A Metric for Opportunistic Routing in Duty Cycled Wireless Sensor Networks

Transcription

1 A Metrc for Opportunstc Routng n Duty Cycled Wreless Sensor Networks Euhanna Ghadm, Olaf Landsedel, Pablo Soldat and Mkael Johansson euhanna@kth.se, olafl@chalmers.se, pablo.soldat@huawe.com, mkaelj@kth.se School of Electrcal Engneerng, KTH - Royal Insttute of Technology, Sweden Chalmers Unversty of Technology, Sweden Huawe Technologes Sweden AB Abstract Opportunstc routng s wdely known to have substantally better performance than tradtonal uncast routng n wreless networks wth lossy lnks. However, wreless sensor networks are heavly duty-cycled,.e. they frequently enter deep sleep states to ensure long network lfe-tme. Ths renders exstng opportunstc routng schemes mpractcal, as they assume that nodes are always awake and can overhear other transmssons. In ths paper, we ntroduce a novel opportunstc routng metrc that takes duty cyclng nto account. By analytcal performance modelng and smulatons, we show that our routng scheme results n sgnfcantly reduced delay and mproved energy effcency compared to tradtonal uncast routng. The method s based on a new metrc,, that reflects the expected number of duty cycled wakeups that are requred to successfully delver a packet from source to destnaton. We devse dstrbuted algorthms that fnd the -optmal forwardng,.e. the optmal subset of neghbors that each node should permt to forward ts packets. We compare the performance of the new routng wth -optmal sngle path routng n both smulatons and testbed-based experments. I. INTRODUCTION Opportunstc routng has shown the potental to sgnfcantly ncrease throughput n mult-hop wreless mesh-networks compared to the tradtonal uncast routng [] [4]. It explots the fact that n wreless mesh-networks, rados are always-on and hence can overhear messages at practcally no addtonal cost. Hence, a sngle transmsson s often receved by multple recevers, each provdng a specfc routng progress to the destnaton. The recever that provdes the maxmum routng progress wll then forward the packet []. In summaton, opportunstc routng leverages spatal reuse to realze two key benefts: t provdes hgh routng progress and lmts the mpact of lnk dynamcs. Ths leads to a substantal throughput mprovement relatve to tradtonal routng schemes [], []. Whle routng protocols for wreless sensor networks (WSNs) also am for hgh routng progress and reslence to lnk dynamcs, exstng proposals for opportunstc routng cannot be drectly appled. In order to guarantee long network lfetme, WSNs are commonly duty-cycled. Nodes n deep sleep states have ther rados turned off to save energy and wll not be able to overhear transmssons from other nodes. The man dstncton of ths work from exstng opportunstc routng schemes s that t consders the practcal ssues of Ths work was partally funded by the Swedsh Research Councl (VR) and the Swedsh Foundaton for Strategc Research (SSF). duty cyclng and presents an opportunstc routng protocol talored to WSNs. A packet s forwarded by the frst awoken neghbor that successfully receves t and offers routng progress towards the destnaton. As a result, by mnmzng the average number of duty-cycles requred for end-to-end packet delvery, we sgnfcantly mprove energy effcency and reduce delay compared to uncast routng n WSNs. We acheve ths by ntroducng a new anycast routng metrc, (Estmated Duty Cycled wake-ups), that focuses on energy effcency and delay nstead of hgh throughput. estmates the on-tme,.e., energy consumpton, of the rados of the nodes that a packet traverses from snk to destnaton. Smlar to routng wth the wdespread metrc [5], that mnmzes the expected number of transmssons requred to forward a packet from snk to source, routng wth mnmzes the energy consumpton of packet forwardng n an opportunstc WSN. Ths paper bulds upon our prevous work [6] whch ntroduces ORW, a practcal opportunstc routng scheme for wreless sensor networks. Whle [6] presents a practcal realzaton of opportunstc routng and evaluates ts benefts n both smulaton and TnyOS based testbed experments, current paper focuses on theoretcal aspects of opportunstc routng n WSNs and makes four core contrbutons: ) We ntroduce a detaled analytcal model to measure the expected number of duty cycled wake-ups as an ndcator of the average end-to-end delay n WSNs. ) We present the metrc as a heurstc to estmate ths value. Compared to the detaled analytcal expressons, s computatonally smple whle mantannng key propertes of loop freeness and local computablty. ) In our evaluaton we show that the analytcal model the and heurstc lead to the nearly the same routng topologes. 4) In smulatons and deployments we compare our anycast metrc to the wdespread metrc for uncast routng, and show that outperforms sgnfcantly n terms of rado duty cycles and delay. The remander of ths paper s structured as follows: After revewng the opportunstc routng n wreless networks n Secton II, we ntroduce the basc concepts of our anycast routng metrc n Secton III. We propose a theoretcal framework to calculate the expected number of wake-ups n Secton IV.

2 Secton V presents metrc. Forwarder set constructon and algorthmc propertes of metrc s dscussed n Secton VI. Secton VII evaluates and compares our metrc aganst. We dscuss related work n Secton VIII. Secton IX concludes. II. BACKGROUND In ths secton, we provde the requred background on opportunstc routng n mesh networks and dscuss why t cannot be drectly utlzed n wreless sensor networks. A. Opportunstc Routng Opportunstc routng [] [4] mproves network throughput n the context of mult-hop, mesh networks. In contrast to tradtonal uncast routng, opportunstc routng delays the forwardng decson untl after the transmsson. In ExOR [] each packet s sent to a set of potental forwardng nodes, prortzed by routng progress. Based on ts prorty, each node n the forwarder set s assgned a tme slot for forwardng, whch t only utlzes f t dd not overhear the packet beng forwarded n a prevous tme slot. Relyng on such a consensus protocol, opportunstc routng avods duplcate forwardng. To sum up, opportunstc routng leverages spatal reuse to ensure hgh routng progress and to lmt the mpact of lnk dynamcs. Ths leads to a sgnfcant throughput mprovement when compared to tradtonal routng schemes [], []. Routng protocols n WSNs follow smlar goals: hgh routng progress and reslence to lnk dynamcs. However, opportunstc routng cannot be drectly appled: Wreless sensor networks and ther applcatons pose specal requrements, such as lowpower networkng and resource constrants, that dstnct them from tradtonal mult-hop mesh networks. These lmt the drect applcablty of opportunstc routng n followng aspects: ) Relablty and Energy Effcency vs. Throughput: Opportunstc routng s desgned to mprove network throughput. However, WSN applcatons commonly demand relable forwardng at hgh energy-effcency and not hgh throughput. In ths paper, we show how opportunstc routng can be adapted to mprove the energy effcency when compared to tradtonal WSN routng. ) Duty Cyclng n Sensor Networks: Commonly, sensor networks are duty-cycled to ensure long node and network lfetme. Hence, nodes are n deep sleep states most of the tme, wth ther rados turned off. Duty-cyclng lmts the number of nodes that concurrently overhear a packet (assumng no pror synchronzaton). As a result, t prevents the spatal reuse n the forwardng process, one of the key benefts of opportunstc routng. B. Adaptng Opportunstc Routng to WSNs After ntroducng the concept of opportunstc routng and dscussng ts lmtatons n the context of WSNs, we dscuss ts adaptaton to the specal requrements of WSNs. Our work targets duty-cycled protocol stacks. For smplcty we here llustrate the basc concept of our opportunstc routng scheme for WSNs utlzng an asynchronous low-power-lstenng MAC, such as n X-MAC [7]. In low-power-lstenng a sender transmts a stream of packets untl the ntended recever wakes up and acknowledges t (see Fg. a and Fg. b). To ntegrate opportunstc routng nto duty cycled envronments, we depart from ths tradtonal uncast forwardng scheme n one key aspect: The frst node that (a) wakes up, (b) receves the packet, and (c) provdes routng progress, acknowledges and forwards the packet, see Fg. c. Our desgn enables an effcent adaptaton of opportunstc routng to the specfc demands of wreless sensor networks: () In contrast to opportunstc routng n mesh networks, forwarder selecton n our scheme focuses on energy effcency and delay nstead of network throughput: It mnmzes the rado-on tme untl a packet s receved by a potental forwarder. () It ntegrates well nto duty-cycled envronments and ensures that many potental forwarders can overhear a packet n a sngle wake-up perod. Thereby, we explot spatal and temporal lnk dversty to mprove reslence to wreless lnk dynamcs. In our routng scheme, a packet s forwarded by the frst awoken neghbor that provdes routng progress. As a result, a node has multple parents and the routng topology towards a destnaton s not a tree anymore as n tradtonal uncastbased routng protocols. It assembles a Drected Acyclc Graph (DAG) wth a sngle destnaton (Destnaton Orented DAG, DODAG). In ths DODAG each packet potentally traverses on a dfferent route to the destnaton (anycast). III. BASIC CONCEPT: ANYCAST ROUTING METRIC To enable energy-effcent opportunstc routng n dutycycled WSNs, we ntroduce (Estmated Duty Cycled wake-ups) as routng metrc. s an adaptaton of [5] to energy-effcent, anycast routng. estmates the number of transmssons requred to delver a packet from source to snk. In contrast, our metrc estmates the rado on-tme,.e.,the rado duty cycle. We rely rado duty-cycles as key metrc as t n contrast to transmsson counts reflects the energy consumpton of the communcaton n duty cycled WSNs. Hence, mnmzng the of the node drectly reduces ts energy consumpton and ncreases node and network lfetme. Furthermore, we show n our evaluaton that also reduces delay when compared to whle achevng smlar hop counts. A. Trade-Offs n Parent Selecton Usng as routng metrc, each node mantans a set of admssble neghbors called forwarder set n whch every member, upon recevng a packet from, s elgble to relay the packets.the optmal forwarder set F of a node s the subset of ts neghbors that leads to the mnmum of. Two factors mpact the choce of the forwarder set F : () addng more neghborng nodes to the forwarder set reduces the tme untl one of the potental forwarders wakes up to receve. Hence, t decreases the sngle-hop of the forwardng node and mproves spatal dversty (see Fg. c). However, () addng too many neghborng nodes to the forwarder set may decrease ts average routng progress, as commonly not all neghbors provde good progress.

3 P P A P A (a) Sample topology: Node reaches va on relable (sold) lnks or drectly on an unrelable (dashed) lnk. P P P P P P P P A (b) Tradtonal uncast routng n WSNs: Although mght overhear some transmsson from, packets are addressed to to ensure stable routng. P P P A (c) Opportunstc Routng n WSNs: wakes up frst receves a packet from, and snce provdes suffcent routng progress t acknowledges and forwards the packet. Fg. : Man dea of opportunstc routng scheme for WSNs s to explot spatal and temporal lnk dversty to reduce energy consumpton and delay. B. Requrements for as Routng Metrc As routng metrc, we requre the followng set of propertes: Loop Free Topology: To ensure stable routng, the resultng topology s requred be loop-free. Dstrbuted Computablty: Computaton of of a node shall only requre nformaton from neghborng nodes. Low Algorthmc Complexty: To match the scare resources of a sensor node n terms of computng capabltes, memory, and energy resources, the our algorthms must be lghtweght. Next we provde an analytcal model to calculate the average number of wake-ups for end-to-end packet delvery. Later, we wll show that, as an approxmaton for the theoretcal model shows a strongly reduced computatonal complexty when compared the analytcal model. IV. EXPECTED NUMBER OF DUTY CYCLED WAKE-UPS We represent the topology of the network as a drected graph G = {N,L,P}, wth a set of nodes N = {,...,N}, a set of lnks L, where a lnk s represented by an ordered par (, j) of dstnct nodes, and a set of probabltes P. The packet loss process on each lnk (, j) L follows a Bernoull process wth success probablty p j, and we assume that packet loss processes on lnks are ndependent of each other. Let F be the set of forwarders of node. For the moment, we assume that the forwarder set of each node s fxed. Later, n Secton VI, we address how ndvdual nodes can perform ths forwarder selecton. Further, we wll assume that nodes use the same duty cycle length T. At duty cycle k and before gong to dormant state, node draws the next wake-up tme t k unformly n the nterval [,T ];.e. node wakes up at t,t + t,t + t, etc. In ths settng, we are nterested n analyzng the expected number of duty cycled wake-ups for a transmsson from source to destnaton. To ths end, let DC be the random number of duty cycled wake-ups requred to complete the end-to-end transmsson, and note that we can dvde t nto two ndependent components. Frst, the number of wake-ups requred for a sngle-hop transmsson from the source node to one of ts forwarders, and second, the number of wake-ups the packet takes to reach from the forwarder node to the snk. Snce lnk losses are assumed to be ndependent, we can wrte E{DC()} = E{DC s ()} + E{DC m ()}, () where E{DC s ()} s the expected number of duty cycled wakeups untl the packet has been receved by one of the forwarders, and E{DC m ()} s the expected number of remanng duty cycled wake-ups t takes to complete the mult-hop transmsson. The number of wake-ups requred for a sngle-hop transmsson can be seen as the sum of two ndependent random varables, DC s () = X s () + Y s () where X s () s the number of faled ntervals (n whch all forwarders wake up once and fal to receve the transmsson from node ) and Y s () s the watng tme wthn a duty cycle wth successful transmsson. A faled nterval requres that all transmssons between and j F fal, hence X s () follows a geometrc dstrbuton wth pdf and mean Pr{X() = k} = j F ( p j ) k E{X s ()} = k= ( j F ( p j ) k Pr{X() = k} = j F ( p j ) j F ( p j ). () To characterze Y s (), note that for node j F to be the forwarder, t must experence a successful transmsson and transmssons to all other nodes that wake up before j must fal. Note that the underlyng event s condtoned on that at least one node wll successfully receve n the current duty cycle. Hence, the probablty of recepton for j F n an arbtrary duty cycle condtoned on at least one recepton s gven by p s ( j) = ) p j k F ( p k ). (),

4 In general, ths event can happen for F cases whch s based on explorng the probabltes of havng all nodes ncluded n the possble subsets of forwarders { f F \ j} have faled before node j. Let F k\ j denote the set of all the subsets of forwarders of node wth cardnalty equal k not contanng node j. The probablty of havng exactly k faled transmsson excludng node j s gven by p f (k\ j) = l F k\ j m l ( p m ). (4) Due to contnuty of the random varable, the probablty of havng two nodes wth the same actvaton tme s zero. Thus, the mean watng tme s acheved by teratng among all the nodes j F wth..d unform wake-ups and dfferent lnk qualtes. Namely, E{Y s ()} = T x j F F k= p s ( j) T p f (k\ j)( x T ) ( ) k T x F k dx. (5) T Note that snce E{Y s ()} does not have dmenson -t s a porton of duty cycle- we normalze the above equaton by dvdng t by T. As an example consder node wth k forwarders wth the same success probabltes p j =. It turns out that n ths case, E{DC s ()} has a closed form. One can see that E{X s ()} = and E{DC s ()} = E{Y s ()} = T T k T x ( T T x)k dx = k+. We observe that the mean sngle hop watng tme decreases hyperbolcally wth ncreasng number of neghbors. E{DC m ()} s the expected number of duty cycled wake-ups whch t takes to send the packet from the forwarder set F to the snk gven that a successful transmsson has already took place between and F. E{DC m ()} s gven by E{DC m ()} = Pr{j s the forwarder}e{dc(j)}, (6) j F where F Pr{j s the forwarder} = k= ) ( F k l F k\ j m l ( p m ) p s( j) F. In words, ths corresponds to the probablty of node j beng the frst successful recever gven that at least one forwarder receves n current duty cycle. Up to now, we have developed an analytcal framework to measure the cost of packet delvery for each sender n terms of the average number of duty cycles. In contrast of a few rudmentary cases -lke when all lnk relabltes are equal - the analyss and even smulatons tend to be ntractable wth respect to ncreased network densty. Thus, the the expected number of duty cycled wake-ups E{DC()} cannot be used for selectng the optmal forwarder set n practcal opportunstc routng protocols. We next ntroduce a new metrc, referred to as, that properly mmcs the behavour the exact E{DC()}. Ths metrc shall be the bass for the desgn of a new low-complexty and dstrbuted algorthm for opportunstc routng, where the selecton and the orderng of the forwarders set of each node s n accordance wth the exact E{DC()} metrc. V. THE METRIC We have seen that an accurate evaluaton of the expected number of duty cycled wake-ups under opportunstc forwardng s qute complex, even when the forwarder sets are fxed. Whle the protocol does not need an analytcal formula for the expected number of wake-ups, t does need a procedure for selectng the optmal forwarder sets. To ths end, we need to defne a lghtweght metrc that captures the essental features of opportunstc forwardng, yet allows us to develop provably correct algorthms for dstrbuted forwarder set selecton. We have found that a metrc whch we call strkes an appealng balance between effectveness n forwarder set selecton and smplcty of protocol analyss. The of a node can be computed recursvely va () = + j F p j ( j) (7) j F p j j F p j The frst term approxmates the expected one-hop forwardng delay E{DC s ()} whle the second term attempts to capture the essental features of the subsequent delay from forwarders to the snk. The sngle-hop cost shares many mportant features of the analytcal model: t s a hyperbolc functon of the lnk relabltes of the forwarders, and addng a forwarder or ncreasng the lnk relabltes decrease the sngle-lop cost. Fgure llustrates a stuaton wth homogeneous lnks (p j = p for all j) and compares E{DC s ()} wth the proposed hyperbolc approxmaton n metrc. We see that the analytcal model and approxmaton agree wth each other when of the number of forwarders ncreases. Expected one hop forwardng delay p=. p=.5 E{DC s ()} metrc p= Number of forwarders Fg. : Comparson of E{DC s ()} versus correspondng term of metrc for F = [,] forwarders. The success probabltes p are equal for each forwarder. In the analytcal model, the complexty of the mult-hop cost comes from the fact that the probablty of j beng a forwarder depends on the lnk relabltes of the other nodes (the probablty of a node j beng a forwarder not only depends on that t could successfully decode the transmsson when t s awake, but t also depends on the probablty that nodes that woke up earler all faled to decode the packet from ). The metrc smply assumes that the probablty

5 that j s a forwarder s drectly proportonal to p j. Wth ths assumpton, the probablty of beng forwarder for each node j s ndependent of others. However, snce probablty of forwarders must add up to one, we normalze each ndvdual forwardng probablty. Hence, n metrc, the probablty p j j F p j. that node j wth relablty p j beng forwarder s Evaluaton results n secton VII confrm the accuracy of metrc compared wth the analytcal scheme under real network scenaros. VI. FORWARDER SET CONSTRUCTION In ths secton, we descrbe how to mantan the metrc n the network. Our key contrbuton s a dstrbuted algorthm for forwarder selecton that mnmzes. In partcular, we show that after the approprate orderng of potental forwarders, nodes can use a greedy algorthm to fnd the optmal forwarder set, and that ths algorthm s loop free. In the forwarder selecton problem, each node s gven a set of potental forwarders N, ther metrcs ( j) for j N, and the probablty of p j successful transmsson from to j N, and should determne the subset of forwarders F N that mnmzes (). To develop our algorthm, we frst revew some rudmentary propertes of the metrc. Lemma 6.: Let p j and c j > for every j N. Defne the set functon f : N R wth f (/) = and f (A) = f () (A) + f () (A) = + j A c j p j, j A p j j A p j for A N. Then f () (A) s strctly decreasng n p j and f () (A) s strctly ncreasng n c j. Proof: The frst result can be verfed by nspectng f () (A {x}) f () (A). For second result one can check that f () (A {k}) f () (A) > gven that c k > c j for all j A. The followng lemma presents a suffcent condton for when the nserton of a new member k N \A n the forwarder set decreases (), Lemma 6.: Let p k >. If c k < f (A) then f (A {k}) < f (A) and vce versa. Proof: The sgn of c k f (A) s the same as the sgn of f (A {k}) f (A), snce f (A {k}) f (A) = p k (c k f (A)) j A p j + p k and p k >. Our result follows. The next result observes the behavor of f (A) after addng a new member nto the forwardng set F. Lemma 6.: If c k < f (A) and p k > then f (A {k}) > c k. Proof: Consder f (A {k}) c k = f (A) c k + p k j A p j Our assumptons mply that the rght-hand sde s postve, hence f (A {k}) > c k. Up to now, we have concluded that t s benefcal for node to add a new neghbor k to the forwarder set f (k) s less than the of node when k s not n the forwarder set. Moreover, after addng node k, the updated of node s greater than (k). The next Theorem characterzes the optmum forwarder set of node. Theorem 6.4: Let π be an orderng of the nodes n N such that {c π() c π() c π( N )}. Then, the optmal forwarder set s F = {π(),...,π(k)} where k satsfes c k < f (F ) and c k+ > f (F ). Proof: Assume that F = {π(),...,π(k)}\π(m) for some m < k,.e. a node m wth c m c k has been excluded from the forwarder set. Accordng to Lemma 6. we have c j < f (F ), j F. Lemma 6. ensures that addng m wth c m c k wll decrease f (F ),.e., f (F {c m }) < f (F ) so F s not optmal and a contradcton acheved. One queston here s what happens f two or more neghbors have equal s but dfferent lnk relabltes. The next lemma shows that even though the node wth hgher relablty results n a larger decrease of the, the optmal forwarder set ether ncludes both nodes or none. Lemma 6.5: f c k = c k < f (A) and p k > p k > then f (A {k}) < f (A {k }) < f (A). Moreover, f c k F, then c k F and vce versa. Proof: The frst part of the proof follows the Lemma 6. and nspectng the nequalty f (A {k }) f (A {k}) = (p k p k )( f (A) c k ) p (p k + j A p j )( k j A p j + ) >. For the second part, assume c k F and c k / F. Snce c k F then by Lemma 6., f (F ) > f (c k ). Now, due to c k < f (F ) and c k / F we conclude that f (F {k }) < f (F ) and consequently contradcton s acheved. So c k F. A smlar argument apples to the nverse case,.e., f c k F, then c k F. Gven a network topology G = {N, L, P}, Lemmas and Theorem 6.4 suggest a greedy algorthm to compute the metrc n the network and to locally construct the set F at each node. Startng from the snk wth =, each node n the network sorts ts neghbors n the set N n ncreasng order of ther s. A potental forwarder j N s added to the set of forwarders F of node f ( j) < (), upon whch () s updated on the bass of the new set F { j}. The procedure repeats untl the forwardng lst and the values of all the nodes reman unchanged. Each teraton k of Algorthm produces a new routng topology R (k) = {N,L (k),e (k) } where L (k) conssts of lnks l = (, j) from a node to all ts forwarders j F, and E (k) network-wde set of updated. We next prove that each routng topology R (k) s loop-free. Lemma 6.6: Any routng topology R (k) = {N,L (k),e (k) } produced by Algorthm s a drected acyclc graph (DAG). Proof: Accordng to Lemma 6., at each teraton k Algorthm a new member j N s added to the forwarder set for node N f (j) < (). By Lemma 6., ths event can only happen snce at teraton k node / Fj,.e. otherwse (j) > (). Furthermore, upon addng j to F we have () = f (F { j}) > ( j) by Lemma 6., whch F

6 Algorthm -based opportunstc routng. Input: G = {N,L,P}, neghbor set N N. Intalze: (Snk), (). repeat Set F = / N for all N do Sort N = {n,...,n N } s.t. (n j ) < (n j+ ). for j = N do f (j) < () then a. Update: F = F {n j }. b. Update: () based on eq. (). end f end for end for untl of all nodes are unchanged. Testbed Sze Snk Tx Power Dameter nodes d dbm hops Motelab 5. Twst TABLE I: Testbed Overvew: In our evaluaton we use PRR traces from two testbeds. ensures that node cannot be added to the optmal forwarder set Fj of j n future teratons of the Algorthm. Thus any two nodes, j N can only be connected by ether an arc (, j) or ( j,) n each rootng topology G (k). Let now consder a path of arbtrary length P = {, j, j,..., j n } from node to the snk n G (k), wth j F, j Fj, and so on. Let assume that P has a loop nvolvng node,.e. there exst a j k P such that Fj k, hence by Lemma 6. () < ( j k ). However, by applyng Lemma 6. to each hop of the path P we have that () > ( j n ), j n P and a contradcton s acheved. A. Valdatng the analytcal model We frst compare the analytcal E{DC} versus smulaton and metrc n a small example. We consder a node wth to forwarders wth fxed average wake-ups and lnk relabltes. Fgure shows the average wake-ups versus forwarder set. Each data pont n the curves corresponds to the updated y-axs values after addng a new forwarder. The frst observaton s the accurate match between theoretcal model and the smulaton. Leveragng on ths match, we wll contnue our evaluatons through analytcal model. Second, wth growng number of forwarders, values eventually tend to the theoretcal values. We ntentonally have sorted forwarders n ncreasng order of average wake-ups. The plot represents the behavor of forwarder selecton algorthm. Startng from the forwarder wth mnmum, sender nserts a new member nto forwardng set, f the of the new forwarder s less than current value of y-axs, n whch n ths example happens untl the thrd forwarder. Avg Delay (n DC) (,.) Analytcal model Smulaton (4.5,.6) (.5,.4) (5,.9) (.6,.5) (4.,.89) (.5, ).5 (4,.75) (,.7) (,.9) Number of nodes n forwarder set Fg. : Comparson of analytcal model versus smulaton and metrc for a node wth [,] forwarders. Forwarder set grows ncrementally wth new members whch are shown by tuple (, relablty). VII. EVALUATIONS We conduct smulatons and real hardware mplementaton to evaluate how metrc performs n terms of average delay, average hop count and average forwarder count. Our evaluaton consst of four parts: () We valdate the analytcal model n extensve smulatons. () We show that our approxmaton reaches a hgh level of accuracy. () We compare our anycast metrc to the wdespread routng metrc. (4) We provde deployment results and compare an based opportunstc routng protocol to the wdespread Collecton Tree Protocol (CTP) [8], whch uses as routng metrc. In the frst three parts we solely focus on the metrc and not protocol mplementatons usng. Hence, we delberately exclude artfacts from protocol mplementatons such the slow spreadng of route updates or packet collsons. To ensure a far and realstc evaluaton our network profle s based on PRR traces from two testbeds: Twst [9] and Motelab [] wth 86 and nodes, respectvely (see Table I). B. versus analytc model To evaluate metrc, we run forwarder set constructon mechansm (Algorthm ) over Twst and Motelab data traces and compare t versus exhaustve search based on analytc model (). The number of forwarders for each node s lmted up to nodes. Ths restrcton s made due to the exponental complexty of the analytcal model as well as the exhaustve search over the forwarder canddates: wth a state of the art PC, current setup requres and 4 hours of smulatons for Twst and Motelab profles, respectvely. Fgures 4a and 4b show optmal duty cycles (E{DC}) versus metrc for each node of the network. We note that values are very close to the analytcal values. Fgures 4c and 4d llustrate the number of forwarders versus node ndex. For each node, the number of optmal forwarders (gven by exhaustve search) and the numbers from the metrc are depcted. Moreover, the number of common forwarders n these two schemes as well as the number of truly ordered common forwarders are plotted. We observe that the last three curves concde to each other.

7 In other words, metrc for each node, pcks a subset of forwarders wth the same order as the optmal set. Roughly speakng, for each node, the best forwarder n optmal set (the one wth lowest E{DC}) s also the frst forwarder that metrc pcks and so on. The values of nodes based on dfferent restrctons on the number of forwarders s llustrated n Fgure 5. For some nodes (the ones closer to the snk) the value does not change. The reason s that due to good paths towards the snk, they do not add more forwarders. In contrast, the nodes farther to the snk ( the ones wth hgher values) wll beneft wth havng more forwarders. We observe that the values for these profles does not change sgnfcantly after forwarders. C. Comparson wth After evaluatng the accuracy of and the mpact of routng table sze, we next compare to the wdespread routng metrc Expected Transmsson Count () [5]. s a uncast routng metrc that estmates the number of (re)transmsson a packet s expected to requre to reach ts ntended destnaton. Routng protocols usng am to mnmze the transmsson count. In contrast to, does not take duty cyclng nto account. Hence, reducng transmsson counts n does not necessarly lead to low delays nor does t reduce rado on-tme. Fgures 6a and 6d show that sgnfcantly reduces delvery delay when compared to n both testbeds. In our deployment results, we also show that ths drectly reduces rado duty cycles and hence rado energy consumpton. Furthermore, we show that dependng on the neghbor table sze, acheves hop counts smlar to (see Fgures 6b and 6e). In some stuatons t even outperforms. Due to ts opportunstc nature, based routng explctly utlzes all neghbors: Instead of watng for one specfc neghbor to wake up as based routng, utlzes the frst neghbor that wakes up and provdes routng progress. As a result, outperforms n terms of delay, whle leadng to more hops. Ths result shows that relyng merely on hop count as an ndcator of delay and energy consumpton s not effcent snce a sender may waste both tme and energy by watng for a best neghbor to wake up. However, lmtng the number of parents n the routng table, we also lmt ths aggressve forwardng and force based routng to select a small number of good parents (see Fgures 6c and 6f). In ths way we trade delay for hop counts and mantenance tme of the forwarder set: By lettng more canddates n the forwarder set we experence less delay meanwhle routng algorthm requres more steps to stablze. Note that even though requres larger forwarder set than, the overhead of routng table management remans unchanged. In practce, also needs to keep the same number of neghbors as to keep track the best routng opton. D. Intal Deployment Results We conclude our evaluaton, by presentng ntal deployment results for our ongong mplementaton of based oppor- Duty Cycle [%] Tx [#] Delay [s]. (CTP, BoX-MAC) (opp. anycast) Node Index Fg. 7: Intal Deployment Results on the Twst Testbed: based routng outperforms based CTP n terms of radoduty cycles by a factor of about and delay by a factor of whle achevng smlar but slghtly hgher hop counts. tunstc anycast routng n TnyOS. We compare our approach to the Collecton Tree Protocol (CTP) [8], the de-facto standard collecton protocol n TnyOS. We use the default TnyOS BoX-MAC []. Based on X-MAC, t s an asynchronous duty cycled MAC layer and has shown good results for CTP. Fgure 7 shows that based opportunstc routng sgnfcantly mproves duty cycles and delay on the Twst testbed. On average, t doubles the energy effcency, ndvdual nodes show mprovements up to a factor of fve. Addtonally, t mproves delay by an average factor of and acheves transmsson counts that are smlar, but slghtly hgher when compared to CTP. VIII. RELATED WORK Smlar to our work, [] [6] consder anycast routng n WSNs. Ther results show that opportunstc routng can mprove energy effcency and delay compared to tradtonal uncast routng. These results strongly motvated our work. LCAR [] assgns a relay canddate-set to each node n order to mnmze the expected cost of forwardng a packet to the destnaton. The expected cost s recursvely constructed by assumng that the relay nodes already know ther own forwardng cost to the destnaton. Mao et al. [] study the selecton and prortzng the forwardng lst to mnmze the overall expected energy consumpton of WSNs. In contrast to our work, they do not consder the duty cyclng n the theoretcal model. Jont study of anycast forwardng and duty cyclng has been done n some recent works. Ashref et al. [4] argues that forwardng to an earlest awoken neghbor can decrease per hop delay. Basu [5] estmates the end-to-end latency of a duty cycled wreless network under random walk routng strategy. Km et al. [6] nvestgates the optmal anycast forwardng polcy for a posson wake-up model to mnmze the expected end-to-end delay n the event-drven WSNs. However, n all of them forwarder selecton merely depends on the wake-up process and the probablty of lnk falure s not consdered:

8 Duty cycled wake ups metrc Analytcal model(optmal) Node ndex (a) Twst: Duty cycled wake-ups Duty cycled wake ups.5.5 metrc Analytcal model(optmal) Node ndex (b) Motelab: Duty cycled wake-ups Number of forwarders Optmal set set Intersecton set Optmally ordered set Node ndex (c) Twst: Forwarder set Number of forwarders Optmal set set Intersecton set Optmally ordered set Node ndex (d) Motelab: Forwarder set Fg. 4: Per node comparson of values and forwarder set n motelab and twst profle. The maxmum number of forwarders s restrcted to. The plots show hgh accuracy of metrc n both duty cycles and forwarder selecton compared wth optmal soluton derved by exhaustve search. Duty cycled wake ups up to forwarders up to forwarders unlmted Node ndex (a) Twst: Duty cycled wake-ups Duty cycled wake ups.5.5 up to forwarders up to forwarders unlmted Node ndex (b) Motelab: Duty cycled wake-ups Fg. 5: Per node comparson of values n motelab and twst profle wth dfferent number of forwarders. We consder ths a key requrement, as due to the low-power nature of the WSNs, ther lnks are hghly dynamc [7]. Opportunstc routng n WSNs also has receved great attenton from a more practcal perspectve. GeRaF [8] and CMAC [9] utlze geographc routng for opportunstc forwardng. Relyng solely on geographc routng, they do not address the key challenges for opportunstc routng n duty-cycled WSNs such as wreless lnk dynamcs, anycast routng metrcs, and energy effcency. DSF [] selects the next hop of a packet based on the sleep schedule of neghborng nodes and dfferent metrcs such delay, relablty, and energy consumpton. Smlar to our work, DSF shows strong mprovements over uncast routng n these metrcs. However, t focuses on synchronzed networks. IX. CONCLUSIONS Ths paper ntroduced a novel routng metrc, Estmated Duty Cycled wake-ups (), for opportunstc routng n dutycycled WSNs. Reducng rado duty-cycles drectly mpacts the key resource n battery-powered sensor networks: the severely lmted energy supples. We establshed key propertes of as routng metrc and showed that t can be computed dstrbutedly and leads to a loop free topology. Comparsons wth a detaled analytcal model establshed that s an accurate

9 , 4,,, Avg. Delay (n Wakeup Intervals), 4,, (a) Motelab: Average delay, Avg. Delay (n Wakeup Intervals) (d) Twst: Average delay, 4,,, Avg. Hop Count (b) Motelab: Average hop count, 4,,, Avg. Hop Count.5 (e) Twst: Average hop count, 4,,, Avg. Parent Count 6 (c) Motelab: Average parent count, 4,,, Avg. Parent Count (f) Twst: Average parent count Fg. 6: Comparng and on Motelab and Twst traces: Independent of routng table sze, outperforms n terms of delay. Addtonally, outperforms n terms of hops for small routng tables. approxmaton of the true number of duty-cycled wakeups requred to forward the packet. Fnally, we showed n both smulatons and ntal deployments that yelds sgnfcantly mproved rado-duty cycle counts and delays compared to. REFERENCES [] S. Bswas and R. Morrs. ExOR: Opportunstc Mult-Hop Routng for Wreless Networks. In SgComm: Proc. of the Conference on Applcatons, Technologes, Archtectures, and Protocols for Computer Communcatons, 5. [] S. Chachulsk, M. Jennngs, S. Katt, and D. Katab. Tradng Structure for Randomness n Wreless Opportunstc Routng. In SgComm: Proc. of the Conference on Applcatons, Technologes, Archtectures, and Protocols for Computer Communcatons, 7. [] P. Larsson. Selecton Dversty Forwardng n a Multhop Packet Rrado Network wth Fadng Channel and Capture. SIGMOBILE Mob. Comput. Commun. Rev., 5,. [4] R. Choudhury and N.H. Vadya. MAC-Layer Anycastng n Ad Hoc Networks. SIGCOMM Comput. Commun. Rev., 4(), 4. [5] S. J. Douglas, D. Aguayo, J. Bcket, and R. Morrs. A Hgh-Throughput Path Metrc for Mult-Hop Wreless Routng. In MobCom: Proc. of the ACM Int. Conference on Moble Computng and Networkng,. [6] O. Landsedel, E. Ghadm, S. Duquennoy, and M. Johansson. Low power, low delay: Opportunstc routng meets duty cyclng. In IPSN: Proc. of ACM/IEEE Int. Conference on Informaton Processng n Sensor Networks,. [7] Mchael Buettner, Gary V. Yee, Erc Anderson, and Rchard Han. X- MAC: a Short Preamble MAC Protocol for Duty-Cycled Wreless Sensor Networks. In SenSys: Proc. of the ACM Int. Conference on Embedded Networked Sensor Systems, 6. [8] O. Gnawal, R. Fonseca, K. Jameson, D. Moss, and P. Levs. Collecton Tree Protocol. In SenSys: Proc. of the ACM Int. Conference on Embedded Networked Sensor Systems, 9. [9] V. Handzsk, A. Köpke, A. Wllg, and A. Wolsz. TWIST: a Scalable and Reconfgurable Testbed for Wreless Indoor Experments wth Sensor Networks. In Proc. of the Int. Workshop on Mult-hop Ad Hoc Networks: from Theory to Realty, 6. [] G.W. Allen, P. Sweskowsk, and M.Welsh. MoteLab: a wreless sensor network testbed. In IPSN: Proc. of ACM/IEEE Int. Conference on Informaton Processng n Sensor Networks, 5. [] D. Moss and P. Levs. BoX-MACs: Explotng Physcal and Lnk Layer Boundares n Low-Power Networkng. Techncal Report SING-8-, Stanford, 8. [] A. Dubos-Ferrè, M. Grossglauser, and M. Vetterl. Valuable Detours: Least-Cost Anypath Routng. IEEE/ACM Trans. Netw., 9(),. [] X. Mao, S. Tang, X. Xu, X. L, and H. Ma. Energy-effcent opportunstc routng n wreless sensor networks. IEEE Trans. Parallel and Dstrbuted Systems, (),. [4] F. Ashref, R.H. Kravets, and N.H. Vadya. Explotng Routng Redundancy usng MAC Layer Anycast to Improve Delay n WSN. SIGMOBILE Mob. Comput. Commun. Rev., 4,. [5] P. Basu and C. Chau. Opportunstc Forwardng n Wreless Networks wth Duty Cyclng. In CHANTS: Proc. of the ACM Workshop on Challenged Networks, 8. [6] J. Km, X. Ln, N. Shroff, and P. Snha. Mnmzng Delay and Maxmzng Lfetme for Wreless Sensor Networks wth Anycast. IEEE/ACM Trans. Netw., 8,. [7] K. Srnvasan, M.A Kazandjeva, S. Agarwal, and P. Levs. The β Factor: Measurng Wreless Lnk Burstness. In SenSys: Proc. of the ACM Int. Conference on Embedded Networked Sensor Systems, 8. [8] M. Zorz and R. Rao. Geographc Random Forwardng (GeRaF) for Ad Hoc and Sensor Networks: Multhop Performance. IEEE Trans. on Moble Computng,,. [9] S. Lu, K. Fan, and P. Snha. CMAC: An Energy-Effcent MAC Layer Protocol usng Convergent Packet forwardng for Wreless Sensor Networks. ACM Trans. Sen. Netw., 5, 9. [] Y. Gu and T. He. Data Forwardng n Extremely Low Duty-Cycle Sensor Networks wth Unrelable Communcaton Lnks. In SenSys: Proc. of the ACM Int. Conference on Embedded Networked Sensor Systems, 7.