Life-Add: Lifetime Adjustable Design for WiFi Networks with Heterogeneous Energy Supplies

Transcription

1 Lfe-Add: Lfeme Adjusable Desgn for WF Neworks wh Heerogeneous Energy Supples Shengbo Chen, Tarun Bansal, Yn Sun, Prasun Snha and Ness B. Shroff Deparmen of ECE, The Oho Sae Unversy Deparmen of CSE, The Oho Sae Unversy Emal: Co-prmary auhors Absrac WF usage sgnfcanly reduces he baery lfeme of handheld devces such as smarphones and ables, due o s hgh energy consumpon. In hs paper, we propose Lfe-Add : a Lfeme Adjusable desgn for WF neworks, where he devces are powered by baery, elecrc power, and/or renewable solar energy. In Lfe-Add, a devce urns off s rado o save energy when he channel s sensed o be busy, and sleeps for a random me perod before sensng he channel agan. Lfe-Add carefully conrols he average sleep perods of he devces o mprove her hroughpu whle sasfyng her operaon me requremen. I s proven ha Lfe-Add acheves near-opmal proporonal-far uly performance for he sngle access pon (AP scenaros. Moreover, Lfe-Add allevaes he near-far effec and he hdden ermnal problem n general mulple AP scenaros. Our ns- 3 smulaons show ha Lfe-Add smulaneously mproves he lfeme, hroughpu, and farness performance of WF neworks, and can coexs harmonously wh IEEE 82.. I. INTRODUCTION WF s one of he mos successful wreless nerne access echnologes, whch has become prevalen for handheld moble devces, such as smarphones and ables. One major concern of he curren IEEE 82. WF desgn s s hgh energy consumpon. Smlar as GPS and Blueooh, WF has been recognzed as one of he bgges energy hogs of smarphones. I was repored ha he IEEE 82. WF desgn may ncrease he smarphone s energy consumpon by up o 4 mes []. Therefore, smarphones may easly suffer from baery ouage wh he curren WF desgn. Currenly, here are wo caegores of works o prolong he operaon me of WF devces. The frs class ams a reducng he energy consumpon of WF rados, e.g., [] [3]. The second class ulzes renewable solar charger or porable baery o provde moble energy replenshmen whou beng confned o he mmovable elecrc power sources on he wall, e.g., [4], [5]. Beyond hese, would be of grea neres o desgn lfeme-unable WF devces whle he hroughpu performance can be also mproved. In hs paper, we propose Lfe-Add: a Lfeme Adjusable desgn for WF neworks, where he devces are powered by baery, elecrc power, and/or renewable solar energy. In hs desgn, a devce senses he channel avalably when has a packe o send. If he channel s sensed o be busy, goes o sleep for an exponenally dsrbued random me perod and hen wakes up o sense he channel avalably agan. If he channel s dle, ransms he packe. Lfe-Add carefully conrols he average sleep perods of he WF devces o mprove her hroughpu and farness performance whle sasfyng her operaon me requremen. We frs formulae a proporonalfar nework uly mzaon problem for asynchronous WF neworks n sngle AP scenaros. Unlke radonal synchronzed wreless neworks, he channel access probables of he WF devces are coupled due o channel conenons. As a resul, he aaned nework uly mzaon problem urns ou o be a dffcul non-convex opmzaon problem. Through reformulaons and manpulaons, we develop a lowcomplexy soluon and prove ha s near-opmal n pracce. In general, for mulple AP scenaros, due o he complcaed nerference envronmen, he WF neworks suffer from he well-known hdden ermnal problem and near far effec. We exend Lfe-Add for he general mulple AP scenaros, where we nroduce congeson conrol o handle he hdden ermnal ssue and leverage devce collaboraon o allevae he near-far effec. The conrbuons of hs paper are summarzed as follows: We propose a new model for operang WF devces, and characerze he hroughpu and energy consumpon performance of each devce. The aaned performance mercs are much smpler han hose obaned from convenonal wo dmensonal Markovan chan model [6]. The reason s ha our model explos he memoryless propery of exponenal sleep perod dsrbuon o smplfy he performance characerzaon. We formulae a non-convex proporonal-far uly mzaon problem for he sngle AP scenaros, and develop a smple soluon,.e., Lfe-Add, o conrol he average sleep me perods. We prove ha Lfe-Add s nearopmal, f he carrer sensng me s neglgble compared o he packe-plus-ack ransmsson me. Ths condon s sasfed for praccal WF packe ransmsson parameers; see he Remark n Secon V-D for deals. We generalze Lfe-Add o deal wh he near-far effec and he hdden ermnal ssue heurscally. Our key conrbuon here s o develop a new devce collaboraon scheme, whch mproves he hroughpu and farness performance. In addon, he Lfe-Add desgn s smple o be mplemened.

2 TABLE I. Performance comparson of dfferen WF desgns. IEEE 82.b IEEE 82.b Lfe-Add wh RTS-CTS Avg Lfeme mn mn mn Avg hroughpu.9568 Mbps.338 Mbps.4 Mbps Jan s farness ndex [7] successful ACK 68.3% 98.6% 87.45% Our ns-3 smulaons show ha Lfe-Add smulaneously mproves he lfeme, hroughpu, and farness performance of WF neworks. A bref performance comparson beween Lfe-Add and IEEE 82.b s provded n Table I for he smulaon scenaro of Fg. 6. We also show ha Lfe-Add can coexs harmonously wh IEEE 82.: f some devces upgrade from IEEE 82. o Lfe-Add, he hroughpu performance mproves for boh he devces swchng o Lfe-Add and hose sckng o IEEE 82.. Compared o IEEE 82., frs, he lfeme mprovemen of Lfe-Add s due o urnng off he rado durng he backoff perod. Second, by carefully desgnng and nroducng collaboraon among he devces, Lfe-Add has a smaller packe collson probably and hus leads o a beer hroughpu performance. Fnally, by successfully provdng hgher prores o he lowhroughpu devces, Lfe-Add can mprove farness performance as a resul. II. RELATED WORKS Performance analyss of carrer sensng mulple access (CSMA schemes for WF neworks have been wdely nvesgaed snce s semnal paper [6]. However, he wo dmensonal Markovan chan model n [6] makes dffcul o conrol he WF ransmssons. Recenly, a queue based schedulng scheme called Q-CSMA, was proven o be hroughpu opmal [8]. These sudes focus on hroughpu enhancemen, assumng he WF rado s urned on all he me for sensng, ransmng, or recevng, whch s no energy effcen. Energy effcen schedulng schemes have been developed for synchronzed wreless neworks (see he recen papers [9] [2] and he references heren. These works focused on sloed wreless neworks, such as cellular neworks. Therefore, hey are no applcable o asynchronous WF neworks. Sleep-wake schedulng schemes have been developed for wreless sensor neworks o prolong he baery lfeme (see [3] [5] and he references heren. Whle hese schemes apply o asynchronous wreless neworks, her focus s on lgh raffc sensor neworks where packe collsons seldom occur. However, packe collson s one of he mos serous problems n WF neworks. Recenly, energy effcen WF desgns have receved sgnfcan research aenon due o he emergng handheld WF devces wh small baery capacy, e.g., [] [3]. In [], he auhors proposed o reduce he power consumpon n dlelsenng by lowerng he clock-rae n hardware. The auhors of [2] found ha IEEE 82. s Power Save Mode (PSM was no effcen n he presence of compeng background raffc, and proposed a schedulng algorhm o resolve. In [3], he devces ener he sleep mode durng he backoff lke our scheme, bu whou conrollng he sleep perod dsrbuon. Whle hese sudes mprove he energy effcency of WF neworks, hey canno mproves he lfeme, hroughpu, and farness performance smulaneously. III. SYSTEM MODEL We frs consder a WF nework wh AP and N devces, where all he devces are assocaed wh he AP. Exensons o general mulple AP scenaro are dscussed n Secon VI. A. Energy Model Consder ha devce n wll be used for a connuous me duraon no shorer han T arge,n before s baery des ou, where T arge,n s called he arge lfeme of devce n. The lfeme consran of devce n s gven by T n T arge,n, n N, ( where T n s he acual lfeme of devce n and N = {, 2,, N} s he se of devces. The energy cos of each devce consss of wo pars: he energy spen on he WF rado and he base energy consumpon n powerng he non-wf componens, such as CPU, screen, ec. Le E RF,n denoe he average energy consumpon rae of he WF crcu n devce n when urned on, and E nonrf,n denoe he average energy consumpon rae of he non-wf componens n devce n. We assume ha, when he WF rado s n sleep mode, s energy consumpon rae s neglgble compared o E RF,n. For example, measuremens showed ha he WF rado n HTC Tl moble phone consumes an average power of 72mW n he sleep mode whle consumes 2 mw n he awake mode [2]. Le B n represen he amoun of energy nally sored n he baery, and r n he average energy replenshmen rae for devce n (eher from renewable energy source or from elecrc power supply, whch can be obaned from hsorcal daa. Then, he mum allowable energy consumpon rae of he WF rado s e con,n = B n T arge,n + r n E nonrf,n, n N. (2 Therefore, he lfeme consran ( can be rewren as he energy consumpon consran as follows e n e con,n, n N, (3 where e n s he acual energy consumpon rae of he WF rado. In pracce, he energy replenshmen rae of he solar charger r n s usually low such ha r n E nonrf,n. In order o make sure ha he lfeme consran s feasble, we requre ha e con,n. Therefore, T arge,n s no greaer han T,n B n /(E nonrf,n r n, where T,n s he mum feasble lfeme of devce n. 2 If a devce reles only on he baery, we have r n =. 2 If a devce recharges from elecrc power supply, hen r n > E nonrf,n and T,n s nfne.

3 Sensng s X-X2<s Collson Devce Packe X Packe Devce 2 Packe X2 Packe Devce 3 Tmeou Packe AP Cycle ACK Channel busy, go o sleep ACK Sleep duraon Cycle Cycle 2 Cycle 3 Tme Fg. : Illusraon of he sleep-wake channel conenon scheme. B. Sleep-Wake Channel Conenon We now descrbe our sleep-wake channel conenon scheme. Consder he uplnk scenaro,.e., from he devces o he AP. When a devce wakes up from a sleep mode, performs carrer sensng mmedaely f has a packe o ransm. We use s o represen he carrer sensng me. Snce s s very shor, we assume ha he energy spen on carrer sensng s neglgble; see he Remark n Secon V-D. If he channel s free, he devce ransms he packe; oherwse, he devce goes back o sleep mmedaely. The sleep perod for each devce n N s an ndependen exponenally dsrbued random perod of me wh mean /R n, and he conrol of R n wll be dscussed laer. If wo devces begn ransmng whn a duraon shorer han he carrer sensng me s, hey may no be able o deec each oher s ransmssons and a collson wll occur. We assume ha he devces are whn each oher s sensng range. 3 Therefore, each devce can perfecly deec he ransmssons of anoher devce as long as he dfference of her wake-up mes s larger han s. If he AP successfully receves he packe, reples wh an ACK. Afer daa ransmsson, he WF rado says awake for an ACK or a meou. Then goes back o sleep for anoher exponenally dsrbued me duraon. The average ransmsson me of a daa packe s denoed by L and he duraon of he ACK s a. Moreover, we assume ha when here s a collson, he average collson me plus meou can be approxmaed o be. Noe ha packe collsons may also occur when some devces wake up before he ACK ransmsson. We om hese collsons n our model o keep he formulaed desgn problem solvable. For smlar reasons, we also om he evens ha some devces wake up durng he meou [6]. However, hey wll be consdered n our ns-3 smulaons n Secon VII. We defne a sleep-wake cycle as he duraon beween he end of wo successve meous or ACKs. Fgure llusraes he sleep-wake cycles of hree conendng devces. Afer he frs ACK, he channel becomes dle and hen he one wh he smalles remanng sleep perod,.e., Devce, wakes up and begns ransmsson. Snce no oher devces s awake n he precedng and he followng perod of lengh s, he ransmsson s successful, and he AP reples wh an ACK. In he nex sleep-wake cycle, snce Devce and 2 wake up 3 Ths assumpon s removed n Secon VI when sudyng he case wh mulple AP scenaros. and ransm whn a me perod shorer han s, leads o a collson. If he ransmng devce does no receve he ACK before he meou, goes back o sleep for anoher exponenally dsrbued me duraon and agan conends for he channel o reransm he packe. For he downlnk scenaro, IEEE 82. defnes a power savng mode (PSM, where he AP perodcally broadcass beacons o nofy whch devces have pendng daa packes n he buffer. Each devce wh pendng packes hen sends a shor packe, called ps-poll packe, o he AP for channel conenon. Afer recevng a ps-poll packe from one wnnng devce, he AP ransms he downlnk packes o he devce [6]. Noe ha he channel conenon of he downlnk case s smlar o he uplnk case. We focus on he uplnk scenaro n hs paper, and wll exend o he general scenaro wh boh uplnk and downlnk raffc n our fuure work. IV. PROBLEM FORMULATION A. Characerzaon of Throughpu and Energy Consumpon Le X n denoe he resdual sleepng perod of devce n when he laes sleep-wake cycle s over. Snce he sleepng perod of devce n s exponenally dsrbued wh parameer R n, X n s also exponenally dsrbued wh parameer R n, owng o he memoryless propery of exponenal dsrbuon. Le β n denoe he probably ha devce n obans he channel and ransms successfully afer a sleep-wake cycle. Accordng o our sleep-wake channel conenon scheme, devce n obans he channel f X X n + s for all N and n. Therefore, β n s gven by β n = Pr(X X n + s, n (a = E[Pr(X X n + s, n X n ] (b = E Pr(X X n + s X n n = = exp( R (x n + s R n exp( R n x n dx n n R n exp(r n s ( R exp( R s, (4 where (a s due o Pr[A] = E[Pr(A B], and (b s due o he fac ha X s ndependen for dfferen devce.

4 Le p n denoe he fracon of me ha devce n ransms successfully wh no collson. Each sleep-wake cycle consss of hree pars: ransmsson/collson, ACK/meou and dle perod. The collson probably s deermned by β col = n β n, because for any sleep-wake cycle, ncludes eher a successful ransmsson or a collson. The dle perod s he shores sleepng perod among N exponenally dsrbued varables wh parameer R, N. I s easy o show ha he dle perod s exponenally dsrbued wh parameer R. In our sleep-wake channel conenon model n Secon III-B, he duraon of each sleep-wake cycle s..d.. By renewal heory [7], p n s gven by β n E[rans] p n = ( β + β col (E[rans] + L[ACK] + E[Idle] β n L = + R R n exp(r n s = R + L exp( R s, (5 ( L+a L where E[rans] represens he average packe ransmsson me L, L[ACK] represens he duraon of ACK a, E[Idle] represens he expecaon of he dle duraon gven by / R, and we have used he assumpon ha he average collson me plus meou can be approxmaed o be. Le Dn be he hroughpu of devce n. In pracce, Dn s proporonal o he fracon of successful ransmsson me p n : D n = p n α n, (6 where α n s a scalng parameer dependng on he physcal layer sgnal srucure, channel codng and modulaon. Noe ha our conrol soluon does no requre knowledge of α n. On he oher hand, besdes successful ransmssons, each devce n may suffer from collsons, whch also coss energy. Thus, we denoe P n as he oal fracon of me ha he WF rado n devce n s urned on,.e., ransmng or wang for he ACK. Smlar o (5, we can show ha P n = [ exp( R n s ] R + exp( R n s R n R +. (7 The dervaon of (7 s provded n [8]. Therefore, he acual energy consumpon rae of he WF rado s e n = P n E RF,n. Hence, he energy consrans (3 can be rewren as P n E RF,n e con,n, n N. (8 Le us defne b n e con,n /E RF,n as he arge energy effcency of devce n, hen (8 can be rewren as P n b n, n N. (9 Noe ha hs consran s always sasfed when b n. B. Problem Saemen Suppose ha each devce n s assocaed wh a proporonalfar uly funcon ln( D n [9]. Our goal s o desgn he average sleep perod R for N o mze he oal uly. Ths desgn problem can be formulaed as ln( D, ( R> N subjec o he per-devce energy consran (9. Subsung (5 and (7 no (, hs problem s rewren as he followng problem: (Problem A ( R > ln R N ln R + (N ( L R s + N ln + s.. [ exp( R n s ] R +exp( R n s R n R + ln α b n, n. V. PROBLEM SOLUTION Problem A s a non-convex opmzaon problem. We frs consder a relaxed verson of Problem A,.e., ( R > ln R N ln R + (N ( L R s + N ln s..r n b n ( + ln α ( R +, n. (2 Noce ha he only dfference beween he above problem and Problem A s he consrans. Snce R n [ exp( R n s ] R + exp( R n s R n, n, he consrans of ( are looser han hose of Problem A. Hence, ( serves as a performance upper bound of Problem A. In he sequel, we solve ( n wo cases: b and b <, and show n Theorem ha he obaned soluon s asympocally opmal for he orgnal Problem A as s A. The Case of b. In hs case, we provde an approxmae soluon o Problem ( n wo seps: ( Defne an auxlary varable y = R. Gven ha y >, R s deermned by he followng approxmae problem: R > ( ln R N ln y + ( L (N y s + N ln (3 + ln α, s.. R n b n y, n N (4 R = y. (5 In [8], we show ha he opmum soluon o (3 s deermned by R n = mn{b n, c }y, (6 where c sasfes mn{b, c } =. (7

5 (2 Subsung (6 and (7 no (3, we ge ( N ln y N ln y + (N y s y> ( L + N ln + ln α + ln[mn{b, c }], (8 whch s an one-dmensonal convex opmzaon problem of y. Takng he dervave of he objecve funcon and seng o be zero, yelds y = 2( + + 4N(L+a (N s 2(. (9 Subsung y = y no (6, he sleep perod parameer {R } s derved. Noe ha Problem (3 has more resrced energy consrans han Problem (. Hence our soluon (6, (7, and (9 s feasble for Problem (. Snce (6, (7, and (9 acheves an objecve value gven by (8, he opmum objecve value of Problem ( s lower bounded by (8. B. The Case of b < Subsung he energy consrans (2 no (, he opmum value of ( s upper bounded by R > s.. ln b (N R n b n ( R s + R +, n. ( Lα ln, (2 In [8], we prove ha he opmum soluon o (2 sasfes ( R n = b n R +, n. (2 Moreover, f (2 holds, he opmum values of ( and (2 are dencal. If b <, he lnear sysem (2 has a unque soluon, whch s gven by R n = b n ( ( b, n. (22 By hs, we have obaned he opmum soluon o Problem ( for b <. C. Implemenaon Procedure We frs express he soluons for b and b < n a unfed form. For b <, he soluon (22 can also be expressed by (6, where c and y are deermned as c =, y = ( ( b. (23 Our ransmsson conrol scheme s descrbed as follows: Lfe-Add: Lfeme Adjusable Desgn for WF Neworks ( The AP gahers he sysem parameers N, L, a and s, and he arge energy effcency parameer b from he devces. (2 The AP checks f b or b <. If b, he AP compues c and y accordng o (6 and (7; oherwse, compues c and y accordng o (23. (3 The AP broadcass c and y o he devces by pggybackng hem on s adversemen beacons. (4 On hearng c and y, he devce n compues R n by (6, and hen ulzes R n o generae s sleep perod. D. Performance Analyss The performance of Lfe-Add s characerzed by he followng heorem: Theorem : Our soluon (6, (7, (9 and (23 s asympocally opmal for Problem A as s. Proof: Here, we provde a proof skech conssng of wo seps. We refer o a more dealed proof n [8]. In Sep One, we show ha our soluon s asympocally opmal for Problem ( as s. If b <, we have derved he exac soluon o Problem ( n Secon V-B. If b, he opmum objecve value of Problem ( s lower bounded by (8, whch s acheved by our soluon (6, (7, and (9. On he oher hand, we shown n [8] ha he opmum objecve value of Problem ( s upper bounded by ( L N ln + ln α + ln[mn{b, c }]. (24 Moreover, he gap beween he lower bound (8 and upper bound (24 ends o as s. Therefore, our soluon (6, (7, and (9 s asympocally opmal for Problem ( as s f b. In Sep Two, we show ha our soluon sasfes R n s as s for boh b and b <. By hs, Problem ( and Problem A ends o be he same problem as s. Therefore, our asympocally opmal soluon o Problem ( s also asympocally opmal for Problem A. Remark: I s worh ponng ou ha he condon s s sasfed n praccal WF neworks. For example, n IEEE 82.b WF sandard, he carrer sensng me s s = 4µs [2], and he ransmsson me of he daa packe and ACK vares from 5µs o 573µs for a packe wh o 46 byes of payload [2]. Hence, s.783. VI. GENERAL WIFI NETWORKS WITH MULTIPLE APS We now exend Lfe-Add o more general scenaros wh mulple APs, where some clens and/or APs canno deec he exsence of each oher because of he large nework sze. The key challenge here s he complcaed nerference envronmen, whch makes he ransmsson conrol problem very dffcul. One such example s he asymmerc nerference scenaro shown n Fg. 2, whch s also known as he near-far effec n wreless communcaons. In hs example, Devce s assocaed wh AP and Devce 2 s assocaed wh AP 2. Snce AP s ou of he nerference range of Devce 2, can successfully receve he packes from Devce. However, he ransmssons of Devce 2 s serously nerfered by Devce. In he IEEE 82. WF desgns, Devce wll keep he mnmum backoff snce s ransmssons are always successful, whle Devce 2 has hgh backoff me due o packe collsons a AP 2. Ths sgnfcanly reduces he hroughpu of Devce 2 and resuls n unfarness beween he wo devces [22]. Noe

6 AP Clen AP 2 Clen 2 Inerference Fg. 2: An llusrang example of he near-far effec. ha he RTS-CTS mechansm has large overhead, hus canno mprove he hroughpu performance sgnfcanly. Anoher challenge of he mulple AP scenaro s he hdden ermnal problem, where a packe collson may occur a a AP even f he ransmsson sarng me of wo packes are more han s apar, because he wo devces canno deec each oher. Therefore, he collson probably β col s under-esmaed. We now exend Lfe-Add o he mul-ap scenaro, and use a heursc desgn o handle hese wo challenges. In order o compue he c and y n mul-ap neworks, each AP overhears he repors of b from he devces whn s communcaon range, ncludng he devces ha are assocaed wh oher APs. Smlar overhearng procedure s suppored n IEEE 82. MAC [23]. For example, o perform vrual carrer sensng, each devce overhears he packes from nearby devces o ge he packe lengh nformaon conaned n he packe header. In addon, each devce receves he beacons broadcasng c and y from all he APs whn s communcaon range. To resolve he near-far effec ssue, Lfe-Add ulzes he followng devce collaboraon scheme: each devce compues he R n s suggesed by nearby APs, and chooses o use he smalles R n value, whch corresponds o he larges average sleep duraon. Ths helps o mprove farness among he devces. For example, for he nework shown n Fg. 2, Lfe-Add wll compue he backoff me of Devce, by consderng channel conenons a boh AP and AP 2. Ths s as f nearby APs ell Devce how many devces ransmssons nerferes wh a each AP (n our example, Devce nerferes wh Devce 2 a AP 2. Therefore, Devce ransms conservavely o provde more channel access opporunes o Devce 2 compared o IEEE 82.. For he hdden ermnal problem, Lfe-Add employs he followng congeson conrol scheme smlar o ha of IEEE 82. [23]: Each devce ncreases s average sleep perod /R n when undergoes a meou, and reduces /R n when receves an ACK, where R n s he acual sleep-wake parameer adoped by he devce. The sleep-wake parameer R n assgned by he APs s used as an upper bound of he acual sleep-wake parameer R n o ensure he lfeme consran. Lfe-Add for he mulple AP scenaro s as follows: ( Each AP gahers he sysem parameers L, a, s and N, where N s he number of devces whn s communcaon range (ncludng hose assocaed wh oher APs. Each AP also collecs b from all hese devces. (2 Each AP checks wheher b or b <. If b, he AP compues c and y by (6 and (7; oherwse, compues c and y by (23. (3 Each AP broadcass c and y o he devces whn s communcaon range by pggybackng hem on s adversemen beacons. (4 Each devce n may receve mulple pars of (c, y from nearby APs whn s communcaon range. For each (c, y, compues he correspondng R n usng (6, and chooses o use he smalles R n value. (5 Each devce compues s Congeson Conrol Facor F n. Inally, he value of F n s. Each me he devce undergoes a meou, doubles s F n (up o a mum value of 32. Each me he devce receves an ACK, s F n s rese o. The acual sleep-wake parameer R n s compued by R n = R n /F n. Fnally, he sleep perod s generaed as an exponenally dsrbued random varable wh mean /R n. Lfe-Add dffers from IEEE 82. MAC n he followng aspecs: ( In Lfe-Add, a devce ransms mmedaely afer senses he channel o be dle. However, n IEEE 82. MAC, he devce keeps sensng he channel for an addonal backoff me, whch consumes much energy. Ths s known as he dlelsenng problem n he leraure []. (2 By usng b n o compue R n, Lfe-Add akes he energy supply and lfeme requremen of he devces no consderaon. (3 Lfe-Add nends o mprove he hroughpu and farness performance by carefully conrollng he ransmsson parameers and nroducng he devce collaboraon scheme. We fnally noe ha a smpler verson of Lfe-Add can be derved by gnorng he lfeme consrans and smply choosng b n >. Ths corresponds o he bes hroughpu performance of Lfe-Add, snce he hroughpu s no sacrfced o sasfy he lfeme consran. Ths case wll be consdered n our smulaons n Secon VII-B. VII. SIMULATION RESULTS We now provde ns-3 [24] smulaon resuls o evaluae he performance of Lfe-Add, where s physcal layer s he same as IEEE 82.b. For he purpose of comparson, we also smulae IEEE 82.b MAC as well as IEEE 82.b MAC wh RTS-CTS. All he smulaon resuls are averaged over 5- sysem realzaons. We evaluae our sysem under UDP sauraon condons such ha he devces always have UDP daa o send. The packe lengh vares accordng o he measuremens n [25]. A. Sngle AP Scenaro We se up a WF nework wh AP and 3 assocaed devces n a feld of sze 5m 5m. The sensng hreshold s se o - dbm resulng n a sensng range of approxmae m. Therefore, all he devces can hear each oher. The AP s assumed o be conneced o he wall power whle each devce s equpped wh a baery and a solar panel ha provdes renewable energy chargng. We assume he devces use HTC Tl smarphones, where f he WF rado s awake, he devce consumes mw, and f he WF rado s n sleep mode, he energy consumpon s 387 mw. Each devce has a baery wh a capacy of 2 mah. 4 I was measured n [2] ha he energy consumpon rae of he WF rado of HTC Tl 89 seres n awake mode s 2 mw and he base energy consumpon rae s whn 55mW 475 mw (an average of 35 mw for a oal consumpon of 435 mw. When he rado s n sleep mode, he oal consumpon s 35 mw + 72 mw = 387 mw.

7 Acual Lfeme (T n (n mnues Wh Rs-Cs Lfe-Add 45 Degree Slope Targe lfeme (T arge (n mnues (a Average acual lfeme vs. arge lfeme Toal Uly Wh Rs-Cs Lfe-Add Acual Lfeme (T n (n mnues (b Toal Uly vs. acual lfeme Fg. 3: Smulaon resuls for sngle AP neworks wh homogenous devces. TABLE II. Parameers of he heerogeneous devces. Node Inal Baery Rechargng Targe lfeme Level (n mah Rae (n mw (n mns. N ,36,,8 N 2 9 9,8,,9 N ,2,,6 Homogeneous Devces: We consder a homogeneous scenaro where all devces have he same nal baery level (3 mah and rechargng rae (6 mw. Fg. 3(a shows he average acual lfeme of he hree desgns wh varyng arge lfeme T arge. The acual lfeme of Lfe-Add ncreases wh respec o he arge lfeme, whle he acual lfemes of he oher wo desgns say consan. Ths fgure shows ha he acual lfeme of Lfe-Add s adjusable and sasfes he lfeme consran (. We noe ha even he mnmum lfeme value of Lfe-Add s longer han ha of he IEEE 82. MACs, because here s no dle-lsenng n Lfe-Add. Fg. 3(b shows how Lfe-Add realzes lfeme exenson by radng he oal uly. The uly of a devce s deermned by U(x = ln(x, f he average hroughpu of he devce s x kbps. Lfe-Add can acheve unable lfeme by adjusng he average sleepng-backoff duraons of he devces. However, for he IEEE 82. MACs, s no possble o adjus he uly and he acual lfeme, and hus, he devces always have fxed uly and lfeme. 2 Heerogeneous Devces: We now explore he performance of Lfe-Add for a heerogeneous scenaro. The nal baery level B n, energy rechargng rae r n, and arge lfeme values T arge,n of he hree devces are provded n Table II, where he varyng sep szes of T arge,n for he hree devces are dfferen. Fg. 4 shows he radeoff beween he hroughpu and acual lfeme of all hree devces. We can see ha Lfe-Add can acheve hgher hroughpu han he IEEE 82. MACs for each devce, whch also mples a larger oal uly. B. Mulple AP scenaro wh Heerogeneous Devces Wh Varyng Number of Devces: We seup a feld of 3m 3m, n whch we randomly deploy 4 APs and varyng number of devces. Each devce s assocaed wh he AP ha has he sronges sgnal, and he devce only sends daa packes o s assocaed AP. The devces have heerogeneous energy supples. In parcular, /3 devces only have access o he energy sored n her baeres. Anoher /3 devces have Throughpu (n Mbps N 82. N N Wh Rs-Cs N 82. Wh Rs-Cs N Wh Rs-Cs N 3 Lfe-Add N Lfe-Add N 2 Lfe-Add N Acual Lfeme (n mnues Fg. 4: Smulaon resuls for sngle AP neworks wh heerogeneous devces. Acual Lfeme (n mnues Wh Rs-Cs Lfe-Add Number of wreless clens (a Average acual lfeme vs. number of devces Toal Uly Wh Rs-Cs Lfe-Add Number of wreless clens (b Toal uly vs. number of devces Fg. 5: Smulaon resuls for mul AP neworks wh heerogeneous devces: varyng number of devces. access o boh baery energy and renewable energy from solar panel. The las /3 devces are conneced o he wall power ha provdes hgh energy rechargng rae. The nal baery levels of all he devces are randomly generaed by a unform dsrbuon whn he range of [2, ] mah. The lfeme consrans are gnored here by choosng b >, whch acheves he bes possble hroughpu performance. Fgure 5(a shows he average lfeme performance versus he number of devces. Lfe-Add prolongs he average lfeme because here s no dle-lsenng. Fgure 5(b shows he oal uly provded by hese hree desgns. One can see ha Lfe- Add acheves a larger proporonally far uly. 2 CDF: Now we consder a feld of 5m 5m, n whch we randomly deploy 4 APs and 3 devces. The energy supply of he devces are se as n Secon VII-B. Fgure 6(a shows he CDF (cumulave dsrbuon funcon of he acual lfeme of he devces. The fgure only plos he CDF for he frs 2 devces snce he las devces have nfne lfeme due o he hgh rechargng rae provded by he wall power. Fgure 6(b shows he CDF of he hroughpu of he ndvdual devces (for all 3 devces. The average lfeme, average hroughpu, Jan s farness ndex [7], and successful ransmsson probably for hs smulaon scenaro s provded n Table I. Lfe-Add has beer hroughpu performance because IEEE 82. has oo many collsons and he RTS-CTS mechansm s no effcen. I s relave easer o undersand he lfeme and farness mprovemen. 3 Coexsence wh IEEE 82.: Fnally, we explore he coexsence beween IEEE 82. and Lfe-Add. We se up he nework as explaned n Secon VII-B2. However, hs me AP and 2 (randomly chosen swch from IEEE 82. (whou RTS-CTS o Lfe-Add whle AP 3 and 4 sck o IEEE 82.. Each devce s assocaed wh he AP wh he

8 REFERENCES CDF Wh Rs-Cs Lfe-Add Acual Lfeme (n mnues (a CDF of he acual lfeme of he devces CDF Wh Rs-Cs Lfe-Add Throughpu (n Mbps (b CDF of he hroughpu of he devces Fg. 6: Smulaon resuls for mul AP neworks wh heerogeneous devces: CDF performance. CDF Pure 82., AP, 2 Coexsence, AP, 2 Pure 82., AP 3, 4 Coexsence, AP 3, Acual Lfeme (n mnues (a CDF of he acual lfeme of he devces CDF Pure 82., AP, 2 Coexsence, AP, 2 Pure 82., AP 3, 4 Coexsence, AP 3, Throughpu (n Mbps (b CDF of he hroughpu of he devces Fg. 7: Smulaon resuls for he coexsence of Lfe-Add and IEEE 82.. sronges sgnal, whch hen deermnes he desgn used by he devce. Fg. 7 shows he lfeme and hroughpu CDFs of he devces assocaed wh AP -2 and AP 3-4, before and afer AP -2 swch o Lfe-Add. One can observe ha, afer AP -2 swch o Lfe-Add, he lfeme dsrbuon of he devces usng Lfe-Add s sgnfcanly mproved, because here s no dlelsenng n Lfe-Add. The lfeme dsrbuon of he devces sck o IEEE 82. does no change much. On he oher hand, he hroughpu dsrbuons for boh groups of devces are mproved. Therefore, upgradng IEEE 82. o Lfe-Add s benefcal for boh he devces swchng o Lfe-Add and hose sckng o IEEE 82., whch provdes he ncenve o employ Lfe-Add. VIII. CONCLUSION In hs paper, we have proposed Lfe-Add, a lfe-me adjusable desgn for WF neworks. By usng a sleep-wake channel conenon scheme, Lfe-Add can resolve he hgh energy consumpon of he curren WF desgn. Then, by conrollng he sleep perod parameers carefully and nroducng collaboraon among he devces, Lfe-Add has a small packe collson probably, whch mples hgh hroughpu. Fnally, by provdng hgh prory o he low hroughpu devces, Lfe-Add he mproves farness performance. Our smulaon resuls show ha Lfe-Add has beer lfeme, hroughpu, and farness performance han IEEE 82.b, and coexss harmonously wh IEEE 82.b. For fuure work, we are evaluang how Lfe- Add behaves under TCP raffc and n he presence of downlnk raffc. Is hardware mplemenaon s under preparaon. [] X. Zhang and K. G. Shn, E-ML: Energy-mnmzng dle lsenng n wreless neworks, n MobCom, 2, pp [2] E. Rozner, V. Navda, R. Ramjee, and S. K. Rayanchu, NAPman: Nework-asssed power managemen for WF devces, n MobSys, 2, pp [3] V. Baamone and C.-F. Chassern, Savng energy durng channel conenon n 82. WLANs, Mob. New. Appl., vol., no. 2, pp , 26. [4] Frenew Technology Company, Solar moble charger, hp://www. frenew.com.cn/cn/produc.asp?nclassd=248&yped=7. [5] Mophe Inc., Exernal USB porable baery charger, hp://www. mophe.com/caegory-s/53.hm. [6] G. Banch, Performance analyss of he IEEE 82. dsrbued coordnaon funcon, IEEE J. Sel. Areas Commun., vol. 8, no. 3, pp , Mar. 2. [7] R. Jan, The Ar of Compuer Sysems Performance Analyss. John Wley & Sons, 99. [8] L. Jang and J. Walrand, A dsrbued CSMA algorhm for hroughpu and uly mzaon n wreless neworks, IEEE/ACM Trans. New., vol. 8, no. 3, pp , Jun. 2. [9] M. J. Neely, Energy opmal conrol for me-varyng wreless neworks, IEEE Trans. Inf. Theory, vol. 52, no. 7, pp , 26. [] L. Ln, X. Ln, and N. B. Shroff, Low-complexy and dsrbued energy mnmzaon n mulhop wreless neworks, IEEE/ACM Trans. New., vol. 8, no. 2, pp. 5 54, 2. [] S. Chen, P. Snha, N. Shroff, and C. Joo, A smple asympocally opmal energy allocaon and roung scheme n rechargeable sensor neworks, n IEEE INFOCOM 22, Mar. 22, pp [2] L. Huang and M. J. Neely, Uly opmal schedulng n energy harvesng neworks, n MobHoc, 2. [3] J. Km, X. Ln, N. Shroff, and P. Snha, Mnmzng delay and mzng lfeme for wreless sensor neworks wh anycas, IEEE/ACM Trans. New., vol. 8, no. 2, pp , Apr. 2. [4] Y. Z. Zhao, C. Mao, M. Ma, J. B. Zhang, and C. Leung, A survey and projecon on medum access conrol proocols for wreless sensor neworks, ACM Compu. Surv., vol. 45, no., pp. 7: 7:37, 22. [5] A. Bachr, M. Dohler, T. Waeyne, and K. Leung, MAC essenals for wreless sensor neworks, IEEE Commun. Surv. Tuorals, vol. 2, no. 2, pp , Quarer 2. [6] G. Anasas, M. Con, E. Gregor, and A. Passarella, 82. powersavng mode for moble compung n W-F hospos: Lmaons, enhancemens and open ssues, Wreless Neworks, vol. 4, no. 6, pp , 28. [7] R. G. Gallager, Dscree Sochasc Processes. Boson: Kluwer Academc Publshers, 996. [8] S. Chen, T. Bansal, Y. Sun, P. Snha, and N. B. Shroff, Lfe-Add: Lfeme Adjusable desgn for WF neworks wh heerogeneous energy supples, 23, Techncal Repor, Deps of ECE and CSE, Oho Sae Unversy. [Onlne]. Avalable: hp:// chens/wop3. pdf [9] F. Kelly, Chargng and rae conrol for elasc raffc, European Transacons on Telecommuncaons, 997. [2] E. Magsre, K. K. Chnalapud, B. Radunovc, and R. Ramjee, WF- Nano: reclamng WF effcency hrough 8 ns slos, n MOBICOM, 2. [2] M. Gas, When Is 54 No Equal o 54? A Look a 82.a, b, and g Throughpu, hp:// wreless hroughpu.hml?page=. [22] C. Hua and R. Zheng, Sarvaon modelng and denfcaon n dense 82. wreless communy neworks, n IEEE INFOCOM 28, 28, pp [23] Wreless LAN Medum Access Conrol (MAC and Physcal Layer (PHY specfcaons, Insue of Elecrcal and Elecroncs Engneers, 27, hp://sandards.eee.org/abou/ge/82/82..hml. [24] ns-3, hp:// [25] R. Snha, C. Papadopoulos, and J. Hedemann, Inerne packe sze dsrbuons: Some observaons, USC/Informaon Scences Ins.[Onlne]. Avalable: hp://neweb. usc. edu/ rsnha/pk-szes, 27.