An Energy Efficient and Accurate Slot Synchronization Scheme for Wireless Sensor Networks

Transcription

1 An Enegy Efficient and Accuate Slot Synchonization Scheme fo Wieless Senso Netwoks Lillian Dai Pithwish asu Jason Redi N Technologies, 0 Moulton St., Cambidge, MA 038 ldai@bbn.com pbasu@bbn.com edi@bbn.com Abstact-Existing slotted channel access schemes in wieless netwoks assume that slot boundaies at all nodes ae synchonized. In pactice, elative clock difts among nodes cause slot misalignment ove time and can esult in catastophic data loss in such systems. We popose a simple netwok-wide slot synchonization scheme (Slot-Sync and Slot-Resync) suitable fo duty-cycling wieless senso netwoks. The poposed scheme attains high accuacy by cicumventing dominant souces of eo inheent in taditional time synchonization potocols. At modeate duty-cycle fequencies, the poposed scheme also has the unique advantage of eliminating e-synchonization (e-sync) ovehead completely, theeby achieving slot e-sync essentially fo fee. We povide an enegy efficient slot guad time and esync inteval design fo the poposed scheme and analyze seveal spanning tee stuctues fo slot-alignment message popagation. In addition, we deive uppe bounds on the synchonization (sync) eo fo a family of tees. Though simulations, we compae the spanning tees we popose to those used fo time sync in liteatue and show up to 80% eduction in sync eo and up to 70% eduction in enegy needed fo slot-alignment message popagation by choosing appopiate tee stuctues. Keywods-wieless senso netwok, slot synchonization, guad time, spanning tee, synchonization eo, clock dift. I. INTRODUCTION In ecent yeas, thee has been phenomenal gowth in the development and deployment of battey opeated wieless senso netwoks (WSN). Since battey enegy is a limited esouce, many systems intelligently conseve enegy by tuning the adio tansceives off though a pocess temed duty-cycling [-3]. oth asynchonous [] and synchonous [, 3] medium access contol (MAC) schemes have been poposed fo such WSNs. In geneal, synchonous MAC with time slotting and some amount of tansmission coodination can achieve highe thoughput than asynchonous schemes; hence ae moe suitable fo fixed senso netwoks with modeate amount of taffic load [-3]. Howeve, implicit in all synchonous MAC schemes is the assumption that slots of neighboing nodes ae aligned within a easonable level of pecision at all times. In pactice, clocks in diffeent nodes suffe fom andom difts, causing slot misalignment ove time. This, in tun, may esult in catastophic data loss in dutycycling WSNs as nodes ae elying on the undelying slotted stuctue fo highe laye pocesses. Pepaed though collaboative paticipation in the Communications and Netwoks Consotium sponsoed by the U. S. Amy Reseach Laboatoy unde the Collaboative Technology Alliance Pogam, Coopeative Ageement DAAD The U. S. Govenment is authoized to epoduce and distibute epints fo Govenment puposes notwithstanding any copyight notation theeon. In this pape, we investigate the slot synchonization (sync) poblem in multi-hop WSNs that employ synchonous MAC. One way to achieve slot sync is to sync the clocks (time-sync) as poposed in [4-8]. y vitue of having attained a common time within a cetain degee of accuacy, slots at neighboing node pais ae tempoally synchonized with bounded offsets. Thee ae vaious souces of eo associated with time-sync potocols, which stem, to a lage pat, fom vaiable softwae delays fo tansmission and eception of time-stamped messages [5, 6]. We note that many slotted netwoks do not have an explicit equiement fo attaining a common time in diffeent nodes [3]. Instead, it is only necessay that the slot boundaies in diffeent nodes ae synced and that nodes agee on which slot they ae cuently tansmitting o eceiving in. This affods an oppotunity to significantly educe the sync eos inheent in time-sync potocols due to time-stamping. We popose a slot sync scheme (temed Slot-Sync and Slot- Resync) that does not exchange time-stamped infomation, hence eliminating vaiable softwae delays associated with channel access, packet queueing, tansmission, and eception. Instead of using time-stamps, ou scheme (descibed in detail in Section III) elies on the inheent popety of the slotted MAC stuctue and an added featue that detemines the signal aival time at each eceive. Since each node tansmits infomation at the beginning of a time slot, each data tansmission infoms othe nodes of a node s slot boundaies. Hence, e-sync is achieved fo fee each time a data tansmission occus. To achieve initial sync in the netwok, slot-align messages ae popagated in the netwok along spanning tees stating fom a efeence node. In effect, with the poposed Slot-Sync scheme, clocks in two neighboing nodes may still epot diffeent times; howeve, the nodes agee on slot boundaies and can poceed to exchange infomation in a common slot. We pefom detailed analytical and simulations studies of the poposed scheme. Ou key contibutions ae:. Slot-Sync and Slot-Resync that can achieve geate accuacy and enegy savings compaed to time-sync.. Enegy-efficient design fo guad time and e-sync peiod. 3. A message-efficient slot fomation and maintenance scheme that uses an appopiately chosen ooted tee stuctue fo slot-align message popagation. 4. An uppe bound on the maximum sync eo. 5. Simulation esults that show up to 80% impovement in sync eo and up to 70% impovement in enegy efficiency fo slot-align message popagation of cetain minimum-hop based tees ove geneal level-based tees such as the apidly constucted tee poposed in [5].

2 Note that contibutions (-5) ae also elevant fo time-sync schemes as applied to slotted wieless systems. In that sense, ou guad time and tee analyses ae of boade inteests. This pape is oganized as follows. Section II povides an oveview of elated wok. Section III descibes the slot sync poblem. Section IV povides analysis of the enegy tadeoffs between guad times, e-sync peiods, and slot utilization. Section V focuses on the poblem of achieving netwok-wide slot sync by popagating slot-align messages along spanning tees. Section VI pesents a compaative simulation analysis of vaious sync tees. Section VII concludes the pape and outlines possible eseach diections. Some eseaches poposed schemes that assume each clock can be appoximated by an oscillato with fixed fequency []. They deived uppe and lowe bounds fo constaints on the elative dift and elative offset between node pais. Othes poposed schemes that aim at minimizing the complexity of achieving time-sync instead of minimizing sync eo [7]. Li and Rus poposed a localized diffusionbased method in which nodes exchange and update clock eading infomation locally with neighbos [8]. Thei algoithm can adapt to node failue, mobility o channel eos, but takes much longe time to convege than tee based sync potocols. II. RELATED WORK The slot sync poblem has been studied in the context of special wieless netwoks such as luetooth. In a luetooth piconet (with a maximum of 8 nodes), a maste node povides the time slot efeence [9]. A slave node esponds to a maste s poll in the second half of the eceived slot, thus achieving slot sync. Adjacent fequency hopping piconets ae inteconnected by bidge nodes which could play maste/slave o slave/slave oles. Since luetooth pefoms slot sync within a piconet alone, such bidges often have to switch between piconet time efeences (and thus waste many slots) duing data fowading. In fact, efficient scheduling of such slots and coodinating tansmission at these bidge nodes is a had poblem and a topic of intense eseach [9]. Ebne et al. also popose a scheme which syncs the slots at each node to those of a neaest neighbo node, foming locally synced node pais on demand [0]. Howeve, thei dynamic slot sync achitectue is designed fo shot lived communications fo highly mobile vehicula systems, not fo geneal pupose o duty cycling WSNs in which nodes ely on the synced slot stuctue to sleep and wake up. Realizing the limitations of the classical Netwok Time Potocol (NTP) [] fom the pespective of enegy efficiency, Elson et al. poposed Refeence oadcast Synchonization (RS) fo time-sync [4]. In RS, nodes send beacons to neighbos using wieless boadcasts. These beacons do not contain explicit timestamps; instead, eceives use the aival time of a beacon as efeence fo compaing thei clocks. RS achieves easonable sync accuacy at the expense of excessive message exchanges between eceives. Ganeiwal et al. [5] poposed a netwok-wide time-sync potocol fo WSNs called Timing-sync Potocol fo Senso Netwoks (TPSN). TPSN has two phases: level discovey and time sync. The level discovey phase assumes that thee exists a known oot node in the netwok. Such a node is assigned a level 0 and the level discovey potocol begins at this node. The level-based sync tee used in this wok has the advantage of apid tee constuction at the expense of lage sync eo as well as long delay and high enegy consumption in popagating the sync messages. We believe that since the sync tee would be used often fo e-sync, one with bette popeties is moe desiable fo achieving significant eduction in synceo and impovement in message (enegy) efficiency. III. SLOT SYNCHRONIZATION FUNDAMENTALS Slotted netwoks equie two fundamental pimitives fo effective opeation: (a) accuate alignment of slot boundaies between neighboing nodes, and (b) coodinated slot usage between nodes in the netwok fo collision fee opeation, and/o duty cycling. While a failue to pefom (b) effectively can esult in loss of netwok thoughput due to collisions and/o dopped packets, a failue to pefom (a) accuately can esult in catastophic data loss ove a peiod of time. In this pape, we focus exclusively on (a). Two nodes X and Y can align thei slot boundaies in seveal ways. If both have GPS eceives, thei clocks ae synchonized to within 00ns of UTC. In the absence of GPS, X and Y can un a time-sync potocol [4,5,8,] to synchonize thei clocks. Slot sync is obtained simply by vitue of two nodes having obtained a common time. If timesync schemes ae used, the misalignment of slot boundaies at X and Y is diectly popotional to the eo in time-sync. Most time-sync potocols in the liteatue exchange messages containing time-stamped infomation geneated in a highe laye of the potocol stack to estimate elative offset, dift and popagation delay. The dominant souce of eo in these potocols is the vaiability in the times spent by this timestamped message in the sende s MAC and the eceive s OS. These delays ae geneally much geate than the signal popagation delay [5]. The availability and use of physical laye timestamps at the eceive node can help to eliminate the delay in the eceive s OS. Howeve, most time-sync schemes with the exception of RS [4] still suffe fom the access time delay on the sende s side. RS, as poposed, pefoms no time stamping at the sende and will only suffe fom the eo due to eceive OS delay. If RS is augmented with the capability of physical laye time-stamping at the eceive, the most dominant souce of eo that would emain is popagation delay. Ou scheme is simila to RS augmented with PHY laye time-stamping and without the exchange of eceive timestamps between nodes. Thee ae seveal advantages of doing this: (a) the only majo souce of eo is popagation delay; (b) no exchange of sende (as in [5]) o eceive (as in [4]) timestamps is necessay as slot sync can be achieved in one shot in a neighbohood; and (c) no exchange of timestamps is necessay fo e-sync at futue times.

3 Ou poposed mechanism achieves slot sync between X and Y without the intemediate step of explicit time-sync. Assume that a peiodic slot stuctue is maintained by the physical laye module (PHY). At local time t, a slot-align message is geneated by a highe laye module at X and contains the slot numbe the message should be sent in. This message is tansmitted by the PHY in the appopiate slot at time t. The slot-align message eaches Y at its local time t. Y then begins its PHY laye time slotting stating at time t. At this point X and Y have achieve slot sync without any futhe infomation exchange. This scheme is shown in Fig.. The only eo incued in this pocess is the popagation delay. Due to the vaiable time delay fom the time the message is geneated to the tansmission time, the slot numbe contained in the packet may be expied at time t. If this occus, PHY notifies the uppe laye pocesses so that a new slot-align message can be geneated with moe lead time. Stating fom a efeence node, slot-align messages ae popagated though the netwok by nodes that have eceived the slot-align message peviously along the edges of a synctee (discussed in geate detail in Section V). Each node maintains a fixed slot duation and eboadcasts the message at its slot bounday, i.e., afte waiting fo time equal to an intege multiple of slot duations. Upon eceiving a message fom a designated paent in the tee, a child node whose slot bounday has difted elative to the paent s, e-syncs its slot to the time of message eception. This pocess is illustated in Fig.. Due to impefections in manufactuing pocesses, changes in ambient tempeatues, mateial aging, and othe extenal conditions [3], a typical clock used in senso nodes may dift up to tens of pats pe million (ppm) which is equal to a few seconds pe day. Since communication equipments typically opeate on the odes of micoseconds, clock difts can significantly degade the pefomance of synchonous communications. Hence esync needs to be an integal pat of any slotted netwok system. To potect against data loss befoe slots ae e-synced, small amounts of guad times ae usually added befoe and afte the data potion of the slot. If thee is enough taffic flowing though the netwok, e-sync can be achieved fo fee unde ou poposed scheme. Othewise, explicit e-sync messages ae tansmitted (See Section IV). Time 6. data tansmission Slot Guad times 5. tansmit data in slot. slot align Slot 4. infom MAC message. begin slot t 3. begin slot alignment t fomation popagation t delay X : MAC X : PHY Y : PHY Y : MAC Fig. Pai-wise Slot Fomation and Slotted Data Tansmission Topology 0 (ef node) 4 3 guad times slot align message (sent at bounday of data potion of slot) Fig. Slot-sync Message Popagation and Alignment Time IV. ENERGY EFFICIENT SLOT DESIGN In a wieless netwok, it is unnecessay to align the slot boundaies of non-neighboing nodes since they do not paticipate in data exchange. Fo each neighboing node pai (tx/x pai), data loss may occu due to elative clock dift, signal popagation delay, and initial slot offset (sync eo) as shown in Fig. 3. All the petinent paametes ae defined in Table I. To mitigate data loss, guad times need to be povisioned in each slot as shown in Fig. 3. Although the amount of time available fo data tansmission is educed in each slot by povisioning guad times, data loss due to slot misalignment can be eliminated fo a numbe of slots. As long as slots of neighboing nodes ae e-synced befoe data loss occus (which may not incu any ovehead as discussed in Section III.), data loss due to slot misalignment can be eliminated completely. The netwok is said to have achieved netwok-wide sync (net-sync) if the slot boundaies between evey neighboing node pai ae synced in evey slot such that data loss is eliminated. Fist, we would like to design the guad times such that net-sync is achieved with minimum e-sync fequency, while maintaining a desied slot utilization, U, which measues the faction of time available fo data tansmission in each slot. This can be posed as a constained optimization poblem. We povide a simple ule-of-thumb esult in scenaios whee the maximum clock dift θ max and the maximum sync eo ae small. Moe details ae pesented in [4]. In this case, TALE I. LIST OF PARAMETERS FOR SLOT DESIGN ψ Slot duation [sec] θ A Relative clock dift between nodes A and d A Popagation delay between nodes A and [sec] A Initial slot offset (sync eo) [sec] s Data slot duation [sec] g init Initial guad time [sec] g end End guad time [sec] T max Max numbe of slots befoe data loss occus (e-sync peiod) T ˆ Re-sync peiod in [sec] = Tmaxψ U Slot utilization = s ψ θ max Maximum clock dift elative to ideal clock [ppm] Maximum sync eo acoss all tx/x pais [sec] d Maximum popagation delay acoss all tx/x pais [sec] slot

4 A C A A ψ ψ ( + θ A ) d A OFF ON OFF lost eceived OFF ON OFF Fig. 3 Tansmission fom node A to with loss. has a slowe clock than A ( θ A > 0 ). All times shown ae times epoted by the clock in node A. (Popagation delay and sync eo ae exaggeated fo illustation puposes). ginit s gend No Data Loss Fig. 4 Tansmissions fom A to and A to C whee, compaed to A, has a slowe clock and C has a faste clock. Afte a numbe of lossless tansmission slots, elative clock difts induce data loss s s ginit ( U ) d, gend ( U ) + d, Tmax time time Data Loss without e-sync U 4θ max () In tems of e-sync inteval T ˆ in time, a simple (appx) expession can be obtained fo the total guad time in a slot g 4 ˆ init + gend θmaxt () This esult is faily intuitive since fo small θ max and, slot boundaies dift apat by at most θ ˆ maxt in duation T ˆ. A g init of θ ˆ maxt is needed fo tansmission fom a node with a slow clock to a node with a fast clock. Similaly, a g end of θ ˆ maxt is needed fo tansmission fom a node with a fast clock to a node with a slow clock. Exact deivations of these quantities have been omitted due to paucity of space and can be found in [4]. Lage esults in lage guad times. Now we addess the issue of optimal slot utilization fo enegy efficient opeation of the Slot-Sync scheme. Fo a given slot utilization, () shows that smalle guad times esult in a shote e-sync peiod. This implies that less enegy is wasted at eceives in each slot whee a tansmission takes place, at the expense of potentially moe enegy consumed to pefom e-sync. The numbe of data and e-sync tansmissions depend on the taffic ate (in an ideal dutycycling netwok, this also coesponds to the duty-cycle fequency). Let the aival of ON slots be a Poisson pocess with aival ate λ. If a data tansmission occus pio to T ˆ, then no exta enegy need to be expended fo e-sync; othewise, fo evey T ˆ inteval that does not have a data tansmission, m numbe of slots ae needed to tansmit esync messages. To fist ode, the expected amount of enegy wasted due to guad times and e-sync is popotional to λtˆ e λ ginit + gend + mψ (3) λtˆ e Substituting (-) into (3), one can numeically solve fo the optimal utilization that minimizes the amount of enegy wasted. Fig. 5 shows a typical cuve fo wasted enegy. Fo highe expected taffic volume, it is moe enegy-efficient to have a lage slot utilization with smalle guad times and esync peiod. Note that implicit in the above deivations, we assumed that a node tansmits to a eceive in one slot and eithe tuns off o tansmits to a diffeent eceive in the subsequent slot. In geneal, a node can tansmit to the same eceive in consecutive slots and need not teminate the tansmission in each slot. If pai-wise tansmissions typically span seveal slots, say n slots, then one may conside edefining a new data slot inteval s = nψ ginit gend. All pevious deivations cay though fo the expanded data slot. One may ague that the guad time at the end of each slot is unnecessay since a eceive can intelligently tun itself off only afte an end-oftansmission signal is eceived fom the tansmitte. Howeve, depending on the duty-cycling and MAC potocols, tuning a eceive off past its slot bounday may cause collisions in the subsequent slot. In ou design, we povide guaanteed slot boundaies to highe layes, although coss-laye design is possible and is subject to futue eseach. V. NETWORK-WIDE SLOT SYNCHRONIZATION In this section, we investigate techniques and popose algoithms to achieve net-sync. Two impotant netwok wide metics ae examined:. Maximum sync eo ( ): maximum slot misalignment between any pai of neighbos afte temination of the netsync algoithm taking acoss all node pais in the netwok.. Message efficiency: the numbe of message exchanges needed to achieve net-sync (this diectly tanslates to enegy efficiency). Fig. 5 Wasted Enegy fo vaying ON slot aival ate λ and slot utilization U

5 The poposed basic Net-Sync algoithm is as follows: One of the nodes in the netwok povides a efeence slot bounday and tansmits a slot-align message at the beginning of a data slot (afte g init ). Neighboing nodes eceive the packet afte some popagation delay, set thei slot boundaies to the time at which the packet is eceived minus g init, and etansmit the slot-align message at subsequent data slot boundaies. The slot-align message is popagated in the netwok though multiple hops until evey node s slots ae aligned. As can be expected, the choice of the efeence node as well as the paths taken by slot-align messages has significant impact on the maximum sync eo and message efficiency to achieve net-sync. Although many time-sync papes povide pefomance analyses on the vaious time-sync potocols, they assume cetain sync message popagation stuctues without much justification. Futhemoe, most eo analyses ae pefomed fo nodes along a single sync path only. A. Model fo Net-Sync and Poblem Statement Conside a senso netwok gaph G = ( V, E) whee V is a set of nodes and E is a set of edges epesenting bidiectional communication links (with maximum tansmission ange ). The efeence node (o oot node) is indexed by. Function + d : E R denotes the popagation delay along each edge of G, and is diectly popotional to the distance between the endpoints of the edge. Let S denote a sync stuctue which is a spanning subgaph of G the net-sync messages ae popagated along the edges of S, stating at node. Clealy, a spanning tee of G is a minimal stuctue along whose edges the sync messages can popagate. Let PS ( w ) denote the shotest path fom to w using edges in S in tems of the following total distance metic: D ( w) = d( x, y) (4) S ( xy, ) PS ( w) This is the minimum delay path fom to w using edges in S. The sync eo between two neighboing nodes, u and v is the diffeence between the total delays accumulated by the espective slot-align messages when they each u and v fom along best paths in the sync stuctue (assuming no delay in fowading at intemediate nodes). It is also desiable that message popagation along S should equie the minimum numbe of boadcast tansmissions bs ( ) fo eaching all nodes in G stating at oot node. This message efficiency metic leads to the consevation of enegy fo pefoming net-sync. The decision vesion of the coesponding constained optimization poblem that minimizes the two afoementioned metics can be fomulated as follows: + + Input: G = ( V, E) ; d : E R ; Z Desied outputs: spanning tee T ; efeence oot node Objective: min max DT( u) DT( v) T ( uv, ) E Constaint: bt ( ) Clealy, this is a vey complex optimization poblem that is NP had fo geneal instances of G. esides, pai wise popagation delay infomation d may not be known (the popagation delays, if known, could easily be compensated fo in a pai wise manne, and thee would be little sync eo.). Hence, in this pape, we popose to constuct heuistic popagation stuctues using connectivity infomation while keeping the two ove-aching metics in consideation. Moeove, fo common popagation stuctues, such as a apidly-constucted level-based tee [5], analyzing sync eo between nodes synchonized along a path is inadequate since the maximum sync eo typically occus fo neighboing nodes that ae synchonized along non-intesecting paths. This is because although slot-align messages ae popagated along the spanning tee, neighboing nodes in the oiginal gaph G may not have paent/child elationships in the spanning tee.. Heuistic Sync-tee stuctues fo Net-sync We fist discuss elements of the sync stuctue that impact maximum sync eo and message efficiency of net-sync. Then, we povide detailed analyses and simulation esults fo seveal candidate sync message popagation stuctues and popose a paticula level-based tee stuctue that has good sync eo and message efficiency popeties. Fo this synctee, we deive uppe bounds on the sync eo. Fig. 6 shows an example of such a level-based spanning tee. We use standad gaph teminologies paent, child, leaf node, and non-leaf node to efe to node elationships in the tee. Maximum sync eo between neighboing node pais is an impotant metic fo a net-sync popagation stuctue. As mentioned ealie, ou slot-sync scheme eliminates dominant souces of eo inheent in time-sync potocols. The dominant souce of eo now is popagation delay, which may be significant fo netwoks with long links. If nodes do not have infomation about the popagation delay between all neighboing node pais, then it is impossible to constuct an optimal spanning tee that minimizes the maximum sync eo using any algoithm. Hence, we can only use hop-based algoithms to appoximate this pefomance. On the othe hand, if nodes indeed possess infomation about pai wise popagation delay, then sync eo can almost be eliminated by an additional handshaking step in the slot-sync potocol. The numbe of slot-align message boadcasts is the othe impotant metic fo the net-sync popagation tee, and it is equal to the numbe of non-leaf nodes in the tee. Hence, the message efficiency (and in tun the amount of enegy) fo Fig. 6 Level-based Spanning Tee fo Slot-align message Popagation. Nodes align slot boundaies to paent nodes pointed to by the aows oot 0 3

6 achieving net-sync is popotional to the numbe of non-leaf nodes; theefoe, minimizing the numbe non-leaf nodes in the spanning tee is a desiable goal. It tuns out that this is equivalent to finding the minimum connected dominating set (MCDS) of G. This has been shown to be NP-had [5]; howeve, seveal heuistic algoithms have been poposed fo the MCDS poblem and the best heuistic we know of in finding the minimum numbe of non-leaf nodes is the beadthfist-seach (FS) spanning tee. It has been shown to be within a constant facto of 8 fom the optimal [6]. Fom an implementation pespective, a FS spanning tee lends itself to simple constuction in wieless senso netwoks. We deive pefomance bounds fo FS spanning tees and show consideable gains ove the apidly constucted level tee used in [5] both in tems of maximum sync eo and numbe of non-leaf nodes, paticulaly if cetain attibutes of the FS tee ae impoved upon. Fist we eview standad gaph theoetic teminology. Let the length of the shotest path (in tems of hop count) between nodes x and y be hxy (, ). The eccenticity of a node i is e = max h( i, j). The diamete and adius of gaph G ae i j V DG = max ei and RG = min ei espectively. The cente of gaph i V i V G is a set of vetices that has node eccenticity equal to the adius. A cental Point is a node in the set of gaph centes. Fo any gaph G, RG DG RG. Fo a FS spanning tee with an abitay oot node (default level 0), the numbe of hops fom to any othe node is the minimum possible. Let the eccenticity of be e, it is easy to show that the numbe of levels of any FS spanning tee ooted at is equal to e. If is a cental point, then the numbe of levels is equal to the adius of G, and hence is equal to the minimum numbe of levels possible. We call such a FS spanning tee that is ooted at a cental point a minimum hop-level spanning tee (MHLST). The FS spanning tee has a few nice popeties: it is elatively easy to constuct; the maximum sync eo is uppe bounded by a linea function of the numbe of levels of the spanning tee; and the numbe of non-leaf nodes is at most a facto of 8 fom the optimal. Additionally, by choosing a cental point as the oot, the numbe of levels is minimized and sync eo uppe bound may be educed by a facto of two. Theoem. The maximum net-sync eo fo a netwok G, that is synchonized using a FS spanning tee ooted at node with e numbe of levels, is uppe-bounded by: e ( + d ), if e = odd =, e d( + ), othewise whee d is the maximum popagation delay ( d = c, whee is the maximum tansmission ange, and c is the speed of light). This bound is tight. Poof: Refe to Fig. 7, one can show that such netwoks, with φ > 60 degees, can be constucted and meet the bound [4]. ε ε A e > φ φ e = Fig. 7 Type of Gaphs that Achieve the Maximum Sync Eo Uppe ound Coollay. The maximum sync eo in a gaph G is uppe R bounded by ( G + R ), if = odd ; ( G + d RG d ), othewise. Poof: The minimum numbe of levels in a FS spanning tee is equal to the gaph adius R G. Hence fo a netwok synced using a MHLST, the uppe bound can be witten fo e = R G. This can seve as an uppe bound on the maximum sync eo fo a netwok synced using any sync stuctue. Coollay. MHLST can educe the maximum sync eo by at most one-half compaed to a FS spanning tee not ooted at a cental point. Poof: A FS spanning tee has a maximum numbe of levels that is equal to the gaph diamete D G, with maximum sync eo uppe bounded by ( DG + ) d. Since DG RG, the uppe bound can be witten fo e = RG. This is less than a facto of two times the uppe bound fo a MHLST. We investigate a plethoa of spanning tees fo distibuting the slot align message fom the oot to all nodes in the netwok. They fall in thee boad categoies: () Rapidly-constucted Spanning Tee [5] The oot node stats by boadcasting a sync message; neighbos that hea this message eboadcast it afte a andom delay. This pocess is continued until all nodes ae synchonized. The esulting tee is level-based, but could potentially have a lage numbe of levels as well as a lage numbe of boadcasting nodes. () Spanning tees based on min hop metic If netwok connectivity (o popagation delay) infomation was widely available, Dijksta s shotest path algoithm can be used to calculate shotest path tees ooted at a given node. (3) FS Spanning tees We investigate two optimizations on the basic FS spanning tee: Node-sot Spanning Tee The oot node stats by popagating a slot-align message. Neighbos popagate this packet to thei neighbos to fom a FS spanning tee. At each level, nodes send the slot-align message in deceasing ode of the numbe of possible childen nodes. This tends to esult in fewe paent nodes than a geneal FS tee ooted at the same oot node. Edge-sot Spanning Tee This tee is simila to the FS Nodesot Spanning Tee. The diffeence is that at each level, nodes send the slot-align message in deceasing ode of the numbe of edges connecting its possible childen. Since childen that A e = A

7 have the same paent tend to have lowe elative sync eo, this tee tends to have bette aveage sync eo pefomances than othe FS tees. The choice of the oot node is othogonal in each of the above tees and has its set of associated tadeoffs. Choosing a cental point as the oot (denoted by CPR) is desiable fo educing the maximum sync eo, but computing this is usually a non-tivial potocol step. On the contay, choosing a oot node heuistically o andomly (denoted by RR) may be faste but may yield suboptimal sync eo and message efficiency pefomance. Min-distance Dijksta CPR Min-distance Dijksta RR Min-hop Dijksta CPR Min-hop Dijksta RR FS CPR FS RR FS Node-sot CPR FS Node-sot RR FS Edge-sot CPR FS Edge-sot RR Rapid CPR Rapid RR VI. SIMULATION RESULTS Ou simulation setup consists of a netwok of 00 nodes unifomly and andomly distibuted in a unit-aea squae egion. Fig. 8 plots the pai-wise sync eo fo all simulated tees nomalized by multiplying by the speed of light. Though moe simulations, we obseve that in geneal, FS based tees and the min-hop Dijksta tee have compaable sync eo and ae significantly bette than the apidlyconstucted tee both in the maximum sync eo and in the mean. The min-distance Dijksta tee achieves even lowe sync eo; howeve, since distance infomation is not known to the netwok, this tee cannot be constucted in pactice. In tems of non-leaf nodes, the apid level-based tee in [5] and the min-distance Dijksta tee have the wost pefomance in geneal, followed by the FS tee. Node-sot and Edge-sot tees have the least numbe of non-leaf nodes in most cases. In geneal, the CPR vesions of tees geneate much fewe nonleaf nodes than the coesponding RR vesions. To veify these obsevations, we simulate 500 andom topologies fo a set of tansmission anges. The aveage numbe of non-leaf nodes and the aveage maximum nomalized sync eo ae plotted in Fig. 9 (the aveage is taken ove the topologies). Figs. 9 also includes plots of pecentage savings in aveage numbe of non-leaf nodes and aveage maximum sync eo ove those geneated by the apidly-foming tee fo pefomance compaisons (the plots show pecentage savings fo CPR only; RR geneates simila plots). As expected fo geometic andom netwoks, thee exists a citical tansmission ange theshold, below which the netwok is disconnected with high pobability. We obseve a second phase tansition theshold, beyond which the netwok is almost fully connected with gaph adius of less than. Fo the 00 node netwok we simulate, this theshold occus at a tansmission ange of appoximately 0.6. Fo most WSNs, the inteesting egion lies between the two phase tansition egions whee the netwok is connected, but not almost fully connected. Hence, the plots we geneate ae ove the tansmission ange of 0.4 to 0.6 only. Fig. 9 shows that the apidly-foming tee and the mindistance Dijksta tee geneate significantly moe non-leaf nodes than FS based tees. Node-sot and Edge-sot tees geneate the least numbe of non-leaf nodes in geneal. When The tansmission adius is 0.. If the opeating aea and tx adius ae scaled by 000, then a nomalized max sync eo of.5 (Rapid tee) coesponds to about 8.3 mu-sec. Fo longe haul links, this sync eo could be much wose. Fig. 8 Nomalized Sync Eo Each dot epesents sync eo of a node pai in the netwok. Cicles maks avg. sync eo ove all node pais; + signs mak uppebounds ooted at cental points, up to 70% savings can be achieved when compaed to the apidly-foming tee ooted at the same nodes. On aveage, all FS based tees have compaable sync eo pefomances. Compaed to the apidly-foming level tee, up to 80% sync eo eduction can be achieved using FS based tees. We also simulated netwoks with fewe and moe nodes as well as ove ectangula egions [4]. Simila cuves have been obtained. Fo all the types of tees simulated, choosing a cental point as the oot node educes the numbe of non-leaf nodes significantly compaed to choosing a andom node as the oot. Up to 40% eductions is achievable fo FS tees. An additional 5% eduction ove FS tees can be achieved if Node-sot o Edge-sot tees ae used [4]. Ou poposed techniques ae applicable to the netwok wide time-sync poblem as well. The tadeoffs between maximum sync eo and message efficiency in achieving sync ae fundamental in natue and ae applicable to both slot sync and time sync poblems. Also, the vaious tadeoffs studied fo slot guad time design in Section IV ae applicable to any slotted netwok system that caes about enegy efficiency. VII. CONCLUSION AND FUTURE WORK In this pape, we pesented a new technique fo achieving slot alignment in wieless senso netwoks temed Slot-Sync. Fist, we povided an enegy efficient slot design fo guad times and e-sync peiods. We then pesented an enegyefficient slot fomation and maintenance scheme that uses an appopiately chosen ooted spanning tee stuctue known as the soted-mhlst fo slot-align message popagation thoughout the WSN. Though simulations, we showed that the choice of the sync tee and that of the oot node ae vey impotant both in minimizing the wost-case sync-eo and the enegy consumption of the sync/e-sync pocess. Up to 80% eduction in sync eo and up to 70% eduction in enegy fo sync message popagation can be achieved ove the apidly constucted tee used in [5]. Using gaph theoetic appoaches, we deived an uppe bound on the maximum sync eo in WSNs and showed that the node pais that have the maximum sync eo typically do not have paent/child elationship in the sync tee.

8 (a) (b) (c) (d) Fig. 9 Simulation esults fo 00 node netwoks in unit aea squae egion; fo each tansmission adius, 500 andom topologies wee geneated. (a) Aveage numbe of non-leaf nodes; (b) Aveage maximum nomalized sync eo; (c) Pecentage eduction in non-leaf nodes ove the apidly-foming tee (d) Pecentage eduction in sync eo ove the apidly-foming tee Although we pesented ou Slot-Sync scheme in the context of WSNs, ou appoach is moe geneal and can be applied to geneal multi-hop wieless netwoks with modeate taffic load and low mobility. We ae investigating solutions to the slot misalignment poblem fo netwoks with geate mobility. In paticula, we ae developing distibuted algoithms fo achieving net-sync in uneliable netwoks whee patitions fom and heal dynamically. We ae also woking on enegy compaisons of the poposed slot-sync scheme when applied to well known synchonous MAC schemes with asynchonous MAC schemes that do not equie sync. Duty cycling pesents additional challenges to the potocol fo maintaining net-sync the time to popagate a message though the netwok inceases as a function of the duty cycling peiod. We ae cuently investigating this issue actively. Additional futue eseach includes a stochastic analysis of guad time and e-sync peiod in contast to the wost-case analysis pesented in this pape. Ou simulations indicated that the mean sync eo can be substantially lowe than the wost case eo. Futhemoe, the mean clock dift is much lowe than the wost case clock dift epoted by the manufactue. Hence, fo duty-cycling netwoks that can toleate occasional data loss, stochastic design of guad times and e-sync peiod may achieve substantial enegy savings. REFERENCES 3 [] K. Sohabi, J. Gao, V. Ailawadhi, and G. Pottie, Potocols fo Self-oganization of a Wieless Senso Netwok, IEEE Pesonal Communications, Oct The views and conclusions contained in this document ae those of the authos and should not be intepeted as epesenting the official policies, eithe expessed o implied, of the Amy Reseach Laboatoy o the U. S. Govenment. [] J. Hill and D. E. Culle, MICA: A Wieless Platfom fo Deeply Embedded Netwoks, IEEE Mico, (6):-4, Nov. 00. [3] J. Redi, I. Castineya, C. Patidge, K. Manning, R. Rosales-Hain, R. Ramanathan, and S. Kolek, Joint Achitectue Vision fo Low Enegy Netwoking (JAVeLEN) DARPA-ATO Connectionless Netwoking Pogam, Phase I, N Technical Repot Dec [4] J. Elson, L. Giod, and D. Estin, Fine-gained Time Synchonization using Refeence oadcasts, Poc. USENIX OSDI, oston, MA, Dec. 00. [5] S. Ganeiwal, R. Kuma, and M. Sivastava, Timing Sync Potocol fo Senso Netwoks, Poc. ACM SenSys, Los Angeles, CA, Nov.003. [6] M. L. Sichitiu and C. Veeaittiphan, Simple, Accuate Time Synchonization fo Wieless Senso Netwoks, Poc. IEEE WCNC, 003. [7] J. Van Geunen and J. Rabaey, Lightweight Time Synchonization fo Senso Netwoks, Poc. ACM Int l. Conf. Wieless Senso Netwoks and Applications, San Diego, CA, Sept [8] Q. Li and D. Rus, Global Clock Synchonization in Senso Netwoks, Poc. IEEE Infocom, 004. [9] T. Salonidis and L.Tassiulas, Pefomance issues of luetooth scattenets and othe asynchonous TDMA ad hoc netwoks, Poc. MoMuC 003. [0] A. Ebne, H. Rohling, M. Lott, and W. Halfmann, Decentalized Slot Synchonization in Highly Dynamic ad hoc Netwoks, Wieless Pesonal Multimedia Communications, vol., pp , Oct. 00. [] D. Mills, Intenet Time Synchonization: The Netwok Time Potocol, IEEE Tans. Communications, 39(0), pp , Oct. 99. [] M. L. Sichitiu and C. Veeaittiphan, Simple, Accuate Time Synchonization fo Wieless Senso Netwoks, Poc. IEEE WCNC, 003. [3] Symmeticom white pape, Symmeticom SmatClock Technology - Impoving Oscillato Long-tem Stability fo Synchonization Applications. [4] L. Dai, P. asu, and J. Redi, Enegy Efficient Slot Synchonization Techniques fo Wieless Senso Netwoks, N Technical Repot, Jul [5] M. R. Gaey and D. S. Johnson, Computes and Intactability A Guide to the Theoy of NP-completeness, W. H. Feeman, San Fancisco, CA, 979. [6] K. M. Alzoubi, P-J. Wan, and O. Fiede, Distibuted Heuistics fo Connected Dominating Sets in Wieless ad hoc Netwoks, Jounal of Communications and Netwoks, 4(), Ma. 00.