This letter presents a simple model for determining energy efficient random sleep-awake schedules. Random sleepawake schedules are more appropriate for sensor networks, where the time of occurrence of an event being monitored, e.g., the detection of an intruder, is unknown a priori, and the coordination among nodes is costly. We model the random sleepawake schedule as a two state Markov process, and maximize the probability of the transmission of sensed data by a given deadline. Our results indicate that for a given duty cycle, the optimal policy is to have infrequent transitions between sleep and awake modes, if the average number of packets sent is greater than the mean number of slots the node is awake

Ercetin, Ozgur

Erçetin, Özgür

Ocakoglu, Ozleyis

Ocakoğlu, Özleyiş

English

Sabanci University Research Database

528 IEEE COMMUNICATIONS LETTERS, VOL. 10, NO. 7, JULY 2006Energy EfficientRandom Sleep-Awake Schedule DesignOzleyis Ocakoglu and Ozgur ErcetinAbstract— This letter presents a simple model for determiningenergy efficient random sleep-awake schedules. Random sleep-awake schedules are more appropriate for sensor networks,where the time of occurrence of an event being monitored,e.g., the detection of an intruder, is unknown a priori, and thecoordination among nodes is costly. We model the random sleep-awake schedule as a two state Markov process, and maximizethe probability of the transmission of sensed data by a givendeadline. Our results indicate that for a given duty cycle, theoptimal policy is to have infrequent transitions between sleep andawake modes, if the average number of packets sent is greaterthan the mean number of slots the node is awake.Index Terms— Sensor networks, battery management, energyefficient protocols.I. INTRODUCTIONONE of the most important research issues in wirelessnetworks is to extend the network lifetime by energyefficient battery management. In a wireless device, most of theenergy is consumed when the device is idle, i.e., when thereis no processing or transceiver operation. In order to minimizethe energy consumption during idle periods, the device isput into low-voltage “sleep” mode. Duty cycle refers to theproportion of time during which a device is active or “awake”.In order to preserve the available energy, wireless devices areoperated at low duty cycles. Although significant amount ofenergy can be saved while operating at low duty cycle, thedevice becomes effectively unavailable and unresponsive toits surrounding during the sleep mode. For example, in sensornetworks the nodes have the task to detect and report theongoing events in their vicinity, e.g., an intruder. However, theinformation regarding the intruder is only useful if deliveredin a timely fashion. When a node is in sleep mode, it cannotperform its tasks, and may miss the event or delay its report.In this letter, we investigate the computation of the bestsleep-awake schedule for a given duty cycle that ensures acertain level of responsiveness of a node. The responsivenessof a node is defined as the proportion of time the node is avail-able (awake) in a certain length of period that has an arbitrarystarting point in time. We especially focus on the design ofrandom sleep-awake schedules for which the durations of sleepManuscript received February 13, 2005. The associate editor coordinatingthe review of this letter and approving it for publication was Prof. SamuelPierre.O. Ocakoglu is with the Information Technologies Institute, TUBITAK-MRC, Gebze, Kocaeli, Turkey. This work was done when the author waswith the Faculty of Engineering and Natural Sciences, Sabanci University,Istanbul, Turkey. (e-mail: ozleyiso@su.sabanciuniv.edu).O. Ercetin is with the Faculty of Engineering and Natural Sciences, SabanciUniversity, Istanbul, Turkey (e-mail: oercetin@sabanciuniv.edu).Digital Object Identifier 10.1109/LCOMM.2006.06218.and awake periods are not constant but determined in a randomfashion. Random sleep-awake schedules are more appropriatein such networks, where it is difficult to attain coordinationamong the nodes or in sensor networks where the eventmonitored occurs randomly in time. There has been someprevious work addressing the issues arising in such networks.For example, [2] offers a new topology management schemecalled STEM, which allows designers to trade off betweendifferent QoS metrics including energy, latency, and density.[3] explores the relationship between the added deploymentredundancy and the amount of reduction in proportion ofawake times for both coordinated and uncoordinated sleepschedules. Chiasserini et. al. in [4] investigates the energyconsumption and latency by modeling dynamics of a sensornetwork with Markov model. [5] uses a Markov model withsix states in order to predict the energy consumption of asensor node and consequently construct the energy map ofthe sensor network.II. SYSTEM MODELWe model a wireless node operating in one of two modes:ON and OFF states referring to active and idle modes ofoperation, respectively. We define sleep-awake schedule as theconsecutive periods of ON and OFF states. Let T be the lengthof the sleep-awake schedule, and TON and TOFF refer to thetotal period during which the node is in ON and OFF statesrespectively during this schedule. Note that T = TON+TOFF .The duty cycle for a node, d, is defined as d = TON/T . Timeis divided into equal length intervals called slots, where slotduration is equal to the transmission time of a single packet.Assume that a node has a battery lifetime of Lb slots, whenit is always in ON state. If the node has a duty cycle, d, thenthe lifetime of the node, L, is extended to L = Lb/(1 − d)slots. If T < L, then the sleep-awake schedule is repeateduntil battery is exhausted. For a given battery lifetime, Lbslots, one can find different sleep-awake schedules with thesame duty cycle, d. For example, a node with 50% duty cycleand a battery lifetime of Lb = 8 slots may have sleep/awakeschedules with different lengths of ON periods, e.g., TON =1, 2, 4, as shown in Fig. 1. Also note that different TON periodsalso show how frequent the node switches between sleep andawake modes.The user/application requirements are defined in terms ofthe number of slots the node is available, K, (as a relay nodein wireless ad hoc networks or as a sensor node in sensornetworks) during any N consecutive slots. Note that sucha requirement specifies the responsiveness of the network.Specifically, in sensor networks the data generated by a sensor1089-7798/06$20.00 c© 2006 IEEEAuthorized licensed use limited to: ULAKBIM UASL - SABANCI UNIVERSITY. Downloaded on November 23, 2009 at 13:38 from IEEE Xplore.  Restrictions apply. OCAKOGLU and ERCETIN: ENERGY EFFICIENT RANDOM SLEEP-AWAKE SCHEDULE DESIGN 529S S S SS SS S S S S S S S AAAAAAAA84 16ONONT      = 1T      = 2ONT      = 4 AAAAAA12Fig. 1. Sleep/awake schedules for a node with 50% duty cycle and Lb = 8.node is useful only a certain period of time after which the databecomes outdated. As an illustrative example, assume that thesensor node generates on the average two packets every timeit observes an event, i.e., K = 2. This data should be sent toa central monitor, say, in four slots in order to be useful, i.e.,N = 4. Also assume that the sensor node has 50% duty cycle.Then, among the deterministic sleep-awake schedules shownin Fig. 1, it is clear that sleep-awake schedules with TON = 1and TON = 2 are the only ones satisfying this requirement.With random schedules, we may not always be able tofind a schedule satisfying such a requirement. Thus, insteadwe aim to maximize the proportion of time the user requestis satisfied. Define, Psuccess, as the probability of the nodebeing available (in ON state) for at least K slots in Nconsecutive slots. We model the random sleep-awake scheduleas the transitions in a two-state markov chain. Let α be theprobability of transition from ON state to OFF state, and βbe the probability of transition from OFF state to ON state.As a result of Markov property, the duration of the OFF stateis exponentially distributed with mean E[TOFF ] = 1/β andthe duration of the ON state is exponentially distributed withmean E[TON ] = 1/α. Then, the duty cycle, d, isd =1/α1/α + 1/β=βα+ β= π0, (1)where π0 is the steady state probability of being in ON state.Note that different random sleep-awake schedules with thesame duty cycle d can be designed by changing the valuesof α and β. Also note that by varying transition probabilities,we also change how frequent the schedule switches betweensleep and awake modes.III. OPTIMAL RANDOM SCHEDULEThe exact analytical expression of Psuccess is derived in [8].This expression is too complicated to be used to determinethe optimal random schedule. Thus, instead we consider anapproximation of Psuccess with Beta-Binomial (BB) distribu-tion:Psuccess = Pr{at least K times in ON state in N slots}=N∑i=K(Ni)B(a+ i,N + b− i)B(a, b), (2)where B(a, b) is the beta function B(a, b) =∫ 10ua−1(1 −u)b−1 du, and a = (N/2)β/(1 − α − β), b = (N/2)α/(1 −α − β). Beta-binomial distribution was previously used indifferent contexts to model the correlated events [6], [7]. Thedetails of derivation of the above formulas and a discussionon the accuracy of the approximation are given in [1]. Weare interested in the solution of the following optimizationproblem:maxα,βPsuccess (3)s. t. β/(α + β) = d, α < 1, β < 1. (4)The objective is to choose the best random sleep-awakeschedule with a duty cycle d by determining the transitionprobabilities α and β that maximizes the proportion of timethe node is available in at least K out of N consecutive slots.Even in this approximate form, the optimization problem ishard to solve due to the discrete objective function. Thus, inorder to have a quick insight, we further approximate Psuccessusing Gaussian distribution resulting in a continuous objectivefunction. With this approximation, we relax the requirementthat the node is available for integer number of slots. Inorder to preserve the accuracy of Psuccess formula, we usea Gaussian distribution with the same mean and variance ofpreviously calculated BB distribution.The objective function in (3) is re-written as follows;max∫ ∞K−1/21/√2πσ2 exp(−(x− µ)22σ2)dx (5)= max 1/2 + 1/2erf(µ−K + 1/2√2σ2), (6)where µ and σ2 are the mean and variance of BB distribution,and erf(x) is the error function defined for zero mean, unitvariance Gaussian distribution. Let m = β/α, which is alsoequal to m = d/(1 − d) from (1). µ and σ2 are defined as,[1]:µ = Nmm+ 1= N · d, (7)σ2 = N2m(m+ 1)22− (m+ 1)α2 + (N − 2)(m+ 1) . (8)Lemma 1: If the required number of times, K, the node isexpected to be awake in N consecutive slots satisfies:1) K = Nd + 1/2, then Psuccess is independent of sleep-awake schedule.2) K > Nd + 1/2, then Psuccess is maximum when themean duration of being awake is also maximum.3) K < Nd + 1/2, then Psuccess is maximum when themean duration of being awake is minimum.Proof The lemma is easily proved by taking the first derivativeof the objective function given in (6). Note that the optimaltransition probability, α, is determined by solving the equationd/dαPsuccess = 0. When K = Nd + 1/2, the value of theerror function in (6) is zero. Thus, regardless of the valueof α, d/dαPsuccess = 0, and one can choose an arbitraryvalue for α. It can easily be shown that when K > Nd +1/2, d/dαPsuccess is always negative. Thus, Psuccess is adecreasing function of α, and the best solution is to choosethe minimum possible value for α. Similarly, when K < Nd+1/2, d/dαPsuccess > 0, and the best solution is to choose themaximum possible value for α.The results presented in this lemma can be intuitivelyverified. As an example, consider again a sensor network.The average number of slots the sensor node is awake duringAuthorized licensed use limited to: ULAKBIM UASL - SABANCI UNIVERSITY. Downloaded on November 23, 2009 at 13:38 from IEEE Xplore.  Restrictions apply. 530 IEEE COMMUNICATIONS LETTERS, VOL. 10, NO. 7, JULY 20060 0.05 0.1 0.15 0.2 0.2500.10.20.30.40.50.60.70.80.91Psuccess1/E[TON]K=4K=8K=11K=12K=13K=14Fig. 2. Psuccess versus inverse of mean duration of time in ON state for asleep-awake schedule with 80% duty cycle.a duration of N slots is Nd. Assume that a sensor nodemust transmit more than Nd packets for each event occurringrandomly in time. Then, it is clear that in order to send allof these generated packets it is better to have a sleep-awakeschedule with mean awake time as large as possible. Similarly,when the number of packets transmitted is less than Nd, thenthe failure of sending all packets is mainly due to finding thenode unavailable for a long period of time. Thus, in that caseit is better to have the node wake up frequently. The resultsof Lemma 1 are demonstrated with a numerical example inthe forthcoming section.IV. NUMERICAL RESULTSThe variation of Psuccess with respect to the inverse ofthe mean duration of time in ON state, E[TON ], when dutycycle is 80% is shown in Fig. 2. In this experiment, a randomsleep-awake schedule is generated with varying E[TON ] andE[TOFF ] values. At a random instance, a group of K packetsis generated and a packet is transmitted at each slot the node isavailable. If all K packets are successfully transmitted withinN slots after the group of packets is generated, then wesay that the application is successful. We count the numberof times the application is successful and divide it by thetotal number of times a group of K packets is generatedto determine Psuccess. The value of N is taken to be 15,so the expected number of slots the node is awake in thisduration, µ, is 12. Psuccess increases with increasing E[TON ]and E[TOFF ], for K > 12.5 and decreases with decreasingE[TON ] and E[TOFF ], for K < 12.5. Thus, our simulationresults support the analytical results derived in the previoussection.In order to maximize Psuccess when a node forwards anumber of packets less than the mean number of availablenumber of slots, E[TON ] and E[TOFF ] should be selectedas small possible. However, there should be a lower boundon E[TON ] and E[TOFF ], since small E[TON ] and E[TOFF ]means that there are frequent state changes. Frequent statechanges between sleep and awake modes may consume moreenergy, since the power amplifier used in the circuitry drawsmore current when it is first powered. Although in this workwe do not aim to model the energy costs associated with thestate changes, we can still draw some conclusions from theabove results. Note that for K = 4, Psuccess increases withincreasing 1/E[TON ], but remains approximately constant for1/E[TON ] > 0.1. Thus, there is no benefit to further reducethe mean duration of time in ON state and increase the numberof state transitions. A random schedule with E[TON ] = 10 andE[TOFF ] = 5 can provide a sufficiently good performance interms of energy consumption.V. SUMMARY AND CONCLUSIONSIn this paper, we propose a random sleep/awake schedulingpolicy for wireless nodes satisfying timeliness and duty cyclerequirements. This problem is especially important for sensornetworks, where the sensor nodes have limited battery energieswhich must be used efficiently while observing an eventrandomly occurring in time. When there is no event occurring,the sensor nodes do not detect anything, and can go into alow energy consuming sleep mode. However, once an eventoccurs the node needs to detect the event and transmit acertain number of packets within a delay bound. The randompolicies are more appropriate for this setting, since the time ofoccurrence of an event is unknown a priori. Our results suggesta simple policy applicable to all systems, once user/applicationrequirements are given.ACKNOWLEDGMENTThe authors would like to thank the Editor-in-Chief Prof.Georghiades for his conscientiousness and valuable guidance.REFERENCES[1] O. Ocakoglu, “Improving network reliability by exploiting pathdiversity in ad hoc networks with bursty losses,” Master’sthesis, Sabanci University, Feb. 2005; available at http://digital.sabanciuniv.edu/tezler/tezler/mdbf/master/ocakogluo/ana.pdf[2] C. Schurgers, V. Tsiatsis, S. Ganeriwal, and M. B. Srivastava, “Optimizingsensor networks in the energy-latency-density design space,” IEEE Trans.Mobile Computing, vol. 1, pp. 70-80, Jan. 2002.[3] C.-F. Hsin and M. Liu, “Network coverage using low duty-cycled sensors:random and coordinated sleep algorithms,” in Proc. IPSN 2004, pp. 433-442.[4] C.-F. Chiasserini and M. Garetto, “Modeling the performance of wirelesssensor networks,” in Proc. IEEE Infocom 2004, vol. 1, pp. 220-231.[5] R. A. F. Mini, B. Nath, and A. A. F. Loureiro. “A probabilistic approach topredict the energy consumption in wireless sensor networks,” in Proc. IVWorkshop de Comunicaceo sem Fio e Computaceo Movel 2002, availableat http://citeseer.ist.psu.edu/mini02probabilistic.html[6] V. F. Nicola and A. Goyal, “Modeling correlated failures and communityerror recovery in multiversion software,” IEEE Trans. Software Eng., vol.16, pp. 350-359, Mar. 1990.[7] D. A. Griffiths, “Maximum likelihood estimator for the beta-binomialdistribution and an application to the household distribution of the totalnumber of cases of a disease,” Biometrics, vol. 29, pp. 637-648, Dec.1973.[8] J. R.Yee, E. J. Weldon, “Evaluation of the performance of error-correctingcodes on a Gilbert channel,” IEEE Trans. Commun., vol. 43, pp. 2316-2323, Aug. 1995.Authorized licensed use limited to: ULAKBIM UASL - SABANCI UNIVERSITY. Downloaded on November 23, 2009 at 13:38 from IEEE Xplore.  Restrictions apply. 

Energy efficient random sleep-awake schedule design

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Energy efficient random sleep-awake schedule design

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