrged. ) Idlig with Reoverig:,, t +,,t+ for + d t < t st, d the trsitio probbility is p λ po () = e-λ. Tht is, there is reovery whe there is o bttery osumptio, d the oseutive idle durtio is lesser th the sturtio threshold t st. d) Idlig without Reoverig:,, t d,, t+ for <+ or t t st, d the trsitio probbility is p λ po () = e-λ. Tht is, there is o reovery whe the omil pity rehes the theoretil pity, or the oseutive idle durtio rehes the sturtio threshold t st. e) Otherwise, the trsitio probbility for ll other pirs of sttes is. I Figs. 9-, we illustrte the stte trsitios i grphil mer, with t st =. We remrk tht there re severl simplifitios i this model. First, we ssume the sturtio threshold t st is idepedet of d. Seod, the reovery proess is the sme for y stte below the sturtio threshold. While these ssumptios ot reflet the omplete o-lier dymis i rel btteries, we ited to pture the essee of geeri bttery behviour. With the miimum umber of prmeters (oly t st ), our model does ot rely o experimets to determie further prmeters s i more omplete model tht otherwise ritilly deped o the types of btteries d other evirometl ftors. Moreover, our model ebles us to obti simple lytil isights for hressig bttery reovery. Let W t m() be the expeted bttery rutime strtig t stte, +m, t i Mrkov hi M bt (i.e., the expeted umber of slots bttery lst util rehig bsorptio stte of ompletely dishrged). By the defiitio of stte trsitios i M bt d the lierity of expeted vlues, it follows tht - W () =+ p λ po (k)w (-k), Wt () =W () () k= Tht is, if the osumptio is of k uits d k, the the expeted bttery rutime will be W (-k)+.otherwise, it will be ompletely dishrged d the expeted bttery rutime is. For m, Eq. () follows. Eqs. ()-() give reursive reltioship of W t m (). But i geerl, Wt m () ppers to hve o simple losed-form solutio. However, severl geerl lytil results be derived s follows. Theorem : The expeted bttery rutime is bouded by: W t m () +m- W m () λ + e -λ This upper boud is ituitive, beuse the bttery rutime should ot exeed Θ(+m) =Θ(). Ideed, the upper boud is tight s show s follows. Theorem : Whe λ is smll or is lrge, for some ostts α, W +m m () λ + α We verified Theorems - for some speifi d m i Fig., where m =. We observe tht the upper boud is ideed tight whe λ is smll or is lrge. Theorem be regrded s pity of bttery rutime. We re iterested i the gp betwee the tul bttery rutime W m() d the pity of bttery rutime. Prtiulrly, we hrterise W m() whe m is lrge. Theorem : Cosiderig t st =, W m () lim m W m () = e λ e λ + e λ λ Theorem shows tht W m() = O() for fixed λ. However, Theorem shows tht the upper boud be O(m+). Therefore, there is gp with order s O(m+). This suggests tht there is lrge potetil for exploitig the udelivered eergy of bttery. Hee, we re motivted to mke use of duty ylig d bufferig to improve eergy effiiey by hressig bttery reovery. Other models (e.g., [9], [], []) ttempt to iorporte more prmeters, suh s omplex rdomised stte trsitios to pture o-lier bttery reovery behviour. However, these models pper ioveiet for lysis, d little lytil isights hve bee obtied.

6 CHAU et l.: HARNESSING BATTERY RECOVERY EFFECT IN WIRELESS SENSOR NETWORKS: EXPERIMENTS AND ANALYSIS 7 +p λ - W t m () = po ()Wt+ m- (+) + p λ po (k)w m (-k) if t < t st k= +p λ - po ()Wtst ()+ p λ po (k)w m (-k) if t = t st m k= () b t= d b t= b t= t= b d W () W () W () W () Fig. 9. Stte trsitios for Mrkov hi M bt t t =. Fig.. Stte trsitios for t =,whet st = B. Duty Cylig Cse with Bufferig I this setio, we lyse the effetiveess of duty ylig d bufferig o the bttery model. We osider simple strtegy tht the sesor will sleep for b buf slots, every time fter the bttery is osumed for trsmissios. Durig the sleep time periods, the sesig uit is still o, d the dt is olleted for bufferig withi the b buf slots. To tke the mximl dvtge of bttery reovery, we set b buf t st. To pture the bove buffered opertios, we defie Mrkov hi M buf, where eh stte is tuple,, b, db mes tht the bttery hs bee i buffered stte for b slots. If b +> b buf, the the buffer will ot hold y dt d proeed to immedite trsmissios. Thus, the set of sttes is: { },, b :,, b re o-egtive itegers, d We ext lyse the expeted bttery rutime of M buf i similr mer s M bt. However, the strightforwrd defiitios of stte trsitios of M buf pper rther itrtble (eve umerilly). For the ese of lysis, i the followig we defie the stte trsitios of M buf i simplified mer, suh tht the bttery osumptio is reorded durig the bufferig slots before tul trsmissios, d hee, the bttery rutime of M buf is smller th the tul bttery rutime. This still serves s lower boud for the tul bttery rutime, d does ot ffet the isights tht we obti. Now the trsitio probbilities of M buf re defied s: ) Dishrgig:,, -k, -k, for k d -k, d the trsitio probbility is p λ po (k) = λk e -λ k!. b ) Completely Dishrged:,, b b,-, d the trsitio probbility is p λ po(k) = k= k= λ k e -λ k!. ) Idlig: { +,, if + (reovery),,,, if <+ (o reovery) d the trsitio probbility is p λ po () = e-λ. d ) Bufferig: { -k+,-k, b,, b + if + (reovery) d -k, -k, b + if <+ (o reovery) for b b buf d -k, d the trsitio probbility is p λ po (k) = λk e -λ k!.wedefie b + b+(mod b buf +) (i.e., the umber of bufferig slots ireses by, util rehig b buf, d the proeed to trsmissios by settig b =). e ) Otherwise, the trsitio probbility for ll other pirs of sttes is. Note tht trsitio d ) is defied to pture bttery osumptio i the bufferig slots before tul trsmissios. I Figs. -, we illustrte the stte trsitios i grphil mer, with b buf =. Similrly, let B b m() be the expeted bttery rutime strtig t stte, +m, b i M buf. We obti: B b () =W () () For m, see Eq. (). Theorem : If b buf = t st, bufferig is lwys better: B b m() W t m() for y b b buf d t t st. Theorem ffirms the usefuless of duty ylig d bufferig. For more qutittive mesure, i Fig., we umerilly solve the solutios of Eqs. ()-() for speifi m d. We observe tht there is sigifit improvemet of the bttery rutime. We exmie the gi of usig duty ylig d bufferig i Fig., where we idetify the speifi s i Fig. tht mximise the differee betwee W () d B () for differet vlues of λ, b buf, t st. We observe tht the mximum gi is up to %. The effetiveess dereses s b buf d t st irese, beuse the lrger sturtio threshold implies more the likely bttery reovery is, d duty ylig d bufferig will ot improve too muh.

7 8 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 8, NO. 7, SEPTEMBER + - p λ B b m () = po (k)bb+ m- (-k+) if b buf b > k= +p λ - () po ()B m- (+) + p λ po (k)b m (-k) if b = k= b= b= b= b= b d d d B () B () B () b B () Fig.. Stte trsitios for Mrkov hi M buf t b =. Fig.. Stte trsitios for b =,wheb buf =. Bttery Rutime slots Upper Boud Duty Cylig Alwys Ative Λ. Mx Gi (%) t st = b buf = t st = b buf = t st = b buf = Λ. Λ.7 Λ. Bttery Rutime slots Upper Boud Duty Cylig Alwys Ative Λ.6 Λ.7 Λ.87 Λ 6 8 Fig.. Whe b buf = t st =, we plot of the upper boud +m- + λ, log with the bttery rutime of lwys-tive se e-λ W (), dthe duty ylig se B (). V. MULTI-HOP SENSOR NETWORKS I multi-hop sesor etworks, sesor ot oly trsmits, but lso listes d reeives from its eighbours. Sie listeig still osumes osiderble eergy, we re motivted to use duty yle to regulte rdio, suh tht i sleep mode the rdio is off, while i tive mode the rdio is o for ll opertios. As i Se. IV, this redue ueessry idle listeig d hress bttery reovery λ Fig.. The mximum gi of the duty ylig se is show gist the lwys-tive se over ll. We obti smooth urves usig movig verge. However, this lso retes problem of requirig oorditio sheme mog the duty yled sesors, suh tht eh sesor disover if its eighbour is tive. A simple sheme is to employ globl oorditor tht ssigs periodi/determiisti duty yle shedule to eh sesor i - priori mer suh tht ll sesors re provided the kowledge of duty yle shedules of their eighbours. However, this sheme suffers from serious slbility issue, d ot ope with the rpid hgig etwork topology due to d ho sesor deploymets. Oe my lso osider otetio-bsed pprohes, suh tht ll sesors re tive time periodilly t the sme time d oted for trsmissio opportuities (e.g., S-MAC). However, this iurs sigifit ollisios d overherig, osumig osiderble eergy. Aother pproh is to tur rdio off d o t eh slot idepedetly d rdomly. The, pkets oly be forwrded whe the trsmittig d reeivig sesors re both tive. This requires o globl oorditor, d is self-ofigurig, with redued ollisios d overherig. But rdom duty yle lso suffers from otrol problem sesor eeds to probe the vilbility of its eighbours. Here, we dpt distributed rdomised pproh from [], by whih eh sesor ifers the rdom duty yle shedule of

8 CHAU et l.: HARNESSING BATTERY RECOVERY EFFECT IN WIRELESS SENSOR NETWORKS: EXPERIMENTS AND ANALYSIS 9 the eighbours bsed o pseudo-rdom sequee. If the trsmitter kows the seed d yle positio of the pseudo-rdom sequee geertor used by the reeiver to geerte the rdom duty yle shedule, it determiistilly predit the tive shedules of the reeiver without probig. Pseudordom sequee hs bee used i other MAC protools (e.g., SEEDEX, O-MAC [], []) for reduig MAC overhed d overherig. Next, we modify pseudo-rdom duty yle to exploit the sturtio threshold of bttery reovery. A. Pseudo-Rdom Duty Cyle Sheme As i Se. IV, we ssume tht whe sesor swithes to sleep mode, oly the rdio trseiver is off, keepig the proessig d sesig uits o for sesig tivities. Hee, it will ot udermie the sesig futiolity of the sesor etwork. All sesors will buffer ll their outgoig dt util the slot whe their respetive reeivers re tive. There is uique sik i the etwork to ollet ll the dt. The pseudo-rdom duty yle sheme is s follows: ) At bootstrppig, the sesors exhge the seed, yle positio d duty yle rte (s the probbility threshold of slot if it is tive or sleep) of their pseudo-rdom sequee geertors with eighbours. At eh slot, sesor determies its stte (beig tive or sleep), d the sttes of ll its eighbours i the ext slot. ) To forwrd pkets, sesor will wit util there is tive eighbour o its shortest pth to the sik, d the trsmit the pkets with orrespodig reeiver ID i the heder. Uiform rdom tie-brekig is used if there re more th oe tive eighbour. The reeiver of the orrespodig ID will rry out the forwrdig of the pkets util rehig the sik. The dvtges of usig pseudo-rdom sequee re tht ) the tive shedules re essetilly uorrelted d rdom mog the sesors, reduig MAC ollisios d overherig; ) sesor dymilly djust its duty yle rte by hgig the probbility threshold of pseudo-rdom sequee geertor, d ) the tive shedules be omptly distributed i the etworks, represeted by the tuple of the seed, yle positio d duty yle rte. Like other syhroised MAC protools (e.g., S-MAC), pseudo-rdom duty yle requires syhroistio, whih will be ddressed i Se. VII. Ad we ssume the rrivl pket rte is ot high, d the ollisio of simulteous trsmitters is egligible. B. Bttery Reovery Awreess To exted the pseudo-rdom duty yle sheme to tke dvtge of bttery reovery, we propose simple sheme by fored sleep. Suppose tht sesor hs bee tive for more th w mx oseutive slots from the urret slot, the it must go to sleep for the ext b buf slots for some b buf t st. This llows suffiiet bttery reovery to improve the Note tht whe eve the sesor s ow pseudo-rdom duty yle shedule presribes the slot is to sleep, it will still be tive to trsmit dt to the tive eighbour. Eve the pket rte is moderte, idepedet rdom duty yle o sesors lredy ut dow the umber of potetil ollisios. Also, oe use stdrd MAC protool withi slot to solve the problem of ollisio. deliverble eergy of bttery. After b buf slots, the sesor deides its tive shedule ordig to its pseudo-rdom sequee geertor. We suppose tht w mx d b buf re kow to ll sesors. Eh sesor still predit its eighbours bttery-wre duty yle sheme ordigly. A typil settig will be w mx =d b buf = t st. C. Evlutios We defie the etwork lifetime s the expeted time tht there is relyig sesor ruig out of its bttery. Prtiulrly, we evlute the etwork lifetime i D lttie etwork, where we idex eh sesor s (i, j) by itegers i, j. There is lik betwee odes (i, j) d (i,j ),if( i-i =d j = j )or( j-j =d i = i ). Without loss of geerlity, we deote (, ) s the sik. We suppose tht eh sesor employs greedy forwrdig (i.e., forwrdig pkets to the eighbour tht is o the shortest pths to the sik d is tive i the ext erliest slot) d rdom tie-brekig whe there re more oe eligible eighbour. We ssume tht the duty yle rtes of ll sesors re the sme. I lttie etwork, the routig lgorithm proeeds s follows: ) For i, sesor(i, ) will forwrd to (i-, ), sthere is oly oe shortest pth. ) For i, j, (i, j) will rdomly forwrd to (i-,j) or (i, j-) with equl probbility. We employ the sme disrete bttery model s Se IV for eh sesor. We ssume tht trsmissio osumes the sme eergy s reeptio, d the sesig evets of ll sesors follow the idepedet Poisso distributio p λ po (k). We defer the study of orrelted sesig evets to the future work. I multi-hop sesor etwork, the Mrkov hi is diffiult to lyse. Hee, we rely o simultio to study the etwork lifetime. By simultio, we ompre the etwork lifetime of bttery-wre, pseudo-rdom duty yle shemes d simple lwys-tive se. To demostrte the effetiveess, we selet some typil prmeters, suh s the duty yle rte s., m = d =. Fig. show tht the gi of pseudo-rdom duty yle sheme is up to %, while the gi of bttery-wre duty yle sheme is up to %. Ad the etwork lifetime of bttery-wre duty yle sheme is geerlly loger th the oe of pseudo-rdom duty yle sheme. VI. LATENCY ANALYSIS Iresig the sleep time period of sesor to mximise bttery reovery will ievitbly irese the ltey of deliverig pket to the sik. I this setio, we provide lytil results for the ltey of dt delivery i sesor etworks with both bttery-wre d pseudo-rdom duty yle. Suppose ode i is witig to forwrd dt, whih hs set of eighbours N i d degree s d i = N i. Eh of these eighbours is performig pseudo-rdom duty yle with probbility ρ d, suh tht i oe time slot, eh ode is tive with i.i.d. probbility ρ d, d is sleep with probbility -ρ d. Let L (i) be the rdom umber of slots for i before eighbour beomes tive. Therefore,

9 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 8, NO. 7, SEPTEMBER Network Lifetime slots Λ 8 Bttery wre Duty Cylig Pseudo rdom Duty Cylig Alwys Ative Mx Gi 8 6 Λ 6 Λ Λ 8 Bttery wre DC vs. Alwys Ative Pseudo rdom DC vs. Alwys Ative Network Size Λ Fig.. I lttie with b buf = t st =, we obtied through simultio the etwork lifetime of bttery-wre duty yle sheme, pseudo-rdom duty yle sheme d simple lwys-tive se. We set the duty yle rte s., m =, =, w mx =. L (i) = mi{l,l,...,l di }, where L j is the rdom witig time for eighbour j N i to beome tive. Theorem : E[L (i) ]= ( ρ d ) di Note tht the expeted per-hop ltey dereses quikly with iresig ode degree d i. For very low duty yle rte (i.e., very smll vlue ρ d ), we obti pproximtio s: E[L (i) ] ( ρ d d i ) = ρ d d i Theorem 6: For D lttie, let l(i, j) be the ed-to-ed ltey from (i, j) to (, ). () E[l(i, )] = + i- d E[l(,j)] = + j- ρ d ρ d () For i, j, E[l(i, j)] + i+j- ρ d I bttery-wre duty yle sheme, sesor tht hs bee tive for more th w mx oseutive slots from the urret slot will go to sleep for the ext b buf slots. Theorem 7: I bttery-wre pseudo-rdom duty yle with fored sleep, E[L j ] b buf + d E[L (i) ] b buf + ρ d ( ρ d ) di For D lttie, let l(i, j) be the expeted ed-to-ed ltey from (i, j) to (, ). () E[l(i, )] +(i-) ( ) b buf + ρ d d E[l(,j)] +(j-) ( ) b buf + ρ d () For i, j, E[l(i, j)] +(i+j-) ( b buf + ρ d ) We ext preset good pproximtio of E[L (i) ].Whe w mx =, we pproximte E[L j ] b buf + ρ d,next, we osider Mrkov hi of the stte of eighbour j. Let p t j be the probbility tht t y slot j is tive. Sie it is -stte Mrkov hi, by stdrd Mrkov hi theory o the reurret times, p t j = E[L j]. Sie the pseudordom duty yle of ll eighbours re idepedet, we b buf + ρ d obti the followig pproximtio i similr s Theorem : E[L (i) ] ( ) di b buf + ρ d I Fig. 6, we observe tht the pproximtio is ideed urte s ompred to simultio. The bove theorems eble sesor etwork desigers useful tool to ble d optimise the trde-off betwee improvig bttery rutime d the iurred ltey of dt delivery. Here we disuss useful pplitio of our theorem. Suppose tht we desig sesor etwork with ltey ostrit. We let the mximum tolerble ltey s E[L (i) ] d E[l(i, j)], d obti the miimum b buf from Theorem 7. Suh b buf be used to ifer the bttery rutime from experimetl dt. VII. DISCUSSION A. Sigifie of Bttery Reovery Eergy effiiey be improved from both the supply side d the demd side. Improvemets from the supply side ilude ew bttery mterils d tehologies. However, the developmet of ew prtil btteries i reet yers hs bee slow. Although fuel ells my brig lrge lep i eergy supply, we rgue tht they re ot vilble i physil formt tht re pproprite for eoomil sesor etworks tht re required to deploy i lrge sle d outdoors i log utteded periods. Aother oeptul ltertive be eergy hrvestig (e.g., solr ells). But the vilbility of eergy soure will sigifitly ostri the pplitios of sesor etworks. Whtever eergy soure is used, effiiet eergy mgemet from the demd side is lwys desirble. I this work, we hve reetly exmied by experimets the beefit of hressig bttery reovery effet, d foud sigifit extesio of bttery rutime (up to % ormlised gi) by tkig dvtge of the itrisi bttery hrteristis. B. Applitios I this pper, we foud tht pproprite (determiisti d rdomised) duty yle shedules irese the deliverble eergy of bttery without jeoprdisig ltey of dt delivery. This is prtiulrly useful to sesor etwork pplitios with eergy d ltey ostrits, suh s seurity d emergee surveille. I these pplitios, duty yle shedules my be used to prolog the etwork

10 CHAU et l.: HARNESSING BATTERY RECOVERY EFFECT IN WIRELESS SENSOR NETWORKS: EXPERIMENTS AND ANALYSIS Ltey E[L (i) ]... Simultio - ( ) - b buf + / Ρ d d i Ltey E [L (i) ]... Simultio d -( i - b buf - / Ρ d ).8.6. w mx =,Ρ d =. w mx =,Ρ d =. w mx =,Ρ d =.. w mx =,Ρ = d.6 w mx =,Ρ d =.9. b buf.. w mx =,b buf = w mx =,b buf =. w mx =,b buf = w mx =,b buf = w mx =,b buf = Ρ d Fig. 6. The figure shows the per-hop ltey E[L (i) ] with d i =d w mx =. The oloured dots re obtied from simultio, while the solid lies re by equtio. di b buf + ρ d lifetime. However, s show by our experimets, duty yle rte is ot the oly ftor to determie the effetiveess of bttery reovery effet. Eve with the sme duty yle rte, some sleep/tive time periods hve sigifit gi by the bttery reovery effet. If we refully set the sleep time periods withi the sturtio threshold, we mximise bttery reovery without exerbtig the ltey of dt delivery. Other pplitios tht tolerte ltey (e.g., moitorig dily temperture) usully hve very log sleep time period, where bttery reovery is fully utilised. C. Syhroistio Protools Like other syhroised eergy optimisig protools (e.g., S-MAC []), we ssume tht the sesors syhroise their lok with eighbours usig populr low-overhed time syhroistio protool (e.g., FTSP []) i spordi itervls. The eed for time syhroistio is due to the possible lok drift o the sesors tht use errors i the duty yle shedules. Smll d low-ed sesors my suffer from iosistet loks beuse of severl ftors (temperture, hrdwre jitter, istbility of the lok rystl). However, we rgue tht tive/sleep time periods re muh loger th the lok drift (withi μs per seod s mesured i []). It does ot require frequet time syhroistio. Moreover, reltively urte time syhroistio is oly required for per-hop bsis. Our duty yle does ot require etwork-wide time syhroistio tht omes with high omplexity. VIII. CONCLUSION This pper exmies the gi of bttery reovery effet d provides lytil results to shed light o hressig the bttery reovery i sesor etworks. I prtiulr, we lyse bttery reovery i the presee of sturtio threshold d rdom sesig tivities, bsed o our experimets. We derive upper bouds of bttery rutime d study the beefit of duty ylig d bufferig. We the propose more eergy-effiiet duty yle sheme tht is wre of bttery reovery, by extedig the pseudo-rdom duty yle sheme. We provide lytil results tht predit the ltey of dt delivery i sesor etworks whe osiderig bttery reovery optimistio. I future work, we im to study broder sope of optimisig bttery reovery effet i ojutio with vriety of qulities of servie observed i sesor etworks, suh s overge, oetivity, relibility. We will lso osider the impt of iterferee i wireless ommuitios o bttery reovery effet, d orrelted sesig tivities. ACKNOWLEDGMENT The uthors thk Yusheg Wg d Xi Yi for helps i the experimets, d the reviewers for helpful ommets. REFERENCES [] D. Lide, Hdbook of Btteries d Fuel Cells. MGrw-Hill, 99. [] I. Buhm, Btteries i Portble World: A Hdbook o Rehrgeble Btteries for No-Egieers. Cdex Eletrois I,. [] J. Redi, S. Kolek, K. Mig, C. Prtridge, R. Rosles-Hi, R. Rmth, d I. Cstieyr, Jvele: A ultr-low eergy d ho wireless etwork, Ad Ho Networks Jourl, vol., o. 8, 8. [] P. Bsu d C.-K. Chu, Opportuisti forwrdig i wireless etworks with duty ylig, i Pro. ACM Workshop o Chlleged Networks (CHANTS), September 8. [] C.-K. Chu, F. Qi, S. Syed, M. H. Whb, d Y. Yg, Hressig bttery reovery effet i wireless sesor etworks: Experimets d lysis, Uiversity of Cmbridge, Teh. Rep., 9. [6] C. Prk, K. Lhiri, d A. Rghuth, Bttery dishrge hrteristis of wireless sesor odes: A experimetl lysis, i Pro. IEEE Seo,, pp.. [7] M. Doyle d J. S. Newm, Alysis of pity-rte dt for lithium btteries usig simplified models of the dishrge proess, J. Applied Eletrohem, vol. 7, pp , July 997. [8] T. F. Fuller, M. Doyle, d J. S. Newm, Modelig of glvostti hrge d dishrge of the lithium polymer isertio ell, J. Applied Eletrohem, vol., pp. 6, 99. [9] C. F. Chisserii d R. R. Ro, Improvig bttery performe by usig trffi shpig tehiques, IEEE J. Sel. Ares i Commu., vol. 9, pp. 8 9, July. [], Eergy effiiet bttery mgemet, IEEE J. Sel. Ares i Commu., vol. 9, pp., July. [] S. Srkr d M. Admou, A frmework for optiml bttery mgemet for wireless odes, IEEE J. Sel. Ares i Commu., vol., o.,. [] V. Ro, G. Sighl, A. Kumr, d N. Nvet, Bttery model for embedded systems, i Pro. Itl. Cof. o VLSI Desig,. [] W. Ye, J. Heidem, d D. Estri, Medium ess otrol with oordited dptive sleepig for wireless sesor etworks, IEEE/ACM Trs. Netw., vol., pp. 9 6, Jue. [] R. Rozovsky d P. R. Kumr, SEEDEX: A MAC protool for d ho etworks, i Pro. ACM MobiHOC,. [] H. Co, K. Prker, d A. Aror, O-MAC: A reeiver etri power mgemet protool, i Pro. IEEE ICNP, 6.

11 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 8, NO. 7, SEPTEMBER [6] Y. Su, O. Gurewitz, d D. Johso, RI-MAC: reeiver-iitited syhroous duty yle MAC protool for dymi trffi lods i wireless sesor etworks, i Pro. ACM SeSys, 8. [7] S. Jyshree, B. Moj, d C. S. R. Murthy, O usig bttery stte for medium ess otrol i d ho wireless etworks, i Pro. ACM MOBICOM,. [8] M. Dhrj, S. Jyshree, d C. S. R. Murthy, A ovel bttery wre m protool for miimizig eergy ltey i wireless sesor etworks, i Pro. HiPC,. [9] C. F. Chisserii, P. Nuggehlli, V. Sriivs, d R. R. Ro, Eergyeffiiet ommuitio protools, i Pro. DAC,. [] M. Mróti, B. Kusy, G. Simo, d A. Lédezi, The floodig time syhroiztio protool, i Pro. ACM SeSys,. Fei Qi reeived the B.Eg i Iformtio Egieerig from HUST, d M.Eg. i Eletroi Egieerig from BIT, 6. He is urretly fuded by DHPA sholrship to work s PhD Cdidte with Dr. Joh Mithell d Dr. Yg Yg i EE Dept., Uiversity College Lodo. Prior to tht, he served s Sr. Applitio Egieer t Crossbow Tehology, Beijig Rep. Offie. Smir Syed reeived his B.S d M.S. degrees i Eletrois d Commuitios Egieerig from Helw Uiversity, Egypt, i 997 d, respetively. Curretly, he is Ph.D. didte t the Deprtmet of EE Dept., Uiversity College Lodo. His preset reserh iterests ilude wireless etworkig, medium ess otrol, qulity of servie, d oopertive ommuitios. Chi-Ki Chu is urretly Reserh Assoite t Uiversity of Cmbridge s primry reserher for the Itertiol Tehology Allie i Network d Iformtio Siee (ITA) progrm tht is joitly fuded by the U.S. Army Reserh Lbortory d the U.K. Miistry of Defese. Previously, he ws Crouher Foudtio Reserh Fellow t the EE Dept., Uiversity College Lodo, wrded two-yer fellowship by the Crouher Foudtio Hog Kog. He reeived the Ph.D. from the Computer Lbortory, Uiversity of Cmbridge, d the B. Eg. (First-lss Hoors) from the Dept. of Iformtio Egieerig, the Chiese Uiversity of Hog Kog. His reserh iterests oer diverse res of etworkig, ommuitios, distributed systems, stohsti etworks d rdomized lgorithms. Muhmmd Husi Whb reeived the BS i Eletrois d Computer Egieerig from Cregie Mello Uiversity d MS from Glsgow Uiversity i 8. He worked o mhie lerig d etworkig protools. He is ow PhD studet i the Computer Siee deprtmet, Uiversity College Lodo, workig o mhie lerig for visio systems uder the Visio d Imgig Siee group. Yg Yg is urretly the Assistt Diretor d Vie CTO t Shghi Reserh Ceter for Wireless Commuitios (WiCO), SIMIT, Chiese Ademy of Siees. Prior to tht, he ws Seior Leturer with EE Dept., Uiversity College Lodo, Uited Kigdom. His geerl reserh iterests ilude wireless d ho d sesor etworks, wireless mesh etworks, d G/G mobile systems.