Towards Energy-Fairness in Asynchronous Duty-Cycling Sensor Networks

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1 38 Towards Energy-Farness n Asynchronous Duty-Cyclng Sensor Networks ZHENJIANG LI and MO LI, Nanyang Technologcal Unversty YUNHAO LIU, Tsnghua Unversty In ths artcle, we nvestgate the problem of controllng node sleep ntervals so as to acheve the mn-max energy farness n asynchronous duty-cyclng sensor networks. We propose a mathematcal model to descrbe the energy effcency of such networks and observe that tradtonal sleep nterval settng strateges, for example, operatng sensor nodes wth an dentcal sleep nterval, or ntutve control heurstcs, for example, greedly ncreasng sleep ntervals of sensor nodes wth hgh energy consumpton rates, hardly perform well n practce. There s an urgent need to develop an effcent sleep nterval control strategy for achevng far and hgh energy effcency. To ths end, we theoretcally formulate the Sleep Interval Control (SIC) problem and fnd out that t s a convex optmzaton problem. By utlzng the convex property, we decompose the orgnal problem and propose a dstrbuted algorthm, called GDSIC. In GDSIC, sensor nodes can tune sleep ntervals through a local nformaton exchange such that the maxmum energy consumpton rate of the network approaches to be mnmzed. The algorthm s self-adustable to the traffc load varance and s able to serve as a unfed framework for a varety of asynchronous duty-cyclng MAC protocols. We mplement our approach n a prototype system and test ts feasblty and applcablty on a 50-node testbed. We further conduct extensve trace-drven smulatons to examne the effcency and scalablty of our algorthm wth varous settngs. Categores and Subect Descrptors: C.2.1 [Computer-Communcaton Networks]: Network Archtecture and Desgn; C.2.2 [Computer-Communcaton Networks]: Network Protocols General Terms: Algorthms, Desgn, Performance Addtonal Key Words and Phrases: Wreless sensor networks, duty-cyclng, energy-farness ACM Reference Format: Zhenang L, Mo L, and Yunhao Lu Towards energy-farness n asynchronous duty-cyclng sensor networks. ACM Trans. Sensor Netw. 10, 3, Artcle 38 (Aprl 2014), 26 pages. DOI: 1. INTRODUCTION Recent years have wtnessed the great success of Wreless Sensor Networks (WSNs). As a promsng technque, WSNs have spawned a varety of crtcal applcatons n practce. In WSNs, sensor nodes are usually powered by batteres, whle frequent replacements of such power sources are normally prohbted. To close the gap between the lmted energy supples of sensor nodes and the long-term deployment requrement n many applcatons, recent research works suggest to operate sensor nodes n a Ths study was supported by Sngapore MOE AcRF Ter 2 grant MOE2012-T Ths study was also supported by NAP M , the NSFC Maor Program No , and NSFC Dstngushed Young Scholars Program A prelmnary verson of ths study was presented at IEEE INFOCOM 2012 [L et al. 2012]. Authors addresses: Z. L and M. L, School of Computer Engneerng, Nanyang Technologcal Unversty; emal: {lzang; lmo}@ntu.edu.sg; Y. Lu, School of Software, Tsnghua Unversty; emal: yunhao@greenorbs.com. Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. Copyrghts for components of ths work owned by others than ACM must be honored. Abstractng wth credt s permtted. To copy otherwse, or republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee. Request permssons from permssons@acm.org. c 2014 ACM /2014/04-ART38 $15.00 DOI: ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

2 38:2 Z. L et al. duty-cyclng work mode [Ye et al. 2002]. In duty-cyclng WSNs, rados of sensor nodes are controlled on a perodcal bass, alternatng between the actve and dormant states. In the actve state, sensor nodes can send or receve data, whle n the dormant state they swtch rados off to save energy. For nstance, wth a 5% duty cycle, sensor nodes have rados on only for 5% of the tme. The duty-cyclng operaton therefore sgnfcantly reduces the energy consumpton rates of sensor nodes and dramatcally prolongs the network lfetme. The duty-cyclng operaton has been employed n a varety of MAC-layer protocols, whch can be bascally classfed nto synchronous and asynchronous two categores. Typcal synchronous protocols, as n Ye et al. [2002, 2006] and Dam and Langendoen [2003], enable sensor nodes to synchronously sleep and wake up, provdng ntermttent network servces. The requred tme synchronzaton ntroduces tremendous communcaton overhead and computaton complcty. Asynchronous protocols, however, allow sensor nodes to operate ndependently. At an arbtrary tme nstance, a subset of sensor nodes operates to provde consstent network servces. Most asynchronous protocols typcally employ Low Power Lstenng (LPL) based approaches [Polastre et al. 2004; Buettner et al. 2006; Lu et al. 2009], ncludng the orgnal LPL technque or some other optmzed technques lke strobed preamble, to acheve asynchronous data transmssons. The basc prncple of those protocols s that pror to the data transmsson, a sender transmts a preamble lastng as long as the sleep perod (.e., sleep nterval) of the recever. The recever s, thus, guaranteed to detect the preamble and receve the data. Compared wth synchronous protocols, asynchronous protocols are free of tme synchronzaton and robust to network dynamcs, whch are benefcal for large-scale deployments. Recently, some varant technques, for example, Low Power Probng (LPP), have been proposed to enable recever-ntated duty-cyclng data transmssons. As all those above technques share smlar energy effcences, for the sake of clear presentaton, we take LPL-based approaches as a vehcle to dscuss the energy farness ssue n asynchronous duty-cyclng sensor networks, and further extend our analyss and soluton to other varant technques. Though the asynchronous duty-cyclng operaton releases the constrant of tme synchronzaton and enables robust sensor networks n dynamc envronments [Lu et al. 2011a], there reman excessve challenges for applyng such an operaton to manage the lmted energy supples of sensor nodes and approach a long network lfetme. Frst, the choce of sleep nterval at any gven node affects not only ts own energy dran to perodcally access the channel, but also the energy consumpton of neghbor nodes communcatng wth t. In partcular, by selectng a relatvely large sleep nterval, one sensor node wll poll the channel less frequently wth reduced energy dran and vceversa. On the other hand, as the LPL technque requres that preambles sent from senders should cover the entre sleep perods of recevers, settng a large sleep nterval unavodably ncreases the energy consumpton of packet senders for the current recpent node. Such an energy tradeoff challenges the approprate choce of sleep ntervals for dfferent sensor nodes, and we call the problem Sleep Interval Control (SIC). Second, the traffc load usually dstrbutes unevenly and vares n the network n many applcatons. As the traffc load drectly affects the preamble and wake-up tme of ndvdual sensors as well, the choce of sleep ntervals cannot be determned separately from the traffc load awareness. If the SIC strategy s not well desgned, certan nodes could rapdly deplete ther energy and become the energy bottleneck, whch severely breaks the network-wde energy farness and thereby shortens the network lfetme. Thus, SIC becomes more challengng as t should be traffc-aware. In addton, the problem wll get even worse f the network scale s large, demandng dstrbuted solutons. There have been excessve studes talored for achevng the energy farness to prolong the network lfetme of sensor networks. Nevertheless, they cannot be drectly ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

3 Towards Energy-Farness n Asynchronous Duty-Cyclng Sensor Networks 38:3 appled to the asynchronous duty-cyclng context [Rangwala et al. 2006; Gu and He 2007; S. J. Tang et al. 2011; Chen et al. 2010; Ma et al. 2011; Zhu et al. 2011]. There have also been attempts made towards the SIC problem n duty-cyclng WSNs. Most of them, however, nvestgate boundng the end-to-end transmsson delay or adustng the energy consumpton of sensor nodes n a centralzed fashon and gnorng the traffc mpact [Wang et al. 2010; Merln and Henzelman 2009; Park et al. 2010; Zhu 2012]. None of them tackles the SIC problem wth a general settng to prolong the network lfetme n a dstrbuted manner. So far as we know, many fundamental ssues n SIC are not well understood and an nstrument to tackle such problems s stll lackng to the communty. In ths artcle, we thoroughly nvestgate the SIC problem to acheve the mn-max energy farness n asynchronous duty-cyclng sensor networks. The contrbutons of ths artcle are as follows. We propose a mathematcal model to descrbe the energy effcency of sensor nodes n exstng LPL based asynchronous duty-cyclng sensor networks, whch captures the essental energy tradeoff between senders and recevers. Based on the proposed model, we observe that exstng smple sleep nterval control mechansms perform far from the optmal one, and there s an urgent need to develop an effcent SIC strategy. Amng at dealng wth the SIC problem n general, we theoretcally formulate such a problem and fnd out that t s a convex optmzaton problem. Based on the convex property, we decompose the orgnal problem nto suboptmzaton problems, and develop a dstrbuted algorthm, called GDSIC, to approach the optmal result. In GDSIC, wth a solely local nformaton exchange, sensor nodes can determne how to adust ther sleep ntervals such that all sensor nodes wthn the network converge to the optmal sleep nterval settngs and the maxmum energy consumpton rate n the network can be mnmzed. The GDSIC algorthm s self-adustable to the traffc load varance and s able to serve as a unfed framework for a varety of underlyng asynchronous duty-cyclng protocols. We mplement a prototype system on a 50 TelosB Mote testbed. The experment results valdate the feasblty and applcablty of the proposed approach n practce. We further conduct extensve and large-scale tracedrven smulatons to examne the effcency and scalablty of the proposed algorthm. The rest of ths artcle s organzed as follows: related works are revewed n Secton 2. In Secton 3, we model the energy effcency of sensor nodes and evaluate the tradtonal SIC strateges. We formulate the SIC problem and propose our soluton n Secton 4. In Sectons 5 and 6, we examne the performance of our approach. We conclude n Secton RELATED WORK In exstng lteratures, the duty-cyclng MAC-layer protocols can be roughly dvded nto two categores: synchronous and asynchronous protocols. Typcal synchronous protocols nclude Ye et al. [2002, 2006] and [Dam and Langendoen 2003]. In S-MAC [Ye et al. 2002], sensor nodes are confgured wth fxed duty-cycle ratos. S-MAC reles on the perodcal synchronzaton among neghbors and a seres of synchronzers to cooperate nodes n the network. The network lfetme can be prolonged compared wth tradtonal always-on networks. However, the energy effcency of S-MAC s usually low. To solve such an ssue, T-MAC n Dam and Langendoen [2003] s further proposed. T-MAC can adust the duraton of the actve state for each node based on varous message rates. Later, n SCP-MAC [Ye et al. 2006], sensor nodes can acheve extremely low duty cycles based on a two-wndow contenton desgn. The maor lmtatons of synchronous protocols are tremendous communcaton overhead and computaton complcty for tme synchronzaton [Y. Wang et al. 2012]. Asynchronous protocols, on the other hand, allow sensor nodes to operate ndependently. The frst reported asynchronous MAC-layer protocol s B-MAC [Polastre et al. 2004], whch apples the orgnal LPL technque. ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

4 38:4 Z. L et al. Afterwards, subsequent protocols, lke X-MAC [Buettner et al. 2006], C-MAC [Lu et al. 2009], and WseMAC [EI-Hoyd and Decotgne 2005], are essentally smlar to B-MAC. However, some optmzatons, ncludng the strobed preamble and predctve wake-up technques, have been ntroduced n those protocols to further reduce the energy consumpton. In X-MAC, senders transmt a seres of short preambles nstead of one long preamble. Two consecutve short preambles are separated va a bref dle tme slot. Whenever recevers wake up and hear the preamble, they wll acknowledge senders durng those dle tme slots. By dong so, the preamble transmsson can be stopped and senders can launch the data transmsson mmedately. C-MAC mplements a smlar dea by usng RTS/CTS. Sensor nodes n WseMAC utlze feedbacks from the recevers to predct ther wake-up tmes. Then, the length of preambles can be shortened to save energy. Snce preambles are sent from senders, aforementoned asynchronous protocols are also referred to as sender-ntated protocols. Dfferent from sender-ntated protocols, recently, some recever-ntated protocols have been proposed, such as RI-MAC [Sun et al. 2008], PW-MAC [L. Tang et al. 2011], A-MAC [Dutta et al. 2010], etc., whch are manly desgned to mprove the channel utlzaton and unfy servces, by employng the LPP technque. Based on [Challen et al. 2010], the energy dran n recever-ntated protocols can be smlarly analyzed as the senderntated ones. In ths artcle, we take the LPL-based protocols as an nstrumental vehcle due to LPL s avalablty n the standard TnyOS dstrbuton, whle dealng wth LPP-based protocols as a promsng extenson. The energy ssue n sensor networks has drawn people s attenton n the past several years. Gu and He [2007] propose DSF to optmze the expected energy consumpton for data forwardng n low duty-cyclng sensor networks. Guo et al. [2009] ntroduces an opportunstc scheme to acheve a rapd and energy-effcent floodng n duty-cyclng wreless sensor networks. Although the routng path can be optmzed based on those prevous studes, traffc loads are stll unevenly dstrbuted. As a result, we stll need to desgn solutons to balance the energy farness of the entre network. On the other hand, to acheve sustanable operatons, a seres of works have exploted the sensor networks wth a harvested power management [Hu et al. 2009] or powered by ultracapactors. Zhu et al. [2009] frst nvestgate the leakage-aware energy synchronzaton n such networks. Then, the study n Zhu et al. [2010] extends to explore the capactor-drven energy storage and sharng for a long-term operaton. Gu et al. [2009] further examnes how to ntegrate the capactor-powered sensor networks wth the duty-cyclng operaton. However, due to the hgh cost of capactors and the desgn complcty, such a new networkng paradgm has not been wdely adopted n large-scale sensor networks. There are also some prmary efforts to control sleep ntervals n WSNs. Wang et al. [2010] propose Dutycon to acheve a dynamc duty cycle control for the end-to-end delay guarantee. The study n Zhu [2012] bounds the communcaton delay n energy harvestng sensor networks. In both Merln and Henzelman [2009] and Park et al. [2010], multobectve optmzaton formulatons are ntroduced, coverng transmsson relablty, end-to-end delay, and energy consumpton. Optmzaton problems are solved by classcal methods n a centralzed manner. IDEA n Challen et al. [2010] ntegrates multple networkng servces, lke LPL adustment, energy-aware routng, and localzaton. Sensor nodes balance the local energy consumpton n a heurstc fashon and t s not clear how close the acheved performance s to the optmal result. As energy s the most sgnfcant ssue lmtng the network performance [Dutta et al. 2008], dfferent from prevous works, we focus on controllng sleep ntervals to acheve the mn-max energy farness so that the network lfetme can be notably prolonged. To make our approach practcal, we requre that the soluton should be completely dstrbuted and self-adustable to the traffc varance, whch s common n many applcatons. In addton, we also requre that our soluton can serve as a unfed framework applcable to a ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

5 Towards Energy-Farness n Asynchronous Duty-Cyclng Sensor Networks 38:5 Fg. 1. Illustraton of the LPL technque. varety of asynchronous MAC protocols. So far as we know, such an nstrument s stll lackng. 3. PROBLEM SPECIFICATION AND DESIGN CHALLENGES In ths secton, we mathematcally characterze the energy effcency 1 of sensor nodes runnng LPL-based asynchronous protocols, and evaluate exstng sleep nterval control strateges n practce. As depcted n Fgure 1 (left), a sender transmts a long preamble pror to the data transmsson wth the orgnal LPL. After the recever wakes up and detects the preamble, t keeps awake to receve data. Later, such a workng mechansm has been further optmzed due to the low energy effcency at the recever sde, and the most representatve example s the strobed preamble technque. As shown n Fgure 1 (rght), nstead of sendng a long preamble, a serals of short preambles are sent such that ntended data can be transmtted wthout watng untl the end of the long preamble. Snce such a technque notably ncreases the energy effcency and t s robust to dynamc envronments, t has been wdely used n large-scale WSNs n practce, lke GreenOrbs [Lu et al. 2011a], and released as the default LPL-based MAC protocol n TnyOS. As optmzed technques are proposed based on the orgnal LPL desgn, we frst nvestgate energy consumpton rates of sensor nodes wth the orgnal LPL technque n ths secton, then we observe that later proposed protocols can be transformed to ts specal cases. Before we proceed, for any sensor node (e.g., ) n the network, we ntroduce two notatons: r s the overall energy consumpton rate of node, T slp s the sleep nterval of node. In general, each r s the summaton of energy consumpton rates for packet transmttng (r tx ), packet recevng (r rc ), channel pollng (r cp ) and overhearng (r oh )atsensor node. As a result, r can be expressed by: r = r tx + r rc + r cp + r oh. (1) After specfyng each term n Eq. (1), we obtan a general expresson for the overall energy consumpton rate of any sensor node n the followng theorem. THEOREM 3.1. Wth the LPL technque, the overall energy consumpton rate at any sensor node can be unfed by r = λ T slp + γ T slp + ζ T slp + τ, (2) 1 Wthout loss of generalty, we focus on the rate of energy consumpton (.e., the energy dran n one unt tme) n ths secton, as the total energy consumpton can be obtaned by multplyng the rate and the tme duraton. ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

6 38:6 Z. L et al. where node receves the packets sent from node, λ, γ, ζ,andτ are coeffcents to smplfy the expresson of r. The detaled dervaton of Theorem 3.1 can be found n Appendx A. Based on Theorem 3.1, we wll (1) evaluate exstng sleep nterval control strateges n practce; and (2) dentfy desgn challenges for the SIC problem Problem Specfcatons To the best of our knowledge, most deployed WSNs n practce employ the dentcal sleep nterval settng due to the desgn and mplementaton smplctes. However, t s well known that the n-network traffc load s usually unevenly dstrbuted [X. Wang et al. 2012; Du et al. 2011; Wang and Lu 2011; Lu et al. 2011b] and recent measurement studes, lke Lu et al. [2011a], have also reported such a phenomenon. We observe that such a smple strategy may lead to heterogenous energy drans and hardly acheve the energy farness n the network. As a result, the network lfetme wll be severely lmted. THEOREM 3.2. The dentcal sleep nterval settng usually results n heterogeneous energy consumpton rates n practce. The rgorous nterpretaton to Theorem 3.2 can be found n Appendx B, whle we brefly explan Theorem 3.2 here. Accordng to Theorem 3.1, we can demonstrate that the energy consumpton rate r of any sensor node s manly determned by ts outgong (transmttng) traffc rate f tx when all sensor nodes are set an dentcal sleep nterval. As mentoned prevously, the network traffc n practce s normally heterogenous. Therefore, sensor nodes n heavy traffc regons are prone to suffer more frequent preamble tme and longer data recevng tme. As a consequence, those sensor nodes tend to run out of energy frst, and traffc loads are prone to domnate the lfetme of sensor nodes when all sleep ntervals are set to be equal. In Secton 3.2, we wll conduct a case study n data collecton to further valdate such a concluson. Theorem 3.2 essentally demonstrates that due to the nherent uneven nature of traffc loads n practce, the wdely adopted sleep nterval settng polcy n exstng sensor networks fals to gan a good performance n terms of the energy effcency. To deal wth such an ssue, sleep ntervals should be controlled dynamcally wth respect to sensors energy dranng speeds and traffc load varances. An ntutve soluton s to ncrease the sleep nterval of a sensor node greedly f ts energy consumpton rate becomes hgher [Challen et al. 2010]. The ratonale behnd s that prolongng the sleep nterval of ths sensor node compensates ts fast energy consumpton. However, as we wll show n Theorem 3.3, the hardness of the SIC problem s beyond such an ntuton. THEOREM 3.3. The greedy SIC strategy by ncreasng sleep ntervals of sensor nodes wth large energy consumpton rates hardly acheve the mn-max energy farness n WSNs. In Fgure 2 and Fgure 3, we show the energy consumpton rate of a sender node wth respect to dfferent sleep nterval settngs. The upper fgure n ether Fgure 2 or Fgure 3 depcts that for any sensor node, how does r n Eq. (2) vary wth T slp when T slp s fxed. If we focus on each ndvdual sensor node, ts energy consumpton rate s ndeed decreased n some scenaros when the sleep nterval ncreases. As depcted n Fgure 3 (upper), the strobed preamble technque belongs to ths category. However, there exst suffcent exceptons. For nstance, sensor nodes adoptng the orgnal LPL technque n the regon wth hgh traffc loads as shown n Fgure 2 (upper). It hnders above ntutve heurstcs to be appled drectly n general. ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

7 Towards Energy-Farness n Asynchronous Duty-Cyclng Sensor Networks 38:7 Fg. 2. r vs. sleep ntervals wth the orgnal LPL technque. Fg. 3. r vs. sleep ntervals wth the strobed preamble technque. On the other hand, from the network perspectve, Eq. (2) mples that after a sensor node ncreases ts sleep nterval, energy consumpton rates of ts senders ncrease accordngly. The lower fgure n ether Fgure 2 or Fgure 3 depcts how does r n Eq. (2) vary wth T slp when T slp s fxed. As a matter of fact, the sleep nterval adustment of one sensor node wll trgger senders to tune ther own sleep ntervals as well. In the greedy strategy, energy drans of sensor nodes are balanced wthn neghborhoods, whch essentally follows the water-levelng mechansm. By dong so, energy consumpton rates of sensor nodes could be converged to a compromsed value. On the other hand, the ntal sleep nterval settng has mplctly defned an nterval, wthn whch the mn-max energy farness can be adusted by the greedy strategy. However, there s no guarantee that the optmal mn-max energy farness falls wthn the formed nterval exactly. Therefore, the greedy strategy s not always effectve, whch challenges the algorthm desgn for SIC. In the next secton, we wll revst both Theorems 3.2 and 3.3 to valdate those conclusons by a concrete case study Case Study n Data Collecton Data collecton s one mportant networkng servce for WSNs [Werner-Allen et al. 2008]. In data collecton, to receve network-wde data, data collecton tree [Gnawal et al. 2009] and Drected Acyclc Graph (DAG) are two maor approaches proposed n exstng lteratures. Whle each sensor node has only one data recever n a collecton tree, n DAG each node can forward data to multple recevers closer to the snk [Ln et al. 2008]. In ths secton, we focus on the data collecton tree snce DAG can be smlarly analyzed. We wll examne both two approaches n Secton 6 va experments and smulatons. LEMMA 3.4. For any node that s l-hop away from the snk node n a data collecton tree, ts outgong traffc can be approxmated by: f tx (l) = ρ(l 2 (l 1) 2 d 2 )/(2l 1)d 2, (3) where d s the average dstance of one hop, ρ ndcates the average traffc generaton rate n the network and L s the maxmum dstance from the network boundary to the snk. The detaled dervaton of Lemma 3.4 s gven n Appendx C. ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

8 38:8 Z. L et al. Fg. 4. r of each sensor node wth the dentcal sleep nterval polcy. Fg. 5. Dstrbuton of energy consumpton rate wth the greedy polcy Revstng Theorem 3.2. Accordng to Lemma 3.4, sensor nodes closer to the snk consume ther energy exponentally faster than other dstant nodes. On the other hand, as we have mentoned, when the dentcal sleep nterval settng s adopted, the energy consumpton rate of one sensor node s manly determned by f tx. Therefore, those heavy traffc burden nodes tend to run out of energy frst, and those nodes are usually located close to the snk node. We perform a smulaton study n Fgure 4, n whch the Y-axs of a red dot represents the energy consumpton rate of one sensor node. As ndcated by Eq. (3), the traffc load s relatvely hgh n the regon near the snk node. Therefore, sensor nodes n such a regon consume energy much faster, whch s consstent to our prevous dscusson Revstng Theorem 3.3. We apply the greedy sleep nterval control strategy for the sensor network and llustrate the energy consumpton rate of each sensor node after the network becomes stable n Fgure 5. In the greedy strategy, sensor nodes adust ther sleep ntervals such that ther energy consumpton rates are set as the average value of ther neghbors, whch s an ntutve way to acheve the mn-max energy farness n the network. Compared wth the dentcal sleep nterval settng polcy, the greedy strategy effectvely reduces the maxmum energy consumpton rates of the network. The acheved energy farness (.e., 4.9 mj/s) s wthn the nterval mplctly formed by the maxmum (.e., 5.8 mj/s) and mnmum (4.4 mj/s) values n Fgure 4. However, n such an example, the optmal mn-max farness s 2.8 mj/s. Fgure 5 shows that the greedy strategy leads the network convergng to a suboptmal value that s far above the optmal result, whch wll cause a non-neglgble gap between the acheved network lfetme and the optmal performance Desgn Challenges Based on these dscussons, we can summarze the desgn challenges for the SIC problem as follows. Increasng the sleep nterval of one sensor node does not necessarly reduce ts own energy consumpton rate. A sensor node ncreases ts own sleep nterval to save energy; nevertheless, energy consumpton rates of the packet senders of the current recever may ncrease. The acheved energy farness may be far away from the optmal result f sleep ntervals are not carefully controlled. ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

9 Towards Energy-Farness n Asynchronous Duty-Cyclng Sensor Networks 38:9 In the next secton, we wll ntroduce our soluton to deal wth those challenges to acheve an optmzed sleep nterval control. 4. PROBLEM FORMULATION AND ALGORITHM DESIGN The sensor network s modeled as an undrected graph G = {V, E}, where V and E represent the sets of sensor nodes and wreless lnks, respectvely. Accordng to Theorem 3.1, the energy consumpton rate of an arbtrary sensor node n the network can be expressed as r = λ T slp + γ /T slp + ζ T slp + τ, where s the recever 2 of node. To control the energy consumpton rate n the network, we ntroduce a set of varables R s and requre that λ T slp + γ /T slp + ζ T slp + τ R for each. As prevously mentoned, by determnng an approprate sleep nterval for each sensor node, the Sleep Interval Control (SIC) problem ams at mnmzng the maxmum energy consumpton rate (.e., the mn-max energy farness) n the network to prolong the network lfetme, whch can be captured by the model from Eq. (4) to Eq. (6) as follows: mn max{r } (4) such that λ T slp + γ T slp + ζ T slp + τ R, (, ) E, (5) 0 < T slp, V. (6) Constrant (5) specfes that the energy consumpton rate of each sensor node s bounded from above by the varable R. Constrant (6) guarantees that sleep ntervals have postve values. The coeffcents λ, γ, ζ,andτ V, are all postve as well. Thus, constrants (5) and (6) mplctly ensure that R > 0. In the end, the obectve functon (4) mnmzes the maxmum R so that the global mn-max energy farness can be acheved n the network. A straghtforward way to obtan the optmal SIC result based on ths formulaton s as follows. Each sensor measures ts own traffc load, calculates λ, γ, ζ,andτ, and reports the calculated coeffcents to a central nformaton collector, for example, the snk. Based on the harvested nformaton from each sensor node, the snk globally solves Eqs. (4) to (6). The snk node dssemnates the optmal sleep nterval settng to the entre network. To be traffc varance-aware, these three steps are repeated perodcally or trggered va the snk when traffc dynamcs are detected. However, such a centralzed soluton normally ncurs tremendous communcaton overhead and complcated cooperaton among sensor nodes, whch hnders the scalablty and applcablty of the soluton for large-scale WSNs. To overcome those lmtatons, we now ntroduce a dstrbuted approach to perform the sleep nterval control at each ndvdual sensor node s sde Dstrbuted Sleep Interval Control Problem We decompose the orgnal SIC problem for each sensor node and focus on a local structure of an arbtrary sensor node n the network. As depcted n Fgure 6, node 2 At the current stage, we focus on the case, n whch sensor node has one recever only. Such a scenaro s common n practce and t can be found when packets are transmtted followng a tree structure, for example, CTP [Gnawal et al. 2009]. However, our proposal s not lmted to the tree structure, and we wll dscuss the multrecever case n Secton 4.3. ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

10 38:10 Z. L et al. Fg. 6. Local structure for sensor. s the recever of sensor and node s k, k = 1, 2,...,K, s a sender of sensor, where K s the total number of potental senders. By exchangng nformaton wth those neghborng nodes, sensor node can determne ts local-optmal sleep nterval based on the formulaton from Eq. (7) to Eq. (10). As T slp affects energy consumpton rates of both node and ts senders n Eqs. (8) and (9), the varable R bounds the energy dran n the local regon from above to control the energy trade-off between and each sender s k. Smlar to the orgnal SIC problem, R n the obectve functon (7) s mnmzed to obtan the local mn-max energy farness. We denote Eqs. (7) to (10) as the Dstrbuted SIC (D-SIC) problem. The followng lemma reveals the essence of both SIC and D-SIC problems. mn R, (7) such that λ T slp + γ T slp + ζ T slp + τ R, (, ) E (8) λ k T slp + γ k T slp + ζ k T slp k + τ k R, (k, ) E k (9) 0 < Tslp, V. (10) LEMMA 4.1. The SIC problem and the D-SIC problem are both convex optmzaton problems. Conclusons made by Lemma 4.1 are clear as all constrants and obectve functons n both SIC and D-SIC problems are convex. In the D-SIC problem, the total amount of constrants s bounded by the number of senders of sensor node. Accordng to Lu et al. [2011a], each sensor node only needs to solve one local D-SIC problem wth a small number of constrants (e.g., <8). As a result, a varety of mature and lghtweght technques can be adopted n practce, such as the nteror-pont method [Boyd 2004], n whch the optmal result can be found wthn guaranteed teratons. Even D-SIC problems can be solved locally, there remans one crtcal ssue not answered yet: how to ensure that such dstrbuted computatons eventually lead to the global optmal result? The answer wll be gven when we ntroduce the Dstrbuted SIC (DSIC) algorthm n the next secton. Before we proceed, we partcularly nvestgate the D-SIC problem for a set of asynchronous protocols based on LPL wth the strobed preamble technque, ncludng X- MAC, C-MAC, and so on, because ts prevously mentoned sgnfcance n practce. Due to the specal propertes, sensor nodes wth ths type of protocols can avod usng teratve algorthms to solve ther own D-SIC problems; nstead, close-form expressons can be obtaned to further smplfy the system desgn. Eqs. (8) and (9) wth the strobed preamble technque n the D-SIC problem can be replaced by Eqs. (11) and ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

11 Towards Energy-Farness n Asynchronous Duty-Cyclng Sensor Networks 38:11 (12), respectvely. As γ and T slp yelds: T slp λ T slp + γ T slp + τ R, (, ) E, (11) λ k T slp + γ k T slp + τ k R.(k, ) E. k (12) are both postve, Eq. (11) mples R >λ T slp + τ, whch further γ /(R λ T slp τ ). On the other hand, snce λ k > 0, based on Eq. (12), (R γ k /T slp k τ k )/λ k. Then, for each sender k, we have: we can further obtan T slp γ R λ T slp T slp R γ k /T slp k τ k, τ λ k R 2 φ,k R = max k R + ω,k 0, (13) { ( (φ φ,k,k) ) / 2,k + 4ω 2}, (14) where R ndcates the selected upper bound for energy consumpton rates n the local regon, φ,k λ T slp + τ + γ k /T slp k + τ k,andω,k (λ T slp + τ )(γ k /T slp k + τ k ) γ λ k. Note that (φ,k ) 2 4ω,k can be transformed to (λ T slp + τ γ k /T slp k + τ k ) 2 + 4γ λ k > 0. As a result, roots of R n Eq. (13) always exst. Then, we have where k = arg max k {(φ,k + T slp (φ,k = ( R γ k /T slp k τ k ) /λk, (15) ) 2 4ω,k )/2} The DSIC Algorthm Desgn To deal wth the traffc load varance, at any sensor node, SIC s performed on a perodcal bass or trggered when traffc dynamcs are detected. Before the algorthm executon, sensor node collects necessary nformaton from neghbor nodes, whch ncludes the current sleep nterval T slp of ts recever, λ k, γ k, ζ k,andτ k of each sender k. Such nformaton s used to update R and T slp by locally solvng the D-SIC problem from Eqs. (7) to (10), or Eqs. (11) to (15) f the strobed preamble technque s adopted. To reduce the communcaton cost, these parameters can be obtaned from regular nformaton exchanges of some underlyng servces, lke lnk estmatons or CTP beacons. One pont worth notng s that f there are dynamcs n the network traffc, the energy consumpton rate of some sensor node (e.g., node ) may suddenly become greater than R. In ths case, R wll not be a vald upper bound and the DSIC algorthm wll not perform correctly. To cope wth such an ssue, we propose a remedal soluton as follows. After node detects ts current energy consumpton rate becomng greater than R, t needs to ncrease R such that R can stll bound ts energy consumpton rate from above. In our mplementaton, R wll be reset slghtly greater than ts current energy consumpton rate. However, snce R should bound energy consumpton rates wthn the local regon of node from above, the ncreasng of R solely accordng to node s energy consumpton rate cannot guarantee that R s greater than the energy consumpton rates of ts neghbors. Therefore, we further rely on the exchangng of R to solve such an ssue. Once recevng R k from each neghbor k, node updates R to be max{r, max k {R k }}. After settng an approprate R,theDSIC algorthm can correctly perform operatons as f the traffc loads were stable. ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

12 38:12 Z. L et al. ALGORITHM 1: The DSIC Algorthm at Sensor Node Input : Current R and sleep nterval T slp. Output: Updated R and T slp, denoted as R and T slp. 1 Collect T slp and R,where s the recever of sensor node. 2 Collect λ k, γ k, ζ k, τ k,andr k from each sender k. 3 Locally solve the D-SIC problem from Eqs. (7) to (10) and obtan the updated R and T slp. 4 f R < R then 5 Set R to be R ; to T slp 6 Update the sleep nterval T slp 7 Inform the updated T slp else ; to ts senders; 8 Keep both R and T slp unchanged; end After R and T slp are updated, sensor node frst checks whether the new R s smaller than the current R.Ifso, adusts ts sleep nterval to be T slp. In addton, R wll be replaced by R for the next updatng. Otherwse, takes no acton. The detaled descrpton of the DSIC algorthm s gven n Algorthm 1. When R < R, the adustment of sleep nterval wll decrease the maxmum energy consumpton rate n the local regon of node. By teratvely executng the algorthm by all the sensor nodes, eventually, no sensor nodes can further decrease ther energy consumpton rates wthout compromsng the maxmum energy consumpton rate acheved wthn ts local regon. In other words, ther energy consumpton rates n ths process are convergng towards a common value, and such a common value keeps decreasng. Moreover, by exchangng R, dfferent sensor nodes wll adust ther own R to the maxmum one wthn ts neghborhood. As a matter of fact, the exchangng of R wll cause the largest upper bound to eventually spread to the entre network. Thus, each local optmzaton process s fnally constraned by the maxmum upper bound n the network, and the updatng operatons n DSIC essentally adust the sleep nterval based on the reducton of ths maxmum upper bound stored locally. In other words, the DSIC solves the global optmzaton problem n a dstrbuted manner wth a local exchange of R. After the performance of DSIC converges, the energy consumpton rate of no sensor node can be further reduced. It mples that the optmal result has been acheved. From a theoretcal perspectve, a rgorous nterpretaton to the correctness of our algorthm s gven n the followng theorem. THEOREM 4.2. By the executon of Algorthm 1 at each sensor node, the maxmum energy consumpton rate n the network approaches to be mnmzed. PROOF. Lne 4 n Algorthm 1 ndcates that whenever the sleep nterval s updated, R becomes smaller, whch results n the decrease of the maxmum energy consumpton rate n each local regon. On the other hand, the orgnal SIC problem and the D-SIC problem are both convex, and each D-SIC s a subproblem of SIC. To fnsh the proof, we assume that the maxmum energy consumpton rate n the network converges to R, whch s dfferent from the optmal result R. Clearly, R > R. Now, we prove ths theorem by contradcton. If the maxmum energy consumpton rate converges to R by our algorthm, t ndcates that there does not exst any R to further reduce the current maxmum rate of the energy dran n the network, mplyng R be a local mnmum pont. However, the orgnal problem s convex, such a concluson yelds that R must be a global optmal pont as well [Boyd 2004], whch s a contradcton. ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

13 Towards Energy-Farness n Asynchronous Duty-Cyclng Sensor Networks 38:13 Fg. 7. Multrecever scenaro Dscussons Multrecever scenaro. So far, we have focused on the case, n whch each sensor node has only one recever. Such a case corresponds to the packet transmsson followng a tree-based routng structure. As aforementoned, packets, however, can be transmtted followng a DAG as well, n whch there may exst more than one potental recever. Wthout loss of generalty, we assume sensor node has n potental recevers. We can slghtly alter our prevous analyss and reach a General Dstrbuted SIC (GDSIC) algorthm, whch can support multple recevers n general. GDSIC can be smply extended from the DSIC algorthm, and the basc prncple s as follows. Snce preambles sent from sensor node must cover the sleep nterval of each potental recever r for 1 n, the length of s preamble can be determned by max {Tr slp } (Fgure 7). Thus, the multrecever case s accordngly transformed to an equvalent sngle recever case as shown by Fgure 8, n whch the sleep nterval of the sngle vrtual recever equals to max {Tr slp }. We can then modfy T slp as max {Tr slp } n lne 1 of Algorthm 1 and apply the DSIC algorthm for the sleep nterval control. Due to the page lmt, the detaled algorthm s gven n Algorthm 2. ALGORITHM 2: The GDSIC Algorthm at Sensor Node Input : Current R and sleep nterval T slp. Output: Updated R and T slp, denoted as R and T slp. 1 Collect Tv slp r and R r from each recever v r of sensor node ; 2 Assgn T slp n the D-SIC problem by max {T slp v r }; 3 Collect λ k, γ k, ζ k, τ k,andr k from each sender k. 4 Locally solve the D-SIC problem from Eqs. (7) to (10) and obtan the updated R and T slp. 5 f R < R then 6 Set R to be R ; to T slp 7 Update the sleep nterval T slp 8 Inform the updated T slp else ; to ts senders; 9 Keep both R and T slp unchanged; end Consderng Resdual Energy Budgets. In prevous dscussons, we focus on mnmzng the maxmum energy consumpton rate n the network. However, after sensor nodes are deployed and have worked for a perod, the resdual energy budget at each ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

14 38:14 Z. L et al. Fg. 8. Illustraton of transformaton from the mult-recever scenaro to the sngle-recever scenaro. node mght have already become uneven. Hereby, we show that the orgnal SIC problem formulaton can be transformed to consder sensor nodes resdual energy budgets. Denote the resdual energy budget of sensor node as e. As a result, the lfetme of node remans e /r. Wth the consderaton of the resdual energy, we naturally hope to maxmze the mnmum lfetme of sensor nodes n the network. Mathematcally, such a desgn target can be expressed as follows: max mn{e } (16) ( ) s.t. e / λ T slp + γ T slp + ζ T slp + τ E, (17) 0 < T slp, 0 < E, V. (18) Snce Eq. (17) can be rephrased as λ T slp + γ +ζ T slp T slp +τ ) e /E, ths formulaton s essentally equvalent to the orgnal SIC problem and the detaled proof s as follows. We defne R to be 1/E. Accordng to Eq. (17), we have: ( ) e / λ T slp + γ T slp + ζ T slp + τ E, ( ) / λ T slp + γ T slp + ζ T slp + τ e 1/E, λ T slp + γ T slp + ζ T slp + τ R, (19) where λ, γ, ζ,andτ equal to λ /e, γ /e, ζ /e,andτ /e, respectvely. Snce E s postve (ndcated by Eq. (18)), R n Eq. (19) s postve as well. As a result, the constrants of both the orgnal SIC formulaton from Eq. (4) to Eq. (6) and the formulaton wth the consderaton of the resdual energy budgets from Eq. (16) to Eq. (18) are shown to be equvalent. Now, we further prove the equvalence of ther obectve functons. max mn{e } mn max{1/e }, mn max{r }. So far, we fnsh the proof the equvalence of these two problem formulatons. As a result, the proposed GDSIC algorthm can be easly extended to consder the resdual energy budgets of sensor nodes Extenson to Recever-Intated Protocols. As a most representatve technque, Low Power Probng (LPP) has been employed n many recever-ntated protocols. The ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

15 Towards Energy-Farness n Asynchronous Duty-Cyclng Sensor Networks 38:15 Fg grd testbed. energy effcences of LPL and LPP are manly dfferent from the followng two aspects. Frst, the energy consumpton to receve the preamble at the recever sde can be omtted n LPP. Second, the energy consumed for overhearng n LPL should be replaced by obtanng the recever s predcted wake-up schedule n LPP. After rephrasng the energy consumpton rate for each sensor node wth LPP based on these two dfferences, our prevous analyss and soluton can be seamlessly extended to the recever-ntated protocols SIC for Leaf Nodes. Snce leaf nodes n the network have no packet senders, they may fal to obtan an effectve sleep nterval adustment based on the GDSIC algorthm. To deal wth such a margnal case, n our mplementaton, those sensor nodes adust ther sleep ntervals such that ther energy consumpton rates are approxmately equal to ther recevers. 5. EXPERIMENTAL EVALUATION In prevous sectons, we elaborate the desgn prncples and mportant propertes of the proposed GDSIC algorthm. In ths secton, we valdate ts feasblty and applcablty n practce Experment Settng We mplement GDSIC on TelosB motes and use a 50-node testbed to examne ts performance. 50 nodes are organzed as a 10 5 grd. 3 (See Fgure 9.) Due to the expermental space lmtaton, the power of each TelosB mote s set to be the mnmum level and the communcaton range s about 10 centmeters. Startng from the left-top conner, sensors are placed followng the bottom-to-top and left-to-rght order based on ther IDs. GDSIC s mplemented at the applcaton layer, whch utlzes two maor standard components, LPL and CTP, adopted n the current TnyOS 2.1 package. On the MAC layer, the default protocol, X-MAC, s adopted n the experment. In the ntal fve mnutes, sensor nodes beacon neghborng nodes to form a stable routng tree rooted at sensor node 0. To ncrease the depth of the formed routng structure, we manually enforce that the recever of a sensor node s selected from ts adacent neghbors on the testbed. For example, the parent of node 15 s chosen from nodes 16, 14, 25, 5, 24, 6, 26, and 4. After the ntalzaton phase, sensor nodes nect packets to the network and cooperatvely delver packets to the snk (root) node. The average 3 Due to the hardware falure, node number 11, n Fgure 9, s excluded and only 49 sensor nodes are fnally used n the experment. ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

16 38:16 Z. L et al. Fg. 10. Energy consumpton rate vs. duraton. traffc generaton rate s one packet every four seconds and the GDSIC algorthm s trggered every 60 seconds Expermental Results Energy Consumpton Rate vs. Duraton Tme. The experment lasts 40 mnutes on the testbed. Based on the collected data, we observe that after GDSIC executes for 20 mnutes, the system performance becomes relatvely stable. For a clear presentaton, we manly demonstrate the transton state of the network after the ntal phase. In Fgure 10, we llustrate energy consumpton rates of fve representatve sensor nodes wth hop counts 1, 3, 5, 7, and 9, respectvely. Each selected sensor node n Fgure 10 experences approxmately the fastest energy dranng speed compared wth other peerng nodes wth the same hop count. Fgure 10 shows that after 800 seconds, energy consumpton rates of those sensor nodes converge to around 3.6 mj/s, and there s no obvous performance varance afterward. At tme 1000 seconds, we take a snapshot of the network and conduct an offlne computaton. The optmal mn-max energy farness s obtaned to be 3.2 mj/s. The mportant nsghts obtaned from Fgure 10 are two-folds: frst, energy consumpton rates of sensor nodes n dfferent network postons are well balanced after the network becomes stable, whch effectvely elmnates the hot spots of the energy consumpton wthn the network. Second, GDSIC has a good convergency speed. In partcular, after the ntal fve mnutes, the overall energy consumpton rates are decreased to be farly low wthn the frst 500 seconds. After several extra teratons, the performance converges eventually. Accordng to Fgure 10, we fnd that the stablzed energy consumpton rates of sensor nodes near the snk node are stll slghtly greater than other dstant sensor nodes n GDSIC and such a performance gap s dffcult to be further closed but remans to be small. Compared wth the equal sleep nterval settng polcy, the mn-max energy farness has been notably mproved by GDSIC Snapshot of Energy Consumpton Rates. In Fgure 11, we llustrate the snapshot of the energy consumpton rate of each sensor node n GDSIC and compare them wth the tradtonal dentcal sleep nterval settng strategy (EQUAL). Accordng to Fgure 11, we can observe that most sensor nodes n GDSIC acheve smlar energy consumpton rates after executng the GDSIC algorthm, and only a small number of sensor nodes ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

17 Towards Energy-Farness n Asynchronous Duty-Cyclng Sensor Networks 38:17 Fg. 11. Snapshot of energy consumpton rates. Fg. 12. Snapshot of sleep ntervals. close to the snk (wth heaver traffcs) suffer slghtly hgher energy consumpton rates. However, compared wth EQUAL, the mn-max energy farness has been mproved by GDSIC up to 64.1%, and the obtaned energy farness s close to the optmal result. In addton, the average energy energy consumpton rate n GDSIC also outperforms EQUAL by 37.2% Snapshot of Sleep Intervals. In Fgure 12, we depct statstcs of sleep ntervals of the sensor nodes n GDSIC accordng to ther hop counts. The statstcs are obtaned after the network becomes stable. In ths experment, sensor nodes are confgured wth the default sleep nterval, that s, 512 ms, ntally. Fgure 12 ndcates that all sensor nodes should ncrease ther sleep ntervals so that the obtaned mn-max energy farness can break the barrer formed by the sleep ntervals selected ntally, whch s dfferent from the ntutve suggestons of the greedy strategy. On the other hand, from Fgure 12, we can observe that the trend, that s, the sleep nterval should be set large f the sensor node s close to the snk node carryng hgher traffc loads, holds after the network becomes stable. However, such a trend only reflects a statstc result. If we focus on each ndvdual node par, such a trend does not always exst. Such results valdate the hardness of the SIC problem, where heurstcs can be hardly borrowed to trvally acheve the optmal sleep nterval control. 6. TRACE-DRIVEN SIMULATION EVALUATION We conduct comprehensve and large-scale smulatons to further examne the effcency and scalablty of GDSIC. We evaluate the system performance of GDSIC n comparson wth the optmal polcy (OPT), the greedy strategy (GREEDY), and the equal sleep nterval strategy (EQUAL). In GREEDY, sensor nodes adust sleep ntervals such that ther energy consumpton rates are set as the average value of ther neghbors. To test a realstc network settng, smulatons are conducted wth a real trace harvested from GreenOrbs [Lu et al. 2011a]. GreenOrbs s a long-term and largescale wreless sensor network deployed n the forest, whch contans 433 nodes and has contnuously worked over one year. From the harvested trace over 6 months, we observe that the dynamcs of wreless lnks result n fluctuatng of the network topology. To mmc the lnk estmaton for real data transmssons, we flter out lossy lnks wth small RSSI values. In partcular, lnks wth the packet recepton rato lower than 30% or RSSI smaller than 80 db are excluded by the flter. By dong so, we obtan a stable network topology for smulatons n Fgure 13. The topology ncludes 6567 lnks wth relatvely good qualtes. ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.

18 38:18 Z. L et al. Fg. 13. GreenOrbs topology. Fg. 14. Maxmum energy consumpton rates 6.1. Expermental Settng In the trace, sensor nodes are deployed n a 700m 200m rectangle feld wth the default transmsson power. Parameters of sensor nodes are set based on the TelosB mote specfcaton [TelosB 2004]. To collect network-wde data, both DAG and data collecton tree are nvestgated n the smulaton. Packet retransmssons due to the lnk loss are consdered n the smulaton. The snk node s placed at ( 200.2, 115.7) and the default traffc generaton rate s one packet every ten seconds. To mmc the traffc dynamcs n real applcatons, we manually trgger the traffc varance and nvestgate the mpact of the traffc dynamcs. The default MAC-layer protocol s X-MAC, whle we also study the GDSIC strategy over a varety of other asynchronous protocols, adoptng the orgnal LPL, strobed preamble and predctve wake-up technques Maxmum Energy Consumpton Rates. In Fgure 14, we frst nvestgate the acheved maxmum energy consumpton rates (mn-max energy farness) wth dfferent approaches on top of DAG. We smulate an 8000-second data collecton process. Durng three tme ntervals of [3500, 4000], [4500, 5000], and [6000, 6500], we double traffc ACM Transactons on Sensor Networks, Vol. 10, No. 3, Artcle 38, Publcaton date: Aprl 2014.