System Level Design for Clustered Wireless Sensor Networks

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1 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO., JANUARY 2007 System Level Design for Clustered Wireless Sensor Networks A. Bonivento Student Member, IEEE, C. Fishione Member, IEEE, L. Nehi, F. Pianegiani, A. Sangiovanni-Vinentelli Fellow, IEEE Abstrat We present a system level design methodology for lustered wireless sensor networks based on a semi-random ommuniation protool alled SERAN, a mathematial model that allows to optimize the protool parameters, and a network initialization and maintenane proedure. SERAN is a two-layer (routing and MAC) protool. At both layers, SERAN ombines a randomized and a deterministi approah. While the randomized omponent provides robustness over unreliable hannels, the deterministi omponent avoids an explosion of paket ollisions and allows our protool to sale with network size. The ombined result is a high reliability and major energy savings when dense lusters are used. Our solution is based on a mathematial model that haraterizes performane aurately without resorting to extensive simulations. Thanks to this model, the user needs only to speify the appliation requirements in terms of endto-end paket delay and paket loss probability, selet the intended hardware platform, and the protool parameters are set automatially to satisfy lateny requirements and optimize for energy onsumption. Index Terms Wireless Sensor Network, Industrial Wireless, Wireless Protool. I. INTRODUCTION ALTHOUGH wireless sensor network (WSN) tehnology experiened great advanements in the last years, still its use in real life appliations is very limited. The main reason for the delay in the adoption is the lak of a system level approah, whih is a design methodology that given a set of appliation onstraints, is able to synthesize a design solution that guarantees the required lateny and quality of servie under unreliable hannel onditions. Partiularly, it is not always lear what are the lateny, reliability and power onsumption performane that the protool stak offers to the appliation, and this is ritial when ontrol is involved []. Designing reliable ommuniation protools is a diffiult task beause in many appliations the environment is unpreditable. However, some appliations have ommon harateristis that an be leveraged for an effetive protool design. For example, important lasses of appliations are haraterized by lustered topologies. In building automation, groups of sensors are deployed in speifi rooms to observe quantities as temperature, humidity, or hemial leakage and report to a A. Bonivento, C. Fishione, and A. Sangiovanni-Vinentelli are all with the Department of Eletrial Engineering, University of California at Berkeley. L. Nehi is with Politenio di Torino, Italy. F. Pianegiani is with the University of Trento, Italy. {alvise, fishion, alberto}@ees.berkeley.edu, lua.nehi@polito.it, fernando.pianegiani@dit.unitn.it. Part of the topis of this work were presented at IEEE MASS 05. C. Fishione aknowledges the support of the San Franiso Italian Institute of Culture throughout the Siene & Tehnology Attahé T. Sapolla. remote entral station in a multi-hop fashion. In manufaturing lines, sensors are typially grouped around speifi points of interest in a manufaturing ell (i.e. the end of a rail or around some robots). From a network perspetive, these are all lustered topologies, and although the size and the position of these lusters may vary signifiantly for different appliations, this similarity allows us to reate protools that an be effetive over all these appliations. In [2] we presented SERAN, a routing and MAC protool for lustered WSNs that provides robustness to environment variability, is energy and storage effiient, an be implemented on a large set of existing hardware platforms, has selfonfiguration apabilities, supports the addition of new nodes, and an be extended with data aggregation algorithms. In that work, a proedure for the start up and the maintenane of the network that allows the system to reat to major hanges in topology onditions and lok drifts was also introdued. In this paper, we further extend the solution and improve the mathematial model to haraterize the delay and power performane of SERAN given an initial topology estimate and traffi requirements without the need of extensive simulation. Consequently, we are now able to propose a omplete system solution that, given the appliation speifiations and a loose desription of the topology, it synthesizes the protool parameters so that end to end lateny requirements of the appliation are satisfied, energy onsumption is minimized, and a proedure for the system to reah the optimal working point is offered. Our solution is different from previous approahes, where single hop performane were optimized and best effort solutions proposed. We do not introdue lustering algorithms beause we assume, as it is the ase of many pratial appliations, that the lusters are already formed and identified by the end user. This is not the first attempt to provide a system level solution for WSN. Both in aademia [3], [4], [5] and industry [6], [7], [8], [9] several system solutions based on different ommuniation protools were proposed, and some more are expeted to be built around standardized low-power protools suh as Zigbee [0] or Bluetooth []. However, none of these solutions is based on a ommuniation protool that learly leverages distintive topology features. Despite existing relevant ontributions in the literature, none of them presents a omprehensive protool, whih inludes all the relevant harateristis of the physial layer, MAC and routing, and whih is able to guarantee lateny performane and optimize for energy onsumption. Our system level design methodology is an appliation of the Platform Based Design (PBD) [2], a methodology that advoates the ombination

2 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO., JANUARY of a top-down approah, where appliation requirements are refined into system onstraints, a bottom up approah, where performane of the implementation options is haraterized, and a meet in the middle phase where a solution is seleted to satisfy onstraints and optimize for a given ost funtion. Although initially developed for lassial embedded systems, PBD was later extended to treat more general ommuniation problems [3]. The paper is organized as follows: in Setion II the routing and MAC solution are presented. To motivate our protool design, we disuss different alternatives at every step of the design flow and indiate how our solution is positioned with respet to previous work. In Setion III we present the mathematial model and show how to optimize the protool parameters for power effiieny, while in Setion IV we present our initialization algorithm for network self-onfiguration and our approah to maintain network operations under adverse onditions. In Setion V, we present testbed results on a ase study, and in Setion VI, we give some onluding remarks. II. THE SERAN PROTOCOL We present our protool stak onsidering the topology of Fig., where five lusters of sensors, with no luster head, are deployed to sense data and report to a ontroller with a lateny onstraint D max Shortest path 4 Shortest path Controller Fig.. Connetivity Graph. Nodes are grouped in lusters, and eah node selets at random the note to whih transmit within nodes in next luster. A. Routing Algorithm Routing over an unpreditable environment is notoriously hard. Our approah leverage density and lusterization, and assumes that if there is a set of nodes within transmission range that ould be andidate reeivers, at least one of them will be likely to offer a good link anytime a transmission is needed. This assumption is reasonable beause the spatial diversity found in wireless transmission an be exploited to give diversity gains [3]. In [26], the idea of deiding next hop after an estimation of the links to neighboring nodes is presented. Although the estimation algorithm has very good onvergene properties, the protool shows stress when applied to fast varying links. In [20], the idea of routing through a random sequene of hops instead of a predetermined one is introdued. In [9], the idea is further explored to redue the overhead aused by the need of oordinating the nodes, and an algorithm is given for determining the optimal shape of the region from whih andidate reeivers should be seleted. In SERAN, the sender has knowledge of the luster to whih a paket will be forwarded, but the atual hoie of forwarding node is made at random. This random hoie is not performed at the network layer, but it is a result of an aknowledgment ontention sheme performed at the MAC layer by all the andidate reeivers (see next subsetion). Consider the luster onnetivity in Fig.. An arrow between two lusters means that all the nodes of the two lusters are within transmission range (not neessarily in line of sight). Assume a partiular node in Cluster has a paket to forward to the ontroller. Our luster-based routing selets at random a node in Cluster 2, so that the node in Cluster forwards the pakets to it. The hosen node determines its next hop by hoosing a node randomly in Cluster 4, and so on. In other words, pakets are forwarded to a randomly hosen node within next-hop luster in the minimum spanning tree to the ontroller. Notie that these operations are done without the need of a luster head node within lusters. B. Hybrid MAC There are several MAC shemes proposed for lustered environments, most of them oupling the MAC with some lusterization algorithm, and eleting a single node to be the luster leader and aumulate all the pakets of the other nodes in the luster [6], [7]. We deided to design a MAC where no single node is eleted to aumulate all the pakets, and whih is able to support the addition of new nodes for preserving the high level of density required to ensure robustness. This flexibility is usually obtained by using CSMA-based aess shemes that may or may not support ollision avoidane, depending on the radio interfaes that are used and the apability of the RF hip to support an effetive lear hannel assessment (see e.g. BMAC [28]). High density unfortunately introdues a large number of ollisions, even if ollision avoidane is supported. To redue ollisions, usually a deterministi MAC is used. A well-known deterministi approah is SMAC [5], where the network is organized in a lustered sheme. Our MAC solution is based on a two-level semi-random ommuniation sheme that provides more robustness to topology hanges typial of a CSMA-based MAC and more robustness to ollision typial of a deterministi MAC. The higher level regulates hannel aess among lusters. A weighted sheme is used suh that at any point in time, only one luster is transmitting and only one luster is reeiving. During a yle, eah luster is allowed to transmit for a number of -slots that is proportional to the amount of traffi it has to forward. The introdution of this high-level struture has the goal of limiting interferene between nodes transmitting from different lusters. The time granularity of this level is the -slot S (see Fig. 2). The lower level regulates the ommuniation between nodes of the transmitting luster and nodes of the reeiving luster within a single -slot. It has to support the semi-random routing protool presented in II-A, and it has to offer flexibility for the introdution of new nodes. This flexibility is obtained

3 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO., JANUARY yle slot slot N slot 2 CSMA slot Fig. 2. -Cyle representation. A slot is omposed of a number of CSMA slots. Eah slot is assoiated to a luster of nodes. by having the transmitting nodes aess the hannel in a p- persistent CSMA fashion [23]. If Collision Avoidane (CA) is supported by the hardware platform, it an be used to improve performane. The random seletion of the reeiving node is obtained by broadasting the paket over all nodes of the reeiving luster, and by implementing in the reeiving nodes a random aknowledgment ontention sheme to prevent dupliation of pakets. Assuming that nodes in Cluster transmit to nodes in Cluster 2, the protool an be summarized as desribed in the following three steps: ) Eah node of Cluster having a paket tries to multi-ast the paket to nodes of Cluster 2 at the first CSMA-slot with probability p. If CA is supported, a Clear Channel Assessment (CCA) for a random bak off time is performed before the transmission, and in ase another transmission is deteted, the node aborts the urrent trial to avoid ollisions. If CA is not supported, the node simply transmits the paket. 2) At Cluster 2, if a node reeives simultaneously more than one paket, it detets a ollision and disards all of them. If it has suessfully reeived a single paket, it starts a bakoff time T ak before transmitting an aknowledgment. The bak-off time T ak is a random variable uniformly distributed between 0 and a maximum value alled T akmax. If in the interval between 0 and T ak, the node hears an aknowledgment oming from another node of Cluster 2, the node disards the paket and does not send the aknowledgment. Note that this random bak-off proedure is different from a CA proedure. This is beause nodes are already awake and listening to the hannel for possible pakets and onsequently suh a sheme an be implemented even on platforms where performing instantaneous CCA is not supported or it is ineffiient. In Setion III-F, we explain how to deal with ineffiienies in this aknowledgment ontention sheme. 3) At the transmitting node of Cluster, if no aknowledgment is reeived (or if only olliding aknowledgments are deteted), the node assumes the paket transmission was not suessful and it multi-asts the paket at next CSMAslot again with probability p. The proedure is repeated until transmission sueeds, or the slots ends. With the approah outlined with previous steps, nodes need to be aware only of next-hop luster onnetivity and do not need a neighbor list of next hop nodes. We believe this is a great benefit beause, while neighbor lists of nodes are usually time-varying (nodes may run out of power and other nodes may be added) and, hene, their management requires signifiant overhead, luster-based onnetivity is muh more stable. In Setion IV, we explain how to deal with permanent fades between lusters within transmission range. In most of the proposed MAC algorithms for WSN, nodes are turned off whenever their presene is not essential for the network to be operational. GAF [4], SPAN [2] and S- MAC [5] fous on ontrolling the effetive network topology by seleting a onneted set of nodes to be ative and turning off the rest of the nodes. These approahes require nodes to maintain partial knowledge of the state of their individual neighbors, thus requiring additional ommuniation. Our dutyyling algorithm leverages the MAC properties and does not require extra ommuniation among nodes. During an entire yle, a node has to be awake only when it is in its listening -slot or when it has a paket to send and it is in its transmitting -slot. For the remainder of the yle, the node radio an be turned off. C. Organization of the -yle Beause of the proposed onverge-ast routing solution, lusters lose to the ontroller have a larger traffi load sine they need to forward pakets generated within the luster as well as pakets oming from upstream lusters. Assuming in the example of Fig. that the average traffi generated at eah luster is the same, the average traffi intensity that luster 4 experienes is three times the traffi intensity experiened by luster. Consequently, we an assign one transmitting -slot per -yle to luster, two transmitting -slots to luster 2 and three transmitting -slots to luster 4. In a similar fashion, on the other path, the number of assoiated -slots per luster an be assigned. Therefore, assuming we have P paths and alling B i the number of lusters in the i th path, we have a total of T f = P i= B i (B i + ) 2 -slots per -yle. For the remaining of the paper, we all T f the topology fator. As we will see later, T f is an important parameter that abstrats the network layout and onnetivity. Notie that in ase the traffi generated is not the same for eah luster, the relative number of -slots per yle for eah luster an be easily realulated hanging the weights in the sheme. For the sake of simpliity, we outline our solution for a ase with uniform traffi rate. The extension to a more generi traffi pattern is straightforward. One we deide the number of -slots per yle for eah luster, we need to deide the sheduling poliy for transmitting and reeiving. We selet an interleaved shedule (Fig. 3). For eah path, the first luster to transmit is the losest to the ontroller (luster 4). Then luster 2 and luster 4 again. Then luster, 2, and 4, and similarly on the other path. This sheduling is based on the idea that evauating the lusters loser to the ontroller first, we minimize the storage requirement throughout the network. ()

4 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO., JANUARY CTRL -p -(k-)p(-p) K-2 -kp(-p) K K- k p (k-)p(-p) K-2 kp(-p) K- Fig. 4. Disrete Time Markov Chain model of the number of pakets that have to be forwarded from one luster to another. Slot Slot 2 Slot 3 Slot 4 Fig. 3. Sheduling: lusters lose to the ontroller are evauated first. Eah slot, only one luster is transmitting, and only another luster is reeiving. III. PROTOCOL PARAMETER DETERMINATION In this setion, we explain how the aess probability p and slot duration S are determined to satisfy appliation requirements (maximum delay D max ), and optimize for power onsumption. First we show how to set the aess probability parameters, then we set the duration of a -slot to offer good lateny performane and optimize for power onsumption. First, we arry on this analysis for the ase in whih ollision avoidane is not supported, and then we show how the model is modified to aount for ollision avoidane. A. Aess Probability Here we would like to determine the aess probability that eah node should use in order to minimize the time to evauate a luster. In partiular, suh a time is then related to the duration of the -slot. Call k the number of pakets that the luster has to evauate at the beginning of a transmitting -slot. We onsider the worst ase senario for ollisions, that is when k pakets are distributed over k different nodes. We abstrat the hannel behavior by a Bernoulli random variable with parameter. Notie that this parameter is lose to sine it abstrats the spatial diversity gain that due to the luster-based onnetivity: is the probability that at least one node in forwarding luster is able to omplete a suessful ommuniation. Indeed, we assume that appropriate hannel and soure oding are applied by eah node, so that the suessful paket loss probability an be met. These are natural assumptions in many WSN appliations [29]. When there are k pakets to be forwarded, the probability of having a suessful transmission at the first CSMA-slot is P r[suess k] = kp( p) k. Note that this model is onservative and does not aount for the luky event of more than one paket transmitted and only a single one suesfully reeived. Assume the transmission was suessful. The luster now has k pakets to forward. This time the probability of a suessful transmission at the first CSMA-slot is P r[suess k ] = (k )p( p) k 2. Again, if the transmission was suessful the luster has k 2 pakets to forward, and so on. This allows us to represent the luster behavior as a Disrete Time Markov Chain (DTMC) where the state is the number of pakets that still need to be forwarded (see Fig. 4). The DTMC has an absorbing state in 0 whih is the steady state Slot 5 Slot 6 Slot 7 Slot 8 Slot 9 solution of the hain. This means that the state 0 is eventually reahed with probability one. We are interested in alulating the expeted time (i.e., expeted number of steps) to reah the absorbing state starting from a given state between and k. This is equivalent to determining the average number of CSMA-slots required for forwarding a number of pakets between and k. Sine expetation is a linear operator and using the fat that the hain an advane only one step at a time, the expeted time to absorption starting from a state k is equivalent to the sum of the expeted time to transition from state k to state k plus the expeted time to transition from state k to k 2 and so on until state 0 is reahed. Given that the hain is in state j, the mass distribution of the required number of steps to transition to state j follows a geometri distribution of parameter jp( p) j. Consequently, the expeted time to transition from state j to state j is τ(j) = jp( p) j. Calling τ k the expeted number of steps to reah the absorption starting from state k, we have τ k = k τ(j) = j= k j=. (2) pj( p) j Considering Eq. (2), we notie that the aess probability that minimizes the transition time from state j to j is p = p j = /j, meaning that a node in the state j hooses an aess probability given by /j. If eah node would use the probability p j when the system is in state j, the expeted number of transmission attempts for eah slot would be exatly one. This is the hoie that maximizes hannel utilization without inurring into exessive ollisions. However, this is not the hoie of the aess probability minimizing the overall Eq. (2). Therefore, we now present two strategies for setting up the aess probability given the number of pakets that need to be transmitted at the beginning of the -slot. In the following subsetions, we present the lateny and energy performane of the two strategies, and in III-E we present a omparison of them. ) Fixed Choie: Aording to this hoie, the aess probability is the same for eah node and it remains the same during the whole -slot duration. Finding a losed form expression of the aess probability p that minimizes τ k in Eq. (2) is a non-trivial problem. However, the expression is a onvex funtion in p. Indeed, (2) is a non negative weighted sum of the funtions /pj( p) j. These funtions are onvex, sine by taking the first derivative there is only a ritial point in the interval [0, ], whih is p j = /j, and the seond derivative is stritly positive. Although (2) is a onvex funtion, its first derivative does

5 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO., JANUARY not help to ompute a losed-form expression of the value of p that minimizes (2). The onvexity allows us to use the bisetion algorithm [27], whih finds iteratively the numerial value minimizing (2) with any desired preision. Note that the algorithm is not omputational demanding, and an be easily implemented on sensor nodes. If the initial guess used to feed the algorithm is good, the onvergene to the optimal value minimizing (2) is very fast. However, it an be proved that suh an optimal seletion of p would be larger than /k. Sine the most ritial stage in our DTMC model, in terms of ollision probability, is from state k to k, suh an aess probability would likely lead to a large number of ollisions at the beginning of the -slot. Consequently, we selet the aess probability p = /k for the whole duration of the slot, whih is suboptimal in terms of expeted forwarding time, but it ensures that at the beginning of the -slot the expeted number of transmission attempts for eah CSMA-slot is. The result is that the hannel is highly utilized, while as time progresses the hannel will be less and less utilized. The expeted absorption time is τ k = k k j= j ( ) j. (3) k In this senario, a simple relation between τ k and k is not easy to find. Nevertheless it is important to have knowledge of it in order to minimize the evauation time and relate it to the slot duration. We an find some useful upper and lower bounds: Proposition : For the fixed hoie, i.e. p = /k, for large k, the expeted time to forward all the pakets is bounded by: α flb k τ k α fub k ln k, where α flb and α fub are positive onstants. Proof: Looking at Eq. (3), we notie that a lower bound is given by the ase in whih all the expeted transition times are the same as the expeted transition time of the first transition (when the hannel is optimally utilized). This expeted transition time is / ( /k) k ( ) and sine lim k > k k = e, we an find a lower bound τ klb = e k. The upper bound an be found onsidering that τ k k ( k k ) k k j= j e k (k ) j. j= The k-th harmoni H k = k j= /j grows as fast as ln k, and it is upper bounded by H k < + ln k. Consequently, defining any γ >, for large k, we have: τ k e (k )( + ln k) e k( + ln k) e kγ ln k. Beause of the interleaved shedule, eah luster evauates all loally generated pakets before reeiving those generated from the one-hop upstream luster. First, we need to ensure that the expeted time for the evauation of pakets in a luster is less then or equal to the duration of a -slot. If this does not happen, pakets keep aumulating and storage apaity is reahed very soon with atastrophi onsequenes on performane. Number of CSMA slots Lower Bound Fixed Choie and Upper Bound Adaptive Choie Upper Bound Fixed Choie Lower Bound Adaptive Choie Number of Forwarding Pakets Fixed Choie Adaptive Choie Fig. 5. Expeted forwarding time for fixed and adaptive parameter hoie (from Propositions and 2). We onsider the upper bound for the forwarding time, so we an simplify our analysis. As we show in Fig. 5 this is already a good enough upper bound, that is τ k = e k ln k. Let us denote with the duration of a -yle and with λ the paket generation rate for eah luster. Sine during a -yle eah luster generates λ pakets, we need to ensure that the -slot duration is S > e λ ln(λ ). Realling the expression of T f in (), and that = ST f, we an simplify previous equation as et f λ S < S max tr = e, (4) λt f whih, given a traffi generation λ, sets a onstraint on the maximum duration of a -slot. Notie that S max tr is the maximum -slot duration due to traffi. As it will be learer in Setion III-E, it is interesting to rewrite previous equation as: λ ln(λst f ) <. (5) et f 2) Adaptive Choie: Aording to this hoie, the aess probability is inreased every time there is a state transition in suh way that for eah transition from state j to j it goes from /j to /(j ). Reall that this is the hoie that minimizes the forwarding time and, hene, maximizes the throughput of the luster. The expeted time to forward all pakets in this ase is: τ k = k ( ) j+. (6) j j= Proposition 2: For the adaptive hoie, for large k, the expeted time to forward all pakets is bounded by: α alb k τ k α aub k, where α alb and α aub are positive onstants. Proof: The upper bound an be found as for the similar ase in the proof of Proposition, so that for large values of k we have τ kub = e k. A lower bound an be found onsidering a suessful transition at every CSMA-slot. This means τ klb = k. Considering the upper bound from previous Proposition, we an now derive some design onstraints in the same way as

6 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO., JANUARY we did in the fixed hoie ase: S e λ. Sine = ST f, we an obtain a limit for the maximum sustainable traffi: λ. (7) et f Notie that, in this ase, we get a onstraint only on the traffi generation rate and it depends on the topology and onnetivity of the network, abstrated by the topology fator T f, and not on the -slot duration, as in Eq. 5. Note also that, given a number of lusters, the onfiguration that minimizes T f (and maximizes the maximum sustainable traffi) is a star topology, where eah luster is a single hop to the ontroller. Conversely, the worst onfiguration is a linear topology, where all the lusters are in a single multi-hop hain. In ase the maximum traffi ondition is not satisfied even using the adaptive hoie, a slot reuse mehanism an be introdued to obtain an operational network. This means to have more than one luster transmitting and reeiving during the same time-slot, provided that they are far enough apart. When the system is faing salability issues, and this an be abstrated by a large T f, slot reuse is an important mean to ope with it. This solution an signifiantly inrease the throughput of the network, but it is also muh more energy expensive. Consequently, it should be onsidered only if the stability requirement annot be satisfied, otherwise a lazy network is preferable. B. Lateny The lusters experiening the largest delay are the furthest from the ontroller. We want to have the delay of pakets oming from those lusters less than or equal to a given D max, the requirement set by the appliation. Consider the pakets generated in luster. These pakets have to wait, in the worst ase, a -yle before the first opportunity to be forwarded to luster 2. Assuming for now that all the pakets of a luster are forwarded within a single -slot, then it takes 3 additional -slots to reah the ontroller. Generalizing to the ase of P paths and B i lusters per path, the worst ase delay is D = + S max,...,p B i = S (B + T f ), where B = max,...,p B i. Consequently, the requirement on S is S S max d = D max B + T f, (8) where S max d is the maximum -slot duration due to lateny. If during a -slot not all the pakets are forwarded, a lateny over the deadline is observed. We an model this phenomenon using the DTMC model introdued in III-A. We want to evaluate the probability that the time to forward λ pakets exeeds the duration of a -slot. Using the Central Limit Theorem, we model the distribution of the time to forward λ pakets as a Gaussian variable whose mean and variane is given by the sum of the expeted times and varianes to advane a step in the hain. Call T ev, the time to evauate λ pakets and all m ev and var ev its mean and variane. Consequently, the time T ev to evauate a luster an be modeled as T ev N (m ev, var ev ), where in ase there is no ollision avoidane we have m ev = m evna = var ev = var evna = λ j= λ j= pj( p) j pj( p) j [ pj( p) j ] 2. Therefore, the probability of not forwarding all the pakets during a given -slot, whih we define as the outage probability of pakets, an be approximated by: P r[t ev S] ( ) S 2 erf mev, (9) varev where erf( ) is the omplementary error funtion. Although it is not possible to find a losed form solution to (9), the requirement expressed in (8) usually ensures an outage probability well below 5%, as we will show in Setion V. C. Energy Consumption We are now interested in determining the total energy onsumed by the network over a period of time. The energy ost is given by the ontribution of the energy spent for transmissions E T x, the energy spent to wake up and listen during the listening luster-slots R, and the energy spent for the lear hannel assessment proedure E Ak in ase ollision avoidane is supported. We onsider the energy spent for reeiving a paket together with the energy onsumption for listening. The energy onsumption for listening for a time δ is given by the sum of a fixed ost (the wake-up ost R) plus a time-dependent ost (listening ost power W ): E ls = R+W δ. During a -yle, nodes in Cluster never wake up for listening, nodes in Cluster 2 wake up one for listening, nodes in Cluster 4 wake up twie for listening, and so on (see Fig. 3). Assume that there are N nodes per luster, and that all nodes wake up in their listening -slot. During a given -yle, the total number of wake ups is: N wu = N P i= B i (B i ) 2. (0) To determine the energy spent for transmissions, we need to derive the average number of attempted paket transmissions during a -yle. In ase ollision avoidane is not supported, we an use the DTMC introdued in III-A. Proposition 3: For large values of the number of pakets aumulated in a luster during a -yle (λ ), the expeted number of attempted transmission is a linear funtion with the respet to the number of pakets to transmit. Proof: We model the number of attempted transmissions for eah transition as the average number of nodes attempting to transmit during a slot multiplied by the average number of slots required for that transition. Assuming k pakets to forward, the average number of attempted transmission during

7 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO., JANUARY a -yle an be modeled as N txna = (num slots /yle) k j= pj, () pj( p) j where (num slots /yle) is the number of slots in a yle (see Setion II-B). We then have the following ases: ) Case Fixed Choie. Sine p = /k, Eq. () an be simplified as N txna = T f (k ) [ ( ) k ]. k For large values of k, [ ( /k) k ] (e ) and k k. Sine there is an average of λ pakets to be forwarded at every slot, we an write N txna = T f (e )λ (2) 2) Case Adaptive Choie. In this ase reall that p j = /j, so that the produt pj at the numerator of Eq. () is always equal to, and the expeted number of attempted transmission is equal to the expeted number of steps required to forward all the pakets. In Setion III-A2, we showed that this number is a linear funtion on the number of initial pakets whose slope is between and e/. Consequently, we an write N txna = A na λ. The number of aknowledgment transmissions is equal to the number of suessful pakets N Ak = T f λ. Realling that E T x is the energy onsumption for the transmission of a paket and E Ak is the energy onsumption for the transmission of an aknowledgment, the total energy onsumption during a time T for the non ollision avoidane ase is E tot (S) = T [N txnae T x + N Ak E Ak + N wu R + N wu W S] = T A na λe tx + T λt f E Ak + T N wu ST f R + T N wu T f W (3) Notie that E T x, E Ak, R, W are parameters that haraterize the physial layer, λ, N are given by the appliation, and T f, N wu depend only on the network topology, so that the only variable in Eq. (3) is S. Sine, from equations (5) and (8), we have S S max = min {S max tr, S max d } and E tot (S) is a monotonially dereasing funtion of S, the optimal working point is S = S max. D. Impat of Collision Avoidane ) Maximum Sustainable Traffi with CA: One again, the behavior of the transmitting luster an be haraterized by a DTMC whose state is given by the number of pakets that remain to be forwarded. Differently from the non CA ase, when ollision avoidane is used, the transition probability from a state j to a state j is larger. This results from the fat that even if two or more nodes deide to transmit, the CA proedure is likely to avoid ollisions and allows at least one paket to be transmitted suessfully. Although very small, the probability of a ollision is still non-zero and it is assoiated to a failure of the CA mehanism. For instane, if TinyOS [8] is used to program the hardware platform, suh a failure may happen if between the posting and the exeution of a sending task of a node, another node starts its transmission. We all φ the probability of suh a failure when two nodes are involved. Consequently, the transition probability from state j to j in a given CSMA-slot an be modeled by the probability of having at least one node trying to aess the hannel multiplied by the probability that other nodes do not interfere with the first that transmits, namely P r[suess j] = [ ( p) j ]( φ) pj. Following the same steps as the non CA ase, we an model the average time to empty the luster using τ k = k j= [ ( p) j. (4) ]( φ) pj In ase the fixed hoie is seleted, the aess probability is /k. Using the same reasoning as in the non CA ase, we an find an upper and lower bound for τ k. The lower bound beomes: ek τ klb = ( φ)(e ), whereas the upper bound does not improve with respet to the non CA ase. Consequently, the onstraint on maximum sustainable traffi and duration of a -slot remains the same. In ase the adaptive hoie is seleted, the upper bound e beomes τ kub = ( φ)(e ) k, whereas the lower bound remains the same. As a onsequene the onstraint on the maximum sustainable traffi is slightly relaxed: λ max ( φ)(e ) et f. 2) Delay with CA: The onstraint on the maximum duration of the -slot does not hange. What hanges is the mean and standard deviation of the Gaussian distribution that abstrats the distribution of the time to empty a luster. Speifially, we have that m ev = m eva = var ev = var eva = λ j= λ j= [ ( p) j ]( φ) pj, [ ( p) j ]( φ) pj { [ ( p) j ] ( φ) pj } 2. 3) Energy Consumption with CA: The differene with respet to the non CA ase is only in the number of attempted transmissions, and in the number of lear hannel assessments. Ignoring the ollision events, the number of attempted transmissions an be easily modeled with the number of suessful transmissions N txa = T f λ. Modeling the number of hannel assessments, is similar to modeling the number of attempted transmissions when ollision avoidane is not used and a similar reasoning may be used involving the manipulation of the relative DTMC. However, a more simple model an be obtained, negleting the ollisions and onsidering the average number of transmission

8 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO., JANUARY tries for eah step. Consequently, we an write N a = T f λ j= pj. (5) Eq. (5) beomes N a = T f 2 (λ + ) T f 2 λ in ase of fixed hoie, and N a = T f λ in ase of adaptive hoie. In any ase, we an model the expeted number of lear hannel assessments as a linear funtion N a = A a λ. Calling t the fixed duration of a CSMA-slot, we have: E tot (S) = T [N txae T x + N Ak E Ak + N wu (R + W S) + N a (R + W t)] = T T f λ(e tx + E ak ) + T N wu R + T N wu W + ST f T f T A a λ(r + W t). (6) Also in this ase we see that the energy onsumption is a monotonially dereasing funtion of S, hene the optimal working point is S = S max. E. Comparison of Aess Strategies Comparing the traffi onstraints in equations (5) and (7), it an be seen that the onstraint relative to the fixed hoie is more stringent. One way to interpret these results is that in a network there is a limit on the sustainable traffi whih is given by the network topology and represented by the topology fator T f. Furthermore, if the fixed hoie is seleted, the onstraint beomes more stringent as the -slot inreases. Consequently, given a traffi to support, the seletion of the fixed hoie may limit the apability of extending the duration of the -slot (unless the onstraint imposed by the lateny requirement is the most stringent). As we showed in Setion III-C, this has a reverse impat on the power performane of the overall solution. The adaptive hoie is more effiient and it allows for a larger throughput. However, suh a strategy is more diffiult to implement in a distributed fashion beause nodes may not be aware of the fat that other nodes ompleted a suessful transmission, and there is no way to tell them without inurring into major overhead osts. The best way to implement this strategy is to have eah node automatially update its aess probability evaluating the expeted time to omplete a transition in the hain. To do this, the node must be able to ompute eah term of the summation in Eq. (2). Failure to ompute those frations, or lak of synhronization among the nodes may have a reverse impat on the effiieny of the solution and reate either too many aesses, hene having more ollisions, or too few aesses, hene wasting bandwidth. In the mathematial analysis we did not onsider these events. Sine we deided to set the aess probability in suh a way that the expeted number of attempted transmissions for a CSMA-slot is at most, ollision avoidane proedures do not improve performane dramatially. However, the greatest benefit is given by the extra robustness against ineffiienies in the implementation of the adaptive hoie. This is a result of the fat that ollision avoidane notoriously helps stabilizing CSMA protools when bandwidth utilization approahes the limit. For all these reasons, we reommend to use the adaptive hoie only when the fixed hoie is not good enough to serve the appliation requirements and the seleted hardware platforms support an effetive ollision avoidane. F. Optimizing the Protool In Setion II-A, we mentioned the problem of dupliate pakets that an happen in our multi-ast sheme. This phenomenon an be simply modeled by introduing a variable ν that represents the probability of having a dupliate paket in eah transmission. To onsider this effet we just need to substitute λ with λ = λ( + ν) in the previous equations. In [9], our aknowledgment ontention sheme is proved to redue ν to 0.. Further power savings an be obtained having only a subset of nodes per luster waking up for their listening duty. The savings ome from three fators: a) The impat of the energy onsumption due to listening dereases. b) If the pakets are forwarded to a smaller number of nodes, then the number of ollisions in the following transmitting -slot is redued. Assume only M out of N nodes wake up. Then, the number of attempted transmissions is no longer a onstant, but a monotonially dereasing funtion of M. ) Sine only few nodes are aumulating upstream pakets, it is possible to implement effiient data-aggregation algorithms. As already mentioned, nodes loser to the data olletor have a higher workload. As a onsequene, these nodes would be subjet to early energy depletion with atastrophi onsequenes for the network lifetime. This problem is typial of single sink networks and not speifially related to our solution. The best way to deal with this issue is implementing some sort of paket aggregation algorithm. Beause of its modularity, SERAN an be extended and integrated with existing paket aggregation algorithms. Note that they would affet the onstrution of the shedule, and not other parts of SERAN. Sine having a paket aggregation proedure dereases the inrement of traffi for lusters loser to the data olletor, the number of -slots dediated to those luster dereases as well, making the design of the final SERAN solution even simpler. Furthermore, a redued number of -slots per -yle will inrease the maximum sustainable traffi for that topology. Having more nodes awake ensures robustness against fades, and, if the number of nodes per luster is large enough, this extra optimization an be explored. Assume we need to wake up an average of M out of N nodes, an effiient and distributed implementation is obtained by having eah node waking up at the beginning of its listening -slot with probability M/N. In [4], [5], [9], and [2], alternative solutions are proposed to obtain this level of optimization. The flexibility of SERAN allows one more the integration of those tehniques. IV. OPERATION OF THE NETWORK In this setion, we introdue a proedure that allows the network to initialize and self onfigure to the optimal working

9 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO., JANUARY point alulated in Setion III, ensures robustness against lok drift of the nodes, and allows for the addition of new nodes. In SERAN, a token is a partiular message that arries information on the duration of a -slot and -yle (S and ), the transmitting and reeiving shedule of a yle, the transmitting probabilities, and a synhronization message arrying the urrent exeution state of the yle. Note that one information on luster loation is given to the ontroller, the ontroller has all information to alulate the optimal set of parameters as in Setion III. Consequently, the ontroller is able to generate a token before the network starts operating. Notie also that one a node reeives a token message, it has all the neessary information to work properly. When the network starts working, eah node is awake and listening. The node remains in this state and annot transmit until it reeives a token. The first transmission omes from the ontroller, whih multi-asts a token to all the nodes of one of the onneted luster. In our example, assume the seleted luster is luster 4. Nodes of luster 4 read information on sheduling and duration of -slot and -yle. Assume the sheduling is the one in Fig. 3. Nodes of luster 4 start transmitting their pakets to the ontroller with the modalities indiated in the token. At the end of the slot, all the nodes of luster 4 listen to the hannel and start a random bak-off ounter. When the ounter expires, if no other node sent a token, they broadast it. Nodes in luster 2 see the token and start behaving aording to the sheduling algorithm. After they transmit their pakets to luster 4, one of them broadast a token so that nodes in luster an hear it. After the first branh of the routing tree is explored, the ontroller sends a token to luster 5, the new branh is explored, and so on. The token passing proedure ontinues even in the following -yles. The routing solution desribed in Setion II-A, is designed to ope with fast time-varying hannels and not with permanent fades between lusters. This is a ase when, e.g., a metal objet is interposed for a long time between two lusters, hene utting off their ommuniation. This phenomenon is deteted by the ontroller that does not reeive pakets (or reeives too little) oming from a partiular luster (or set of lusters). When this event ours, the ontroller reomputes a minimum spanning tree, without onsidering the orrupted link and generates a new sheduling and protool parameters, then for a limited number of -yles (typially from 2 to 5) it sends a token with a message to void the urrent sheduling, and finally it re-initializes the network sending a token with the new optimal parameters. This re-initialization happens in general more often at the beginning of the network life-yle, but one the orrupted links are deteted, it is less and less frequent. In [2], we have shown that lok drift onditions that were an order of magnitude worse than the ones reported in literature for off-the-shelf platforms do not influene the protool stability. V. CASE STUDY Industrial monitoring appliations offer a great opportunity to exploit natural lusterization and node density [30]. We onsider a ase study of a typial robot monitoring and maintenane appliation. Sensors are plaed around robots in a manufaturing line to sense vibrations, and data must be delivered to a ontroller with a lateny onstraint. The ontroller is usually plaed lose to the manufaturing line. We rereated the topology of Fig. in a testbed environment, where 5 MICA2dot motes [22] are plaed in eah luster and disonneted lusters are separated by metal walls. The main goal of our validation is to test the validity of our mathematial analysis. In partiular, prove that the analysis of Setion III drives to a solution that satisfies lateny onstraints and minimizes power onsumption. We onsidered a lateny onstraint on the end-to-end delay of D max = 90s. This value was seleted to allow for an implementation over the available platform and generate interesting synthesis senarios. We implemented the power saving tehniques desribed in Setion III-F. Speifially, nodes wake up for listening with probability 2/5, and if a node has in its buffer pakets generated by the same luster, it alulates the average of the data and forwards a single paket. We abstrated the physial layer using a CSMA-slot duration t = 0.s whih we assume to be enough for two nodes to exhange a paket and an aknowledgment. We onsider two senarios. In the first one we seleted a paket generation rate per luster λ = pkt/5s, and for the seond we have λ 2 = pkt/0s. In both ases we used the fixed hoie for the hannel aess probability alulating the aess probability p as explained in Setion III-A, and we do not onsider ollision avoidane (notie that this means to turn off the ollision avoidane mehanism present in the ommon distribution of TinyOS). In Table I, we summarize the synthesized parameters. During initialization, all nodes were operational after the first -yle. The introdution of a permanent fade between luster 2 and luster 5 fored the minimum spanning tree to the shortest path tree of Fig.. The re-initialization of the network was suessful after two -yles in both senarios. For the first senario, sine the most stringent onstraint was due to the traffi sustainability (S max tr in Eq.( 4)), the solution was fast and the delay onstraint always satisfied. In the seond senario, the most stringent onstraint was due to the delay requirement and more interesting results were obtained. Senarios 2 D max 90s 90s λ pkt/5s pkt/0s S max tr 3.9s 54s S max d 6s 6s p TABLE I SYNTHESIZED PARAMETERS FOR BOTH SCENARIOS As it is shown in Fig. 6, the optimal solution offered an outage probability around 2%. At this working point, we observed an average node duty-yle around.4% that would projet a network lifetime of several months. As it an be seen in Fig. 7, better power performane an be obtained

10 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO., JANUARY Outage probability Duration of the slot (in number of CSMA slot) Fig. 6. Outage probability vs. -slot duration for Senario 2. Average Duty Cyle Duration of the slot (in number of CSMA slots) Fig. 7. Average Duty-Cyle vs. -slot duration for Senario 2. having longer -slot, but this would have the side effet of entering a region of exponential growth of the outage probability. For this reason, we onsider the optimal alulated solution as the one that offers the best trade-off. The reason for the perfet math of the results is that a CSMA-slot duration of 00ms is enough for a omplete paket-aknowledgment exhange and no unexpeted problems appeared. When trying to repliate the same example using a muh smaller CSMAslot duration (less than 50ms), we notied a high level of unaknowledged pakets that results in a network instability. We believe that a CSMA-slot duration of 50ms is the limit of the proposed solution when implemented over suh a node platform. VI. CONCLUSIONS AND FUTURE WORK We presented a system level approah for the design of wireless sensor networks in lustered environments. We believe lustered topologies abstrats very important appliation lasses and the apability of leveraging their harateristis as well as providing a methodology to effetively design these systems is what distinguish our approah from the previous system level solutions. Our solution is based on a semi-random ommuniation protool alled SERAN, a mathematial model that desribes the performane and trade offs of the protool, and an algorithm to initialize and maintain the network. We validated our mathematial model with some testbed experiments. Future work inludes performing a large set of experiments with a wide experimental evaluation of the SERAN protool, in several senarios of traffi load, node lustering, luster size, hannel onditions, and performane requirements. Furthermore, we will inlude in the framework aggregation algorithms to inrease the effetive throughput at no power ost, whenever aggregate information is required. Symbol Meaning D max Lateny onstraint p CSMA-slot paket aess probability T ak Bak off time before transmitting an aknowledgment T akmax Maximum bak off time before transmitting an aknowledgment P Number of paths of luster B i Number of lusters in the i th path T f Topology fator, or -slots per -yle k Number of pakets to evauate per luster (at the beginning of a transmitting -slot) Suessful paket reeption probability, or hannel behavior τ(j) Expeted time to transition from state j to j τ k Time to evauate k pakets from a luster τ klb Lower bound of the time to evauate k pakets from a luster τ kub Upper bound of the time to evauate k pakets from a luster p j Aess probability that minimize the transition time from state j to j Duration of a -yle λ Paket generation rate for eah luster S -slot duration S max tr Maximum -slot duration due to traffi S max d Maximum -slot duration due to delay lateny T ev Time to evauate λ pakets from a luster m ev Mean value of T ev var ev Variane of T ev E T x Energy spent for transmissions R Energy spent to wake up and listen during the listening luster-slots E Ak Energy spent for the lear hannel assessment proedure E ls Energy onsumption for listening W Time dependent ost for listening N wu Number of wake up during a yle N txna Average number of attempted transmission during a -yle N Ak Number of aknowledgment transmissions φ Probability of failure of the Collision Avoidane mahanism N txa Number of attempted transmissions, with Collision Avoidane N a Number of hannel assessments t CSMA-slot duration TABLE II MAIN SYMBOLS USED IN THE PAPER. REFERENCES [] B. Sinopoli, C. Sharp, L. Shneato, S. Shaffert, S. Sastry, Distributed Control Appliations within Sensor Networks, IEEE Proeedings, Speial Issue on Distributed Sensor Networks, [2] A. Bonivento, C. Fishione, A. Sangiovanni-Vinentelli, F. Graziosi, and F. Santui SERAN: A Semi Random Protool Solution for Clustered Wireless Sensor Networks, Mobile and Ad-Ho Sensor Systems (MASS) 2005, Nov [3] S. Madden, The Design and Evaluation of a Query proessing Arhiteture for Sensor Networks, Ph.D. Dissertation, UC Berkeley, 2003.