Multi-hop Coordination in Gossiping-based Wireless Sensor Networks

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1 Mult-hop Coordnaton n Gosspng-based Wreless Sensor Networks Zhlang Chen, Alexander Kuehne, and Anja Klen Communcatons Engneerng Lab, Technsche Unverstät Darmstadt, Germany Emal: {z.chen,a.kuehne,a.klen}@nt.tu-darmstadt.de Abstract Gosspng-based wreless sensor networks provde a communcaton paradgm wth whch all sensors n the network can aggregate messages from the entre network wthout specfyng a routng tree and a snk sensor. Random gosspng provdes a robust aggregaton, however, t also leads to based aggregaton and long aggregaton tme n terms of the number of communcatons between sensors. In a prevous work, we proposed a scheme to reduce and even elmnate the bas of the aggregaton wth a smaller number of communcatons by ntroducng an ndcatng header to each message that s communcated n the network. In ths paper, we extend our work by a mult-hop coordnaton of sensors such that when a sensor wakes up n a random gosspng-based sensor network, t can coordnate the message exchange wth sensors whch are more than one hop away. In order to measure the stablty of the network topology, we ntroduce the reflectng how often a senor fals to perform message exchange wth other sensors. We provde smulaton results to show the reducton of the number of communcatons that are requred for every sensor to aggregate all messages of the entre network. I. INTRODUCTION Wreless sensor networks (WSNs) are data-centrc networks where messages are exchanged and aggregated between sensors [1]. In order to aggregate the messages of all sensors, two typcal technques are appled. In the frst one, a gateway s defned for the sensor network and a routng tree s bult wth the gateway beng the root and all sensors beng ether leaves or branches of the tree [2]. In ths confguraton, the communcaton of the messages has only one drecton,.e., from sensors to the root. The sensors n the routng tree wll receve messages from ther chldren sensors, perform computatons and forward to ther father sensors. The communcaton stops n the network when the gateway receved messages from all ts chldren sensors. The second technque s random gosspng. It specfes a communcaton paradgm n a WSN that sensors are randomly waked up and exchange messages wth ther neghbor sensors,.e., the communcaton of messages s not constraned n one drecton. Wth applcaton examples n [3] and [4], random gosspng s used for all sensors to acheve consensus of ther measurements. In [5], random gosspng s appled to dynamc rado access n networks. In ths technque, all sensors are aggregatng messages from the sensors of the entre network,.e., the aggregated messages can actually be retreved from any sensor n the network. Random gosspng provdes a more robust communcaton method n WSNs aganst lnk falure Ths work was performed wthn the LOEWE Prorty Program Cocoon ( supported by the LOEWE research ntatve of the state of Hesse/Germany. and topology changes than routng because no gateway s specfed and no communcaton path shall be mantaned from each sensor to the gateway [3]. In our work, we combne the robust random gosspng algorthm ntroduced n [3] and [4] and the routng based message communcatons n [2] such that every sensor n the network wll aggregate messages from the entre network. We extend the aggregaton n WSNs from calculatng consensus to dvsble functons whch nclude some most common functons we are nterested n, e.g., summaton, averagng, max, mn, hstogram, etc.[6]. In[7], we proposed two methods whch are jontly used to reduce the aggregaton bas and the aggregaton tme n gosspng-based WSNs. The property of dvsble functons s explored for cancellng the bas of the aggregaton by usng the messages stored n the buffer of sensors. We ntroduced an ndcatng header to each message communcated n the network ndcatng whether the data of a certan sensor has been aggregated n the current message. Two strateges how a sensor can exchange messages wth ts neghbor sensors have been compared as well. The goal of ths paper s to further decrease the number of communcatons that are requred for all sensors to aggregate all messages n the network n random gosspng-based WSNs by extendng the schemes we proposed n [7]. Ths shall be acheved by enablng the coordnaton of message exchange wth sensors whch are more than one hop away. Mult-hop n random gosspng was prevously dscussed n [8] and [9] n consensus problems. In [8], the averagng s performed along a path whch s randomly bult towards another random target sensor n the network when a sensor randomly wakes up. In [9], a gosspng algorthm for consensus s preformed n a grd sensor network. A sensor can gossp wth a sensor that s wthn several hops and determned by the gradent of the measurements at sensors. In[8] and[9], only a consensus problem s dscussed, whereas our work extends the aggregaton functon n WSNs to all dvsble functons. Furthermore, the possblty of bas reducton s not consdered n [8] and [9]. In ths paper, we contnue our prevous work n [7]. The mult-hop random gosspng based on the ndcatng headers of the messages n the network for calculatng dvsble functons s dscussed. Furthermore, we consder the possblty that a sensor fals to communcate wth other sensors and analyze the mpact on the aggregaton tme. The remander of ths paper s organzed as follows. In Secton II, we gve the system model and the notatons. In Secton III, we brefly revew the content of our prevous work. In Secton IV, we ntroduce the scheme of the mult-

2 hop coordnaton. Secton V shows the performance results and Secton VI concludes ths paper. II. SYSTEM MODEL AND NOTATIONS Throughout ths paper, N denotes the number of sensors whch are randomly deployed. The set of sensors s denoted by V = {v 1,v 2,,v N }. The exstence of the connecton between sensors v and v j s solely determned by ther dstance whch s denoted by d j. Let d c be a threshold such that for any two sensors v V and v j V the connecton between v and v j exsts when d j d c. In order to guarantee the connectvty of the network, d c s chosen n such a way that the Laplacan matrx of the network has a postve second smallest egenvalue [10]. N denotes the set of neghbor sensors of sensor v,.e., the set of sensors havng connectons to v. In ths paper, we use the term data to ndcate the nformaton generated at sensors by measurement. Sensors perform computatons to the data that they generated themselves and that they receved from other sensors. The term message ndcates the bt sequence output from computatons,.e., there may be data from several sensors n one message. The messages wll be transmtted and receved by sensors. We use the term aggregaton of messages to ndcate that the computatons are performed to the data n the messages. The term data s also referred to as parameters of functons n the context of dvsble functons. III. BIAS OF GOSSIPING-BASED AGGREGATION AND INDICATING HEADERS In ths secton, we revew the schemes that we ntroduced n [7] to reduce aggregaton bas and tme n gosspng-based WSNs as far as needed to understand the rest of the paper. We base our scheme of reducng the bas of aggregaton on dvsble functons. Let s denote the data generated at sensor v. An applcaton n WSNs correspondsto a set F of dvsble functons [6]. Each dvsble functon f l F has l parameters and the functons f 1,f 2,f 3, form the set F. Let S, = 1,2,,L denote dsjont non-emptysets whose elements are chosenfromtheparametersets = {s 1,s 2,,s K },.e.,s S, whch corresponds to the set of measured data from all sensors n the network. Let vector s S denote the parameters gven n set S and vector s denote all parameters n S. The dvsble functon gves a type of functon n WSNs whch can be calculated n a dvde-and-conquer fashon [6]. Ths means that for the parameter set S and any partton Π(S) = {S 1,S 2,,S L } of t, there s a functon g Π(S) such that f K (s S ) = g Π(S) (f l1 (s S1 ),f l2 (s S2 ), f ll (s SL )), (1) where l, = 1,,L denotes the number of parameters n subset S, = 1,,L. In random gosspng, sensors wake up themselves and are waked up by ther neghbor sensors randomly. Due to the lack of the dentty of the data n the messages, one cannot tell whch data has been ncluded n the computaton. In consequence, the output message may contan a message from a sensor several tmes or does not contan the message from a sensor at all. We call such aggregaton as based aggregaton. For two sensors v C V and v R V, ther correspondng parametersetsare S C ands R, respectvely.functonsf lc F and f lr F are ther correspondng dvsble functons, respectvely. The respectve parameters n S C and S R are s SR are s SR. If S C S R φ, the aggregaton f (lc+l R)(s SC,s SR ) = g Π({SC,SR}) (f lc (s SC ),f lr (s SR )) (2) s based,.e., there are parameters whch have been aggregated unequally n the output. In order to reduce the bas n the results of (2), n [7] we defne the bas-elmnaton set Ψ CR = {S 1,S 2,,S ψ } of parameter set S C S R, where ψ s the number of parameter sets n Ψ CR. We use the operaton whch apples ether the unon or the ntersecton to the parameter set n the set Ψ CR. The bas-elmnaton set fulflls ψ =1 S = S C S R = S B. (3) We defne the parameter set S A = S C S B. The aggregaton f lc (s SC ) = g Π({SA,SB}) (f la (s SA ),f lb (s SB )) (4) s followed by a functon g Π 1 ({S C,S B}) such that f la (s SA ) = g Π 1 ({S C,S B}) (f lc (s SC ),f lb (s SB )). (5) The unbased aggregaton of the parameters n S C and S R s therefore achevable by f (la+l R)(s SA,s SR ) = g Π({SA,SR}) (f la (s SA ),f lr (s SR )). (6) In [7], we also ntroduce the concept of an ndcatng header whch s a fxed length bt sequence pared wth each message that s generated and computed at sensors. For a WSN wth N sensors, the ndcatng header of an aggregated message s an N-bt message feld. The ndcatng header of the message of sensor v s denoted by I. If the current message of sensor v has aggregated the data generated at sensor v j,j = 1,2, N, the j-th bt n I, I (j) s marked 1, otherwse 0. Therefore, the ndcatng header tells only whether the correspondng data has been aggregated wthout showng ts duplcaton. We use the nvertble functon Θ to map the parameter set S to the ndcatng header I wth I = Θ(S ) and S = Θ 1 (I ). When two sensors v and v j wake up to exchange messages, they frstly exchange ther ndcatng headers of ther messages and decde whether a transmsson of the message on a drecton,.e., v j to v or v to v j s needed [7]. The concept of ndcatng headers can be used to reduce the aggregaton bas n combnaton wth the property of dvsble functons shown from (2) to (6). The realzaton s made through memorzng by consderng the fact that sensors have buffers to store prevous receved messages. When sensor v receves a message from ts neghbor sensor v j, t uses the ndcatng header I j of the receved message to check the bas of the aggregaton, S B = S S j = Θ 1 (I ) Θ 1 (I j ). If S B s non-empty, sensor v uses the messages n ts buffer to fnd the bas-elmnaton set Ψ j of S B. If sensor v cannot fnd the bas-elmnaton set Ψ j, sensor v wll then neglect the bas and perform a based aggregaton. In ths case, the bas aggregaton wll be propagated when sensor v performs further communcatons wth other sensors.

3 IV. MULTI-HOP COORDINATION In ths secton, we extend our work n [7] by consderng a mult-hop coordnaton n the message exchange process. Our scheme of mult-hop coordnaton n gosspng-based WSNs s that when a sensor wakes up t can exchange messages wth sensors whch are several hops away. Multhop coordnaton can extend the range of sensors wth whch the awake sensor exchanges ther messages. The motvaton of such mult-hop coordnaton s to ncrease the aggregaton effcency.fromthepontofvewofonesensornthenetwork, t s most effcent to set ths sensor as the root and buld a routng tree to connect all sensors n the network when t s about to aggregate all messages n the network. For a sensor network wth N sensors, when a tree s bult wth sensor v beng the root, t requres N communcatons of messages untl sensor v aggregates all messages. Because the wake-up s random and the communcatng sensor pars are not scheduled, the random gosspng cannot guarantee such small number of communcatonsforsensorv, evenwththe ndcatngheaders we proposedn [7] who can reduce the numberof unnecessary communcatons. However, as a communcaton paradgm wth less topology and stablty requrements than buldng a routng tree, random gosspng benefts from ts robustness and ts flexblty. The mult-hop coordnaton combnes the capablty of a connected network for buldng a tree rooted at any sensor wth the flexblty of a gosspng based communcaton paradgm. Ths natural extenson of gosspng-based WSN s based on the fact that a sensor n a sensor network always plays two roles n terms of communcaton: a recever and a transmtter. For a sensor v V n a connected WSN, the depth δ j () of another sensor v j V wth respect to sensor v s defned as the mnmum number of hops wth whch v can send ts message to v j and vce versa. In the followng, we defne the coordnaton depth c of sensor v as the maxmum depth that sensor v can coordnate message exchanges wth other sensors. From ths, t followsthat sensor v can exchange message wth all sensors v j whose depth δ j () s smaller than c whentwakesupforcommuncatons.wthn l denotngthe set of sensors whose depth wth respect to v s l, all sensors n c l=1 Nl are the possble sensors who can exchange messages wth v. Due to the falure of communcatons, the falure of the wake-ups, etc., the query nformaton may not be receved or responded by a sensor. We model the rate of falure wth a parameter whch s referred to as r of sensor v whch ndcates the probablty that sensor v fals to receve query nformaton or to respond to another sensor n the network. In our prevous work [7], we propose two message exchange strateges when a sensor wakes up. In the case that a sensor exchanges message wth only one sensor wthn ts neghbor sensors, we call the sensor a humble sensor. In the case that a sensor exchanges ts messages wth all the sensors wthn ts neghborhood, we call the sensor a greedy sensor. When the mult-hop coordnaton s enabled n the network, we use the term humble sensor to ndcate that the sensor v wll coordnate a sngle path wth length c. For the greedy sensor of v, a tree, whose root s sensor v, s constructed among sensors n c l=1 Nl. In the case when the humble sensor strategy s appled n the network,let P denotethe path that s ntatedby sensor v wth the maxmum possble depth beng c and let P (0) = v and P (l) ndcate the root sensor and the sensor on the l-th hop of ths path, respectvely. The awake sensor v broadcasts a query message to all ts neghbor sensors n N 1. In ths query message, the nformaton s contaned that sensor v asks all sensors n N 1 for ther ndcatng headers and the nformaton tellng sensors n N 1 that a path s gong to be constructed. Sensors n N 1 receve ths query nformaton and respond to t wth r j,v j N 1. We denote the set of sensors n N 1 who successfully receve and respond to ths requrement from v by P(N 1). Sensors v j P(N 1) wll sendbacktherndcatngheadersi j.sensorv wllchoosethe sensor whch sends back ts ndcatng header and whch results n the greatest b-drectonal message dfferences to be ts next hop. The chosen sensor broadcasts the query nformaton to N 2 and chooses ts next hop. Such process contnues untl ether the maxmum coordnaton depth c s reached or no more sensors respond to jon the path when c has not been reached. In general, the crteron to choose the sensor for the l-th hop s gven by P (l) = arg max v j P(N l ) N P (l 1) I P(l 1)XOR b I j, (7) where the operatonxor b performsthe XOR-operatonto the bt-sequencen I and I j and gves the number of postve bts n the output. The algorthm of constructng path P s gven n Fgure 1. 1: P (0) = v ; 2: l = 1; 3: whle l c do 4: P (l 1) broadcasts query messages to sensors n N l 5: Determne the set P(N l ) 6: Determne P (l) wth (7) 7: l = l +1 8: end whle Fg. 1. Algorthm of constructng a path ntated by sensor v The actually acheved path depth s denoted by c α, where c α c. We denote v as the header of path P and P(c α ) as the tal sensor, respectvely. Once the path P s constructed, the transmsson of the messages starts from the tal sensor. P(c α ) transmts ts message to P(cα 1), sensor P(cα 1) aggregates t wth ts own message and the combned message s transmttedto P(c α 2). Ths procedures doneuntl sensor v has the aggregated message whose ndcatng header s I = Θ ( c l=0 Θ 1( I P(l))). (8) Afterwards, sensor v starts to transmt ts message along the path P towards the tal sensor untl every sensor v j P updates the aggregated message wth ndcatng header I j = I. In the case that sensors n the network are greedy sensors, each sensor v V wll attempt to coordnate a tree whose root s v and the maxmum depth s c. Let T be the tree rooted at sensor v. T (l) denotes the set of sensors whose

4 depth wth respect to sensor v s l and T (0) = v. The father sensor of sensor v j n the tree T s denoted by T f (v j). When sensor v wakes up,t broadcastsaquerymessage wth ts own ndcatng header I. Sensors n N 1 receve the query message and respond to t wth r j, where v j N 1. The set of sensors who successfully receve and respond to the query s denoted by P(N 1) and hence T (1) = P(N 1 ). Each sensor n T (1) contnues ths tree constructon by forwardng the query message wth ts ndcatng header. If a sensor v j whose depth wth respect to v s l,.e., v j P(N l),l = 2,,c, receves query messages and ndcatng headers from several sensors, t decdes tself whch sensor shall be ts father sensor T f (v j). Let N T j = N j P(N l 1 ) denote the set of sensors from whch sensor v j receves ndcatng messages. The crteron of sensor v j to choose ts father sensor s gven as T f (v j) = arg max I k XOR b I j. (9) v k N T j The algorthm of constructng the tree T s gven n Fgure 2 1: T (0) = v ; 2: l = 1; 3: whle l c do 4: for v l T (l 1) do 5: v l broadcasts query message to sensors n N l+1 6: Determne the set P(N l+1 N l ) 7: end for 8: for v m vl T (l 1)P(N l+1 9: Determne N T m 10: Determne T f 11: end for 12: l = l+1 13: end whle (vj) wth (9) N l ) do N l Fg. 2. Algorthm of constructng a tree ntated by sensor v The actually acheved tree depth s denoted by c β, where c β c. The communcaton n T stars wth sensors n T (c β ) transmttng ther messages to ther father sensors n T (c β 1). After a sensor n T (c β 1) receves messages from all ts chldren, t forwards the aggregated messages to ts father sensors. Ths procedure fnshes untl sensor v receves messages from all ts chldren. Sensor v wll have an aggregated message whose ndcatng header s I = Θ ( vj T Θ 1 (I j ) ). (10) Afterwards, sensor v broadcasts ts newly aggregated messages whch contans messages from all sensors n T to T (1) and sensors n T (1) forward ths messages to ther chldren sensors. Ths procedure stops when all sensors n T have receved the aggregated messages from v. Every sensor v j T wll now have an updated message wth ndcatng header I j = I. Note that for both humble and greedy cases we assume that the sensors only suffer from falures n the phase of constructng paths or trees, respectvely. V. PERFORMANCE RESULTS In ths secton, we demonstrate the performance of the schemeweproposednsectoniv.inthesmulatons,n = 30 sensors are randomly deployed n a two-dmensonal squared area. acheved coordnaton depth maxmum coordnaton depth acheved coordnaton depth maxmum coordnaton depth Fg. 3. Maxmum coordnaton depth versus acheved coordnaton depth wth. Left: humble sensors, rght: greedy sensors. Along the drecton of the arrow, r = 0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9 In Fg. 3, we depct the relaton between the maxmum coordnatondepthofallsensorsnthenetwork,.e.,c,v V and the actually acheved coordnaton depth n the network under dfferent s of sensors. As shown n the fgure, wth both humble and greedy sensor strateges, t s unlkely that the maxmum coordnaton depth can be acheved when the ncreases. In comparson, the greedy sensor strategy results n a larger acheved coordnaton depth due to the fact that all neghbor sensors who decde not to reject the requrement wll jon the tree. number of message communcatons Fg. 4. Average number of message communcatons requred n the network untl the aggregaton s fnshed for humble sensors. In Fg. 4, we demonstrate how many message communcatons n the network have been performed untl the aggregaton s fnshed when all sensors are humble sensors,.e., a path s constructed when a sensor wakes up. As shown n the fgure, when the ncreases, more message communcatons are needed due to the falure of the communcaton. Meanwhle, ncreasng the maxmum coordnaton depth decreases the number of requred message communcatons. A sgnfcant reducton of the number of message communcatons can be wtnessed by just ncreasng the coordnaton depth from c = 1 whch corresponds to the scheme n [7] to c = 2. For coordnaton depths c > 3, the addtonal reducton by further ncreasng the maxmum coordnaton depth s small. When sensors n the network are greedy sensors,.e., a tree

5 number of message communcatons number of equvalent communcatons Fg. 5. Average number of message communcatons requred n the network untl the aggregaton s fnshed for greedy sensors. Fg. 7. Average number of equvalent communcatons requred n the network untl the aggregaton s fnshed for greedy sensors. s constructed when a sensor wakes up, the performance of the number of message communcatons s shown n Fg. 5. In comparson to humble sensors, less message communcatons are needed wth the greedy sensor strategy. In order to take nto consderaton the communcatons that have to be spent to exchange ndcatng headers, we assume that the ndcatng header requres 10% of the message length. We defne equvalent communcatons as the sum of the number of message communcatons and 0.1 tmes the number of communcatons spent for ndcatng headers. The performance of the humble sensor case s shown n Fg. 6 and of the greedy sensor case s shown n Fg. 7, respectvely. As shown n Fg. 6, wth the humble sensor strategy, a larger coordnaton depth stll results n a lower number of communcatons. However, wth the greedy sensor strategy, such beneft by ncreasng coordnaton depth can only be acheved wth small r < 0.3. As seen n Fg. 7, wth a larger, the number of equvalent communcatons for a larger coordnaton depth s even worse compared to the case wth smaller coordnaton depths. number of equvalent communcatons Fg. 6. Average number of equvalent communcatons requred n the network untl the aggregaton s fnshed for humble sensors. VI. CONCLUSION In ths paper, we extend our prevous work n gosspngbased wreless sensor networks. We ntroduce a mult-hop coordnaton to sensors when sensors randomly wake up to exchange messages wth ther neghbor sensors. To take nto account the falure of communcatons between sensors, a of sensors s also proposed. Smulaton results show the reducton of the number of communcatons needed for performng aggregatons n the whole network wth the proposed schemes. REFERENCES [1] I. F. Akyldz, W. Su, Y. Sankarasubramanam, and E. Cayrc, A survey on sensor networks, IEEE Communcatons Magazne, vol. 40, no. 8, pp , Aug. 2. [2] R. Rajagopalan and P. K. Varshney, Data-aggregaton technques n sensor networks: A survey, IEEE Communcatons Survey and Tutorals, vol. 8, no. 4, pp , 6. [3] S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, Randomzed gossp algorthms, IEEE Transactons on Informaton Theory, vol. 52, no. 6, pp , 6. [4] T. C. Aysal, M. E. Yldz, A. D. Sarwate, and A. Scaglone, Broadcast gossp algorthms for consensus, IEEE Transactons on Sgnal Processng, vol. 57, no. 7, pp , 9. [5] P. D Lorenzo, S. Barbarossa, and A. Sayed, Bo-nspred swarmng for dynamc rado access based on dffuson adaptaton, n Proc. 20th European Sgnal Processng Conference, [6] A. Grdhar and P. R. Kumar, Computng and communcatng functons over sensor networks, IEEE Journal on Selected Areas n Communcatons, vol. 23, no. 4, pp , 5. [7] Z. Chen, A. Kuehne, and A. Klen, Reducng aggregaton bas and tme n gosspng-based wreless sensor networks, n Proc. 14th IEEE Internatonal Workshop on Sgnal Processng Advances n Wreless Communcatons, [8] F. Benezt, A. G. Dmaks, and P. Thran, Order-optmal consensus through randomzed path averagng, IEEE Transactons on Informaton Theory, vol. 56, no. 10, pp , [9] D. Ustebay, B. Oreshkn, M. Coates, and M. Rabbat, Mult-hop greedy gossp wth eavesdroppng, n Proc. Internatonal Conference on Informaton Fuson, 9. [10] S. Sardelltt, S. Barbarossa, and A. Swam, Optmal topology control and power allocaton for mnmum energy consumpton n consensus networks, IEEE Transactons on Sgnal Processng, vol. 60, no. 1, pp , 2012.

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