Quantifying Application Communication Reliability of Wireless Sensor Networks

Transcription

1 Inernaional Journal of Performabiliy ngineering Vol. 4, No., January 008, pp RAMS Consulans Prined in India Quanifying Applicaion Communicaion Reliabiliy of Wireless Sensor Neworks AKHILSH SHRSTHA and LIUDONG XING * lecrical and Compuer ngineering Deparmen, Universiy of Massachuses Darmouh 85 Old Wespor Road, Norh Darmouh, MA 0747, USA (Received on June 8, 007) Absrac: In his paper, we consider he problem of modeling and analyzing he applicaion communicaion reliabiliy of wireless sensor neworks (WSN) wih differen opologies, including sar, ree, mesh, and hierarchical clusering. We propose reliabiliy measures ha inegrae he convenional conneciviy-based nework reliabiliy wih he sensing coverage measure of WSN. We apply a reduced ordered binary decision diagram (ROBDD) based progressive approach for evaluaing he proposed coverage-oriened applicaion communicaion reliabiliy of WSN. Our sudy will provide useful insighs for he WSN designers in choosing he appropriae nework opology. We illusrae he basics and advanages of our approach by working hrough he analysis of an example WSN. Keywords: applicaion communicaion, coverage, reduced ordered binary decision diagram, reliabiliy, wireless sensor nework. Inroducion Due o recen advances in micro-elecro-mechanical-sysems (MMS) and wireless echnology, wireless sensor neworks (WSN + ) have araced remendous research ineres in commercial, indusrial, and academic areas o build an environmenally aware inelligen nework of mulimodal sensors. WSN offer a remarkable poenial o bridge he gap beween he physical world of in-siu sensors and he virual world of informaion services, hereby enabling us o assimilae a deep and broad undersanding and conrol of he environmen. However, before WSN is ruly esablished as he environmen-aware ubiquious sensing, neworking, and compuing infrasrucure, i is criical ha hese smar sensors deliver he promised sensing coverage and have reliable and dependable communicaion. Coverage analysis and reliabiliy evaluaion are, herefore, imporan asks before he successful deploymen of he WSN. Reference [] gives differen axonomy o classify sensor neworks and proposes ha communicaion wihin WSN can be concepually classified ino wo caegories: applicaion and infrasrucure. Infrasrucure communicaion relaes o he delivery of conrol, configuraion, and mainenance daa (e.g. query, pah discovery, various policies like degree of coverage) beween base saion and sensor nodes. Applicaion communicaion relaes o he acquisiion of sensed daa abou he phenomena and reliable delivery of hese observed daa * Corresponding auhor s ldxing@ieee.org. + The singular and plural of an acronym are always spelled he same. 43

2 44 A. Shresha and L. Xing from sensor nodes o he sink node. Therefore, in addiion o he conneciviy requiremen, applicaion communicaion requires ha WSN mainain he desired sensing coverage ha indicaes he qualiy-of-service (QoS) of WSN. Thus, he measure for describing he applicaion communicaion reliabiliy (ACR) should inegrae he conneciviy reliabiliy wih he coverage QoS measure of WSN. In our earlier paper [], we proposed measures and mehodologies suiable for infrasrucure communicaion reliabiliy (ICR) of WSN. In his paper, we sudy he ACR of WSN wih differen opologies (described in Secion ). The coverage concep and he conneciviy-based nework reliabiliy are boh widely researched opics. Bu only lile work [3] has sudied he wo conceps in a unified framework. And no exising work, o he bes of our knowledge, has provided quaniaive measures inegraing he wo noions for he reliabiliy analysis of WSN. Therefore, in his paper, we propose new ACR measures ha inegrae he convenional conneciviy reliabiliy wih he sensing coverage of WSN. The new measures will provide a more accurae represenaion of he WSN reliabiliy behavior han he exising measures for applicaion communicaion paradigm. We presen reliabiliy expressions for a few prominen WSN opologies, including sar, ree, mesh, and hierarchical clusering. We also propose an efficien approach for evaluaing he proposed ACR measures of WSN in an accurae manner. The remainder of he paper is organized as follows: Secion presens a brief background on differen opologies of WSN. Secion 3 gives he moivaion of his research, he problem saemen, and assumpions. Secion 4 describes an illusraive example WSN. Secion 5 presens he general ACR measure and specific reliabiliy expressions for WSN wih differen opologies. Secion 6 presens he proposed progressive reliabiliy analysis approach. Secion 7 gives an illusraion of he proposed measures and approach hrough he analysis of he example WSN. The las secion presens our conclusions and fuure work.. Background WSN consis of numerous small and inexpensive sensor nodes wih embedded inelligence. The limied power, memory, processing, sensing, and communicaion capaciy of sensor nodes necessiae he dense deploymen of sensor nodes in he area of observaion. Moreover, due o hese resource consrains and operaion in unaended and harsh environmens, sensor nodes are prone o failures. Therefore, a large number of redundan sensor nodes are usually deployed o achieve faul olerance and required sensing coverage. Redundancy also faciliaes he energy preservaion hrough careful duy-cycle adjusmen of sensor nodes [4]. The lack of exising energy and communicaion infrasrucure in WSN demands ad hoc power-aware muli-hop rouing operaions, collaboraive compuing, and efficien mainenance of dynamic WSN opology wihou any cenralized adminisraion. The deployed nodes auonomously organize hemselves ino a communicaion framework. The communicaion opology affecs he componen conneciviy and hereby various performance merics. Presenly, sar, ree, mesh and hierarchical clusering opologies have emerged as he choice opologies for WSN []. Sar Topology In sar opology, all he peripheral nodes are conneced o a cenral node via direc, poin-o-poin links, i.e. all he nodes in he WSN are wihin a single hop from he cenral node. The cenral node, being he hub, is logically (and/or physically) a he cener of he nework. The cenral node can be eiher he base saion iself or a gaeway node ha is in

3 Quanifying Applicaion Communicaion Reliabiliy of Wireless Sensor Neworks 45 direc communicaion wih he base saion. Tree Topology A naural and logical exension of he sar opology is he ree opology where he sink node is he roo and nodes a differen levels in hierarchy are conneced via direc links. Mesh Topology In mesh opology, each sensor node no only sends and receives is own message bu also funcions as a rouer o relay messages for is neighbors hrough he nework. Mesh opology faciliaes muli-hop communicaion and muliple communicaion pahs from sensor nodes o he base saion. Hierarchical Clusering Topology In he hierarchical clusering opology [5], all nodes in he WSN are joined a he lowes level. The sensors use heir local neighborhood informaion o form a se of clusers and use some negoiaion mechanisms o elec a cluser head (CH) for each cluser. The CH elecion process can be based on various parameers such as available energy resources, proximiy o he base saion, and number of neighbors. The CH manages he clusers by assigning duy cycles o sensor nodes and coordinaing inra- and iner-cluser ransmissions. Usually, i is he CH ha performs daa aggregaion by processing and filering he possibly redundan daa received from is member nodes [6]. In hierarchical clusering opology, he CH a he lowes level are arranged ino clusers in a higher level, and a CH is assigned for each cluser a his level. The process is repeaed unil he highes level in he hierarchy is reached. The number of levels may depend on various crieria including coverage requiremen, deploymen region, node densiy, and ransceiver and sensing range. The hierarchical clusering opology mainains a ree rooed a he sink node, wih a hierarchy of CH as inernal nodes and sensor nodes as leaf nodes of he ree, for nework addressing and organizaion. Whenever a sensor node needs o send a message o he sink or anoher sensor node, i sends he message o is CH along a muli-hop roue. The message is roued progressively o he immediaely higher-level CH unil i reaches he CH ha is he common ancesor of boh he source and desinaion nodes and herefore has he rouing informaion abou he desinaion node. The message is hen roued progressively o lowerlevel CH unil i reaches he desinaion node. Noe ha unlike he ree opology, he hierarchical clusering opology sill mainains he muli-hop mesh rouing for acual daa communicaion, i.e. each pah from a lower level o a higher level and vice versa is acually a muli-hop roue. 3. Moivaion and Problem Saemen I has been shown ha he complexiy of he nework reliabiliy analysis algorihms increases sharply wih he increasing number of nodes [7]. Therefore, he radiional analyical nework reliabiliy analysis approaches, suiable for neworks of moderae size (0~00 nodes), canno be, a leas direcly, applied o WSN consising of hundreds o housands of nodes. Besides he inadequacy of he exising analysis approaches, radiional nework reliabiliy measures based solely on conneciviy is no adequae for describing he applicaion communicaion behavior of WSN. In WSN, reliable monioring of he phenomenon depends on boh he sensing coverage and he communicaion of he colleced daa provided by he subse of sensors in he proximiy of he phenomenon o he observer. Therefore he reliabiliy in WSN incorporaes he reliabiliy of boh daa acquisiion and daa disribuion processes. The daa disribuion behavior can be modeled appropriaely by he radiional conneciviy-

4 46 A. Shresha and L. Xing based reliabiliy measures. Daa acquisiion aspec of WSN, however, needs o be modeled by he coverage concep [4]. To he bes of our knowledge, only lile work has been done in modeling and analyzing he reliabiliy of WSN, and he exising approach employs a measure ha is similar o he radiional end-o-end erminal-pair reliabiliy measure based solely on he conneciviy [8]. In his paper, we consider he problem of evaluaing he applicaion communicaion reliabiliy of WSN by proposing new reliabiliy measures ha inegrae he convenional conneciviy reliabiliy wih he sensing coverage of he WSN, and by proposing efficien approaches o compuing he proposed coverage-oriened reliabiliy of WSN wih various opologies. Due o a large variey of WSN applicaions, coverage is subjec o a wide range of inerpreaion. For example, coverage can be defined in erms of spaial or emporal observabiliy. For our sudy, we consider area (or poin) coverage where sensing coverage of a region of ineres is defined as he abiliy o monior every poin in he region by a leas one sensor node [3], [4]. In paricular, we consider a more general concep of coverage, called K- coverage, which requires every poin o be covered by a leas K sensors [4]. We define K- coverage-se as a se of sensor nodes such ha all he poins in he sensed field are covered by a leas K nodes. The degree of sensing coverage required by a WSN depends on he specific applicaion requiremens. Therefore, he value of K, which is a leas one, indicaes he fauloleran capabiliy and QoS of WSN. In his work, we assume ha he nodes providing coverage are saionary. However, as sudied in [9], mobile nodes offer beer coverage han saionary nodes; albei he link reliabiliy may deeriorae. Our fuure work will invesigae he effecs of node mobiliy and oher coverage conceps on ACR. We make he following assumpions in our analysis: The conneciviy aspec of he WSN is modeled by an undireced probabilisic graph G (V, ) [7]. Boh links and nodes fail s-independenly wih known probabiliies. The failure probabiliy for each link or node is given as a fixed probabiliy for a given mission ime or in erms of a lifeime disribuion. All he sensor nodes are saionary during he mission ime. In he case of WSN organized using hierarchical clusering opology, each sensor node belongs o a single cluser a any given ime. The accurae reliabiliy analysis of WSN heavily depends on he realisic esimae of he failure parameers or disribuions of is componens (wireless links and sensor nodes). In paricular, esimaion of wireless link failure parameers is a challenging ask because lowpower radio communicaion is highly variable due o exernal sources of inerference in he specrum, conenion wih oher nodes, muli-pah effecs, obsrucions, fading, and oher changes in he RF condiions, as well as node mobiliy [0]. Various sophisicaed saisical models have been proposed o characerize he failure parameers (e.g., iner-error inervals) of wireless channels, including he simple sraegy like he characerizaion of conneciviy beween nodes a a poin in ime using he probabiliy of successful packe ransmission [0]. However, mos of he exising approaches, primarily based on coninuous ime Markov chains, for link reliabiliy esimaion use only a wo-hop scenario due o he complexiy of analyical models for muli-hop scenarios []. In his paper, we assume componen failure parameers are given as inpu parameers of he problem and we only focus on he sysem-level reliabiliy analysis. Follow-up research

5 Quanifying Applicaion Communicaion Reliabiliy of Wireless Sensor Neworks 47 will include invesigaion of mehods for componen failure parameer esimaion as well as sensiiviy of WSN reliabiliy o changes in he inpu componen parameer values. 4. Illusraive xamples Figure (a) shows he deploymen of 8 sensor nodes in a recangular sensor field and he posiion of he base saion in our example WSN. Figures (b), (c), and (d) show he mesh, ree, and hierarchical clusering configuraions respecively for he same deploymen in Figure (a). Noe ha each level in he ree configuraion in Figure (c) has a sar opology Sensor Node Sensor Node Base Saion 5 4 (a) Deploymen of Sensor Nodes (b) Mesh Topology Base Saion Roo Node Level- Cluser Head Paren Node Ordinary Sensor Node CH Level-0 Cluser Head Level-0 Gaeway Node Level- Gaeway Node Ordinary Sensor Node CH3 CH (c) Tree Topology Base Saion Base Saion 3 (d) Hierarchical Clusering Topology Fig. : Illusraive WSN In he hierarchical clusering WSN (Figure (d)), nodes ha are conneced o nodes in neighboring clusers are referred o as gaeway nodes. And, gaeway nodes ha connec wo level-i clusers are referred o as level-i gaeway nodes. The cluser head of each cluser i is idenified by he node labeled CH i. These cluser heads represen he lowes level-0 cluser heads in our hierarchy. The single base saion represens he sink node. In level- of he hierarchy (and highes level for his example), clusers,, and 3 are organized ino a single cluser, and CH is assigned as he level- cluser head. In he following secions, we use his example for illusraing he analysis of ACR for WSN wih differen opologies. 5. Definiions of Applicaion Communicaion Reliabiliy (ACR) Reliabiliy is generally defined as he probabiliy ha he sysem will perform is inended funcion under saed condiions for a specified period of ime []. In paricular, he applicaion communicaion reliabiliy (ACR) of WSN is defined as he probabiliy ha every

6 48 A. Shresha and L. Xing poin in he sensed field can be observed by a leas K sensor nodes (i.e., he field of ineres is K-covered) and here exiss an operaional pah from he subse of nodes ha provides K- coverage o he sink node [3]. The value of K should be configurable based on he specific applicaion QoS requiremens. Nex we elaborae he above definiions of ACR for differen opologies of WSN. The following noaions are used: represens he even ha here exiss an operaional communicaion pah beween a pair of nodes, and k represens he even ha here exiss an operaional communicaion pah beween each pair of he k nodes. Also, we assume sensor nodes ha provide K-coverage for he area of ineres consiue he subse U i here. If here exis n such coverage ses, hen each subse U i (i =,,, n), which may conain differen number of nodes U i, guaranees K-coverage. In passing, if here are n K-coverage-ses, hen he lifeime of he nework is increased by a fracion of n. Sar The ACR of sar opology is he probabiliy ha here exiss a subse U i ha provides K-coverage such ha all he nodes in U i can communicae direcly wih he sink node. U ACR sar = Pr(K - coverage) = Pr U (sink o node i) () i Tree The ACR of ree opology is he probabiliy ha here exiss a subse U i ha provides K-coverage such ha all he nodes in U i can communicae direcly wih is paren node, which in urn can communicae direcly wih heir paren nodes, and so on, ill lasly he highes level ancesors of nodes in U i can communicae direcly wih he sink node. Le PN (k) denoe he level-k paren node of nodes in U i, denoe he highes hierarchical level in he archiecure, and H k denoe he se of paren nodes above he subses of nodes of ineres a paren level k, 0 k, hen: ACR ree = Pr U, j - m, n 0 U (sink o PN (PN (PN ( ) ( ) () i) i o PN ( -) m o PN (paren of node i o node i) j) n) * If we assume ha each of he coverage ses U i conains he subses of nodes ha are hierarchically below he same se of PN, hen each of he erminal-pair evens in () (excep he las even) are idenical for each of he U i. Therefore, () can be represened as (3) below: ACR ree = Pr, j - m U (sink o PN, n (PN (PN ( ) ( ) () i) i o PN ( -) m o PN j) n) * 0 ( (PN of node i o node i) ) U quaion (3) can be represened by (4) provided ha we accoun for he failure funcion of each PN (k) only once. () (3)

7 Quanifying Applicaion Communicaion Reliabiliy of Wireless Sensor Neworks 49 ACR ree = Pr (sink o PN () i) *, j Pr - (PN () i o PN (-) j) *...* m, n Pr (PN () m o PN n) * Pr(K-coverage probabiliy), (4) where H 0 Pr(K-coverage) = Pr U i U (PN of node i o nodei) (5) Mesh The ACR of mesh opology is he probabiliy ha here exiss a subse U i ha provides K-coverage such ha all he nodes in U i can communicae wih he sink node. ACR mesh = Pr(K - coverage) = Pr (sink and nodes in he subse U ) k U, (6) k = U sink node Hierarchical Clusering In general, he area of ineres may cover a subse of clusers. The ACR of a WSN wih hierarchical clusering opology is he probabiliy ha here exiss a subse U i ha provides K-coverage such ha here exiss operaional pahs from all he nodes in U i o he level-0 CH, from hese level-0 CH o he respecive paren level- CH and so on up o he op level CH, and from hese op level CH o he sink node. Le CH (k) denoe he level-k CH, denoe he highes hierarchical level in he archiecure, R denoe he se of clusers ha conain he nodes of ineres in U i, H 0 denoe he se of CH for clusers in R, and H k denoe he se of CH ha is hierarchically above R a paren level k, k, hen: ACR cluser = Pr U, j - m, n 0 w R ( ) (sink o CH i) ( ) ( -) (CH i o CH j) (7) () (CH m o CH n) * k (CH of cluser w nodes of U in cluser w) If we assume ha each of he coverage ses U i conains he subses of nodes ha are conained in he same se of clusers R, hen each of he erminal-pair evens in (7) are idenical for each of he U i. Therefore, (7) can be represened as below: ACR cluser = Pr, j - m U (sink, n o CH (CH (CH ( ) ( ) () i) i o CH m o ( -) CH n) * ( ) 0 (CH of cluser nodes of in cluser ) w R k w U w Furhermore, (8) is ighly lower-bounded by (9), i.e., ACR cluser in (8) is a leas he value given by (9). This is an imporan simplificaion because i is compuaionally inensive o sore and manipulae he huge expressions represened by sub-expressions in (8). Also his is a realisic simplificaion under he pracical assumpion ha he clusers are non-overlapping, and nodes ha paricipae in communicaion beween CH (k+) and CH (k) do no generally paricipae in communicaion beween CH (k) and CH (k-) ; and when hey do paricipae, heir j) (8)

8 50 A. Shresha and L. Xing conribuion is insignifican. ACR cluser = m, n 0 Pr (sink o CH () i) *, j - Pr (CH () i o CH (-) j) *...* Pr (CH () m o CH n) * Pr(K-coverage probabiliy), (9) where Pr(K-coverage) = Pr U w R k (CH of cluser w nodes of U in cluser w) 6. Proposed Approach Revisiing he opologies discussed in Secion and he reliabiliy definiions in Secion 5, i is easy o find ha he hierarchical clusering opology is a generic archiecure ha covers oher opologies. Therefore, we use hierarchical clusering opology as a vehicle in describing he generic reliabiliy evaluaion algorihm for WSN. The sar, mesh, and ree archiecures are special cases of our proposed reliabiliy models and evaluaion mehods. 6.. The Progressive Approach o Reliabiliy Analysis Consider he fac ha he complexiy of nework reliabiliy analysis algorihms increases sharply wih increasing number of nodes [7]; a progressive reducion scheme [] is used o reduce he nework graph level by level. The number of levels of reducion process is decided by he number of levels in he nework hierarchy (refer o Secion ). ach reduced graph will be used for evaluaing nework reliabiliy relaed o he corresponding level. Specifically, consider he example hierarchical clusering WSN in Figure (d). The original nework graph is referred o as level-0 graph. Therefore, CH, CH, and CH 3 are referred o as he level-0 cluser heads (CH) of clusers,, and 3 respecively. The level-0 CH are arranged ino a single level- cluser, and CH is assigned as he CH for his level- cluser. The level-0 graph in Figure (d) is used o evaluae he las erm in (8) (a cluser s k-erminal reliabiliy) or in (a cluser s K-coverage probabiliy). The level-0 graph is also analyzed o obain he occurrence probabiliy of he wo-erminal even (i.e., wo-erminal reliabiliy) beween he level-0 cluser head (denoed by CH ) and he level-0 gaeway node ha connecs wo level-0 clusers (denoed by g ). CH Level- CH Level-0 CH Level- Gaeway Level-0 Gaeway Level- CH Level- Gaeway CH 3 CH CH 3 Base Saion Base Saion (a) Level- graph (b) Level- graph Fig. : Reduced Graphs The level-0 graph in Figure (d) is reduced o a level- graph conaining only he CH, g, and g () as shown in Figure (a). The wo-erminal reliabiliy beween CH and g

9 Quanifying Applicaion Communicaion Reliabiliy of Wireless Sensor Neworks 5 compued based on level-0 graph is assigned o he corresponding CH o gaeway link a he level- graph. The level- graph in Figure (a) is used o evaluae he second o he las erm (wo-erminal even/reliabiliy beween CH () and CH ) in (8) or (9). The level- graph is also analyzed o obain he wo-erminal reliabiliy beween CH () and g (). The level- graph in Figure (a) is furher reduced o a level- graph conaining only he CH () and g () as shown in Figure (b). The wo-erminal reliabiliy beween CH () and g () compued based on level- graph is assigned o he corresponding CH o gaeway link a he level- graph. The level- graph in Figure (b) is used o evaluae he hird o he las erm (i.e., he firs erm, wo-erminal reliabiliy beween he sink and CH () for his specific example) in (8) or (9). In general, in he progressive reducion scheme, a level-i graph is reduced o a graph conaining only he level-i CH i.e., CH (i) and level-j iner-cluser gaeways, i.e., g (j), where j >= i. This process is ieraed unil he graph is reduced o he op level of he hierarchy. Those reduced graphs are used o solve he differen sub-problems in (8) and (9). Specifically, he las erm is calculaed from level-0 graph, he second o he las erm is calculaed from he level- graph, he hird las erm is calculaed from he level- graph and so on. Finally, he firs erm is compued from he op-level graph. The reliabiliy resuls are inegraed using (8) or (9) o obain he exac or lower-bounded ACR for he enire WSN, respecively. Noe ha when using (9) o obain he igh lower bound on ACR, if a componen s failure probabiliy has been considered a a lower-level graph, i is considered zero in higher-level graphs. For example, he failure probabiliy of each CH and each gaeway node g are already considered in he level-0 wo-erminal reliabiliy evaluaion, failure probabiliy of zero is assigned o he CH and he gaeway nodes in he reduced higher-level graphs. However, he iner-cluser gaeway-o-gaeway link (g i, g j ) failure probabiliies need o be considered a level- graph, as hey were no considered a level-0. For evaluaing he wo-erminal, all-erminal, and in general k-erminal nework reliabiliy, an efficien reduced ordered binary decision diagrams (ROBDD) based mehod [4], [5] is adoped. The main seps of he mehod are reviewed as follows:. Order he nework nodes and links using a good variable ordering heurisic. A heurisic is good in he sense ha i yields a compac ROBDD model [6].. Generae ROBDD from he probabilisic (reduced) graph of he WSN a he corresponding level, i.e. each sub-expressions in he above reliabiliy definiions are represened by a ROBDD srucure. 3. valuae nework unreliabiliy recursively from he final ROBDD. 6.. Coverage-Oriened Reliabiliy Measure The las erm of (8), (9) is he cluser K-coverage even/probabiliy. Based on our pracical assumpion in Secion 3 ha a sensor node belongs o a single cluser, we analyze each cluser individually o evaluae he K-coverage probabiliy. In general, he K-coverage probabiliies for various WSN opologies, viz. sar in (), ree in (5), mesh in (6), and hierarchical clusering opology in can be calculaed via he mehod oulined in his secion. Firs, we find he K-coverage-ses. This is an exension of he classic ar gallery problem ha deals wih deermining he se of observers necessary o cover an ar galley room such ha every poin is seen by a leas one observer (i.e., -coverage se). A poin p is covered by a node v if heir uclidean disance is less han he sensing range R s of v, i.e., d (p, v) < R s. A K-

10 5 A. Shresha and L. Xing coverage-se is defined as a se of sensor nodes in a sensor field such ha all he poins in he field are covered by a leas K nodes [3]. Similar o he radiional minimal cu-se/pah-se based reliabiliy evaluaion mehods [7], we need o idenify all he K-coverage ses for finding he K-coverage probabiliy. As in radiional cu-se/pah-se generaion, he problem of enumeraing he K-coverage ses is a NP-complee problem and he mos sraighforward soluion is he brue force way. Specifically, we check each subse in he sample space (wih n subses, where n represens number of sensors in he field of ineres), idenifying wheher ha subse can K-cover he field. Reference [4] proposes a soluion o he decision problem of wheher every poin in he moniored area is covered by a leas K sensors via checking he perimeer of every sensor s sensing range. Reference [8] proposed echniques o formulae and solve he -coverage as ineger linear programming (ILP) problems. In his work, we adaped he algorihm in [8] o solve he K-coverage problem by redefining sensor inensiy marix as he coverage marix and redefining he minimum inensiy value as K. Specifically, we formulae he minimum K-coverage problem in WSN as follows: Inpu: A sensor se S = {s, s,, s n }; a sensor field A, where {a, a, a m } is a pariioning of A; an area coverage marix C m n, where each elemen C i,j is if sensor s j S covers area a i A and i is 0 oherwise. Problem: Find he minimum K-coverage ses of sensors, each se represened by vecor X n, where X i is if sensor s i S is in he se ha K-covers A, and 0 oherwise. All he sensors s i wih X i = in he vecor X n consiue a minimal K-coverage se. The ILP formulaion of he problem is: Minimize: n X n Where: C m n X n m.k The objecive funcion being minimized is he number of sensors represened by he sum of elemens of vecor X. The consrains o be saisfied are ha each region a i mus be covered by a leas K sensors as represened by he inequaliy. LP_SOLV, a noncommercial ILP solver can be used o obain he soluion for he above problem [9]. The above procedure can be used o find a single K-coverage se. However, noe ha here can be muliple K-coverage ses. Therefore, he above procedure is repeaed unil all he K- coverage ses are obained. A i h ieraion, he (i-) K-coverage ses obained so far, i.e. {U, U,, U i- }, is added o he consrain U i {U, U,, U i- } and U j U i (j < i) of he above opimizaion problem. Le U i be composed of i nodes {n i,, n i,,, n i,i }. Then he probabiliy of obaining his coverage-se is he probabiliy ha here exiss a Seiner ree ha connecs all he nodes {n i,j, j i } in he coverage se wih he cluser head(s), which is a k-erminal reliabiliy problem [7], [5] wih k = U i cluser head. Afer obaining he K-coverage ses, we apply he BDD-based mehod o find he K- coverage probabiliy. Specifically, assume here are w K-coverage-ses denoed by {U, U,, U w }. The K-coverage probabiliy is simply he probabiliy ha a leas one of he K- coverage ses is operaional, i.e., k () U Pr(K-coverage) = Pr { (CH nodes in he subse U ) } To solve his equaion, a BDD is generaed for each K-coverage se U i by finding he k-

11 Quanifying Applicaion Communicaion Reliabiliy of Wireless Sensor Neworks 53 erminal reliabiliy beween CH and he nodes in U i. The final BDD is obained by ORing he sub-bdd for all he K-coverage ses. The evaluaion of he final BDD using he recursive evaluaion algorihm [4] gives he K-coverage probabiliy. 7. Resuls In his secion, we illusrae he applicaions and advanages of our proposed measures and evaluaion approaches via he analysis of he ree, mesh and hierarchical clusering opologies of he example WSN in Secion 4. We consider he mission ime of 0,000 hours. We assume ha boh links and nodes fail s-independenly and exponenially. Table I shows he consan failure raes of WSN componens. Alhough we assign exponenial failure disribuion o he nodes and links, our analysis mehodology is suiable for any failure disribuion. Noe ha he link failure parameer is a funcion of disance and ransmission power. However, for simpliciy of illusraion, we assume each link in he mesh and hierarchical clusering opologies has he same failure parameer. Also, we assume ha he long range ransmission power in ree opology of Figure (c) is suiably increased so ha he links have he same failure parameers as links in mesh and hierarchical cluser. Inuiively, his will give an upper bound on he reliabiliy of ree WSN wih similar ransmission energy o ha of he mesh and hierarchical clusering WSN. Our fuure work includes he simulaion sudy of he rade-off in communicaion energy efficiency and reliabiliy. Table I: Failure raes (hr - ) for WSN componens Links Base saion Cluser head Nodes e-6 e-7 e-6 e-6 We consider -coverage as he QoS requiremen for each region (idenified by he clusers,, and 3 in Figure (d)) and he enire WSN wih ree, mesh and hierarchical clusering opologies. The -coverage-ses can be found via he mehod oulined in Secion 6.. We assume ha he -coverage-ses are generaed as follows: Cluser : CS = {0, 8,, 5}, CS = {0, 8, 6, 4, 5} Cluser : CS = {7, 5,, }, CS = {7, 5, 8, 3} Cluser 3: CS 3 = {8, 6,, 4}, CS 3 = {8, 6, 5,, } nire field: CS = CS CS CS 3, CS = CS CS CS 3, CS 3 = CS CS CS 3, CS 4 = CS CS CS 3, CS 5 = CS CS CS 3, CS 6 = CS CS CS 3, CS 7 = CS CS CS 3, CS 8 = CS CS CS 3. Noe ha alhough he coverage ses for he enire field has been specified as inersec of he coverage ses of clusers,, and 3; his is no a general rule for obaining he coverage ses of he enire field (as here may be overlapping areas of coverage in he hree clusers). For illusraion, we presen he ACR expression of he enire field for he hierarchical clusering opology in Figure (d). According o (9), ACR for he enire field is given by, ACR cluser = {3} Pr (sink o CH () i) * {3}, j {,) Pr (CH () i o CH j) * Pr(Kcoverage), where { } Pr(K-coverage) = Pr ( k (CH of cluser w nodes of U in cluser w) ) U { CS,..., CS8} w {,,3}

12 54 A. Shresha and L. Xing The ACR expressions for each cluser of he hierarchical clusering opology and for oher opologies can be similarly esablished. We abulae he resuls of ACR for ree, mesh, and hierarchical clusering opologies for regions wihin cluser, cluser, cluser 3, and he enire sensor field of he example WSN from Secion 4 in Table II. Table II. ACR resuls of example WSN Cluser Hierarchical Tree Mesh # Clusering nire WSN Noe ha in our analysis of ACR for he enire WSN wih mesh opology, because here are eigh K-coverage ses corresponding o eigh k-erminal reliabiliy sub-problems, we need o generae, sore, and manipulae eigh ROBDD. Due o memory limiaions, we were unable o obain he exac value of he ACR for his scenario. As we menioned in Secion 3, his is also due o he NP-complee naure of he nework reliabiliy problem. The value given in he Table II for his scenario is he lower bound obained via muliplicaion of he reliabiliies for cluser, cluser, and cluser 3. Our fuure work involves invesigaing mehodologies and heurisics for improving he efficiency of our analysis approach. For all he scenarios, he mesh opology offers he highes ACR due o muliple pahs hrough he nework. The ree opology has he lowes reliabiliy due o he use of only a single direc link beween nodes a successive levels in he hierarchy. The hierarchical clusering opology is a compromise beween he wo exremes. Is ACR is beer han he ree s ACR as i sill mainains muli-hop pahs, while i has lower reliabiliy han mesh because each communicaion beween nodes a differen clusers mus roue hrough affiliaed cluser heads, which are single-poin of failures. Also, in a very naïve inerpreaion, cluser 3 wih he lowes reliabiliy is he bes candidae o improve WSN coverage-oriened applicaion communicaion reliabiliy. Neverheless, a beer approach for idenifying he candidae regions is o perform sensiiviy analysis [4], [0] which is our fuure work. 8. Conclusions We proposed a novel approach of inegraing sensing coverage wih convenional nework conneciviy for he applicaion communicaion reliabiliy analysis of sar, mesh, ree, and hierarchical clusering WSN. The coverage-oriened reliabiliy of WSN provides a beer measure of he performance of he WSN han he ones based solely on conneciviy or coverage. As illusraed hrough he example, our reliabiliy measures can reflec he QoS of WSN hrough he inegraion of sensing coverage. The proposed approach for he reliabiliy analysis is pracical and easy o implemen because i is progressive and is based on he compuaionally efficien ROBDD approach. However, here is a scope for improvemen of he algorihm for exac reliabiliy evaluaion. Our fuure work also includes he consideraion of sensor nodes mobiliy ino he reliabiliy analysis, sensiiviy analysis, and inegraing oher sensing coverage models.

13 Quanifying Applicaion Communicaion Reliabiliy of Wireless Sensor Neworks 55 Acknowledgmens An earlier version of his paper [] was presened a he h ISSAT Inernaional Conference on Reliabiliy and Qualiy in Design. We appreciae he feedback given o us on his opic by conference aendees. References [] Tilak, S., N. B. A. Ghazaleh, and W. Heinzelman, A Taxonomy of Wireless Micro-Sensor Nework Models, Mobile Compuing and Communicaions Review, Vol., No., June 00. [] Shresha, A., L. Xing, H. Liu, Infrasrucure Communicaion Reliabiliy of Wireless Sensor Neworks, In Proceedings of he nd I Inernaional Symposium on Dependable, Auonomic and Secure Compuing, Indianapolis, Indiana, pp , Sepember 9 Ocober, 006 [3] Wang, X., G. Xing, Y. Zhang, C. Lu, R. Pless, and C. Gill, Inegraed Coverage and Conneciviy in Wireless Sensor Neworks, In Proceedings of he s ACM Inernaional Conference on mbedded Neworked Sensor Sysems, pp. 8-39, November 003. [4] Huang, C. F., and Y. C. Tseng, The Coverage Problem In a Wireless Sensor Nework, In Proceedings of he nd ACM Inernaional Conference on Wireless Sensor Neworks and Applicaions, pp. 5, Sepember 003. [5] Banerjee, S., and S. Khuller, A Clusering Scheme for Hierarchical Conrol in Muli-Hop Wireless Neworks, I INFOCOM, Anchorage, Alaska, April 00. [6] Krishnamachari, B., D. srin, and S. Wicker, Modelling Daa-Cenric Rouing in Wireless Sensor Neworks, I INFOCOM, 00. [7] Colbourn, C. J., The Combinaorics of Nework Reliabiliy, The Inernaional Series Of Monographs On Compuer Science, Oxford Universiy Press, 987. [8] AbolFooh, H. M. F., S. S. Iyengar, and K. Chakrabary, Compuing Reliabiliy and Message Delay for Cooperaive Wireless Disribued Sensor Neworks Subjec o Random Failures, I Transacions on Reliabiliy, Vol. 54, No., pp , 005. [9] Liu, B., P. Brass, O. Dousse, P. Nain, and D. Towsley, Mobiliy Improves Coverage of Sensor Neworks, In Proceedings of he 6 h ACM inernaional Symposium on Mobile Ad Hoc Neworking and Compuing, Urbana-Champaign, IL, USA, May 5-7, 005. [0] Woo, A., and D. Culler, valuaion of fficien Link Reliabiliy simaors for Low- Power Wireless Neworks, Technical Repor UCB/CSD-03-70, CS Deparmen, Universiy of California, Berkeley, 003. [] Chen, D., S. Garg, and K. S. Trivedi, Nework Survivabiliy Performance valuaion: A Quaniaive Approach wih Applicaions in Wireless Ad-Hoc Neworks, In Proceedings of he 5 h ACM Inernaional Workshop on Modeling Analysis and Simulaion of Wireless and Mobile Sysems, Sepember 00, Alana, GA. [] Rausand, M., and A. Hoyland. Sysem Reliabiliy Theory: Models and Saisical Mehods, Wiley Series in Probabiliy and Mahemaical Saisics, John Wiley & Sons, 004. [3] Xing, L., and A. Shresha, QoS Reliabiliy of Hierarchical Clusered Wireless Sensor Neworks, In Proceedings of he 5 h I Inernaional Conference on Performance Compuing and Communicaions (esco-wi 06), Phoenix, AZ, pp , April 006. [4] Zang, X., H. Sun, and K. S. Trivedi, A BDD-Based Algorihm for Reliabiliy Graph Analysis, (Rerieved on April 6, 007) hp://cieseer.is.psu.edu/387.hml.

14 56 A. Shresha and L. Xing [5] Yeh, F. M., S. K. Lu, and S. Y. Kuo, OBDD-Based valuaion of k-erminal Nework Reliabiliy, I Transacions on Reliabiliy, Vol. 5, No. 4, December 00. [6] Bouissou, M. An Ordering Heurisic for Building Binary Decision Diagrams from Faul- Trees, In Proceedings of Annual Reliabiliy & Mainainabiliy Symposium, pp. 08-4, January 996. [7] Dugan, J. B., and S. A. Doyle, New Resuls in Faul-Tree Analysis, Tuorial Noes of he Annual Reliabiliy and Mainainabiliy Symposium, January 996. [8] Meguerdichian, S., and M. Pokonjak, Low Power 0/ Coverage and Scheduling Techniques in Sensor Neworks, Technical Repors 03000, Universiy of California, Los Angeles, January 003. [9] Berkelaar, M., LP_SOLV: Linear Programming Code, (Rerieved on April 6, 007) hp:// [0] Xing, L., Faul-oleran Nework Reliabiliy and Imporance Analysis using Binary Decision Diagrams, In Proceedings of he 50 h Annual Reliabiliy and Mainainabiliy Symposium, Los Angeles, CA, January 004. [] Shresha, A., L. Xing, and H. Liu, Applicaion Communicaion Reliabiliy of Wireless Sensor Neworks, In Proceedings of he h ISSAT Inernaional Conference on Reliabiliy and Qualiy in Design, Chicago, Illinois, USA, pp , Augus 006. Akhilesh Shresha was awarded he M.S. degree in Compuer ngineering from he Universiy of Massachuses Darmouh in 005. He is currenly a Ph.D. suden in he lecrical and Compuer ngineering Deparmen a he Universiy of Massachuses Darmouh. His curren research ineress include faul oleran and dependable compuing, wireless sensor neworks, and daabase sysems. He is a suden member of I since 003. Liudong Xing received her M.S. and Ph.D. degrees in lecrical ngineering from he Universiy of Virginia, Charloesville, VA in 000 and 00, respecively. Since 00, Dr. Xing has been an Assisan Professor wih he lecrical and Compuer ngineering Deparmen, Universiy of Massachuses - Darmouh. Dr. Xing served as a program co-chair for he 006 I Inernaional Symposium on Dependable, Auonomic and Secure Compuing, a program vice chair for he 007 Inernaional Conference on mbedded Sofware and Sysems, and an associae gues edior for he Journal of Compuer Science on a special issue of Reliabiliy and Auonomic Managemen. She is currenly an dior for Shor Communicaions of he Inernaional Journal of Performabiliy ngineering. She is he recipien of he I Region Technological Innovaion (Academic) Award in 007. Her curren research ineress include dependable compuing and neworking, reliabiliy engineering, faul-inrusion oleran compuing, and wireless sensor neworks. She is a senior member of I and a member of a Kappa Nu and AS.