A System Context-Awre Approh for Bttery Lifetime Predition in Smrt Phones Xi Zho, Yo Guo, Qing Feng, nd Xingqun Chen Key Lbortory of High Confidene Softwre Tehnologies (Ministry of Edution) Shool of Eletronis Engineering nd Computer Siene, Peking University, Beijing, Chin {zhoxi,yoguo,herry}@sei.pku.edu.n,fengqing@os.pku.edu.n ABSTRACT Energy is bottlenek in smrt phone systems, nd knowing the sttus of the bttery lifetime nd being ble to use it effiiently is n importnt requirement from users. We propose system ontext-wre pproh for prediting bttery lifetime, whih llows user to know the urte bttery sttus nd to utilize the power effiiently. We refer to olletion of system omponent sttes s system ontext nd model the quntittive reltion between system ontext ttributes nd the bttery dishrge rte by multiple liner regressions. When the user hnges pplitions or opertions, we n dynmilly predit the remining bttery lifetime s well s its vritions by monitoring system ontext ttributes. We implement the CABLI system with our pproh s on n HTC G smrt phone running the Android operting system. Experiments show tht our model desribes how the hnges of system omponent sttes ffet the bttery lifetime, nd tht it improves the ury of online bttery lifetime predition. Ctegories nd Subjet Desriptors D.4. [Operting Systems]: Orgniztion nd Design Rel-time systems nd embedded systems, Performne Modeling nd predition Generl Terms Mngement, Mesurement, Experimenttion, Humn Ftors Keywords Smrt Phone, bttery lifetime, energy onsumption, system ontext-wre.. INTRODUCTION A smrt phone hs extended its funtionlities beyond the trditionl role of phone nd beome pervsive omputing devie. The lwys-on bkground pplitions inrese the omplexity of the system environment s well s the power onsumption. For smrt phone users, bttery lifetime is one of the primry usbility onerns. Knowing the sttus of the bttery lifetime nd using it effiiently is n importnt requirement from users. Trditionl solutions tke the form of bttery inditor, informing users the remining bttery hrge level with four to seven brs. However, it is hrd for users to know how long the bttery lsts if they perform vriety of tsks, nd how their Permission to mke digitl or hrd opies of ll or prt of this work for personl or lssroom use is grnted without fee provided tht opies re not mde or distributed for profit or ommeril dvntge nd tht opies ber this notie nd the full ittion on the first pge. To opy otherwise, or republish, to post on servers or to redistribute to lists, requires prior speifi permission nd/or fee. SAC, Mrh 5,, TiChung, Tiwn. Copyright ACM 978--453-3-8//3 $.. hnges of opertions ffet the bttery lifetime. If the operting system n provide more urte nd quntittive informtion bout remining bttery energy nd lifetime, then the users n djust the opertions to extend the bttery life nd enjoy more qulity time. Prior reserhes tried to monitor the bttery energy level during the exeution of some trget pplitions nd then to predit the bttery lifetime bsed on the bttery dishrge mesurements of pst period #,[]. These pprohes work well when the trget pplition is the only running pplition in the system nd hs onstnt worklod. However, in multi-proess OS environment with bkground onurrent pplitions, it is diffiult to identify whih pplition should ount for energy onsumption in ertin period. Furthermore, the ssumption tht the future energy onsumption ws the sme s the historil mesurement is in generl not vlid. In this pper, we propose system ontext-wre pproh for bttery lifetime predition in smrt phone systems. We obtin the ritil system omponents tht ffet energy onsumption of smrt phone nd refer to olletion of their sttes s system ontext. We then build quntittive model for the system ontext nd the bttery dishrge rte by using multiple liner regressions. In ddition, we monitor the system ontext nd dynmilly predit the remining bttery lifetime nd its vrition. We implement this pproh on n HTC G smrt phone running the Android operting system. In our experiments, we nlyze the predition effiieny of the model nd ompre it with n existing pproh []. The results show tht our model desribes how the hnges of system omponent sttes ffet the bttery lifetime, nd it improves the ury of online bttery lifetime predition. We orgnize the rest of the pper s follows. Setion desribes the relted work. Setion 3 presents the proess of the pproh nd the system ontext-wre bttery lifetime model. After presenting experimentl results in Setion 4, we onlude with Setion 5.. RELATED WORK There hs been lot of work on lptop bttery lifetime predition. Most of erly reserhers dopted eletrohemil fetures to predit bttery lifetime nd optimize the energy usge [, 3]. The bttery lifetime reserh of mobile phones reeived lot of ttention over the yers. Rhmti et l. studied humn-bttery intertions nd improved the intertion between users nd bttery dishrge of smrt phones [4]. They pointed out tht users need higher resolution bttery inditors, whih enble them to hrge phones more onveniently. However, they did not disuss how to urtely predit bttery lifetime. In order to enhne user experienes of using smrt phones, some reserhers mesured nd nlyzed energy onsumption nd 64
bttery lifetime under different pplitions nd usge ptterns [5][6][7]. They did not onsider how the system omponents ffet the bttery lifetime nd how to use this informtion to predit the bttery lifetime. Rvi et l. proposed bttery mngement pproh for mobile phones [8]. They used bse urve nd the dishrge speedup ftor to predit the bttery life. However, their pproh n only be pplied to given set of pplitions observed in dvne. Our pproh is pplied to the entire smrt phone systems, not limited to some speil pplitions. Wen et l. proposed n online pproh for prediting bttery lifetime []. They ssumed tht the future energy onsumption is the sme s the historil mesurements. This pproh works on vrious pplitions, but it hs reltively lrge men errors for vrible worklods. In our method, the sttes of system omponents re more ruil for bttery lifetime predition. Our experiment results show tht our pproh performs with higher ury nd provides users better usge experienes thn their pproh. Shye et l. studied mobile rhitetures by logger pplition tht olleted rel user tivity nd the tres of power onsumption [9]. They dopted liner regression nlysis method nd system prmeters similr with ours. But they didn t onsider the reltionship between the bttery lifetime nd the system omponent sttes. We model the quntittive reltionship mong the bttery dishrge rte, bttery lifetime nd the system omponent sttes. One of our distinguished ontributions is tht we pplied the model to bttery lifetime predition, nd hieved muh more ury thn the existing pprohes. Their work onfirms our finding tht the system omponent sttes re the key nd strightforwrd inditors for bttery energy onsumption nd lifetime predition. 3. SYSTEM CONTEXT-AWARE BATTERY LIFETIME PREDICTION Through extensive profiling, we found tht the hnges of system omponent sttes re driven by pplitions, nd tht the system omponent sttes re good inditors for worklods in the system. The bttery lifetime is ffeted by the summtion of energy onsumption of ll system omponents. Energy onsumption of omponent depends on its power stte (whih n be mpped to the opertion stte) nd the durtion it remins in tht stte. Therefore, we n use regression nlysis to quntify the reltion between system omponent sttes nd bttery energy onsumption. 3. System Context In mobile phone, the mjor energy onsumers re the CPU, LCD bklight, nd network interfe [9, ]. However, no existing work hs onduted the quntittive nlysis on the reltion between these omponent sttes nd bttery dishrge rte. We nlyze lrge mount of profiling dt quntittively, nd find out tht there re pproximtely liner reltion between the bttery dishrge rte nd some system omponent stte ttributes (Tble ). For some omponents, we use their resoure utiliztions to desribe their sttes beuse the resoure utiliztions more urtely express the worklod intensiveness nd n be mpped to energy onsumption of the omponents. For exmple, we use verge CPU utiliztion during time intervl to desribe CPU stte, nd use dt trnsfer rte to desribe the stte of the network interfe. We refer to set of system omponent sttes s system ontext nd tret eh stte s n ttribute of the system ontext. We denote system ontext nd its ttributes s tuple C brt,pu,wifi,io,spd. Tble shows the system ontext ttributes we use in our urrent predition model. The vlues of the ontext ttributes vry ording to differently running pplitions nd user s opertions. Tble. System Context Attributes Attribute Desription & Rnge Exmple CPU Utiliztion The rtio between the idle time to the (pu) totl time of intervl, [-]. LCD Bklight Brightness (brt) Rnge from [3,55] in HTC G 55 Wireless Stte (wifi) Disble or Enble [, ] IO Idle Rte (io) IO idle rte during time intervl.6 Dt Trnsfer rte(spd) Volumes of dt trnsferred (KB) It is well known tht intensive usge of omponents tends to redue bttery lifetime. However, in order to urtely predit the bttery lifetime, we need to present the quntittive reltion between the system ontext nd the bttery dishrge rte. 3. The Proess of Our Approh Our pproh for bttery lifetime predition onsists of two stges: modeling nd prediting. Figure shows the proess of this pproh. Figure. Proess of dynmi bttery lifetime predition During the modeling stge, we ustom speifi senrios tht hve stble system omponent sttes for whole bttery lifetime durtion. For exmple, we run video plyer pplition tht plys movie with the mximum LCD bklight brightness vlue 55. For the whole bttery lifetime, the verge CPU utiliztion, wifi, io, nd spd re ll pproximtely stble, s listed in the third volume in Tble. Then we profile the bttery energy level vs. time under this senrio during the whole bttery lifetime by using the API provided by the Jv frmework nd the operting system. Figure () shows the bttery dishrge urves nd bttery lifetime of the VideoPlyer pplition under this senrio. The bttery energy level is in terms of perentge. The slope of the fitted line of the urve is the dishrge rte, whih mens the bttery energy level deresement per minute. In this exmple, its bsolute vlue on verge is.574. If we hnge the brightness to nother vlue (for HTC G, this vlue rnges between 3 nd 55), suh s 3, while keeping other omponent sttes fixed, we n get nother dishrge rte.347 shown in Figure (b). 64
remining bttery lifetime. Furthermore, by lulting the differene of the urrent nd the lst predition, we n tell the vrition of predited bttery lifetime used by the hnges of the system omponent sttes. bttery energy level (%) 55brt liner55 8 6 4 y =.564x +.98 R² =.9949 3 44 7 3 3.3 Regressions of Dishrge Rte In order to predit the remining bttery lifetime, we first need to estimte the dishrge rte by using the system ontext ttributes. As shown in Figure, the dishrge rte is the energy onsumption rte of the system. We build quntittive model of system ontext nd dishrge rte by using multiple liner regression nlysis. time(min.) 33 64 94 () bttery energy level (%) We tke system ontext ttributes s independent vribles nd bttery dishrge rte s dependent vribles. We use the multiliner regression model shown in eqution to desribe their reltionship. 8 3brt liner3 6 4 y =.347x +.99 R² =.9936 A X time(min.) 3 44 7 3 33 64 94 5 56 86 where, (b) Figure. Bttery dishrge urve nd bttery lifetime of VideoPlyer pplition with the brightness of 55 nd 3. In this mnner, we ollet series of dishrge rtes under different system ontexts. The Tble shows smple list of system ontext ttributes nd the bttery dishrge rte. Tble. A smple list of system ontext ttributes nd bttery dishrge rte (brt, pu, wifi, io, spd) () Bttery Dishrge Rte 55,.,,.8,.56 9,.,,,.8,.47 8,.,,,.8,.4 3,.,,,.8,.35 55,,,,.6 55,.9,,,.58 55,.73,,,.55 55,.63,,,.5 55,.38,,,.5 55,.3,,,.48 55,.,,,.47 55,.,,,.46 55,.6,,, 4.69 55,.4,,, 3.67 55,.3,,,.66 55,.,,,.65 With the olleted dt, we ondut multiple liner regressions nd hieve quntittive model to desribe how the dishrge rte of the bttery hnges long with system omponent sttes. We sve the model s oeffiient sets. The modeling work is one-time work for smrt phone bttery, nd the results built from the dt n be used gin for long period before the bttery ges. In the prediting phse, we monitor the bttery energy level nd system omponent sttes under the urrent pplition senrio. Then, we use the model oeffiients nd the monitored ttributes to ompute the dishrge rte of the bttery. With the dishrge rte nd the urrent bttery energy level, we n predit the 643 x x xk x x xk A, X,,nd ε xn xn xnk n k n A is n ( n ) dependent vrible vetor representing the bsolute bttery dishrge rte, where n is the number of dishrge rtes. X is n (n k) mtrix of ttribute vlues, where k is the number of ttributes. is ( k ) vetor of regression oeffiients. is n ( n ) vetor of rndom errors, nd they ount for derivtions of the tul dt from the predited vlues. We usully think of s sttistil error nd ssume tht it is normlly distributed with men zero nd vrine, bbrevited s N,. In order to find out how the system ontext ttributes ffet the predition ury nd identify the most proper set of system ontext ttributes, we dpt model fmily of six equtions, whih inludes different ttributes seleted from (brt, pu, wifi, io, spd). Tble 3 lists the nmes of the equtions nd their desriptions. The dr eqution only onsiders the LCD brightness, nd other system ontexts re treted s onstnts. The dr eqution only onsiders CPU utiliztion. The dr3 eqution onsiders the LCD brightness nd CPU utiliztion. The subsequent equtions inorporte more nd more system ontext ttributes in the model. Tble 3. Different System Context Attributes Eqution k brt pu wifi io spd drbrt drpu dr3 3 4 5 The experiment results presented in the next setion illustrte tht different ombintions of system ontext ttributes result in different predition ury, nd there is trde-off between the omplexity nd the predition ury of the model.
We put the bsolute vlues of bttery dishrge rte nd system ontext ttributes in the mtrix nd use the method of lest squres to ompute the oeffiients. With different ombintions of ontext ttributes, we get different equtions by the regression model. They re shown s set of equtions in formul. = 36. +.8brt = 5. +.56 pu 3 = 34. +.6brt 5. pu 4 = 34. +.6brt 5. pu 8. wifi 5 = 5. +.8brt 8. pu. wifi 79. *io = 5. +.8brt 8. pu 5. 9wifi 79. *io.7*spd 6 The bove equtions desribe how the hnges of system ontext ttributes ffet the vritions of bttery dishrge rte nd the bttery lifetime. For exmple, suppose tht the urrent bttery energy level is 86. If user hnges the LCD bklight brightness vlue from 8 to 9 while keeping other ontexts fixed, then with the eqution we lulte tht the bsolute dishrge rte hnges from.43 to.49. In ddition, we n predit tht the bttery lifetime will shrink from minutes to 75 minutes. This gives the user quntittive informtion bout the hnge of the bttery lifetime nd the impts of his opertions on the bttery lifetime. 3.4 Dishrge Rte-Bsed Bttery Lifetime Predition In this prt, we will present how to predit the bttery lifetime by using the estimted dishrge rte. Refer to the bttery dishrge urve in Figure, we use formul 3 to desribe the reltionship between the bttery energy level nd the remining time: v=f t where, v is the bttery energy level in terms of perentge, represents the ontext tuple, nd t is the time in minutes. We write the liner regression funtion of the bttery dishrge urve under the ontext tuple s in formul 4: v t where, nd (- ) re the interept nd slope of the trend line, respetively. In order to illustrte the predition model more lerly, we plot the line with vrible nmes in Figure 3. ( ) mesures the hnge in the men of v for unit hnge in t, whih is the dishrge rte of the bttery. Figure 3. A trend line of bttery dishrge urve Suppose t the time t, the bttery energy level is v ur, nd the trget bttery energy level is v tr t t. Then, we lulte the bttery lifetime from t to t by the formul 5. () (3) (4) 4. EXPERIMENTS AND EVALUATION We implement the CABLI system using our pproh in n HTC G smrt phone running the Android operting system (Linux kernel.6.7). The phone hs 58MHZ Qulomm MSM7A ARM proessor nd 56MB flsh memory. It is equipped with n 5mAh/3.7V lithium-ion bttery, nd the pity of the bttery is 538mJ in terms of energy. We develop set of tools in the CABLI system. A system ontext monitor servie tool ollets the profiling dt in the running system. A modeling tool nlyzes the dt nd hieves the oeffiients of the model. A bttery lifetime inditor monitors the system ontexts nd predits the bttery lifetime online by using the prepred model oeffiients. In order to hieve good results for the regression model, we ollet lrge mount of dt from more thn 4 different test senrios. We selet 6 group smples to build the model nd use other dt to evlute the model. These smples re olleted under the senrios with stble system omponent sttes, whih re CPU utiliztion, LCD bklight brightness, WiFi stte, I/O idle rte, nd network dt trnsfer rte. We use the benhmrks listed in Tble 4 to test the predition ury. For exmple, VideoPlyer provided by HTC G produes pproximtely onstnt worklod; Simulte- written by ourselves produes vrible CPU utiliztion whih we n ontrol. Furthermore, we rndomly run pplitions, suh s settings, ontts, notes, et., to produe vrible worklod, nd nme these senrios s MisOper. Benhmrk Worklod T(v,v ) t t ur tr Tble 4. Benhmrk Desriptions Desription VideoPlyer Constnt An video plyer Jv progrm Ping Vrible An operting system ntive utility, sends dt to the server by WiFi QuikSort Constnt A sorting Jv progrm with quik sort lgorithm Dijkstr Constnt A grph serh Jv progrm tht solves the single-soure shortest pth BubbleSort Constnt A sorting Jv progrm with bubble sort lgorithm MisOper Vrible Misellneous nd pplitions, suh s settings, ontts, notes Simulte- Constnt A CPU-intensive Jv progrm with onstnt CPU utiliztion Simulte- Vrible A CPU-intensive Jv progrm with vrible CPU utiliztion In the following setions, we first show n nlysis on the energy onsumption distributions of the smrt phone. Then we evlute the fitness of the regression model. Lst, we present the omprison of our pproh with previous pproh on effiieny nd performne. 4. Energy onsumption distributions As desribed bove, the bttery dishrge rte expresses the bttery energy dissiption by the smrt phone in the unit time. Bsed on the regressive model of the bttery dishrge rte, we vur v tr (5) 644
.35 Tble 5. System omponent sttes.6 9. spd 4 io..8.8 No.3 55 4.8 No.4 55..7 No. No.3 dr3 drpu dr brt -.5 -. -.5 -. -.5 First, we ompre Wen s pproh [] (denoted s HBI) with ours (denoted s CABLI). We exeute the bove benhmrks nd monitor the bttery energy level vs. time. We predit the bttery lifetime with two different pprohes t every bttery energy level nd get the predition errors. Beuse of the limited spe, we tke VideoPlyer senrio nd ping wireless dt trnsfer senrio s exmples to illustrte the effiieny of the pprohes. From the results in Figure 6, we find tht the predition error of HBI is bout -35%~55%, while tht of CABLI is only bout -% ~%. The reson is tht HBI ssumes tht the future bttery power dringe tends to be the sme with the history. In ontrst, CABLI thinks tht the system omponents re the mjor power onsumers nd predits the bttery power dringe bsed on the urrent vlues of their sttes. Therefore, it n reflet the vrition of the remining bttery lifetime more urtely. 9 9 8 8 7 7 6 6 6 5 5 4 4 3 3 BtteryLevel Context-bsed History-bsed 7 No.4 Ping with 3KB Dt Trnsferred VideoPlyer with Brightness 55 8. No. Eqution 9.. -.5 4.3 A Comprison with Wen s Approh BtteryLevel Energy Distribution.3. Figure 5. Predition errors nd residuls of dishrge rte other io spd wifi pu brt.4.5. -.5.9.5..5 -...6.5. -.5 Our model lso n be used to support the online dynmi power mngement. For exmple, during the system exeution, we monitor the system omponent sttes nd estimte energy onsumption distributions of system omponents, nd then we n djust the worklods or sttes of the system omponents online to mke trde-off between the performne nd energy onsumption..7..5 -. As shown in Figure 4, the energy onsumption distributions of the system omponents re diret proportionl to their sttes nd resoure utiliztions, whih is in onformity with our ommon sense. For exmple, the ontext No. hs the sme brt, wifi, io nd spd ttribute vlues with ontext No.3, but its pu utiliztion is.6, whih in less thn tht of No.3. Then, the CPU energy onsumption of No. is less thn tht of No.3 by bout 4%. This demonstrtes tht our model n be used to evlute how the omponent sttes ffet energy onsumption of the smrt phone system..8.5 - - - BtteryLevel wifi.5 9 BtteryLevel Context-bsed History-bsed 8 7 6 5 5 4 4 3 3 - - - - - -3-3 -3-4 -4-4 5 System Context Time 5-3 -4 () 4 Time 6 8 (b) Figure 6. Predition errors of the pprohes. Figure 4. Energy onsumption distributions of the system omponents 4.4 Predition Errors of the Equtions We evlute the fitness of the predition model by using residuls nd predition errors of the bttery dishrge rte. The differene between the smpled vlue whih is used to build model nd the estimted vlue is lled residul. The predition error is the differene between the observed vlue nd the estimted vlue. The residuls nd predition errors of the dishrge rte re shown in Figure 5. From the results, we n find tht, the men residul of is less thn.%, nd the men predition error is less thn %. The drbrt model hs the worst bsolute residul of not more thn % nd the drpu hs the worst bsolute error of not more thn 3%. This mens tht the model with ontext ttributes inluding LCD 645 Vrible Worklod with Mis Opertions Simulte- with Vrible CPU Utiliztion 6 4 Men Errors (%) 4. Model Evlution - HBI dr3 drpu drbrt -4-6 -8 - - -4 () pu_3 pu_38 pu_63 pu_78 pu_ Men Errors (%) 55 pu.3 Men Errors Men Residuls Men Error (%) No. brt.4.35.3 Men Errors Context Number No. Men Errors nd Residuls of Dishrge Rte.4 Men Error (%) We selet four exmples tht re listed in Tble 5, nd nlyze energy onsumption distributions of the system omponents under these system ontexts. bklight, CPU utiliztion, WiFi stte, I/O idle rte nd network dt trnsfer rte performs the best, nd tht the too few system ontext ttributes ffet the performne of the regression model. Men Residuls n understnd the ontribution of eh system omponent to the dishrge rte under given ertin system ontext. HBI dr3 drpudrbrt - pu_rm_ pu_rm_3 rndom- rndom- -4-6 (d) -8 Figure 7. Men predition errors of different equtions In CABLI, different model equtions represent different omplexity levels of the model. We ompre the predition results
of bttery lifetime obtined by different equtions. In Figure 7, we tke Simulte- nd MisOper s the exmples. The results show tht, the men error of is the smllest nd is within -% ~ %, nd performs best mong the six equtions. 4.5 Predition Errors of Vritions of the Bttery Lifetime for Chnged Worklods When user hnges the worklod, whih pproh n urtely notify the user the vritions of the bttery lifetime used by the hnges? In order to nswer this question, we ompre the predition errors of vritions of the bttery lifetime given by the two pprohes. In Figure 8, we present the errors nd the perentge errors of the predited hnges under five senrios. The lbels 55->8, 55->3, 3->55 represent three senrios of the VideoPlyer pplition. Under these senrios, the user hnges bklight brightness from 55 to 8, 55 to 3, nd 3 to 55, respetively. The lbel Video->sort represents senrio, under whih, the user hnges VideoPlyer to Quiksort. The lbel pu.8->.5 represents senrio of the simulte- progrm, under whih, the user hnges CPU utiliztion from.8 to.5. From the Figure 8, we n find tht the mximum perentge error of CABLI is less thn 6%, while tht of HBI is lose to 4%. CABLI predits the bttery lifetime hnges more urtely thn HBI, nd performs better thn HBI. Predition Errors nd Perentge Errors 8 8 6 Errors 4 6 4 - Perentge Errors (%) CABLI_Err CABLI_Err% HBI_Err HBI_Err% - 55->8 55->3-4 3->55 Video->Sort pu.8->.5-4 Figure 8. Predition Errors nd Perentge Errors under hnged worklods 5. CONCLUSION We propose system ontext-wre pproh for online bttery lifetime predition. We uses multiple liner regressions to build quntittive bttery lifetime predition model for smrt phones. The model desribes how the hnges of system ontext ttributes ffet the vritions of energy onsumption nd bttery lifetime. Using this pproh, we dynmilly predit the remining bttery lifetime bsed on monitored system ontext ttributes. We implement our pproh in the HTC G smrt phone running the Android operting system. Experiments show tht our pproh predits bttery lifetime with higher ury thn prior works. The urte predition of remining bttery lifetime n provides smrt phone users with better usge experienes. 646 6. ACKNOWLEDGEMENT This work ws supported by the Ntionl High Tehnology Development Progrm of Chin (863) under Grnt No. 8AAZ33, the Ntionl Bsi Reserh Progrm of Chin (973) under Grnt No. 9CB373, the Siene Fund for Cretive Reserh Groups of Chin under Grnt No. 683, nd the Chin Postdotorl Siene Foundtion under Grnt No. 94534. 7. REFERENCES []Y. Wen, R. Wolski, C. Krintz, nd R. Krintz, "Online Predition of Bttery Lifetime for Embedded nd Mobile Devies," in Issue on Embedded Systems: Springer-Verlg Heidelberg Leture Notes in Computer Siene, 4, p. 4. []D. U. Suer nd H. Wenzl, "Comprison of different pprohes for lifetime predition of eletrohemil systems-using led-id btteries s exmple," Journl of Power Soures, vol. 76, pp. 534-546, 8. [3]L. Benini, G. Cstelli, A. Mii, E. Mii, M. Ponino, nd R. Srsi, "Disrete-time bttery models for system-level lowpower design," IEEE Trns. Very Lrge Sle Integr. Syst., vol. 9, pp. 63--64,. [4]A. Rhmti, A. Qin nd L. Zhong, "Understnding humnbttery intertion on mobile phones," in MobileHCI '7: Proeedings of the 9th interntionl onferene on Humn omputer intertion with mobile devies nd servies, New York, NY, USA, 7, pp. 65--7. [5]A. Crroll nd G. Heiser, "An nlysis of power onsumption in smrtphone," in Proeedings of the USENIX Annul Tehnil Conferene, Boston, MA, USA,. [6]J. Kng, C. Prk, S. Seo, M. Choi, nd J. W. Hong, "UserCentri Predition for Bttery Lifetime of Mobile Devies," in APNOMS '8: Proeedings of the th Asi-Pifi Symposium on Network Opertions nd Mngement, Berlin, Heidelberg, 8, pp. 53--534. [7]N. Blsubrmnin, A. Blsubrmnin nd A. Venktrmni, "Energy onsumption in mobile phones: mesurement study nd implitions for network pplitions," in IMC '9: Proeedings of the 9th ACM SIGCOMM onferene on Internet mesurement onferene, New York, NY, USA, 9, pp. 8--93. [8]N. Rvi, J. Sott, L. Hn, nd L. Iftode, "Context-wre Bttery Mngement for Mobile Phones," in PERCOM '8: Proeedings of the 8 Sixth Annul IEEE Interntionl Conferene on Pervsive Computing nd Communitions, Wshington, DC, USA, 8, pp. 4--33. [9]A. Shye, B. Sholbrok nd G. Memik, "Into the wild: Studying rel user tivity ptterns to guide power optimiztion for mobile rhitetures," in Proeedings of the Interntionl Symposium on Mirorhiteture (MICRO 9), 9. []H. Flki, R. Mhjn, S. Kndul, D. Lymberopoulos, R. Govindn, nd D. Estrin, "Diversity in smrtphone usge," in MobiSys ': Proeedings of the 8th interntionl onferene on Mobile systems, pplitions, nd servies, New York, NY, USA,, pp. 79--94.