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Perforance Modeling and Siulation Studies of MAC Protocols in Sensor Network Perforance Heran Sahota Ratnesh Kuar Ahed Kaal Dept. of Electrical and Coputer Engineering, Iowa State University, Aes, IA 50011

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Perforance Modeling and Siulation Studies of MAC Protocols in Sensor Network Perforance Heran Sahota Ratnesh Kuar Ahed Kaal Dept. of Electrical and Coputer Engineering, Iowa State University, Aes, IA Abstract he use of wireless sensor networks is essential for ipleentation of inforation and control technologies in precision agriculture. We present our design of network stack for such an application where sensor nodes periodically collect data fro fixed locations in a field. Our design of the physical (PHY) layer consists of ultiple power odes in both the receive and transit operations for the purpose of achieving energy savings. In addition, MAC layer is designed which uses these ultiple power odes to save energy during the wake-up synchronization phase. We also present analytical odels and siulation studies to copare the energy consuption of our MAC protocol with that of the popular S-MAC protocol and show that our protocol has better energy efficiency as well as latency in a periodic data collection application. I. INRODUCION Precision agriculture refers to the use of inforation and control technologies in agriculture. In [1], we presented the design of our sensor network for autoated collection of soil data fro a far-field. he application requires the collection of soil data over the entire duration of crop season(s) at a sapling frequency of about once an hour and a spatial resolution of about square-eters (see Fig. 1). Sensor nodes are placed in a rectangular grid at the required spatial resolution and are integrated into a network that collects data periodically. he data is relayed to a sink node located at one of the corners of the rectangular field at regular tie intervals, consistent with the easureent period. the MAC protocol (ours and the standard S-MAC []) under a given routing strategy. We validate our analytical odels by developing siulations in nesc and Python using event driven fraework provided by OSSIM. Counication between sensor nodes in a field and the satellite nodes at the corners of the field is asyetric, in the sense that a transission fro a satellite node can reach all sensor nodes in the field, but a transission fro a sensor node reaches adjacent sensor nodes only, and can reach a satellite node if it is close enough (see Fig. 1). he satellite nodes take turns acting as sink nodes and collect inforation fro the sensor nodes in a field to relay the collected inforation to the basestation where the inforation is processed. Additionally, satellite nodes also dispatch routing and scheduling inforation to the nodes in the field and participate in the sensor localization process. Given a sink node for a round, a routing tree rooted at that node is constructed for achieving load-balancing (a node will forward its data to that neighbor which has witnessed least depletion of energy so far). See Fig.. he scheduling is done coplying with the order iposed by the routing. Fig.. Routing tree R used for perforance evaluation. Fig. 1. Wireless sensor network, showing sensor and satellite station deployents. he following are the contributions of this paper: We present an analytical approach to odel the perforance (throughput, latency and energy consuption) of his work was supported in part by the National Science Foundation under the grants CNS-0668, NSF-ECS , NSF-ECCS , NSF- CCF , and NSF-ECCS II. ENERGY EFFICIEN WAKE-UP AND DAA COLLECION Data collection in our sensor network occurs periodically in rounds, where a round is the tie during which the nodes attept to relay the sensed data readings towards a sink node (one of satellite nodes). All nodes receive coon routing and scheduling data at the beginning of each round fro the sink node of that round and use this event to synchronize their clocks. However the clocks drift during the course of the round owing to the fact that sensor nodes are ipleented using inexpensive crystals that can drift of the order of 40 parts per illion. When two nodes are ready to synchronize, their clocks could drift by an aount ± relative to a true clock. herefore in the worst case, the receiver of a wake-up signal needs to wake up for a tie that is on the order of 4 [1] in order to ake sure it can capture the wake-up synchronization signal fro its transitter. herefore, the energy consued by the receiver can be significant if is large, which is the case for long data-collection rounds. In our application, nodes are synchronized at the beginning of each data-collection round, and during this period the node clocks drift, requiring synchronization between sender and receiver nodes. Our strategy is aied at reducing the energy consuption during the wake-up synchronization phase of the transission. In the current designs of MAC protocols ([3], [], [4]), the wake-up synchronization between a transitter and a receiver is established using the noral transissionpower and receiver-sensitivity levels. We consider a odified wake-up synchronization schee in which a node saves its battery energy consuption by reducing its own receiver sensitivity level. In contrast, we increase the transissionpower level of the wake-up synchronization signal to allow for a successful detection by a lower sensitivity level receiver. It turns out that this new schee saves the overall energy consuption during the synchronization phase since the protocol uses a relatively short pulse for wake-up signal [1]. Additionally, we take advantage of the convergecast nature of sensor network traffic to iniize the nuber of high energy pings transitted. his is achieved by aking the downstrea node wake up all its upstrea neighbors with a coon ping signal. Existing sensor network MAC protocols such as S- MAC [], -MAC [4] and WiseMAC [3] establish individual link counications independently, regardless of whether two or ore links share a coon node. Besides the savings at the MAC level, our routing level strategy ais at balancing the energy consuption aong the sensor nodes in the entire field. We refer to the ode of short-duration and high-power wake-up signal transission as the ping ode. Likewise, the ode of operation of the receiver circuit in the degraded sensitivity is tered as drowsy. hese two odes of the radio are used in the wake up strategy eployed by our MAC protocol to save on energy for wake-up synchronization. We call our MAC protocol PD-MAC (letters P and D stand for ping and drowsy, respectively). III. MAHEMAICAL ANALYSIS AND SIMULAION We establish the perforance iproveents in latency and energy achieved by PD-MAC by coparing its perforance with that of the ost coonly used S-MAC protocol, in the setting of our application, using analytical odels as well as siulations. For coparison purposes, both protocols operate under the sae routing and scheduling inforation ade available by the network layer. For the siulation studies we consider a 5 node network placed in a 5x5 rectangular grid, and the routing tree as depicted in Fig.. A corner node, node 0 acts as the sink at which all the data fro the network is collected. he scheduling strategy ensures that no two links in the network are active at the sae tie to avoid interference and also ensures that a node begins transitting data to its downstrea node only after it has already attepted to collect data fro all of its upstrea nodes. he differences between S-MAC and PD-MAC lie in the ipleentation of the routes and schedules and also the synchronization protocol. In S-MAC, the synchronization handshake as well as the data/ack exchange occurs in a pairwise anner between one sender node and one receiver node. If a node has ore than one upstrea neighbors, then the respective sender receiver links are scheduled in a sequence, and for each pair a axiu of N s synchronization attepts is allowed, and once the synchronization is established, a total of N d data attepts is allowed. (a) An execution scenario of ultiple senders to one receiver counication links with PD-MAC. (b) An execution scenario of ultiple senders to one receiver counication links with S-MAC. Fig. 3. In S-MAC, when a node wakes up to establish a counication link with its neighbor, it waits for a predefined duration before transitting a synchronization request packet so as to guarantee that the other node on the link is awake to receive the synchronization request. he duration of this period is accordingly chosen to be the worst case relative drift ( ) between the clocks of the two nodes. Accordingly, letting S denote the tie to send synchronization request and receive reply packet, the discovery duration ( DD ), which is defined as the period of tie a node ust use when it wakes up to discover any existing neighboring sleep-listen schedules, lasts DD = + S units of tie. he node that receives the synchronization request packet replies with a synchronization reply packet. Keeping the priary goal of coparing latency and energy savings, we ake a siplifying assuption that the reply packet is delivered error free. In addition, in regular S-MAC, the synchronization reply (a.k.a rebroadcast of the synchronization packet) by the node that receives a synchronization request happens after a rando back-off to prevent ultiple nodes fro transitting at the sae tie. However, in our application setting, only a senderreceiver pair can be active at a tie. Hence, a back-off is not required. he two nodes keep awake (i.e., aintain a 100% duty cycle) until they expend all synchronization and data transfer attepts or until data transission succeeds. his way S-MAC is not penalized with a longer round duration by being forced to sleep part of the tie due the choice of a less that 100% duty cycle. Also, a sender node is guaranteed to have data to send to its downstrea neighbor when it wakes up eliinating the need for a sleep-listen schedule. Fig. 3 shows a possible execution scenario of a schedule consisting of one receiver and two sender nodes by S-MAC, under the choice of paraeters N s = and N d = 1. On the other hand, in PD-MAC, a node synchronizes all of its upstrea nodes with a coon ping. A axiu nuber (N s ) of ping attepts are allowed in case of unsuccessful synchronization. Between successive pings, the upstrea neighbors are allowed a axiu of N d data transission attepts in a tie division anner. his process of synchronization and data collection constitutes the counication tie of a node in PD-MAC. A possible execution of PD-MAC under the sae scenario as S-MAC is also shown in Fig. 3. Next, we present our analytical odels as well as siulation results to copare the perforance (throughput, latency and energy consuption) of two MAC protocols. Note throughput is deterined by the average nuber of data packets collected per unit tie, and can be obtained by taking the ratio of the average data-count at the sink node per round and the average latency of the round. So it suffices to deterine data-count and latency per round. A. Modeling data-count at sink We odel the probability distribution of nuber of data readings collected at each node at the end of each round. PD (i) denotes the probability that node gathers i data readings (including locally generated reading) after it has attepted to collect data fro its upstrea neighbors, U. We evaluate PD (i) recursively as shown in Equation (1). he leaf nodes of the routing tree do not have any upstrea neighbors and so they collect exactly one data unit. herefore, the base case of the recursion is: For all leaf nodes, PD (i) = 1 for i = 1 and PD (i) = 0 for i 1. For the non-leaf nodes, PD (i) is given by the following forula: 8! X Y PD (i) = PD(i k k )Psuc(i k ). P S U : k S : k S i k=i Y = PD(i k k )P fail (i k ) A (1) k U \S ; he above expression coputes the probability that a subset of upstrea neighbors, S U, collectively transits i 1 data units to node, where the upstrea neighbor k S transits i k data units such that k S i k = i 1. Psuc(i k ) denotes the probability that synchronization is established in at ost N s attepts and a data packet containing i k data units is transitted successfully in at ost N d attepts, whereas P fail (i k ) = 1 Psuc(i k ). N s N d ( Psuc(i k ) = (1 q)q s 1 (1 p e ) D(i k) s=1 (1 (1 p e ) D(i k) ) r 1), () where q is probability of synchronization failure, p e is the bit error rate, D(i k ) denotes the bit length of a data packet containing i k data units. he expression for the data-count probability for PD-MAC and S-MAC reains the sae as given in Equations (1) and () except for the value of the q paraeter. For S-MAC, this is coputed in accordance with the bit error probability and the nuber of bits in the synchronization packet while for PD-MAC, this denotes the probability of failure of ping, which is a uch lower value owing to its shorter length and no data content. Average Data-count at node S MAC, Model PD MAC, Model S MAC, Si PD MAC, Si Fig. 4. N s (Synchronization opportunities allowed) Expected data count stored at sink. We used a bit error rate of 0.01, ping transission error probability of 0.1, 8-bits per data unit, 8-header bits per packet, 8-bits payload per S-MAC synchronization request/reply packet, ping pulse duration of 0.1s, and a baudrate of 100bps was used for our perforance evaluation studies. he expected data-count at the sink-node 0 is given by N i=1 ip D 0 (i), where N is the total nuber of nodes in the field. Fig. 4 shows the expected data count at node 0 versus the nuber of synchronization attepts allowed for the two protocols. Both protocols have coparable perforance as far as the data-count at the sink node is concerned. his behavior is expected because we allow the sae nuber of synchronization and data transission attepts for the two MAC protocols. B. Modeling latency or round duration We define the counication tie of a node as the tie taken by a node to synchronize with and collect data fro all its upstrea senders. Round duration is the su of the counication ties for all nodes in the routing tree. In the following two subsections we odel the counication tie for a node for the two MAC protocols. 1) Modeling counication tie for S-MAC: Let k denote the expected counication tie for a receiver node, corresponding to an upstrea neighbor k as odeled in Equation (3). Here Psync(i) denotes the probability that synchronization succeeds in ith attept (i N s ) and P sync-fail denote the probability that synchronization fails all N s attepts. If synchronization fails N s attepts, data phase does not take place. However, if synchronization succeeds in at ost N s attepts, the two nodes attept to exchange the data packet for up to a axiu of N d attepts. N s [ ] k = Psync(i). sync(i) + data k + i=1 P sync-fail.no-sync, (3) where sync(i) denotes the expected duration of the synchronization phase given that synchronization succeeds in i th attept, data k denotes the expected data phase duration consisting of a axiu of N d attepts (its value depends on k as different upstrea neighbors have different nuber of data units to send), and no-sync denotes the expected duration of the synchronization phase when synchronization fails all N s attepts. Equation (4) coputes sync(i), whereas the forulae for no-sync and data k are given in Equations (5) and (6) respectively. i + 1 sync(i) = DD + {(i + 1) od } E(Y ) (4) Equation (4) can be understood as follows: the two nodes that are attepting to synchronize with each other take turns in sending synchronization request packets to each other. herefore, if synchronization occurs in i th attept, the node that starts first takes a total of i+1 turns, each of which lasts for the discovery duration of DD. In addition, if the synchronization succeeds in an even-nubered attept, an additional delay corresponding to the difference in the wakeup ties of the two nodes, denoted Y in Equation (4), is also incurred denoting synchronization request transission by node that wakes up second. For exaple, Fig. 5 shows sync(5) and Y. Siilarly, Ns + 1 no-sync = DD + {(N s + 1) od } E(Y ) (5) Note, Y = X k X, where the rando variables for wake-up tie of k and, X k, X U(0, ). hen the expected value of Y is given by: E(Y ) = 3. We now copute data k, the expected tie to transit data by an upstrea neighbor k in a total of N d attepts. Let R k denote the sub-routing-tree rooted at node k. hen, since this subtree has size and since each node senses one data unit, node k can have at ost data units to transit to its downstrea node (since soe data packets ay Fig. 5. Synchronization phase in S-MAC. Y represents the absolute difference between the wake up ties of the sender and receiver nodes. be lost). he probability distribution of the nuber of data packets contained at every node is expressed by Equation (1). Let D (l) denote the tie-slot for l data units and A (s) denote the tie-slot for an acknowledgeent vector for s nuber of senders (for S-MAC s = 1, always). Note D (l) = D(l)/BP S and A (s) = A(s)/BP S, where BP S denotes the bit rate of the radio transceiver and A(s) denotes the bit length of an acknowledgeent packet containing a bit vector of length s. hen the size of tie-slot needed to accoodate the axiu-sized data fro node k (of size ) and one acknowledgeent to node k is given by k DA = D() + A (1). We can odel the expected data phase duration as follows: data k = PD(l) k ( Nd P r suc(l).r. k DA + P N d fail (l).n d. k DA where PD k (l) is defined in Equation (1), P suc r (l) is the probability of successful transission of a data packet containing l data units in the r th attept. Since the packet error rate for a data packet containing l data units is given by p l = 1 (1 p e ) D(l), the forulae for Psuc r (l) and P N d fail (l) are as follows: Psuc(l) r = (1 p l )p r 1 l ; P N d fail (l) = pn d l. (7) ) Modeling counication tie for PD-MAC: In PD- MAC, node attepts to synchronize with all of its upstrea neighbors U using a coon ping. Here, we obtain a recursive odel for the counication tie of a node. Let (i, r, S, D, Q ) denote the reaining counication tie, given that i 1 synchronization attepts have taken place and r 1 data attepts associated with the i th synchronization attept have taken place. S U denotes the subset of upstrea neighbors that are synchronized so far, D S denotes the subset of upstrea nodes that have successfully delivered their data so far, and Q U \ S denotes the subset of upstrea nodes that have synchronized in the ost recent (i th ) synchronization attept. Q gets updated only following a synchronization attept (and reains unaltered following a data transission attept). A recursive odel for (i, r, S, D, Q ) is given by Equation (8), where SY N denotes the duration of ping, and DA = ) (6), 0, if C := [(D = U ) (i = N s + 1)] (i, r, S, D, Q ) = SY N + R U \S C R DA + q U\S\R (1 q) R Psuc(C )P fail (R \ C ) (i + (r/n d ), (r od N d ) + 1, S R, D C, R ), if C, r = 1 C Q \D DA + Psuc(C )P fail (Q \ D \ C ) (i + (r/n d ), (r od N d ) + 1, S, D C, Q ), if C, r 1, (8) A ( U )+ k U D () represents the duration of entire tie-slot accoodating data packets by all senders and acknowledgeent packet by the downstrea node. hen, (1, 1,,, ) gives the total counication tie for node. Case 1 in Equation (8) denotes the base condition. he reaining counication tie (S, D, Q, i, r) is zero if node has already received data fro all its upstrea neighbors (captured by the condition: D = U ), or if it has already expended all N s synchronization attepts along with the N d data attepts associated with each synchronization attept (captured by the condition: i = N s + 1). Case odels the i th ping transission which takes a duration of SY N and the ensuing (first) data attept which takes a duration of DA. In a synchronization attept (r = 1) a subset R U \ S ay get synchronized (captured in the first suation) with a probability of q U\S\R (1 q) R and participate in at ost N d data attepts. During the first data attept a subset C R of nodes ay be successful in data transission (captured in the second suation) with a probability of Psuc(C )P fail (

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