Real-Time Transmission Mechanism Design for Wireless IoT Sensors with Energy Harvesting under Power Saving Mode

Transcription

1 1 Real-Tme Transmsson Mechansm Desgn for Wreless IoT Sensors wth Energy Harvestng under Power Savng Mode Jn Shang, Muhammad Junad Faroo, Student Member, IEEE, and Quanyan Zhu, Member, IEEE arxv: v1 [cs.sy 6 Dec 218 Abstract The Internet of thngs (IoT) comprses of wreless sensors and actuators connected va access ponts to the Internet. Often, the sensng devces are remotely deployed wth lmted battery power and eupped wth energy harvestng eupment such as solar panels. These devces transmt real-tme data to the base statons whch s used n the detecton of other applcatons. Under suffcent power avalablty, wreless transmssons from sensors can be scheduled at regular tme ntervals to mantan real-tme detecton and nformaton retreval by the base staton. However, once the battery s sgnfcantly depleted, the devces enter nto power savng mode and s reured to be more selectve n transmttng nformaton to the base staton (BS). Transmttng a partcular pece of sensed data wll result n power consumpton whle dscardng t mght result n loss of utlty at the BS. The goal s to desgn an optmal dynamc polcy whch enables the devce to decde whether to transmt or to dscard a pece of sensng data partcularly under the power savng mode. Ths wll enable the sensor to prolong ts operaton whle causng mnmum loss of utlty of the applcaton. We develop a mathematcal model to capture the utlty of the IoT sensor transmssons and use tools from dynamc programmng to derve an optmal real-tme transmsson polcy that s based on the statstcs of nformaton arrval, the lkelhood of harvested energy, and desgned lfetme of the sensors. Numercal results show that f the statstcs of future data valuaton can be accurately predcted, there s a sgnfcant ncrease n the utlty obtaned at the BS as well as the battery lfetme. Index Terms Internet of thngs, low power wde area network, long range wde area network. I. INTRODUCTION The Internet of thngs (IoT) comprses of wreless sensors and actuators connected va access ponts to the Internet. The wdespread adopton of the IoT coupled wth energy effcent protocols have tremendous applcatons and use cases n transportaton, healthcare, smart ctes, and nfrastructure systems [2. Many IoT applcatons n these scenaros such as waste water montorng, smart garbage collecton, smart street lghtng systems, ar ualty montorng, etc., reure contnuous low-rate streamng data reported from battery powered devces over a long perod of tme [3. Usually sensors are reured to contnuously send real-tme sensed data to a BS for further processng and to be converted nto actonable nsghts. Hence, power savng s essental n such applcatons to satsfy the operatonal lfe tme targets. Jn Shang s wth the Department of Mathematcs, New York Unversty Abu Dhab, UAE. Muhammad Junad Faroo and Quanyan Zhu are wth the Department of Electrcal & Computer Engneerng, Tandon School of Engneerng, New York Unversty, Brooklyn, NY 1121, USA, E-mals: js8544, mjf514, z494}@nyu.edu. Fg. 1: Illustraton of an uplnk IoT system. A battery powered sensor eupped wth energy harvestng devce transmts sensed data to the base staton, whch s subseuently used for data analytcs. Energy effcent medum access control (MAC) protocols are reured to ncrease the operaton tme of battery powered IoT sensors and devces. More energy effcent MAC protocols are beng developed known as the low power wde area networks (LPWANs) [1. One such protocol developed for IoT devces s referred to as the long range wde area network (LoRaWAN) [4 protocol, whch s optmzed for battery-powered end-devces. These MAC protocols allow for the remotely deployed devces to operate several years wthout the need for replacng the battery. LoRa networks [5 Three dfferent classes of LoRa [3 devces have been developed namely Class A, B, and C, out of whch Class A and B are battery powered whle Class C are mans powered [6. Class A devces only have two short receve wndows after transmttng a packet. After the receve wndows, Class A devces goes to sleep for conservng energy. Class B devces, on the other hand, have extra receve wndows at scheduled ntervals [6. RF transmssons cost the most n terms of energy n all classes of the LoRa protocol [7. In ths paper, we focus on desgnng a power savng mode for IoT sensors that comes nto play once a set amount of battery s remanng and the target number of measurements by the sensor s hgher than the number of transmssons that the battery can support. Therefore, the developed framework ams to assst n maxmzng the utlty of data sent to the BS usng the avalable battery resources. Whle research s beng done on mprovng the physcal layer effcency of these MAC protocols, we propose a crosslayer approach towards a more cogntve MAC. A crtcal component that leads to battery depleton s the uplnk transmssons by the IoT sensor[. Therefore, the key to reducng the energy consumoton and subseuently extendng battery lfetme n IoT devces s to mprove the transmssons to get more utlty wth mnmum battery power. The

2 developed framework beleves that usng nformaton about the amount of remanng battery, the usefulness of nformaton, and the channel state nformaton, the sensor can effectvely decde on transmttng or dscardng sensed data. We make use of dynamc decson theory to mprove the transmsson effcency of the sensors. As more and more powerful computatonal capabltes are beng embedded onto IoT devces, there s more room to ncorporate ntellgence onto them. Exstng work focuses on desgnng energy effcent sleep schedules for IoT devces to ensure a gven QoS and consder metrcs such as bt-rate, packet delay, and packet loss rate. Whle these metrcs are mportant for contnuous data transmssons n sensor network, n most IoT networks, the data s transmtted only at the occurrence of an event. For dfferent types of sensed data, an optmal transmsson polcy mght be dfferent. For nstance, for spked data, e.g., one comng from a moton sensor, the optmal transmsson polcy mght be dfferent as compared to a temperature sensng applcaton. In ths paper, we consder real-tme or msson-crtcal IoT applcatons, whch cannot tolerate delay n the transmsson. In other words, data not sent to the base staton mmedately after generaton s consdered to be futle. We hope that ths research wll pave the way for the development of more cogntve and strategc transmsson mechansms and protocols to enhance the operatonal lfetme of battery powered devces whle achevng msson specfc goals. A. Problem Descrpton Although energy effcent mechansms are avalable. However, the transmssons may be redundant, e.g., when the data sent by the sensors s not mportant. Snce the IoT sensors have embedded computng capabltes, they can evaluate the usefulness of transmttng the data as opposed to conventonal wreless sensor networks. Partcularly, the cognton s mportant once the devce s n power savng mode to prolong ts perod of operaton wthout reurng a battery replacement. The problem under consderaton s to desgn a polcy for realtme transmsson decson based on the potental utlty of the nformaton. Perodc transmsson of data mght result n ms-detecton of mportant real-tme data The goal n ths paper s to mprove the utlty obtaned from transmttng data by beng more selectve and adaptve n the transmsson decsons. We leverage theores from dynamc programmng and stochastc processes to construct an optmal dynamc transmsson framework for use under a power savng mode n Wreless IoT sensors. B. Related Work Power savng has been one of the key focus areas for researchers workng on wreless sensors and IoT endpont devces [8. Recently, the Defense Advance Projects Agency (DARPA) has started a Near Zero Power RF and Sensor Operatons (N-ZERO) program that s amed at developng sensors for mltary purposes, whch can stay dormant wth neglgble power consumpton untl awakened by an external trgger [9. Apart from reducng the power consumpton of devce crcutry, t reures the development of more cogntve MAC protocols to support the low power operaton. However, for tradtonal IoT applcatons, the cogntve MAC may suffce as a power savng mode under specal crcumstances snce data may have to be transmtted more freuently as compare to mltary applcatons. Developng energy effcent transmsson polces for communcaton systems has been a long standng area of research. Most exstng works develop onlne and offlne transmsson polces for tradtonal communcaton data. The mportance of the data s not consdered n the frameworks. Generally try to maxmze the long term average throughput by adjustng the transmt power of the transmtter n real-tme [1. The goal s to transfer maxmum amount of data from the source to the destnaton. However, n our work, the goal s to transmt the most valuable nformaton to the base staton. The ratonale behnd ths objectve s that many IoT sensng applcatons partcularly, the sensng applcatons, wll only be transmttng the most valuable data to the base statons nstead of transmttng all the sensed data. [11 [12 Sleep modes have been desgned for mprovng energy effcency n LTE networks [13. Generally, the alternatve sleep/wake cycles are proposed for delay tolerant applcatons where the data s buffered to be transmtted when the sensor s n the actve stage [14. To manage power consumpton for contnuously transmttng devces, a new mechansm referred to as dscontnuous recepton/transmsson (DRX/DTX) [15 has been ncorporated nto the 3GPP LTE-A standard, whch allows devces to go to sleep by turnng off ther rado nterfaces n dfferent patterns. A sgnfcant amount of work has been done n the lterature to optmze these sleep-wake patterns by consderng the ualty of servce constrants [16. However, the regular sleep wake schedules mght not be the best polcy partcularly when data of varyng mportance s beng generated and has to be transmtted mmedately to the BS. Exstng approaches towards achevng energy effcency n data transmsson s lmted to effectve schedulng of transmssons and algnng them wth the harvested energy. Add references from WSN lterature and cellular uplnk cases. Fewer efforts have been made towards real-tme transmsson mechansm consderng the energy effcency. Whle offlne transmssons can be scheduled accordng to the harvested energy, the real-tme data needs to be transmtted mmedately. Otherwse, t loses the utlty. In ths paper, we propose a data cognzant framework for real-tme transmsson decsons n the uplnk of IoT sensors. The allocaton of stochastc seuentally arrvng tasks to resources has been well studed n management scence and operatons research lterature [17. We leverage the developed models and methodologes to make onlne transmsson decsons and expand t to encompass energy harvestng. Dynamc allocaton of resources to stochastc and seuentally arrvng reuests has been studed n the cloud com-

3 TABLE I: Lst of symbols used. Symbol Descrpton N Z + Number of avalable battery unts n Z + Number of target measurements remanng x R Valuaton of the measurement n the th tme slot f X (x) Probablty densty functon of sensed data valuaton F X (x) Probablty dstrbuton functon of sensed data valuaton [, 1 Probablty of transmsson success from sensor to BS U(.) R Utlty obtaned by successful transmsson of sensed data [, 1 Probablty of harvestng a unt of energy n each tme slot h R Fast fadng wreless channel gan ρ th R Channel ualty threshold α 1 Probablty of transmsson success under hgh channel gan α Probablty of transmsson success under hgh channel gan g( 1 ) Dstrbuton of condtonal on the prevous value V N,n (, x) The expected maxmum total utlty functon putng context n [18. However, t s based on a contnuous tme model as the reuests arrve at random tmes. In ths paper, we consder a dynamc transmsson decson problem where sensng data s generated contnuously wth stochastc valuaton. C. Contrbutons A summary of the man contrbutons s provded below: 1) We propose an optmal model that maxmzes the total receved utlty to determne whether a captured data s transmtted. 2) We develop a reslent and dynamc algorthm that runs n real-tme. The developed decson support framework s dynamcally optmal. 3) We desgn and run several numercal tests to demonstrate the optmalty of the algorthm n comparson wth exstng protocols. The rest of the paper s organzed as follow: Secton II provdes a descrpton of the system model and ts assumptons. Secton III shows the methodology for solvng ths problem. Secton IV descrbes the reslent and dynamc algorthm. Sectons V shows the numercal test results for several cases and comparson wth other methods. II. SYSTEM MODEL In ths secton, we provde a descrpton of the network model. For the convenence of readers, the notatons used throughout ths paper are summarzed n Table I along wth a bref descrpton. A. System Model We consder an Internet of Thngs network consstng of IoT sensors and Base Statons (BS). Sensors are deployed remotely wth lmted battery. They are desgned to operate for a prolonged tme perod as battery replacement s costly and dffcult. They collect data and transmt them to the base staton, whch has a utlty based on the value of the data. Sensors are also eupped wth energy harvestng devce such as solar panels that enable them to generate battery power. To mnmze cost, sensors are eupped wth lmted memory and computatonal power, therefore an offlne algorthm wth bufferng s not allowed. We consder a tme slotted system, n whch sensng data s generated at ntervals of duraton τ s. A target operaton tme, denoted by T s set for the sensor, whch mples that n = T τ Z+ s the target number of measurements that wll be made by the sensor. We assume that the energy consumpton of crcut processng and dle operaton of the sensor s neglgble as compared to the power consumpton of uplnk transmsson. At each tme nstant, data s generated by the sensor and ts valuaton or sgnfcance for the applcaton, denoted by X s modeled as a random varable wth probablty densty functon (pdf) f X (x) and cumulatve dstrbuton functon (cdf) F X (x). The sgnfcance of the data generated at the th tme slot s denoted by x, 1. At each tme slot, a unt of renewable energy may be generated wth a probablty [, 1. 1 B. Channel Model We use a sgnal capture model to determne the successful recepton of packets from the sensor to the base staton. Ths means that the sgnal power receved at the BS s expressed as P t h ν η, where P t s the transmt power, h denotes the channel gan at tme slot, ν s the dstance to the BS, and η s the path loss exponent. We assume that the wreless channel experences Raylegh fadng,.e., the random channel gan, denoted by h, follows an..d. exponental dstrbuton wth mean µ 1 and h s a realzaton of the channel at tme slot. In our model, We assume that complete channel state nformaton (CSI) s avalable to the IoT devce 2. It means that both nstantaneous (or short term) CSI and statstcal (or longterm) CSI s known to the sensor. The nstantaneous CSI s used to make real-tme decsons on transmssons whle the expectaton about future channel condtons comes from the statstcal CSI. We use a bnary abstracton model for the state of the wreless channel. The fast fadng wreless channel gan s modeled as ndependent and dentcally dstrbuted (..d.) random varables at each tme nstant. At any partcular tme nstant, the channel can be n ether good or bad state based on the realzaton of the channel gan. Ths dstncton can be made based on an arbtrary threshold denoted by ρ th. The average probablty of successful transmsson durng good and bad channel state s denoted by α 1 and α respectvely. The channel gan essentally determnes whether a transmtted packet wll be receved at the recever successfully or not. However, there are other factors that nfluence the successful recepton of a packet f metrcs based on the sgnal-tonterference-plus-nose-rato (SINR) are used. We ncorporate the average mpact of these factors such as the dstance dependent sgnal decay and the nterference nto the parameters α 1 and α. Therefore, the probablty of successful transmsson 1 The slot nterval τ can be adjusted to ensure that a unt of energy can be generated that s suffcent to support a sngle transmsson. 2 Ths assumpton s reasonable for practcal systems snce the devce may be recevng dscovery beacons from the BS. Moreover, there mght be dedcated control channels avalable to convey such nformaton.

4 condtonal on the knowledge of the channel gan, denoted by P s can be expressed as follows: α1 f h ρ P s = th, (1) α f h < ρ th. Note that the the probablty of success s a random varable that depends on the state of the channel. The expected probablty of successful transmsson can be expressed as follows: E[P s = α 1 (1 F h (ρ th )) + α F h (ρ th ), (2) = α + e µρth (α 1 α ), (3) where (3) follows from the Raylegh fadng assumpton,.e., exponentally dstrbuted channel gans. C. Energy Harvestng We assume a unt transton Markovan energy harvestng model,.e., at each tme slot, there s a probablty that a unt of energy wll be harvested. Therefore, the number of battery unts avalable at the th tme slot evolve as follows: N + 1, w.p., N +1 =, = 1,..., n 1, (4) N, w.p. 1. If there s only one remanng measurement to acheve the target, then the data s transmtted and the sensor shuts down completng ts desred lfetme. Therefore, the battery status s not updated at the last stage 3. D. Assumptons For our model, we made several reasonable assumptons as follow: 1) Every uplnk transmsson costs the same amount of battery power. 2) The transmsson channel s always avalable for the sensor,.e., every transmsson s successful and utlty s ganed. 3) The dstrbuton of data values s condtonal on the prevous value(s). 4) Energy harvestng for the sensor s a Markov process. It s pertnent to menton that the developed framework s desgned for utlty maxmzaton n power savng mode. Under normal operaton mode,.e., when suffcent amount of battery power s avalable, the sensor may apply standard or more customzed transmsson protocols optmzed for other performance metrcs such as false alarm rate, ms-detecton probablty, etc. However, once the target measurements are hgher than the number of battery unts remanng, then the optmal transmsson mechansm for utlty maxmzaton may be employed. We assume that the power savng mode s actvated when n measurements are remanng to reach the target lfetme of the sensor and only N n battery unts are avalable. E. Problem Formulaton The utlty of successful recepton of the measurement, whose valuaton s x, at the BS s denoted by U(x ) : R R. 3 Note that at the last measurement, the sensor s desgned to transmt by default and effectvely shuts down unable to receve further energy to contnue operaton. The problem of the sensor can be formally expressed as follows: [ n V (N, n) = maxmze E U(x k ) k y k y Y k=1 subject to Battery level dynamcs n (4). where y k, 1}, k = 1,..., n, and n k=1 y k = N. Hence, the vector y denotes the transmsson polcy, whereby N out of n measurements are selected to be transmtted. Note that the battery level at each tme slot N evolves stochastcally accordng to the dynamcs expressed n (4). Y denotes the set of all possble permutatons of the vector [1 N, n N T. In essence, the problem s to select the best data to transmt to the BS under when the data s arrvng seuentally whle consderng the nstantaneous channel ualty. The III. METHODOLOGY In ths secton, we present a soluton to the above problem usng dynamc programmng. A. Decson Sub-problem In order to use dynamc programmng to solve our problem, we need to frst formulate a decson sub-problem for every stage. At the -th stage, the sensor collects data of value x and harvested battery unts. It has N battery unts remanng (ncludng the new harvested unts) and n stages to go. Now the sensor needs to decde whether to transmt x or not gven the above condtons. In order to make the optmal decson, we consder ts revenue of utlty from both optons. 1) If t transmts x, 1 battery unt s consumed and t wll gan a revenue of U(x). Then at round (+1)-th, the sensor wll have N battery unts, and n 1 data to be collected. 2) If t dscards x, no battery s consumed and no utlty s ganed. At round (+1)-th, the sensor wll have N + +1 battery unts, and n 1 data to be collected. Let V N,n (, x) denote the maxmal revenue for a sensor wth N battery unts, n more data to collect, whch just harvested unts and collected x. The optmal decson s to take the opton whch gves maxmal revenue of utlty. Therefore we can establsh the followng relaton regardng V N,n (, x ): U(x ) + V N++1 1,n 1( +1, x +1 ), V N,n (, x ) = max V N++1,n 1( +1, x +1 ) the sensor should transmt the message f: U(x ) > V N++1 1,n 1( +1, x +1 ) V N++1,n 1( +1, x +1 ) Theorem 1. If the sensed data valuaton at the th tme slot has valuaton x, the nstantaneous channel gan s h, and the utlty acheved by the BS on successful recepton of data (5) (6)

5 s U(x ), then the IoT sensor should transmt the data f ts valuaton x a [ n N, where a n N = U 1 (1 ) E[V (N, n 1) V (N 1, n 1)+ E[V (N + 1, n 1) V (N, n 1), (7) P s and the value functon, denoted by V (N, n), f N battery unts are avalable and n measurements are targeted, s expressed as follows: V (N, n) = Proof. See Appendx A. U(x )P s + E[V (N, n 1)+ (1 )E[V (N 1, n 1), f x a n N, E[V (N + 1, n 1)+ (1 )E[V (N, n 1), f x < a n N. (8) The expected value functon can be obtaned accordng to the followng lemma. Lemma 1. The expected value functon f N battery unts are avalable and n measurements are targeted, denoted by V (N, n) s expressed as follows: E[V (N, n) = E[P s [ a n N U(x)f X (x)dx + (1 F X (a n N)) E[V (N, n 1) + (1 )E[V (N 1, n 1) F X (a n N) [ E[V (N + 1, n 1) + (1 )E[V (N, n 1) Proof. The proof follows from takng the expectaton of the value functon V (N, n) defned n Theorem 1. The transmsson decson polcy can be computed usng backward nducton. The termnal condtons can be expressed as follows: 1) n = If n =, then the lfetme measurement target of the sensor has been acheved. Hence, the value V (N, ) = for all values of N. Ths restrcton s mposed by desgn. 2) N = If N =, there s no battery power left: Dscard the data V,n (, x ) = V +1,n 1( +1, x +1 ) V s not zero because t wll harvest energy n later stages. 3) N = n If N = n,.e., there are eual number of battery unts as the number of remanng measurements. In that case, the optmal polcy s to transmt n all tme slots,.e., y = 1 N. 4) If N > n, there s suffcent battery power: Transmt the data V N,n (, x ) = V N++1 1,n 1( +1, x +1 ) Same as exstng protocols. 5) N < n +. (9) B. Specal Cases In ths subsecton, we provde some analytcal results for specal cases. We assume that U(x) = x. In ths secton, we provde some analytcal expressons for the thresholds to decde on real-tme transmssons. 1) Exponental dstrbuted data valuaton: f X (x) = Λe Λx. Corollary 1. a 2 1 = (1 )E[XE[P s P s = (1 )(α + e µρ th (α 1 α )) Λ, a 3 1 = (3 2 )E[XE[P s + (1 2)(1 + e 2Λa1 2 (Λa )) + e Λa1 2 ( 1)E[XE[ = (3 2 + e Λa1 2 ( 1))(α + e µρ th (α 1 α )) Λ + (1 2)(1 + e 2Λa1 2 (Λa ) (1) P s Usng a smlar methodology, the remanng thresholds can be computed teratvely from the boundary cases. Proof. See Appendx B. 2) Unformly dstrbuted data valuaton: f X (x) = 1 x x. Corollary 2. Smlarly, we get a 2 1 = (1 )E[XE[P s = (1 )( x + x)(α + e µρ th (α 1 α )) 2, a 3 1 = ( )( x + x)(α + e µρ th (α 1 α )) 4P s + (3 x2 + 2 xx + x 2 )(1 2)(α + e µρ th (α 1 α )) 16( x x)p s 3) No energy harvestng ( = ) : (11) Corollary 3. a 2 1 = E[XE[P s = xf X(x)dx(α + e µρ th (α 1 α )), ( ) a 3 1 = E[P s F X (a 2 1)E[X + (1 F X (a 2 1)) xf a 2 X (x)dx 1 = (α + e µρ th (α 1 α ))F X (a 2 1) xf X(x)dx + (α + e µρ th (α 1 α ))(1 F X (a 2 1)) xf a 2 X (x)dx 1 (12) IV. RESULTS In ths secton, we present the dynamc and reslent decson algorthm based on the dynamc programmng soluton we developed n the last secton. EV s the 2 D array that stores the expected total revenue gven N and n. The tme complexty of RUNTIME s O(1) per operaton, whch means t s a realtme algorthm. The space complexty s O(Nn), whch s the

6 Fg. 2: Cogntve Process Flow Fg. 3: Example Trace of Exponentally Dstrbuted Data Fg. 4: Example Trace of Unformly Dstrbuted Data sze of the threshold table. For a devce of N = 13 and n = 13, the storage space needed s approxmately 4M B. Therefore, ths mechansm s effcent for devces wth lmted computatonal power and storage space. The work flow s shown n Fgure 2. V. C OMPARISON AND N UMERICAL E XPERIMENTS In ths secton, we test our proposed optmal dynamc transmsson polcy for power savng mode on..d. data whose valuaton s generated accordng to a known dstrbuton and compare ts performance wth other transmsson polces. The duraton of each tme slot s selected to be τ = 1 ms. We set the average probablty of successful transmsson n good and bad channel states as α1 =.8 and α =.2 respectvely. ρth and µ are set to.5. In order to test the effcency of our mechansm, we ran several numercal tests and compare t wth exstng protocols. We performed tests for exponental dstrbutons and unform dstrbutons. We also tested the effect of energy harvestng. The metrcs we used for evaluatng the performance are total utlty ganed and battery lfetme. For each test, we random draw 1 data x1, x2,..., x1 accordng to ther dstrbuton. The valuaton of data s the data tself, whch s, U (x) = x. 1 tests are run for each of the sensors startng wth N battery unts, N = 1, 2,..., 1. Each sensor follows a fxed strategy. At the -th stage, each sensor decdes on whether to transmt the data based on ts strategy untl t runs out of battery or the test ends. Then we wll compare the total utlty ganed and battery lfetme. For each data valuaton dstrbuton and energy harvestng condton, the tests are taken 5 tmes to average out the random errors. The comparson strateges we tested are as follows: 1) Greedy Transmsson: Ths s the normal protocol for data transmsson. Sensors transmt every data they capture when t has enough battery regardless of the valuaton of data. 2) Perodc Transmsson: Ths polcy s a sleep-wake cycle nspred polcy that does not use any ntellgence n transmttng data. Instead, t transmts data perodcally regardless of the valuaton of data. 3) Statc Threshold: We mpose a constant threshold on the data valuaton for transmsson. In other words, the data s transmtted f ts valuaton determned by the sensor s hgher than a partcular level. Several dfferent levels are nvestgated as part of our comparson. Fg. 5: Optmal Threshold for transmttng data wth unformly dstrbuted data valuaton and no energy harvestng,.e., =. Fg. 6: Optmal Threshold for transmttng data wth exponentally dstrbuted data valuaton and no energy harvestng,.e.,wth = Fg. 7: Optmal Threshold for Exponentally Dstrbuted Data wth =.1 Fg. 8: Average Total Utlty for Unformly Dstrbuted Data wth = Fg. 9: Average Total Utlty for Exponentally Dstrbuted Data wth = Fg. 1: Average Total Utlty for Exponentally Dstrbuted Data wth =.1 Fg. 11: Average Battery Lfetme for Unformly Dstrbuted Data wth = Fg. 12: Average Battery Lfetme for Exponentally Dstrbuted Data wth =

7 Fg. 13: Average Battery Lfetme for Exponental Dstrbuted Data wth =.1 A. Unform Dstrbuton wth No Energy Harvestng In ths test, the dstrbuton of data valuaton and the energy harvestng condton s:.5 f x 2 f(x) =, = (13) otherwse An example of the randomly drawn data set s shown n Fgure 4. The dstrbuton of the valuaton of data s unform n [, 2. The optmal threshold calculated s Fgure 5. We plotted the optmal thresholds for varng battery levels and desrable measurements. We can observe that as the expected number of measurements ncreases, the threshold gets hgher, whch means that the optmal algorthm holds the battery and wats for larger data when there are more data to come. When the sensors have more battery unts to spend, the sensor lowers the threshold to acheve maxmum total utlty. For smaller N, the thresholds converge to x max = 2 very uckly because transmttng data s very costly the chance of a data wth valuaton close to 2 s very hgh. For any battery level, when the number of measurements s less than the number of battery unts, whch s n N, there s suffcent battery and the optmal transmsson polcy s to transmt every data, and thus the optmal threshold s zero. In comparson wth other strateges, Fgure 8 and Fgure 11 show the average total utlty and average battery tme for dfferent strateges wth dfferent startng battery level. Every lne n Fgure 8 s approxmately lnear and the optmal polcy acheves the hghest total utlty, but the margn s relatvely small. For all Statc Threshold strateges, the average utlty t gans from transmttng one data s the same and f there s nsuffcent battery, : E[Total Utlty) = NP s U(x)f X (x)dx (14) s a constant where t represents the fxed threshold. Ths s because the expected revenue from spendng every battery unt s the same, and every battery unt s consumed when there s nsuffcent battery. We can also vew Greedy and Perodc Transmsson as Statc Threshold wth t = because there s no selecton of data. Ths fact also explans why Perodc and Greedy transmssons have the same revenue when the battery s nsuffcent and why hgher threshold yelds hgher revenue. The optmal polcy also has a lnear curve because the threshold converges to 2 very fast. The battery lfetme shown n Fgure 11 shows that the optmal polcy acheves a huge gan n operaton tme when the battery s nsuffcent. The optmal polcy reaches almost t 1 wth very lmted startng battery level, whch means that t can almost work untl the desred operaton tme ends wth few battery whle gans maxmal utlty. To show why the comparson polces are straght lnes, we can also derve the formulas for the comparson strateges. For the Statc Threshold, We can prove that the expected battery lfetme of Statc Threshold transmsson polcy wth N battery unts and n desred data s: N E[Battery Lfetme = (15) 1 F X (t) when n s suffcently larger than N. Ths s because the chance of havng a data wth valuaton more than t s 1 F X (t), and thus one n every 1/(1 F X (t)) data s trasmtted. For Perodc Transmsson polces, t s obvous that: where p s the perod. E[Battery Lfetme = pn (16) B. Exponental Dstrbuton wth No Energy Harvestng In ths test, the dstrbuton of data valuaton and the energy harvestng condton s: e x f x f(x) = otherwse, = (17) An example of the randomly drawn data trace s shown n Fgure 4. Ths s the exponental dstrbuton wth λ = 1. Compared to the unform dstrbuton, the most of the data have a valuaton less than 2. Fgure 6 shows the optmal threshold for varyng battery levels and desrable measurements. Compared to the unform dstrbuton, the threshold does not converge because the dstrbuton of x has no upper bound. Fgure 9 plots the average total utlty aganst dfferent startng battery levels. It s obvous that the curve for optmal polcy s not lnear any more because the threshold does not converge, whle the rest of the strateges reman lnear. And therefore the optmal strategy receves more utlty by a hgher margn. Fgure 12 s the average battery lfetme of the polces. It s almost dentcal to the unform case where the optmal polcy wns wth a large gap ahead of the comparson polces. C. Exponental Dstrbuton wth Energy Harvestng In ths test we examne the effect of energy harvestng. The condtons are: e x f x f(x) =, =.1 (18) otherwse whch s the same as the prevous test added.1 change of energy harvestng at every stage. The thresholds are shown n Fgure 7. Compared to the test wth no energy harvestng, t seems lke the curves n Fgure 6 extended. Intutvely, energy harvestng allows more battery unts to be consumed for transmttng, and therefore the curves are of the same shape as the prevous test but wth x-axs extended. Fgure 1 shows the average total utlty. An exceptonal phenomenon s that the optmal polcy gans much more utlty

8 than the others when fewer battery are avalable, and the gap decreases as battery level ncreases. Ths can be explaned by the pattern n the thresholds. Wth small N, the threshold ncreases very fast as battery ncreases. But the threshold curves saturate wth very large N and the utlty curve thus become straght lnes. The battery lfetme s dsplayed n Fgure 13. Wth energy harvestng, the gap between the optmal polcy and the comparson strateges s huge from the begnnng. When battery s very lmted, the optmal polcy wats longer than the ones wth statc thresholds and thus receve the full benefts of energy harvestng. Polces wth low threshold are shut down very early and no further harvested energy s ganed. In the results, we have demonstrated that there can be sgnfcant gans n the performance as well as operaton lfetme of the IoT sensors usng the developed transmsson framework. However, these numbers depend on the specfc utlty functon employed as well as the target number of measurements set by the sensor. Hence, the gans cannot be generalzed for arbtrary cases. VI. CONCLUSION & FUTURE WORK In ths paper, we develop an onlne transmsson mechansm for power savng mode for IoT sensor devces. In practce, f the statstcs of data valuaton can be accurately predcted, there s a potental for sgnfcant mprovement n the utlty as well as battery lfetme of the sensor. Several dfferent drectons can be pursued as part of the future work. The case where the data valuaton at each tme step depends on the valuaton of the prevous one can be explored. A markov chan modelng s reured to model the data valuaton representng dfferent applcaton scenaros. APPENDIX A PROOF OF THEOREM 1 For the general case, f the sensor has N 1 unts of battery remanng and n > n target measurements at the th tme slot, then the decson has to be made to transmt the current measurement x or skp transmsson n the hope of beng able to transmt data wth hgher valuaton n the future. If the data s transmtted, a utlty U(x ) wll be receved at the BS wth a probablty P s,.e., f the data successfully gets transmtted, and N 1 battery unts are remanng for future n 1 measurements. On the other hand, f the decson s to skp the transmsson, then there s zero utlty at the BS wth certanty and N battery unts are stll avalable for the remanng n 1 measurements. However, once the decson has been taken at the th tme slot, there mght be an addtonal battery unt avalable for transmsson from the harvested energy wth a probablty of. Therefore, there s an addton of a battery unt wth a probablty of makng N and N + 1 battery unts avalable n the cases when the sensor transmts and skps respectvely. The decson problem s llustrated n the form of a tree n Fgure 14 where the leaves pont towards the expected future utlty wth the remanng battery unts and target measurements after the ntal decson has been made. Conseuently, at the root node, the value functon f N battery E[V (N, n 1) U(x )P s 1 E[V (N 1, n 1) N battery unts n measurements E[V (N + 1, n 1) 1 E[V (N, n 1) Fg. 14: Decson tree for the th tme slot f N battery unts are avalable and n measurements are remanng. E[U(X)E[P s U(x )P s 1 N = 1, n = 2 E[U(X)E[P s Fg. 15: Decson tree at th tme slot wth N = 1 and n = 2. unts and n transmssons are remanng can be expressed as follows: V (N, n) = max y ( U(x ) + E[V (N, n 1)+ y,1} (1 )E[V (N 1, n 1)), (1 y) (E[V (N + 1, n 1)+ } (1 )E[V (N, n 1)), (19) where the varable y = 1 mples that the sensor should transmt at the current tme slot, whle y = mples that the transmsson should be skpped. The soluton to (19) s y = 1,.e., to transmt, f U(x ) + E[V (N, n 1) + (1 )E[V (N 1, n 1) E[V (N + 1, n 1) + (1 )E[V (N, n 1) and y = otherwse,.e., not transmt. It leads to the transmsson condton n Theorem 1 based on the nstantaneous data valuaton x and transmsson success probablty. We denote the comparson threshold on x when N battery unts are avalable and n measurements are remanng as a n N. It s then straghtforward to show that the value functon n (19) can be expressed as n (8). APPENDIX B PROOF OF COROLLARY 1 If there are two measurements remanng to acheve the target and one unt of battery,.e., N = 1 and n = 2, then at the measurement of data at the (n 2) th tme slot, the decson tree s shown n Fgure 15. The decson problem s max The decson problem for the case when n = N s trval snce the problem reduces N to max y k=1 U(x k) k y k. In other words, the soluton s to transmt n all avalable tme slots,.e., y = 1 N. the sensor should transmt the message f: (1 ) E[U(X)E[P s, (2) where the value functon s expressed as follows: U(x ) V (2, 1) = + E[U(X)E[P s, f x a 1 2, E[U(X)E[P s, f x < a 1 2. (21) x > U 1 [

9 U(x ) 1 N = 1, n = 2 N =, n = 2 1 N = 1, n = 3 1 N = 2, n = 2 1 N = 1, n = 2 1 Fg. 16: Decson tree at th tme slot wth N = 1 and n = 3. For notatonal convenence, = E[U(X)E[P s. [15 C. S. Bontu and E. Illdge, DRX mechansm for power savng n LTE, IEEE Communcatons Magazne, vol. 47, no. 6, pp , Jun. 29. [16 J. Lang, J. Chen, H. Cheng, and Y. Tseng, An energy-effcent sleep schedulng wth QoS consderaton n 3GPP LTE-Advanced networks for nternet of thngs, IEEE Journal on Emergng and Selected Topcs n Crcuts and Systems, vol. 3, no. 1, pp , Mar [17 C. Derman, G. J. Leberman, and S. M. Ross, A seuental stochastc assgnment problem, Management Scence, vol. 18, no. 7, pp , [18 M. J. Faroo and Q. Zhu, Adaptve and reslent revenue maxmzng dynamc resource allocaton and prcng for cloud-enabled IoT systems, n Annual Amercan Control Conference (ACC 218), Mlwaukee, WI, USA, Jun The tree s three levels deep when there are three measurements remanng. From Fgure 16 we know that x should be transmtted f: [ x > U 1 (E[V (2, 2) E[V (1, 2)) + 1 (E[V (1, 2) E[V (, 2)) By computng the respectve expected value of V Lemma 1 we get the desred threshold. REFERENCES from [1 U. Raza, P. Kulkarn, and M. Sooryabandara, Low power wde area networks: An overvew, IEEE Communcatons Surveys Tutorals, vol. 19, no. 2, pp , Second Quarter 217. [2 A. Al-Fuaha, M. Guzan, M. Mohammad, M. Aledhar, and M. Ayyash, Internet of thngs: A survey on enablng technologes, protocols, and applcatons, IEEE Communcatons Surveys Tutorals, vol. 17, no. 4, pp , Fourth Quarter 215. [3 U. Noreen, A. Bounceur, and L. Claver, A study of LoRa low power and wde area network technology, n Internatonal Conference on Advanced Technologes for Sgnal and Image Processng (ATSIP 217), May 217. [4 LoRaWAN Specfcaton, LoRa Allance, Beaverton, OR, USA, 215. [Onlne. Avalable: lorawantm specfcaton -v1.1.pdf [5 A. Augustn, J. Y, T. Clausen, and W. M. Townsley, A study of LoRa: Long range & low power networks for the Internet of thngs, Sensors, vol. 16, no. 9, 216. [6 P. S. Cheong, J. Bergs, C. Hawnkel, and J. Famaey, Comparson of LoRaWAN classes and ther power consumpton, n IEEE Symposum on Communcatons and Vehcular Technology (SCVT 217), Nov [7 G. Hassan, M. ElMaradny, M. A. Ibrahm, A. M. Rashwan, and H. S. Hassanen, Energy effcency analyss of centralzed-synchronous lorabased mac protocols, n 14th Internatonal Wreless Communcatons Moble Computng Conference (IWCMC 218), Jun. 218, pp [8 M. Taneja, A framework for power savng n IoT networks, n Internatonal Conference on Advances n Computng, Communcatons and Informatcs (ICACCI 214), Sept 214. [9 D. R. T. Olsson, Near Zero Power RF and Sensor Operatons (N- ZERO ), DARPA. [Onlne. Avalable: near-zero-rf-and-sensor-operatons [1 A. Arafa and S. Ulukus, Moble energy harvestng nodes: Offlne and onlne optmal polces, IEEE Transactons on Green Communcatons and Networkng, vol. 2, no. 1, pp , Mar [11 K. Tutuncuoglu, A. Yener, and S. Ulukus, Optmum polces for an energy harvestng transmtter under energy storage losses, IEEE Journal on Selected Areas n Communcatons, vol. 33, no. 3, pp , Mar [12 K. Tutuncuoglu and A. Yener, Energy harvestng networks wth energy cooperaton: Procrastnatng polces, IEEE Transactons on Communcatons, vol. 63, no. 11, pp , Nov [13 R. Wang, J. S. Thompson, and H. Haas, A novel tme-doman sleep mode desgn for energy-effcent LTE, n 4th Internatonal Symposum on Communcatons, Control and Sgnal Processng (ISCCSP 21), Mar. 21. [14 Y.-W. Kuo and L.-D. Chou, Power savng schedulng scheme for Internet of thngs over LTE/LTE-Advanced networks, Moble Informaton Systems, no , 215.