Taking Advantage of Overhearing in Low Power Listening WSNs: A Performance Analysis of the LWT-MAC Protocol

Transcription

1 DOI.7/s Taking Advantage of Oveheaing in Low Powe Listening WSNs: A Pefomance Analysis of the LWT-MAC Potocol Cistina Cano Bois Bellalta Anna Sfaiopoulou Miquel Olive Jaume Baceló Spinge Science+Business Media, LLC 2 Abstact LWT-MAC is a new Low Powe Listening MAC potocol fo WSNs designed to apidly eact to instantaneous inceases of the netwok load. It takes advantage of oveheaing by waking up all nodes at the end of a tansmission to send o eceive packets without needing to tansmit the long peamble befoe. In this wok, detailed analytical models of the LWT-MAC and B-MAC potocols, fo both satuated and unsatuated conditions, ae pesented. Moeove, the key LWT-MAC paametes ae optimized in ode to minimize the enegy consumption, constained to obtain the same thoughput as the IEEE 82. (CSMA/CA) MAC potocol. Fom the behavio of the optimal LWT-MAC paametes, a heuistic configuation is poposed. Finally, the LWT-MAC is compaed to B- MAC, in both single and multi-hop scenaios, showing impovements in enegy consumption, thoughput and delay. Keywods WSNs low powe listening B-MAC LWT-MAC analytical model Intoduction Wieless Senso Netwoks (WSNs) consist of small devices that sense envionmental data and send it to C. Cano (B) B. Bellalta A. Sfaiopoulou M. Olive J. Baceló NeTS Reseach Goup, Depatment of Infomation and Communication Technologies, Univesitat Pompeu Faba, C/ Tange, 22-4, 88, Bacelona, Spain cistina.cano@upf.edu a cental collecto. Nomally, senso nodes have educed pocessing, memoy and battey esouces and ae deployed in emote and lage aeas. The battey eplacement in these netwoks is, theefoe, too costly o even impossible, making enegy consumption the most impotant constaint. Fo this eason, the Medium Access Contol (MAC) potocol is cucial as it diectly influences the tansceive opeation that is the most consuming component of a senso node. The common appoach to educe enegy consumption in WSNs is to peiodically put the tansceive into sleep mode, woking in a low duty cycle opeation instead of continuously listening the channel as in taditional wied and wieless netwoks without powe constaints, like in IEEE 82. Caie Sense Multiple Access with Collision Avoidance (CSMA/CA) []. A well-known MAC potocol fo WSNs is Bekeley MAC (B-MAC) [2]in which each nodepeiodicallyand independently of the othes samples the adio channel to detect activity, what is known as Low Powe Listening (LPL) opeation. Then, when a node wants to send a message, it fist sends a peamble long enough to ovelap with the listening time (active pat of the duty cycle) of the eceive. Using B-MAC the enegy consumption of the senso nodes is extemely educed at vey low loads. Howeve, as the load inceases, fo instance, due to events occuence, the collisions of peambles become a significant enegy waste, even moe impotant in lage scale WSNs with hidden teminal poblems. The Low powe listening with Wake up afte Tansmissions MAC (LWT-MAC) potocol (pesented by the authos in [3]) was designed to maintain a low enegy consumption at low loads while, at the same time, being able to eact to instantaneous inceases of the

2 netwok load. A local synchonization afte tansmissions, that ensues that all nodes that have ovehead the last tansmission will be awake to eceive a new message, is adopted, hence without equiing the long peamble tansmission. Analytical models of WSNs MAC potocols allow to deive pefomance optimizations of the diffeent paametes involved: duty cycle, Contention Window (CW) o packet size among othes, depending on diffeent netwok scenaios. Howeve, existing analytical models of WSNs MAC potocols (fo instance, the ones used in [2, 4]) ae extemely simple as they only conside the time to tansmit a packet without analyzing the time and enegy wasted in collisions. Although these simple analytical models ae valid fo low taffic loads they become inaccuate when the taffic load inceases. Moe detailed analytical models of scheduled MAC potocols such as the Senso-MAC (S-MAC) [5] and nanomac [6] have been pesented, howeve, the LPL opeation has not been studied so exhaustively. In this wok, the LWT-MAC potocol is studied fom an analytical point of view. The pesented LWT-MAC analytical model consides the enegy waste due to collisions and oveheaing in a single-hop netwok unde satuated and unsatuated conditions. The analytical model pesented is adapted to model the B-MAC potocol and it can also be extended to model othe LPL MAC potocols (like the X-MAC potocol [7]). Using the analytical model, the LWT-MAC key netwok paametes ae identified and optimized to minimize the enegy consumption but maintaining a good pefomance in tems of delay and thoughput. Fom the optimization pocess, a heuistic configuation is deived. The LWT-MAC with the heuistic configuation is compaed with B-MAC in a single-hop netwok and in a multi-hop scenaio with peiodic and event-based taffic pofiles. The est of the pape is oganized as follows: Section 2 povides a compaison of the poposed appoach with simila existing mechanisms, then, in Section3 the LWT-MAC is descibed. The LWT-MAC analytical model and the adaptation to model the B- MAC potocol, as well as thei validation ae pesented in Section 4. The optimization analysis of the LWT- MAC potocol is pefomed in Section 5 while the pefomance esults ae discussed in Section 6. Finally, some concluding emaks ae given in Section 7. 2 Related wok LPL MAC potocols as B-MAC [2] pefom well when the taffic load of the netwok is low, howeve as the taffic load inceases the continuous collisions of peambles consideably deceases the netwok pefomance. The LWT-MAC potocol aims at impoving the pefomance by waking up neighboing nodes at the end of a tansmission in ode to send o eceive packets [3]. Some simila mechanisms have aleady been defined in ode to addess the same poblem. Fo instance, the multi-hop steaming capability defined in the Scheduled Channel Polling MAC (SCP-MAC) potocol [8] that inceases the duty cycle upon a message eception in ode to educe the end-to-end delay. Anothe example is descibed in [9] whee the sende of a message activates a send moe bit in the heade of the packet indicating that thee is moe data pending to be tansmitted. The destination of the message stays awake at the end of the tansmission to eceive the packet, thus eliminating the need of the long peamble tansmission. In scheduled MAC potocols the same idea can be followed: in S-MAC [4] and Timeout-MAC (T-MAC) []each node that oveheas an Request To Send (RTS) o Clea to Send (CTS) stays awake just in case it should fowad the message. All those mechanisms diffe fom the appoach pesented in this wok in the sense that in LWT-MAC evey node that has ovehead a tansmission is allowed to tansmit at the end, not only the sende o the ecipient of the last tansmission. This appoach impoves the pefomance when the taffic load of the netwok inceases. The load of the netwok can incease, fo instance, due to an event detection, in this situation a set of neaby nodes ty to tansmit a packet to infom the sink about the event occuence. Othe appoaches like the X-MAC potocol [7] aim at estimating the taffic load of the netwok and then adapt the duty cycle accodingly. Those potocols povide bette pefomance but they suffe fom an inceased complexity. The LWT-MAC potocol, in contast, adapts to the taffic load in a simple manne, only by waking up all neighboing nodes afte a tansmission. 3 Taking advantage of oveheaing: the LWT-MAC potocol The LWT-MAC extends the opeation of B-MAC by taking advantage of the local synchonization of all nodesthatoveheaa tansmission [3]. The LWT-MAC defines that all oveheaing nodes wake up simultaneously at the end of each successful tansmission in ode to send o eceive packets. Since all nodes that have ovehead the last tansmission will be awake, the long

3 Sende Receive Oveheaing Contende Sende Cycle Sleep=U(,SleepTime) NAV Time LONG PREAMBLE DATA ACK CTS ACK t NAV Time t BO RTS t DATA t new packet aival Listen Sleep UNSCHEDULED PHASE SCHEDULED PHASE (a) LWT-MAC Potocol Cycle LONG PREAMBLE DATA ACK t educes the time equied to send a packet impoving the netwok pefomance. Howeve, it should be noted that the pefomance benefits of LWT-MAC mainly depend on the pobability that the next tansmission eceive has ovehead the last tansmission, that in tun depends on the topology and on how the outes to the sink ae selected. If a packet tansmission fails, a etansmission pocedue is initiated. The details of this pocedue ae diffeent in the scheduled and unscheduled modes of opeation. Receive Oveheaing Contende new packet aival (b) B-MAC Potocol LONG PREAMBLE DATA Listen ACK t t t Sleep Fig. Compaison of LWT-MAC and B-MAC medium access mechanisms peamble is no longe necessay (the medium access mechanism is depicted in Fig. a). In this scheduled phase it is mandatoy to compute a andom backoff (BO) befoe attempting tansmission, howeve in the unscheduled phase it is optional. This foces all nodes to listen afte each tansmission at least the value of the CW. Duing the andom BO of the scheduled phase nodes should keep listening to the channel in case any othe node stats a tansmission. The use of the RTS/CTS tansaction befoe the packet tansmission in the scheduled phase is ecommended. The fou-way handshake will help in alleviating hidden teminal poblems and it is useful to let oveheaing nodes sleep duing the entie packet tansmission. The duation of the tansmission should be included in RTS, CTS and Data messages and will allow the oveheaing nodes to set a Netwok Allocation Vecto (NAV) time (as defined in []) and sleep until the tansmission finishes. If no message is sent duing the listening afte tansmissions peiod, nodes go to sleep fo a andom time (with a maximum value equal to the sleep time of the duty cycle) moving towads the unscheduled phase. Obseve that, compaed to B-MAC (Fig. b), thee is a eduction of the enegy waste, both in tansmission and eception, due to the suppession of continuous long peamble tansmissions. Moeove, by suppessing long peambles the delay and the channel occupation duations ae educed as well. Additionally, at instantaneous inceases of the netwok load the potocol 3. Retansmission pocedue in the unscheduled access If a tansmission failue occus duing the unscheduled access, the acknowledgement (ACK) is not eceived, the sende etansmits the packet by sending an RTS afte waiting a andom BO. As the tansmission failue can be caused by collisions of peambles, the etansmission inceases the pobability to eceive the RTS coectly. Afte that, in case the CTS is not eceived (thee ae two consecutive tansmission failues), it is assumed that the intended ecipient is eithe involved in anothe tansmission o waiting fo a tansmission to finish. In ode to alleviate consecutive collisions, the sende does not immediately etansmit the message. Instead, it waits a Collision Avoidance (CA) time (set to the duation of a peamble and a fame tansmission). Duing the CA time the node keeps listening to the channel, that povides the oppotunity to get synchonized with the cuent ongoing tansmission (if any) afte oveheaing a message involved. If that is the case, it can sleep until the tansmission finishes and ety tansmission using the scheduled method. Othewise, if the CA time expies, the node eties tansmission using the long peamble again. The CA time has been added as an optional mechanism to educe hidden teminal poblems, howeve, it can be deactivated when needed, fo instance in single-hop netwoks in which all nodes ae inside the coveage ange of the othes. The RTS/CTS mechanism can also be activated in the unscheduled mode [2], i.e., an RTS is sent afte the tansmission of the long peamble. In this case, if a tansmission failue occus (CTS not eceived) the sende assumes that the ecipient is involved in anothe tansmission and waits the CA time as peviously descibed. Note that, afte a collision among hidden teminal nodes, the eceive will hopefully eceive at least one of the RTS sent. By activating the RTS/CTS in the unscheduled mode the use of the NAV time

4 will also allow to let oveheaing nodes to sleep as peviously explained. 3.2 Retansmission pocedue in the scheduled access If a tansmission fails duing the scheduled access it can be eithe because the CTS o the ACK ae not eceived. In case the RTS fails (CTS not eceived), it is assumed that the ecipient has not ovehead the past tansmission and, theefoe, it is sleeping (notice that the long peamble has not been peviously sent). In this case, the node will ety to send the message by sending the long peamble fist in ode to wake up the eceive. If the packet tansmission is not acknowledged the sende waits a CA time as aleady explained in the unscheduled access. The detailed specification of the potocol behavio is depicted in Fig Pefomance benefits Fo illustation puposes the enegy consumption and thoughput of LWT-MAC compaed with the esults obtained using IEEE 82. [] and B-MAC in a - node single hop netwok ae shown in Figs. 3 and 4 (the paametes used ae depicted in Table ). Obseve that the thoughput is significantly impoved if compaed to B-MAC at the cost of a slightly highe enegy consumption at low loads, whee idle listening afte tansmission peiods occu. Howeve, the enegy consumption is educed at high loads due to the suppession of the long peamble tansmission. 3.4 Addessing collective Quality of Sevice (QoS) The LWT-MAC wake up afte tansmissions capability makes it a good candidate to be used in event-based New packet to tx Init PktTx++ Set State = Peiodic Sleep Peiodic Sleep CATime Expies State == Peiodic Sleep? yes Set State = Non Peiodic Sleep Backoff Listen(Tlisten) Channel Busy Set State = Non Peiodic Sleep Listen Packet eceived Channel Idle Packet ovehead Sleep(Tsleep) Send Peamble Set Mode = Unscheduled Stop CATime (if set) Stop CATime (if set) no Is the RTS/CTS activated? yes Receive Peamble Receive RTS Receive CTS Receive Data Receive ACK Set NAV Time Send Data Send RTS Send CTS Stop CTSTime Send ACK Stop ACKTime PktTx Sleep(NAVTime) Set ACKTime Set CTSTime Send Data yes Is PktTx > no CTSTime Expies Set ACKTime Channel Busy Backoff Channel Busy Listen(Tlisten+CW slot) Channel Idle Channel Idle no Mode == Scheduled? yes ACKTime Expies Send RTS Set Mode = Unscheduled Set CATime Channel Busy Backoff no Mode == Scheduled? yes Set Mode = Scheduled Sleep(Random(Tsleep)) Channel Idle Send Peamble Set Mode = Unscheduled Backoff Channel Busy Set CATime Set CTSTime Channel Idle Send Data Send RTS Set ACKTime Set CTSTime Fig. 2 Flowchat of the LWT-MAC potocol. The Mode value is initialized to Unscheduled and PktTx is initialized to zeo

5 Thoughput (bps) IEEE 82. B MAC LWT MAC Fig. 3 Thoughput of IEEE 82., B-MAC and LWT-MAC in a -node single hop netwok WSNs whee instantaneous inceases of the taffic load occu due to event detection at neaby senso nodes. The QoS obseved by event-based messages is cucial in ode to assue the coect and fast event detection at sink. Howeve, this QoS diffes fom the taditional definition in which the QoS measuement is made packet by packet. In event-based WSNs the QoS should efe to the goup of messages elated to an event, it is known as collective QoS. Collective QoS is defined as the QoS (delay, bandwidth, packet loss, etc.) of the set of packets elated to a specific event []; i.e., the delay Enegy Consumption (J) IEEE 82. B MAC LWT MAC Fig. 4 Enegy consumption of IEEE 82., B-MAC and LWT- MAC in a -node single hop netwok Table Default paametes Paamete Value Paamete Value (data ate) 2 kbps T listen /T sleep 24.5/75.5 ms σ (empty slot) ms L data (packet size), bits DIFS ms L ts, L cts, L ack 64 bits SIFS 5 ms E tx mw CW 64 E x, E idle 3.5 mw K (queue size) pkts E sleep.5 mw R (ety limit) 7 T (time) 5 s of the individual messages is not cucial but the latency fom the event geneation until the event detection at sink is citical. A MAC potocol that efficiently eacts to event-based taffic will incease the collective QoS of the messages involved. The LWT-MAC potocol is designed in ode to impove the collective QoS of event messages while maintaining a low enegy consumption. As fa as the authos know, thee is not any othe MAC potocol designed keeping in mind collective QoS metics. Those which ae focused on QoS ae based on end-to-end taditional QoS metics instead [2 7]. The behavio of the potocol with peiodic and event-based taffic pofiles and its ability to incease the collective QoS was studied in [8]. 4 LWT-MAC analytical model In this section an analytical model of the LWT-MAC potocol in single-hop WSNs is descibed. The analytical model assumes ideal channel conditions (no channel eos o hidden teminal poblems) and that each node computes a andom BO (between and CW) befoe each tansmission attempt. Fo simplicity easons the senso nodes ae consideed to be homogeneous (equal taffic pofiles and capabilities). Table 2 povides the desciption of some elevant vaiables used. The extension of the analytical model to a multi-hop netwok is a challenging task since collisions can happen due to hidden teminal poblems [9]. Moeove, in WSNs, whee hidden teminals can wake up at any moment duing an ongoing tansmission, the multi-hop analysis becomes even moe difficult than in taditional wieless netwoks whee nodes ae always listening to the channel. Theefoe, the multi-hop analysis is left fo futue study. The effect of the CA time peviously descibed has not been studied, it is consideed that collisions move the system to the unscheduled mode.

6 Table 2 Notation Notation Desciption n Numbe of nodes L data Packet size (bits) λ Rate of packet geneation (packets/s) K Queue size (packets) L ts,cts,ack RTS,CTS,ACK packet size (bits) L p Peamblesize(bits) Tansmission ate (bits/s) T Time (s) S Thoughput (bits/s) M Aveage numbe of tansmission attempts pe packet B Aveage numbe of slots in BO p sch Scheduled pobability p w Pobability to wake up afte a tansmission ρ Queue utilization τ Tansmission pobability in a given slot CW Contention window of the andom BO σ Empty slot duation (s) ζ Refes to the metics: S, M, B, p sch, p e,ρ T sleep Sleep time of the duty cycle (s) Listen time of the duty cycle (s) T listen 4. Netwok pefomance metics The LWT-MAC analytical model is based on the one descibed in [2] whee an IEEE 82. (CSMA/CA) analytical model to compute taditional metics such as thoughput, delay and queue occupation is pesented. A senso node is modeled as a single queue of length K packets. Each node geneates packets following a Poisson distibution with ate λ packets/s and aveage packet length L data bits. Fom these assumptions the following metics can be computed: A = λx, ρ = A( P b ), P b = ( A)AK A K+ () whee A is the offeed load, ρ is the queue utilization, P b denotes the blocking pobability and X efes to the sevice time (the time since the packet aives at the head of the queue until it is eleased fom it, assuming that it follows an exponential distibution). The sevice time can be calculated as: X = (M ) (Bα + T c ) + Bα + T s (2) whee M is the aveage numbe of equied tansmission attempts pe packet, B is defined as the aveage numbe of slots selected befoe each tansmission attempt, α is the aveage slot duation and T c and T s ae the duations of a collision and a successful tansmission espectively. The aveage numbe of attempts pe packet successfully tansmitted o discaded (M) due to maximum ety limit (R) eached is computed as: M = pr+ (3) p whee p is the conditional collision pobability (assumed to be constant fo all tansmission attempts): p = ( τ) n (4) Being n the total numbe of nodes in the netwok and τ the steady state pobability that a node tansmits in a andom slot given that it has a packet eady to be tansmitted: τ = ρ (5) B + Assuming that the BO is unifomly distibuted in the ange [-CW], B can be obtained as shown in Eq. 6. B = CW (6) 2 The aveage slot duation (α), is calculated consideing the duation of the slot depending on the channel state (Eq. 7). As the channel is assumed to be eofee, itcanonlybeinempty, successf ul o collision states with thei coesponding pobabilities p e, p s, p c. α = p e σ + p s (T s + σ)+ p c (T c + σ) (7) whee σ is the empty slot duation. The channel state pobabilities ae elated to the stationay pobability that the est of the nodes (except the one that is in BO) ty to tansmit in a given andom slot. These ae given by: p e = ( τ) n p s = (n )τ( τ) n 2 p c = p e p s (8) Finally, the thoughput pe node can be computed as: S = ρ L data X ( p d) (9) whee p d is the pobability to discad a packet due to maximum ety limit eached: p d = p R+ () The channel occupation duations (Eqs. and 2) can be computed consideing the length of the messages involved and the time intevals between them. Note that in the unscheduled mode the peamble is sent befoe each packet tansmission attempt. The analytical

7 model pesented in this wok only consides the tansmission of packets peceded by RTS/CTS messages, although the model is easily adaptable to also conside the basic access method. Obseve also that it has been consideed the use of the DIFS, SIFS and EIFS time peiods as in the IEEE 82. (CSMA/CA) []. T c = DIFS + (L p p unsch ) + L ts + EIFS () T s = DIFS + (L p p unsch ) + L ts + L cts + L data + L ack + 3SIFS (2) whee L p, L ts, L cts and L ack ae the lengths of the peamble, RTS, CTS and ACK messages espectively, while efes to the tansmission ate. The pobability of tansmitting a packet in scheduled mode (p sch )is the pobability that afte a successful tansmission, any othe node has still data to be tansmitted. On the othe hand, the pobability to tansmit a packet in the unscheduled mode (p unsch ) is obtained as the complementay of the fome: p sch = p ss ( ( ρ) n ), p unsch = p sch (3) p es whee p ss and p es ae the pobabilities of successful and empty slots fom the netwok point of view: p es = ( τ) n, p ss = nτ( τ) n (4) The analytical model is solved using a fixed point appoximation. With the metics obtained the enegy consumption of a senso node duing a cetain amount of time can be computed. 4.2 Enegy consumption The total enegy consumption of a senso node can be divided in fou pats: (i) the enegy spent to tansmit and (ii) eceive messages, (iii) the enegy wasted in oveheaing, and (iv) the enegy spent in duty cycle (sleeping and waking up in inactive peiods): e = e tx + e x + e ov + e dc (5) Let N s be the total numbe of messages a node successfully sends duing a time T, it can be deived using the ( thoughput S and the packet length L data as S N s = T L data ). The enegy spent to tansmit N s messages is computed taking into account the enegy needed to successfully tansmit a packet (e s,tx ) and the enegy spent in collisions fo each unsuccessful attempt (e c,tx ): ( ) e tx = N s es,tx + (M )e c,tx (6) The values of e s,tx and e c,tx can be obtained consideing the enegy spent to tansmit and eceive the messages involved and the empty time intevals (Eqs. 7 and 8). Moeove, the empty slots of the BO pocedue must be consideed (note that the busy slots of the BO countdown ae pat of the eceiving o oveheaing enegy consumptions). ( e c,tx = E idle DIFS + Bσ p e + 2SIFS + L ) cts + E tx (L p p unsch ) + L ts e s,tx = E idle (DIFS + Bσ p e + 3SIFS + T e ) + E tx (L p p unsch ) + L ts + L data (7) L cts + L ack + E x (8) whee E tx, E x and E idle denote the enegy consumptions of being in tansmission, eception and idle modes. Notice that, afte a successful tansmission, all nodes in the netwok keep listening to the channel in case anothe node has something to tansmit. If thee ae no moe data to send, this time emains empty and each node stays in the idle mode duing a T listen (added to avoid synchonization poblems) plus the CW, this is: T e = ( ρ) n (T listen + σ CW) (9) Fo simplicity easons, it has been consideed that each node eceives N s packet destined to it. Theefoe, the total enegy consumption to eceive those messages is computed as: e x = N s e s,x (2) The colliding packets have not been consideed hee. It is assumed that the unsuccessful tansmissions of a node collide with those that ae destined to it and that the pobability to collide with moe than one packet can be neglected. The enegy consumption to eceive a packet is: e s,x = p sch e b + p unsch e p + E idle (3SIFS + T e ) ( ) ( ) Lts + L data Lcts + L ack + E x + E tx (2) whee e b is the enegy of a busy listening afte tansmissions peiod, i.e., the idle time inteval befoe sending a packet in the scheduled mode. Obseve that, those nodes without data to send must also wait the emaining BO of the othe nodes.

8 This time has been appoximated by Bσ as shown in Eq. 22. This appoximation does not affect when the taffic load is low (the scheduled pobability is small) o high (the pobability that a node has no data to tansmit is negligible). Howeve, it affects the esults with modeate taffic load and its effect depends on the numbe of nodes. When n is high the enegy consumption is oveestimated (as the pobability that a node has a small emaining BO inceases) while with small n the enegy consumed is undeestimated (since the pobability to tansmit a packet that aives at the queue duing the listen afte tansmission peiod inceases). Then: e b E idle (DIFS + Bσ( ρ)) (22) The paamete e p efes to the enegy spent eceiving the long peamble. If a node has something to tansmit it will be listening to the channel, theefoe it will eceive the entie long peamble of any othe tansmission in the medium. Othewise, the node will be in duty cycle mode and on aveage it will wake up in the middle of the othe s long peamble tansmissions plus its own T listen : ( ) L p e p = ρ E idle DIFS + E x + ( ρ) ( Eidle T listen + E x L p 2 ) (23) Similaly, the enegy consumption due to oveheaing is computed as: ( e ov = N s (n 2) e s,ov + M ) e c,ov (24) 2 whee e s,ov and e c,ov ae the enegy consumption to ovehea a successful tansmission o a collision espectively: L ts e c,ov = p sch e b + p unsch e p + E x ( + E idle 2SIFS + L ) cts (25) L ts e s,ov = p sch e b + p unsch e p + E idle T e + E x ( ) Lcts + L data + L ack + E sleep + 3SIFS (26) whee E sleep denotes the enegy of being in sleep mode. Finally, the est of time (T inactive ), that can be obtained using the equations above computing the time instead of the enegy, and the total time T, each node pefoms a low duty cycle opeation, listening and sleeping accoding to the duty cycle: ( ) T listen T sleep e dc = T inactive E idle + E sleep (27) T ci T ci whee T ci is the check inteval: T ci = T listen + T sleep (28) 4.3 B-MAC analytical model The pevious analytical model can be adapted to model the behaviou of the B-MAC potocol. To achieve that aim two modifications ae needed: (i) the pobability of being in scheduled mode (p sch ) has to be fixed to, meaning that the potocol always woks in the unscheduled mode and (ii) the empty listen time afte a successful tansmission has not to be consideed (T e = ) when computing the enegy consumption of a senso node since the listen afte tansmissions capability does not apply in B-MAC. 4.4 Analytical model validation The SENSE simulato [2] has been used to validate the esults obtained with the analytical model. The scenaio consists of n nodes andomly placed in an aea smalle than the maximum coveage ange, thus, assuming ideal channel conditions, a full connectivity among them is assued. The default paametes used fo the evaluation ae shown in Table (see Section 3). Figue 5 shows the analytical and simulation esults of B-MAC and LWT-MAC with diffeent numbe of senso nodes. Obseve how the scheduled pobability of LWT-MAC (Fig. 5a) inceases with the taffic load until a cetain point at which the numbe of collisions (that move the system to the unscheduled mode) is noticeable. With a highe numbe of nodes, the scheduled pobability inceases faste (since the taffic load is highe), howeve it also becomes constant soone as the collision pobability is also highe. The total enegy consumption of LWT-MAC (Fig. 5b) is stongly elated to the scheduled pobability. Note how the model undeestimates the enegy consumption appoaching satuation fo two and five nodes and oveestimates it with ten nodes. The eason fo this discepancy is the afoementioned appoximation on the value of e b.in contast, fo B-MAC, since it always woks in unscheduled mode, its accuacy is not affected by the e b appoximation. It is also inteesting to obseve the thoughput (Fig. 5c) that slightly inceases, in both potocols, with the numbe of nodes, howeve the satuation though-

9 psch LWT MAC Model n=2 LWT MAC Sim n=2.2 LWT MAC Model n=5 LWT MAC Sim n=5. LWT MAC Model n= LWT MAC Sim n= (a) Scheduled Pobability Enegy Consumption (J) (b) Enegy Consumption B MAC Model n=2 B MAC Sim n=2 LWT MAC Model n=2 LWT MAC Sim n=2 B MAC Model n=5 B MAC Sim n=5 LWT MAC Model n=5 LWT MAC Sim n=5 B MAC Model n= B MAC Sim n= LWT MAC Model n= LWT MAC Sim n= Thoughput (bps) B MAC Model n=2 5 B MAC Sim n=2 LWT MAC Model n=2 4 LWT MAC Sim n=2 B MAC Model n=5 B MAC Sim n=5 3 LWT MAC Model n=5 LWT MAC Sim n=5 2 B MAC Model n= B MAC Sim n= LWT MAC Model n= LWT MAC Sim n= (c) Thoughput Fig. 5 Scheduled pobability, total enegy consumption and thoughput with diffeent numbe of senso nodes put deceases with ten nodes as the collision pobability inceases. Figue 6 shows the esults with ten nodes and diffeent check intevals (the T listen value is maintained while T sleep changes to fit the given check inteval). The scheduled pobability of LWT-MAC (Fig. 6a) emains equal fo all the check intevals at high loads, howeve at lowe loads it inceases faste with highe values of the check inteval. This diffeence occus because with longe check intevals the pobability that a node has eceived something to tansmit duing an ongoing tansmission inceases. In the enegy consumption (Fig. 6b) it can be seen, fo both potocols, that at low loads the use of shot time intevals notably penalizes the enegy consumption as nodes wake up unnecessaily moe often. Howeve, as the load inceases, to have longe check intevals in LWT-MAC implies highe enegy consumption caused by the collisions that move the netwok to the unscheduled mode (moeove, afte a collision nodes wait awake listening the entie peamble tansmission). Howeve, the obtained enegy consumption values at high loads ae substantially lowe than the ones obtained using B-MAC. In the thoughput (Fig. 6c), it can be obseved that lowe satuation values ae obtained when longe peambles ae used, in both cases: using B-MAC and LWT-MAC. In this case, once again, it can be seen how the LWT-MAC impoves the B-MAC pefomance inceasing notably the satuation thoughput. 5 Optimization analysis In this section, a pefomance optimization is done in ode to deive the best paamete configuation of the LWT-MAC potocol fo a single-hop scenaio. A fist goal is to identify how the diffeent paametes that define the LWT-MAC opeation affect its pefomance and how they can be tuned to minimize the enegy consumption without significantly educing the thoughput and delay. 5. Key paametes optimization One of the paametes of cucial impotance is the sleep time of the duty cycle (T sleep ) as it diectly affects psch B MAC Model Tci=5 ms B MAC Sim Tci=5 ms.2 LWT MAC Model Tci=5 ms LWT MAC Sim Tci=5 ms. B MAC Model Tci= ms B MAC Sim Tci= ms (a) Scheduled Pobability Enegy Consumption (J) B MAC Model Tci=5 ms B MAC Sim Tci=5 ms LWT MAC Model Tci=5 ms 6 LWT MAC Sim Tci=5 ms B MAC Model Tci= ms B MAC Sim Tci= ms 4 LWT MAC Model Tci= ms LWT MAC Sim Tci= ms B MAC Model Tci=2 ms 2 B MAC Sim Tci=2 ms LWT MAC Model Tci=2 ms LWT MAC Sim Tci=2 ms (b) Enegy Consumption Thoughput (bps) B MAC Model Tci=5 ms 5 B MAC Sim Tci=5 ms LWT MAC Model Tci=5 ms 4 LWT MAC Sim Tci=5 ms B MAC Model Tci= ms B MAC Sim Tci= ms 3 LWT MAC Model Tci= ms LWT MAC Sim Tci= ms 2 B MAC Model Tci=2 ms B MAC Sim Tci=2 ms LWT MAC Model Tci=2 ms LWT MAC Sim Tci=2 ms (c) Thoughput Fig. 6 Scheduled pobability, total enegy consumption and thoughput with diffeent values of the check inteval

10 the pefomance of the netwok. High values of the T sleep allow to decease the enegy consumption but at the cost of educing the thoughput and inceasing the delay. Additionally, it is possible to define a pobability of waking up afte successful tansmissions (p w ), based on which senso nodes decide to wake up at the end of a successful tansmission o go to sleep emaining in the unscheduled access. Obseve that, an additional mechanism should be implemented to infom nodes to wake up at the end of each tansmission based on this pobability, othewise eceives can be sleeping when nodes send packets without using the long peamble. The sende can, fo instance, notify senso nodes to wake up at the end of the tansmission in the data o RTS messages. At low taffic loads, setting that pobability to small values allows to educe the enegy consumption as fewe idle listening afte tansmission peiods will occu, howeve, as load inceases, highe values of p w educe the enegy waste since the numbe of long peamble tansmissions ae educed. Note that by defining this pobability Eqs. 3, 8, 2 and 26 should be ewitten as shown in Eqs. 29, 3, 3 and 32, espectively: p ss p sch = p w ( ( ρ) n ), p unsch = p sch p es (29) e s,tx = E idle (DIFS + Bσ p e + 3SIFS + p w T e ) + E tx (L p p unsch ) + L ts + L data + E x L cts + L ack (3) e s,x = p sch e b + p unsch e p + E idle (3SIFS + p w T e ) ( ) ( ) Lts + L data Lcts + L ack + E x + E tx (3) L ts e s,ov = p sch e b + p unsch e p + E idle p w T e + E x ( ) Lcts + L data + L ack + E sleep + 3SIFS (32) Othe paametes such as the CW, used to compute the andom BO, also affect the pefomance, but compaedtothet sleep and p w thei influence is limited. Paametes like the packet length o the taffic load ae consideed fixed. 5.2 Optimization function The main goal of the optimization pocess is to minimize the enegy consumption (e) but constained to achieve the same thoughput as the IEEE 82. (CSMA/CA) MAC potocol. The IEEE 82. has been chosen as a efeence as it does not implement the duty cycle opeation, esulting in an uppe bound in tems of pefomance (given that the othe common paametes, such as the CW and the RTS/CTS option ae equally configued in both appoaches). The optimization analysis consides the thoughput as the only constaint since the aveage packet tansmission delay will necessaily incease to allocate space fo the long peamble tansmission, which is the pice that the LWT-MAC pays to obtain a lowe enegy consumption than the IEEE 82. without educing its thoughput. The optimization function is shown in Eq. 33. [T sleep, p w ] = ag min T sleep [,.5],p w [,],S S 82. e ( n, L data,ζ,t, T sleep, p w ) (33) Obseve that, the metics efeed by ζ (see Table 2) ae a function of n, λ and L data and can be obtained using the peviously descibed analytical model. 5.3 Optimization esults By applying Eq. 33 the optimal sleep time (Tsleep ) and wake up pobability (p w ) can be obtained fo a given scenaio. The optimal values ae those that minimize the enegy consumption and achieve the same thoughput as the IEEE 82.. To see how the optimal paametes change fo diffeent taffic loads (A) and numbe of nodes (n), a single-hop netwok with the paametes shown in Table (see Section 3) has been evaluated. Results ae shown in Fig. 7. Note that, once the thoughput of IEEE 82. cannot be achieved the metics ae not longe depicted. The minimum enegy consumption (Fig. 7b) fo the achieved thoughput is depicted in Fig. 7a. Obseve, in Fig. 7c, how the optimal pobability to wake up afte a successful tansmission (p w ) inceases apidly fom to when the taffic load stats to be noticeable. In contast, the Tsleep (Fig. 7f) takes high values at low loads, meaning that, fo the load equiements, senso nodes can be sleeping duing a longe time in each duty cycle. As the load inceases, the value of Tsleep deceases, howeve it shows an inflection point and begins to incease. This effect is caused by the listening afte tansmissions pobability that suddenly inceases to educing the offeed load of the netwok as it educes the time needed to send a message. Afte this behavio, the Tsleep continues deceasing in ode to maintain the thoughput but also

11 Enegy Consumption (J) n=2 n=5 n= (a) Enegy Consumption Thoughput (bps) n=2 n=5 n= (b) Thoughput pw* n=2. n=5 n= (c) p* w 7 6 n=2 n=5 n= n=2 n=5 n= Delay (s) 4 3 psch t*sleep (s) n=2. n=5 n= (d) Delay (e) Scheduled Pobability (f) T * sleep Fig. 7 Pefomance metics with optimum Tsleep and p w in a single-hop netwok to educe the duation of collisions. Moeove, as it has been consideed that afte a collision nodes also keep listening to the channel, thus eceiving the entie next long peamble tansmission, the consumption with high taffic loads inceases with the value of the sleep time (that makes the long peamble to incease). The values Tsleep and p w diectly influence the delay and the scheduled pobability. The delay, depicted in Fig. 7d, shows a small incease at vey low loads caused by the long sleep time and emains moe o less constant until the queues become satuated. Regading the scheduled pobability (Fig. 7e), it is diectly affected by p w that bounds its value at low loads. Fom these esults, it can be concluded that, if the load can be estimated, the best configuation is: a) at low loads set the T sleep to long values and p w equal and b) at high loads decease the T sleep value and set p w equal. 5.4 Heuistic configuation of the LWT-MAC paametes The estimation of the taffic load is a difficult task, even moe in event-based WSNs whee the taffic pofiles diffe fom the taditional ones, showing spoadic and instantaneous inceases of the taffic load due, fo instance, to events occuence. Moeove, senso nodes ae devices with limited capabilities in tems of pocessing and memoy esouces making the load estimation an aduous task. Howeve, if the load can be estimated in a fast and eliable way, the best option will be to use the LWT-MAC with the optimal values fo T sleep and p w. Othewise, fom the obsevations made in the optimization analysis pefomed in the pevious section, a heuistic paamete configuation to povide low enegy consumption, high thoughput and small delay though the entie load ange can be made. The majo disadvantage of LWT-MAC is that it consumes moe enegy than B-MAC at low loads due to idle listening afte tansmission peiods, howeve a modeately long value of T sleep can help to decease the enegy consumption at low loads. To benefit fom the advantages of LWT-MAC, if the T sleep is fixed to a long value, the p w pobability should always be set to one. With this configuation, the LWT-MAC will consume less enegy at low loads and it will maintain its capability to eact to instantaneous inceases of the netwok load. Figue 8 shows fo diffeent numbe of senso nodes the value of the enegy consumption and thoughput

12 Enegy Consumption (J) Tsleep=5ms 2 Tsleep=ms Tsleep=2ms Tsleep=3ms.5.5 (a) Enegy Consumption n = Enegy Consumption (J) Tsleep=5ms Tsleep=ms Tsleep=2ms Tsleep=3ms (b) Enegy Consumption n =5 Enegy Consumption (J) Tsleep=5ms 5 Tsleep=ms Tsleep=2ms Tsleep=3ms (c) Enegy Consumption n = Thoughput (bps) Thoughput (bps) Thoughput (bps) Tsleep=5ms Tsleep=ms Tsleep=2ms Tsleep=3ms.5.5 (d) Thoughput n = 2 Tsleep=5ms Tsleep=ms Tsleep=2ms Tsleep=3ms (e) Thoughput n =5 2 Tsleep=5ms Tsleep=ms Tsleep=2ms Tsleep=3ms (f) Thoughput n =2 Fig. 8 Pefomance metics fo diffeent T sleep and p w = in a single-hop netwok with diffeent values of T sleep and vaying the taffic load. It can be seen that fo T sleep = 5 ms the enegy consumption at low loads is significantly highe. Howeve, it deceases substantially with T sleep = ms and, still a bit moe, with T sleep = 2 ms. Howeve, with T sleep = 3 ms the eduction of enegy consumption at low loads is extemely small, compaed to the obtained with 2 ms, and at the cost of a lowe thoughput. Theefoe, a T sleep aound 2 ms povides a consideably eduction of the enegy consumption at low loads maintaining an acceptable value fo the thoughput. Howeve, once the netwok satuates the enegy consumption inceases with highe values of T sleep since it is consideed that all nodes keep listening to the channel afte a collision, thus eceiving the entie long peamble of the etansmissions. Nevetheless, in the nomal opeation, the netwok is expected to wok fom low to modeate load conditions, not in satuation. Thus, the suggested heuistic configuation is: T sleep = 2 ms and p w =. MAC with T sleep = 75 ms in a single-hop and a multihop netwok. The esults of LWT-MAC with T sleep = 75 ms and p w = have also been included to keep them Sink Senso Node 6 Pefomance evaluation In this section, the heuistic configuation of T sleep = 2 ms and p w = is evaluated and compaed to B- Fig. 9 Single-hop scenaio Peiodic Messages

13 Enegy Consumption (J) Thoughput (bps) Delay (s) LWT MAC Tsleep=2ms LWT MAC Tsleep=2ms LWT MAC Tsleep=2ms (a) Enegy Consumption n =5 (b) Thoughput n =5 (c) Delay n = Enegy Consumption (J) Thoughput (bps) Delay (s) LWT MAC Tsleep=2ms B MAC Tsleep=75ms LWT MAC Tsleep=2ms LWT MAC Tsleep=2ms.5.5 (d) Enegy Consumption n = (e) Thoughput n = (f) Delay n = Fig. Pefomance metics with ecommended heuistic T sleep and p w in a single-hop netwok with five and ten senso nodes as a efeence. Fo a fai compaison the RTS/CTS pocedue is used in both B-MAC and LWT-MAC (fo the scheduled and unscheduled accesses), theefoe an RTS is sent immediately afte the long peamble tansmission. Afte oveheaing an RTS o CTS message, nodes go to sleep fo the ongoing tansmission duation in both B-MAC and LWT-MAC. In the multi-hop case event-based taffic pofiles will be also consideed. The SENSE simulato [2], as explained befoe, has been used to obtain the esults. In this case the simulato has also been extended with the B-MAC potocol and the event-based taffic pofile. The channel has been consideed eo-fee. The single-hop scenaio consists of n nodes andomly placed in an aea smalle than the maximum coveage ange. All senso nodes geneate messages following a Poisson distibution and send them to the sink (Fig. 9). The default paametes used fo the evaluation ae shownintable (see Section 3). In this scenaio the CA time is deactivated. Obseve that this scenaio povides the best conditions fo the LWT-MAC potocol since without hidden teminals and channel eos all senso nodes will synchonize to ongoing tansmissions and theefoe, will be able to send thei packets afte them without making use of the long peamble. Moeove, since all the nodes ae inside the coveage ange of the othes, eceives ae always awake in the scheduled phase, i.e., they ovehea all tansmissions taking place. The only Senso Node 6. Single-hop netwok Event Radius Sink Peiodic Messages Event Data Fig. Multi-hop scenaio with peiodic and event-based taffic pofiles

14 Table 3 Default paametes Paamete Value Paamete Value (data ate) 2 kbps T listen 24.5 ms σ (empty slot) ms L data (packet size) 24 bits DIFS ms L ts, L cts, L ack 64 bits SIFS 5 ms E tx mw CW 64 E x, E idle 3.5 mw K (queue size) pkts E sleep.5 mw R (ety limit) 5 T (time) 5 5 s limitation of this scenaio is the occuence of collisions. It has been assumed that collisions move the system to the unscheduled phase in which nodes should use the long peamble befoe a data tansmission. Howeve, afte the initial tansmission in the unscheduled phase the system will immediately move to the scheduled phase again. Results (Fig. ) show that the enegy consumption of LWT-MAC with the heuistic paamete configuation is simila to the one obtained by B-MAC at low loads as can be obseved in Fig. a and d. Howeve, at high loads the suppession of the long peamble educes the enegy consumption of the LWT- MAC potocol. The suppession of the long peamble tansmission is the cause of the highe thoughput of the LWT-MAC compaed to the B-MAC as depicted in Fig. b and e. Howeve, the incease of the T sleep to maintain the enegy consumption makes the delay to slightly incease at low loads as can be seen in Fig. c and f. Compaed to the LWT-MAC with T sleep = 75 ms, the heuistic configuation povides slightly wose esults in tems of thoughput and delay but consideably educes the enegy consumption at low loads. 6.2 Multi-hop netwok The multi-hop scenaio consists of a multi-hop eventbased WSN with nodes andomly placed in a m 2 aea. The adio ange of each node is 43 m and the Floyd algoithm has been used to compute the shotest path between any pai of nodes. Each senso node geneates two kinds of taffic pofiles: (i) messages geneated following a Poisson distibution and (ii) event-based messages (see Fig. ). A andom event geneato selects andomly the event position and notifies the senso nodes that ae inside the coveage adius of the event in ode to send event-based messages 5 x LWT MAC Tsleep=2ms 25 2 LWT MAC Tsleep=2ms LWT MAC Tsleep=2ms Enegy Consumption (J) Total Thoughput (bps) 5 5 Peiodic Delay (s) Peiodic Message Inteaival Peiod (s) (a) Enegy Consumption Peiodic Message Inteaival Peiod (s) (b) Thoughput Peiodic Message Inteaival Peiod (s) (c) Delay of peiodic messages 9 8 LWT MAC Tsleep=2ms 5 Collective Delay (s) Collective Bandwidth (bps) Peiodic Message Inteaival Peiod (s) (d) Collective Delay LWT MAC Tsleep=2ms Peiodic Message Inteaival Peiod (s) (e) Collective Bandwidth Fig. 2 Pefomance metics with ecommended heuistic T sleep and p w in a multi-hop netwok with peiodic and event-based taffic pofiles

15 Table 4 Collective eliability fo peiodic inteaival time equals and 25 s MAC potocol s 25 s B-MAC T sleep = 75 ms LWT-MAC T sleep = 75 ms LWT-MAC T sleep = 2 ms to the sink. Events have a constant coveage adius of 3 m, the time between events follows an exponential distibution with mean 6 s and the numbe of event messages needed at sink to eliably detect an event has been set to 5. In this scenaio the CA time is activated. The paametes used ae shown in Table 3. The esults obtained ae shown in Fig. 2. It is obseved that at low loads the enegy consumption of the LWT-MAC with the heuistic configuation is consideably lowe than using the B-MAC (Fig. 2a). This effect appeas due to the longe T sleep but also due to the CA time that avoids continuous collisions of peambles and bette manages hidden teminal poblems. The LWT-MAC povides also bette esults in thoughput, depicted in Fig. 2b, with a highe value of the satuation thoughput and delay (Fig. 2c). The collective QoS metics ae shown in Fig. 2d, e and Table 4. The LWT-MAC with heuistic configuation achieves lowe collective delay (Fig. 2d), defined as the time span between the event occuence and the event detection at sink [22]. It also povides bette collective bandwidth fo the event-based messages as shown in Fig. 2e and bette collective eliability (see Table 4) fo a message inteaival peiod equals and 25 s. Fo othe loads the eliability is almost %inall the cases. Collective bandwidth efes to the bandwidth equied to detect an event while collective eliability is the faction of coectly detected events among all events geneated [8]. Obseve that, the LWT-MAC with T sleep = 75 ms povides, as seen in the single-hop scenaio, bette esults in thoughput and delay but also in the collective metics. Howeve, the heuistic configuation allows to noticeably decease the enegy waste at low loads by obtaining bette collective and individual metics than B-MAC. 7 Concluding emaks In this wok an analysis of the LWT-MAC potocol has been pefomed. A LWT-MAC analytical model that computes the netwok pefomance metics and the enegy consumption taking into account collisions in both satuated and unsatuated conditions has been pesented. Moeove, the optimal configuation fo the pobability to wake up afte a successful tansmission (p w ) and the sleep time of the duty cycle (T sleep ) have been obtained depending on the numbe of nodes and the load of the netwok in a single-hop scenaio. Fom the optimization esults, a heuistic configuation fo the T sleep and the p w is suggested. The use of the poposed heuistic paamete configuation avoids the complexity of othe mechanisms that, fo example, adapt the paametes based on the taffic load estimation, which can be unfeasible in WSNs, and povides a nea-optimal pefomance in a wide ange of situations. Additionally, the LWT-MAC with the heuistic paamete configuation has been compaed with B- MAC in a single-hop netwok as well as in a multi-hop scenaio with event-based taffic. Results show that the enegy consumption of the senso nodes is maintained simila o lowe to the consumed by B-MAC and that the othe pefomance metics, specially those egading to collective QoS, ae substantially impoved. Although the heuistic paamete configuation has been obtained fo a single-hop scenaio, it has been shown that it is also valid in a multi-hop netwok. Acknowledgements This wok has been patially suppoted by the Spanish Govenment unde the pojects TEC28-655/TEC (GEPETO, Plan Nacional I+D) and CSD28- (COMON- SENS, Consolide-Ingenio Pogam) and by the Catalan Govenment (SGR29#67) Refeences. 82., IS (999) Wieless LAN medium access contol (MAC) and physical laye (PHY) specifications. ANSI/IEEE Std 82.. Revised Polaste J, Hill J, Culle D (24) Vesatile low powe media access fo wieless senso netwoks. In: Poceedings of the 2nd intenational confeence on embedded netwoked senso systems (SenSys 4) 3. Cano C, Bellalta B, Sfaiopoulou A, Baceló J (29) A low powe listening MAC with scheduled wake up afte tansmissions fo WSNs. IEEE Commun Lett 3(4): Ye W, Heidemann J, Estin D (24) Medium access contol with coodinated adaptive sleeping fo wieless senso netwoks. IEEE/ACM Tans Netw 2(3): Haapola J (25) Multihop medium access contol fo WSNs: an enegy analysis model. EURASIP J Wiel Comm 25(4): Zhang Y, He C, Jiang L (28) Pefomance analysis of S- MAC potocol unde unsatuated conditions. IEEE Commun Lett 2(3): Buettne M, Yee G, Andeson E, Han R (26) X-MAC: a shot peamble MAC potocol fo duty-cycled wieless senso netwoks. In: Poceedings of the 4th intenational confeence on embedded netwoked senso systems (Sensys 6), pp Ye W, Silva F, Heidemann J (26) Ulta-low duty cycle MAC with scheduled channel polling. In: Poceedings of the