Ad Hoc Networks 11 (2013) Contents lists available at SciVerse ScienceDirect. Ad Hoc Networks

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1 Ad Hoc Networks 11 (213) Contents lsts avalable at ScVerse ScenceDrect Ad Hoc Networks journal homepage: Generc predcton asssted sngle-copy routng n underwater delay tolerant sensor networks Zheng Guo a,,1, Bng Wang b, Jun-Hong Cu b a X an Unversty of Posts and Telecommuncatons, X an, Chna b Department of Computer Scence and Engneerng, Unversty of Connectcut, Storrs, CT 6269, USA artcle nfo abstract Artcle hstory: Receved 7 February 212 Receved n revsed form 19 November 212 Accepted 19 November 212 Avalable onlne 3 January 213 Keywords: Delay tolerant networks Underwater sensor networks Sngle-copy Routng Algorthm One challenge n delay tolerant networks (DTNs) s effcent routng, as the lack of contemporaneous end-to-end paths makes conventonal routng schemes napplcable. Although many DTN routng protocols have been proposed, they often have two lmtatons: many protocols are not moblty cognzant, so they only sut specfc moblty models and become neffcent when the envronment changes; some protocols employ mult-copy replcaton to accommodate moblty dversty for ncreased delvery probablty or reduced delay, but they usually do not perform well n resource constraned networks. Due to the unque characterstcs of underwater sensor networks (UWSNs), effcent DTN routng becomes even more challengng. In ths paper, we propose a generc predcton asssted sngle-copy routng (PASR) scheme that can be nstantated for dfferent moblty models. PASR frst collects a short-duraton trace wth network connectvty nformaton and employs an effectve off-lne greedy algorthm to characterze the underlyng network moblty patterns, depct the features of best routng paths and provde gudance on how to use hstorcal nformaton. Then t nstantates predcton asssted sngle-copy onlne routng protocols based on the gudance. As a result, the nstantated protocols are energy effcent and cognzant of the underlyng moblty patterns. We demonstrate the advantages of PASR n underwater sensor networks wth varous moblty models. Ó 213 Elsever B.V. All rghts reserved. 1. Introducton Many routng protocols have been proposed to deal wth the lack of contemporaneous end-to-end paths n delay tolerant networks (DTNs) [1 8]. These protocols, however, have the followng lmtatons. Frst, many protocols are desgned for specfc moblty models [9 12]. For nstance, the protocols n [13,14,7,15,16] are for networks n socal envronments; the protocols n [17,18] focus on random way pont and random walk moblty models; Correspondng author. E-mal addresses: guozheng@engr.uconn.edu (Z. Guo), bng@engr. uconn.edu (B. Wang), jcu@engr.uconn.edu (J.-H. Cu). 1 He was wth the Department of Computer Scence and Engneerng, Unversty of Connectcut, Storrs, CT 6269, USA. He s now wth X an Unversty of Posts and Telecommuncatons, X an, Chna. and the protocol n [11] s for networks wth pre-determned node trajectores. Although some other protocols are desgned for general moblty models, they are not moblty model cognzant [19]. Snce the underlyng moblty domnates the contact and nter-contact pattern [2], these moblty ncognzant protocols can have superor performance for one model whle much degraded performance for another model [19]. Another drawback of most exstng routng protocols s that they use mult-copy replcaton, whch allows multple replcas of a packet to exst n a network smultaneously. These protocols establsh several vrtual spatal temporal routes (ether usng floodng [4,19,21] or controlled floodng [15,22]) to ncrease delvery probablty and decease end-to-end delay. On the other hand, they exhaust network resources (such as bandwdth, storage and power) much more quckly than sngle-copy routng strateges. Thus, mult-copy routng /$ - see front matter Ó 213 Elsever B.V. All rghts reserved.

2 Z. Guo et al. / Ad Hoc Networks 11 (213) schemes always lead to poor performance n resource strngent networks. Underwater sensor networks (UWSNs), an area that has attracted sgnfcant attenton from both academa and ndustry [23 27], can be treated as DTNs [28] due to node moblty and sparse deployment. Compared to other DTNs, UWSNs are extremely resource strngent snce acoustc communcaton, the most practcal communcaton method for UWSNs, has very lmted bandwdth and very hgh power consumpton. Furthermore, the moblty pattern n an UWSN can vary dramatcally over tme dependng on the envronment. These two characterstcs render exstng DTN routng protocols, especally mult-copy replcaton schemes, unsutable n UWSNs. Therefore, an effcent sngle-copy routng scheme, whch can also be self-adaptve to the varyng moblty, s desrable. In ths paper, we propose a generc scheme, predcton asssted sngle-copy routng (PASR), for UWSNs to acheve mnmum delvery delay at low energy consumpton. PASR can be nstantated to effcent sngle-copy routng protocols under dfferent moblty models. PASR conssts of two phases, learnng phase and routng phase. In the learnng phase, PASR collects a short-duraton trace wth network connectvty nformaton and employs an effectve off-lne greedy algorthm to characterze the underlyng moblty patterns, depct the common features of best routng paths and provde gudance on how to use hstorcal nformaton. In the routng phase, t nstantates a predcton asssted sngle-copy onlne routng protocol based on the gudance. Our man contrbutons are: (1) we propose a short-duraton trace-based greedy algorthm, named aggressve chronologcal projected graph () n the learnng phase and analyze the computatonal complexty; (2) we desgn a generc scheme on nstantatng heurstc predcton asssted sngle-copy routng protocols based on the gudance from n the routng phase; and (3) we evaluate ths generc scheme n UWSNs wth three dfferent moblty patterns through comprehensve smulaton. Our smulaton results show that ndeed captures the relatonshp between hstorcal nformaton and best routng paths under dfferent moblty patterns and provdes effectve gudance to nstantate heurstc sngle-copy routng protocols, that acheve close to optmal results and outperform other exstng schemes. A prelmnary verson of ths paper appeared n [29]. The rest of ths paper s organzed as follows. We frst dscuss related work n Secton 2. We then ntroduce the network model and convert t to an extended space tme graph n Secton 3. Afterwards, we present the greedy algorthm and compare t wth an optmal algorthm n Secton 4. Secton 5 descrbes the generc scheme PASR and how to nstantate predcton asssted sngle-copy routng protocols n UWSNs for dfferent moblty models. Secton 6 presents performance evaluaton. Fnally, Secton 7 concludes the paper and proposes future research drectons. 2. Related work Snce many types of networks (e.g., planet networks [3], sensor networks [24], vllage networks [31], vehcle networks [11]) can be treated as delay tolerant networks, much effort has been put on the challengng routng problem and many schemes have been proposed. Dependng on whether the complete nformaton of the networks s avalable or not, DTN routng can be categorzed as determnstc routng and heurstc routng Determnstc routng Determnstc routng schemes are to optmze a certan performance metrc (e.g., shortest average delay, hghest delvery rato, mnmum energy consumpton, longest network lfetme and so on) when complete nformaton s avalable. The complete nformaton may nclude the locaton of nodes, the contacts between nodes, the power or storage status of nodes, the traffc demands and so on. Based on the complete nformaton, determnstc routng schemes can acheve the optmal results n respect to a certan performance metrc. Merugu et al. bult a space tme graph to select routng paths usng dynamc programmng and shortest path algorthm n [32]. Jan et al. formulated a lnear programmng problem upon the avalablty of all knowledge oracles n [5]. The rgorous requrement on the complete nformaton of networks makes all algorthms above not practcal n real networks, snce even mssng partal nformaton can sgnfcantly ncrease the complexty [5]. Dfferent from above schemes, we propose a practcal predcton asssted scheme. In ths scheme, we apply an off-lne determnstc algorthm on a short-duraton trace to gude the desgn of onlne heurstc routng schemes Heurstc routng In most networks, t s mpossble to obtan complete nformaton n advance, thus only heurstc routng s sutable. Accordng to how many replcas of a packet can exst n the network smultaneously, we classfy exstng heurstc routng schemes nto two categores: mult-copy routng and sngle-copy routng Mult-copy routng Mult-copy routng means that a node can replcate a packet on multple relay nodes and expect any of them can reach the destnaton quckly. [4] was a representatve mult-copy routng scheme. To mnmze the end-to-end delay, replcated a packet to every node n the network. However, ths floodng scheme consumed too many resources and made tself nfeasble n harsh network envronments. To avod unconstraned resource consumpton, many other mult-copy routng schemes that lmt the number of copes have been proposed. These schemes forward packets accordng to some crtera,.e. utlty functon, forwardng probablty and so on. Harras et al. proposed several controlled floodng schemes n [21], such as basc probablstc, tme-to-lve, kll tme and passve cure. Spyropoulos et al. presented spray and wat [19], n whch a certan number of copes of a packet were replcated to the frst encountered nodes. Ths scheme only strctly controlled the total number of copes, but dd not choose the relay nodes wsely, causng

3 1138 Z. Guo et al. / Ad Hoc Networks 11 (213) wasteful replcaton. Later, Spyropoulos et al. and Xue et al. mproved the performance of spray and wat wth better dstrbuton schemes n [33,34] separately. In [35], Burgess et al. suggested a mult-copy routng scheme, called Max- Prop, usng prortes based on the path lkelhood. Lndgren et al. proposed PROPHET to lmt the number of copes [15], n whch an ntermedate node only forwarded a packet to the neghbors that have hgher probabltes to reach the packet s destnaton n a short tme. Balasubramanan et al. presented an ntentonal DTN routng protocol, Rapd, to optmze a specfc routng metrc [36]. Rapd treated DTN routng as a resource allocaton problem by translatng the targetng metrc to per-packet utlty and determnng the packets replcaton n the network. Sandulescu et al. exploted the context of moble nodes to estmate the sze of a contact wndow and proposed OR- WAR to make better forwardng decsons [37]. In addton, Jones et al. utlzed the contact hstory to fnd routes wth mnmum estmated expected delay [38]. Wu et al. proposed a scheme that forwarded packets to relays wth ncreasng utlty to ncrease relablty [22]. The scheme by Carde et al. made routng decsons based on the probablstc trajectory predcton [39]. Lu et al. presented optmal probablstc forwardng (OPF) to maxmze the expected delvery rate usng forwardng thresholds as functons of remanng hop-count and resdual tme-to-lve n [6]. Guo et al. adaptvely classfed packets wth dfferent prortes and assgned correspondng replcas n [28]. These mult-copy routng schemes replcate packets usng some crtera, whch are talored for specfc network mobltes and the performance can degrade sgnfcantly when the underlyng moblty changes. So they requre to know the underlyng moblty n advance and cannot drectly apply to other network scenaros. Moreover, mult-copy routng schemes consume too many resources (e.g., power, buffer and bandwdth) and are not sutable for resource strngent networks. In ths paper, we propose a generc moblty cognzant sngle-copy routng scheme. Ths scheme does not requre the underlyng moblty n advance, whle t apples a greedy algorthm on a shortduraton trace collected to characterze the moblty, and gudes to nstantate a correspondng heurstc sngle-copy scheme for ths network. Therefore, our scheme s applcable to any network scenaro, especally when the underlyng moblty s unknown or not constant. In addton, our sngle-copy routng schemes are energy effcent Sngle-copy routng In the lterature, only few studes focus on sngle-copy routng. In connected networks, routng schemes take only sngle copy on a sngle path because t s easy to determne the best routng crtera. However, n DTNs, t s challengng, f not mpossble, to decde whch relay s the best canddate durng each contact opportunty. Chen et al. only focused on the cross-cluster dsconnecton n cluster-based networks, whch was only applcable to stuatons where the nodes nsde a cluster were well connected and clusters were occasonally connected [4]. Musoles et al. proposed Context-Aware Routng (CAR) to send messages to host wth the hghest delvery probablty, whch was predcted from avalable context (the set of attrbutes that descrbed the aspects of the system and could be used to optmze the process of message delvery) [41]. Spyropoulos et al. dscussed a number of basc sngle-copy routng protocols n [18]. Yuan et al. presented predct and relay (PER) to forward a packet based on the predcton of the probablty dstrbuton of future contact tmes [7]. They assumed that nodes could only move around a set of landmarks followng a tme-homogeneous sem-markov model. As a sngle-copy routng scheme, the forwardng crtera become even more strct and closely related to the underlyng moblty. Thus the aforementoned routng schemes can only be used n specal networks, because one crteron may be not meanngful, or even not avalable, n other networks. In ths paper, we solve ths problem by proposng a general predcton asssted scheme, whch characterzes the network moblty and gves gudance on whch nformaton can be used for predcton and whch forwardng crtera can be used for forwardng packets. 3. Prelmnares 3.1. Network model We consder a data collecton underwater sensor network, whch conssts of M layers. Multple underwater sensors are deployed n each layer, and can passvely move wth water currents n the horzontal plane and vbrate slghtly n the vertcal drecton. Ths knd of deployment can be acheved by smple buoyancy control of underwater sensors at certan depths [24]. Fg. 1 shows a smple example of such a network wth three layers, where the dashed lnes ndcate the nstantaneous connectvty. In ths network, for smplcty, we assume that one data snk s anchored n the mddle of the water surface. Snce underwater sensors float wth currents (we assume passve moblty n the target UWSN model), ther movements are drven by the movement of water currents and are tractable to some extent [42]. We adopt the knematc model [43] to descrbe the moblty. The current feld s assumed to be a combnaton of a tdal and a resdual current felds. The tdal feld s a spatally unform oscllatng current n one drecton and the resdual current feld s assumed to be an nfnte sequence of clockwse and counter-clockwse rotatng eddes. The movement s Surface Layer 1 Layer 2 Layer 3 Fg. 1. A smple example of a three-layers underwater sensor network.

4 Z. Guo et al. / Ad Hoc Networks 11 (213) constraned n the horzontal plane and ndependent of the depth. The moblty model can be approxmated as V x ¼ k 1 kv snðk 2 xþ cosðk 3 yþþk 1 k cosð2k 1 tþþk 4 V y ¼ kv cosðk 2 xþ snðk 3 yþþk 5 ð1þ where V x and V y are the nstantaneous veloctes on the X and Y axes respectvely; k ( =1,...,5), k and v are varables related to the envronment, such as tdes and bathometry. We vary these parameters n Secton 6 to nstantate three dfferent mobltes and demonstrate that the proposed PASR can adapt to the correspondng underlyng moblty. Further we assume the network operates n a slotted manner, each slot of duraton T. Sensors n the lowest layer generate packets to be transmtted to the snk usng nodes n the mddle layers as relays. All sensors use store-andforward mechansm; a packet receved or generated n a slot can be forwarded from the next slot. At the begnnng of each slot, each sensor broadcasts a short HELLO message to ts neghbors to declare ts exstence and exchange nformaton. Each sensor s equpped wth a buffer that can accommodate W packets and a battery that can transmt P packets. Sensors work n a half-duplex mode (.e. they cannot transmt and receve smultaneously), and transmt or receve data at the rate of k packets per second. The objectve s to delver packets to the snk wth mnmum delay at low energy consumpton Extended space tme graph Snce the connectvty changes over tme, we can represent the evolvng network n both spatal doman and temporal doman as a drected extended space tme graph [44]. We assume the network contans M layers and N nodes n each layer (excludng the snk on the surface). We also model a super source v s that generates packets and dstrbutes them to the correspondng sources wthout delay, and a super snk v d (the snk on the surface) to collect all packets. The slots are ndexed as,1,2,... Thus, we can construct a drected extended space tme graph G(V, E). V: the set of nodes, ncludng v s, v d and node nstances at dfferent slots v t j ; ¼ 1; 2;...; M; j ¼ 1; 2;...; N; t ¼ ; 1; 2;... E: the set of edges, ncludng holdng edge set E h and forwardng edge set E f,.e. E = E h [ E f. E h : an edge v t j ; v tþ1 j 2 E h denotes that a packet can be held on node v j durng the slot t; an edge v s ; v t j 2 E h denotes packets generaton. E f : an edge v t j ; v tþ1 kl 2 E f ff node v j can transmt to v kl ( k or j l) durng slot t. C (u, v): the capacty of edge (u, v), defned as: C ðu;vþ ¼ þ1; ðu; vþ 2E h sk; ðu; vþ 2E f ð2þ where k s the transmsson rate, and s s the contact duraton between u and v n that slot, 6 s 6 T. Cv: the capacty of node v, whch s defned as the avalable buffer space. To completely descrbe the specal constrants of the network, we ntroduce the followng notatons: d(u, v): the cost of edge (u, v). Snce our objectve s to mnmze the delay, the cost s defned as dðu; vþ ¼ ; u ¼ v s ð3þ T; o:w: whch ndcates a delay (cost) of T when a packet traverses an edge. P: the resdual battery capacty of a node, ndcatng how many transmssons a node can stll afford. kt: the transcever capacty,.e. the maxmum number of packets a node can transmt and receve n one slot. q v : the traffc demand,.e. the number of packets that node v generates durng the th slot. Fg. 2 gves an example extended space tme graph for a three-layer network. A vertcal vertex set at slot t (as crcled) represents the node nstances at the end of that slot. Vertces n the set are arranged accordng to the layer and node sequence, not related to the geographc locatons. The horzontal drecton represents the evolvng network n temporal doman. The dashed lnes are holdng edges and the sold lnes are forwardng edges. v s and v d represent the super source and super snk, respectvely. 4. Determnstc routng algorthm The drected extended space tme graph G(V, E) can be constructed based on a small trace, regardng the node connectvty, recorded durng a short perod. After that, we can use determnstc algorthm, such as nteger lnear programmng (ILP), to fnd the optmal routng soluton wth mnmum delay. However, ILP has hgh computatonal complexty and only provdes the lower bound of achevable mnmum delay. Hence, we develop a greedy algorthm, aggressve chronologcal projected graph (). not only produces routng results that are close to the mnmum delay, but also characterzes the underlyng moblty pattern and depcts the common features of routes. v 1N super snk Layer 1 v12 v v 2N Layer 2 v22 v 21 v 3N 1 2 Layer 3 v super source Tme slot Fg. 2. An example of extended space tme graph.

5 114 Z. Guo et al. / Ad Hoc Networks 11 (213) Integer lnear programmng We assume F s a feasble flow on graph G(V, E) and f(u, v) s the flow through the edge (u, v). Dfferent from Ref. [5], we requre all flows contan an nteger number of packets. Followng the notatons n the prevous secton, we formulate the mnmum delay problem as an ILP: X mnmze : dðu; vþf ðu;vþ ð4þ f ðu;vþ2f subject to : f ðv s ;v Þ¼q v X f ðu;vþ¼x u2v w2v f ðu;vþ 6 C ðu;vþ X f ðu;vþ 6 C v u2v X X ¼;1;2;... f ðv;wþ; v 2 V nfv s ;v d g ðu ;v þ1 Þ2E f f ðu ;v þ1 Þ 6 P ð5þ ð6þ ð7þ ð8þ ð9þ X X f ðu ;v þ1 Þþ f ðv ;w þ1 Þ 6 kt ð1þ ðu ;v þ1 Þ2E f ðv ;w þ1 Þ2E f X ðu;v d u2vnfv s;v d gf Þ¼X X q v ð11þ v where u or v s the nstance of sensor u or v n the th slot. The constrants from Eqs. (5) to (11) represent the traffc demand, flow conservaton, channel capacty, node capacty, power capacty and transcever capacty, respectvely. By solvng these equatons, ILP can provde the optmal soluton to satsfy all flow requrement wth mnmum average delay. However, ILP s NP hard wth extremely hgh computatonal complexty Aggressve chronologcal projected graph We next propose a greedy algorthm named aggressve chronologcal projected graph () based on a much smpler undrected graph G o (V o, E o ). The man nspraton s that the vertces at dfferent tme slots n G(V, E) are not fully ndependent. They are dfferent nstances of the same node at dfferent tme slot, so they are spatally dentcal and temporally related. Moreover, the essentalty of routng s forwardng a packet to another approprate canddate towards the destnaton, whch happens over forwardng edges only n the extended space tme graph. Therefore, we can construct a smple graph G o (V o, E o ), where V o only represents the overlay network nodes (the same vertex set n G) and E o s dynamcally updated by addng the connectng edges recorded n the short-duraton trace chronologcally. It can be seen as that G o (V o, E o ) s compressed from the full extended space tme graph G(V, E) by projectng the forwardng edges n G to the same vertex set slot by slot from the begnnng one. Optmal algorthms, such as ILP, need to construct the complete statc graph G, whle aggressvely fnds out possble flows n the dynamc graph G o along wth the graph constructon. In the followng, we present the constructon of G o and the operatons of. For smplcty and comparson purpose, we construct G o by compressng G. In practce, wthout constructng G n advance, we can drectly construct G o from the short-duraton trace Constructon of G o The projected graph G o (V o, E o ) can be smply represented as the overlay graph of the network topology. Vertex v j 2 V o ( =1,...,M, j =1,...,N) s the jth node n the th layer, and edge (v j, v kl ) 2 E o s the projecton of edges v t j ; vtþ1 2 Eðt ¼ ; 1;...Þ. Snce edges n dfferent tme kl slots n G can be projected to the same edge n G o,we use (u, v, t, C) to represent an edge n G o, where u t and v t+1 are the connectng nodes n G and C s the capacty of that edge. The edge set E o s ntalzed to be empty and updated n at each tme slot. We frst ntroduce some basc concepts of the projected graph G o : Defnton 1 (Actve node and nactve node). At a tme slot, a node v 2 V o s actve f there exsts at least one route from the super source to t n G o, whch means that t s possble there could be packets arrved at ths node from the super source untl current tme slot; otherwse, t s nactve. In G o, an actve node has at least one connectng edge and an nactve node has no assocated edges. Defnton 2 (Upstream node of a node v 2 V o,uv). Node u s the upstream node of v ff (u, v, t, C) 2 G o has the smallest value t among all edges assocated wth v. Intally, all nodes except for the super source v s are nactve. Because we consder a real network scenaro wth lmted transcever capacty, buffer and power, we also mantan the followng resource nformaton for each node v 2 V o : Iv(): the maxmum number of packets that can be transmtted or receved durng the th slot, ntalzed to be kt. Cv(): the avalable storage n the th slot, ntalzed to be buffer sze W. Pv: the resdual power for transmssons, ntalzed to be battery capacty P. Iv() and Cv() are nstant node propertes at the th slot, so we need to mantan multple entres for a node. Each of them has an ntal value and s updated n the teratve processes of. However, Pv s a node property, whch cannot be recovered after consumpton, so we only need to mantan one entry for a node Operatons of s operated n a slot by slot manner along wth the constructon of G o. At each slot t, t >, t ncludes two routnes: (1) edge projecton, durng whch edges n G are projected to G o (n practce, edges are added by examnng the connectvty records at slot t n the short-duraton trace) and (2) routes reservaton and graph update, durng whch routes are dscovered and G o s updated Edge projecton. To descrbe the edge projecton process, we classfy the edges E 2 E f as necessary edges and unnecessary edges.

6 Z. Guo et al. / Ad Hoc Networks 11 (213) Defnton 3 (Necessary edge and unnecessary edge). An edge (u t, v t+1 ) 2 E f s necessary f t s a forwardng edge and ether u 2 G o or v 2 G o s actve. All holdng edges and other forwardng edges n G are not necessary edges. Necessary edges mean that there are possble flows through these edges. In the routne of edge projecton at a tme slot t, only the necessary edges n G wll be projected to G o, whle unnecessary edges wll be gnored drectly because they cannot contrbute for forwardng packets. The reasons are twofold: (1) nodes do not forward packets through holdng edges and (2) the forwardng edge, whch connects two nactve nodes, u 2 G o and v 2 G o, s mpossble to be used for forwardng packets snce no packets can arrve at ether u 2 G o or v 2 G o before the tme slot t when the edge s present, otherwse u 2 G o or v 2 G o should be actve at ths tme slot t. After the projecton of (u, v, t, C) 2 E o, both u and v become actve and update ther upstream nodes respectvely. If multple edges have been projected to edge (u, v) 2 E o up to the current slot t, only the one wth the lowest tme slot value can be used for the route dscovery untl t s replaced by the next earlest edge. Because we remove all holdng edges and partal forwardng edges, can sgnfcantly reduce the problem sze Routes reservaton and graph update. The second routne fnds possble routes up to slot t, reserves the resources and updates G o. The second routne s only executed when the super snk v d 2 G o s actve at slot t, because there must exst at least one flow from the super source v s to v d, whch can be traced back along the upstream nodes from v d wth complexty O(M N). Theorem 4.1. The dscovered route by tracng back along upstream nodes s loop-free and the complexty of fndng ths route s upper bounded by M N, where M s the number of layers and N s the number of nodes n each layer. Proof. For a node v 2 G o, the drecton to ts upstream node Uv always ponts to another edge wth smaller tme slot, whch further connects to the upstream node of Uv, untl the super source. Ths property s guaranteed by the constructon of G o and the process of graph update n Secton Assume there s a loop of length k on the dscovered route as v 1? v 2 v k? v 1.Ifk =2, v 1 and v 2 become mutual upstream nodes (see Defnton 4), whch cannot exst n the graph. If k > 2, there must exst one node, for example v 1, whch s the upstream node of v k through the edge (v 1, v k, t k, C k ) and has ts own upstream node u 2 through the edge (v 2, v 1, t 1, C 1 ). In ths case, v k should be the upstream node of v 1, whch s contradctory to the fact that v 2 s the upstream node of v 1. Snce the dscovered route by tracng back along upstream nodes s loop-free, ths route can at most traverse all (M N) nodes, whch s the worst case. h After fndng a route, we reserve the necessary resources wth the route capacty, whch s the mnmum node capacty, power capacty, transcever capacty or edge capacty along the route. After reservaton, nodes whose batteres are exhausted and edges whose capactes are reached become dead, and hence should be removed from G o. Afterwards, related nodes should update ther upstream nodes. The removal of nodes or edges and the update of upstream nodes may cause mutual upstream nodes and outdated edges, whch are defned as follows. Defnton 4 (Mutual upstream nodes and outdated edge). Two nodes are mutual upstream nodes f they are the upstream nodes of each other and the edge connectng mutual upstream nodes s defned as an outdated edge. Both mutual upstream nodes and outdated edges cannot exst n G o. Because f nodes u and v are mutual upstream nodes, then the edge (u, v, t, C) (t s the earlest tme slot among all projected edges between u and v) s outdated and mpossble to be utlzed snce no packets can arrve at u or v before tme slot t through other routes. Therefore, outdated edges should be removed from G o and the connectng nodes u and v should update ther upstream nodes respectvely untl no mutual upstream nodes exst. If all edges assocated wth a node have been removed, ths node goes back to be nactve. Ths update wll guarantee that any route by tracng back along upstream nodes at any tme n G o s thus guaranteed to be loop-free. These two routnes are operated alternately untl all traffc demands are satsfed. Through the aggressve route dscovery along the earlest avalable edges, not only quckly fnds low delay routes wth sgnfcantly reduced complexty, but also summarzes the characterstcs of the greedy routes, whch reflect the propertes of the underlyng moblty pattern (see Secton 6). Fg. 3a shows an example of the projected graph for 12 nodes n 3 layers at slot 9 after addng forwardng edges n ths slot, where we only mark the tuple (t, C) on an edge (overlapped edges are arranged chronologcally and only the frst edge s used for route dscovery). There are possble flows on the graph snce v d s actve. Followng the upstream nodes, we can buld the frst route v 9 d v 7 12 v 3 22 v 1 31 v s wth capacty of 5 packets and delay of 8 slots, where represents the packet s transmtted n the th slot. After reservng the resources on nodes and edges on the route, edges (v 31, v 22,3,5) and (v s, v 31, 1, 5) are removed and node v 22 (v 31 ) changes ts upstream node to v 23 (v 22 ). Then we can fnd another route v 9 d v 7 12 v 5 22 v 4 23 v 2 33 v s wth capacty of 2 packets and delay of 7 slots. Ths route exhausts edge (v 22, v 12, 7, 2), so we remove edge (v 22, v 12, 7, 2) and the outdated edge (v 12, v d, 9, 3), and make v 12 and v d nactve. The resdual graph after routes reservaton and graph update s shown as Fg. 3b Complexty analyss In order to analyze the computatonal complexty, we assume the collected short-duraton trace records the node connectvty durng a perod of S tme slots n a network wth M layers and N nodes n each layer. Therefore, we can construct the complete extended space tme graph

7 1142 Z. Guo et al. / Ad Hoc Networks 11 (213) vd vd Layer 1 v v v v v11 v12 v13 v14 Layer 1 v11 v12 v13 v14 (7 7,7) Layer 2 (6,6) (5,3) v21 v22 v23 v24 /(8,5) Layer 2 (6,6) (5,1) v21 v22 v23 v24 /(8,5) Layer 3 (4,6) v31 v32 v33 v34 Inactve node Layer 3 (4,4) v31 v32 v33 v34 Inactve node vs Actve node vs Actve node (a) After edge projecton. (b) After graph update. Fg. 3. An example of projected graph for 12 nodes n 3 layers at slot 9. G(V, E), where jvj = M N (S +1) O(M N S), je h j = M N S and je f j s dynamc dependng on the network stuaton. Although je f j s not determnstc, we can assume je f jo(je h j) accordng to the defnton of DTN. Although the ILP aforementoned potentally provdes the optmal soluton, t s NP hard. Even when we relax the condtons to be a lnear programmng, the computatonal complexty s stll as hgh as O(n 6 )(n s the number of vertex n G) usng ellpsod method [45]. In our extended space tme graph, n O(M N S). Thus n may be huge, leadng to extremely hgh computatonal complexty. Moreover, ILP s operated on the complete extended space tme graph, causng sgnfcant spatal complexty. In contrast, for, we buld a much smpler graph G o (V o, E o ), whch only contans M N vertces, and elmnate all holdng edges. Ths smplfcaton reduces the spatal complexty sgnfcantly. As we presented above, the operatons of nclude two routnes, (1) edge projecton and (2) routes reservaton and graph update. The frst routne, edge projecton, examnes all forwardng edges n the trace and project them to G o, whch ntroduces the complexty of je f j. The second routne s executed only when there s a flow n the graph, and every executon fnds out a flow of an nteger amount whch s at least 1. Thus there are at most F executons, where F s the total flow demand. In each executon, there are two steps, routes reservaton and graph update. As proven n Theorem 4.1, the complexty of fndng a route by tracng back along upstream nodes s upper bounded by M N, makng the total routes reservaton for all flows s upper bounded by M N F. Moreover, each route reservaton leads to node status and edge update (a node mght be changed to be nactve and an edge mght be removed form G o ). Durng each executon, a node s updated at most once and each edge s removed at most once, leadng to the total complexty of graph update for all flows s upper bounded by (M N F)+jE f j. Therefore, we can conclude that the computatonal complexty for s je f j +(M N F)+ (M N F)+jE f jo(m N F)+o(M N S). Apparently,, compared to ILP, can also reduced the computatonal complexty sgnfcantly, whch s demonstrated n Secton Performance of We evaluate the performance of by comparng t wth optmal solutons from nteger lnear programmng (ILP). The ILP formulaton s based on an expanded space tme graph. It, however, may not be able to provde feasble solutons (because not all traffc demands can be satsfed)., on the other hand, s a greedy algorthm that aggressvely searches for routes usng the earlest avalable edges. As we shall see, t not only acheves close to optmal solutons, but also characterzes the propertes of the near optmal routes accordng to the moblty pattern. We consder a three-layer underwater sensor network. Each layer covers a 6 m 6 m horzontal area and the dstance between two adjacent layers s 9 m. Four nodes are ntally randomly deployed n each layer and move followng the determnstc moblty model descrbed n Eq. (1) (.e. k 4 = k 5 = ). The smulaton n a small network s due to the hgh complexty of ILP (the proposed s scalable, we nvestgate larger networks n Secton 5). Each sensor has buffer sze of 3 packets and transmsson range of 1 m. Sensors n the 3rd layer take turns to generate packets from the 5th second to the 1th second wth the rate of one packet per second n a round-robbn manner. The smulaton runs to the 3th second and the slot nterval s chosen to be 1 s. We vary the power capacty from 5 to 1 transmssons, and unlmt means both the buffer and power capactes are not constraned. Fg. 4 compares the performance of ILP and. The curves are plotted based on the average results of 1 runs and the numbers assocated wth the sold lne n Fg. 4a ndcate the number of runs n whch ILP obtans feasble solutons. Although ILP s not feasble n some smulaton runs because not all traffc demands can be satsfed, always provdes solutons to delver as many packets as possble. We observe that ILP and overlap for both delvery rato and average delay n the unlmted condton, ndcatng that can perform as well as the optmal algorthm when there are no power, buffer and bandwdth constrants. It s nterestng to note that ILP fals to provde feasble solutons n more and more runs when the power

8 Z. Guo et al. / Ad Hoc Networks 11 (213) (1) (8) (8) (8) (6) 3 25 ILP Dlvery rato Average delay (s) unlmt ILP 1 5 unlmt (a) Delvery rato. (b) Average delay. Fg. 4. Performance comparson of ILP and. capacty decreases, whle provdes good solutons wth only slghtly lower delvery rato and hgher average delay. Especally when the power capacty s as low as 1 transmssons, ILP provdes no feasble solutons for all the runs, but provdes results for almost 6% of all packets. If we exclude the unfeasble runs n ILP, can perform as well as the optmal ILP. In Fg. 5, we plot the runtme of dfferent algorthms, whch represents the computatonal complexty. It s clear to see that ILP requres more and more tme when the power capacty s lower (more flow splts and conjunctons), but always renders solutons n short tme (around.1 s). In summary, for all the scenaros we nvestgate, provdes results close to the optmal ones. Moreover, can explore the relatonshp between the close to optmal routes and avalable hstorcal nformaton, whch s related to the underlyng moblty pattern, and provde gudance on how to utlze the hstorcal nformaton for nstantatng predcton asssted sngle-copy routng protocols (see Secton 5). 5. Predcton asssted sngle-copy routng Many routng protocols desgned for DTNs predct future contacts based on some hstorcal nformaton. The more precse the predcton s, the better performance the routng acheves. Ths s especally true for sngle-copy routng. However, even the same hstorcal nformaton and predcton methods may lead to completely dverse performance under dfferent moblty envronments. Thus, what nformaton can be used and how to predct the future become the man challenges. To address these challenges, we propose predcton asssted sngle-copy routng (PASR), that utlzes n a learnng perod to capture the characterstcs of the moblty pattern, and provde gudance on route selecton. Actually, does not examne the moblty model drectly. In, we frst demonstrate that can provde close to optmal soluton by comparng wth ILP, whch means the routes dscovered n are approprate under current moblty Runtme (s) unlmt ILP 5 model. Then we characterze the common features of these greedy routes and explore ther relatonshp wth the hstorcal nformaton, whch are both closely related to the underlyng moblty model. Fnally we can conclude whch hstorcal nformaton can be used and how to be used to predct future contacts and buld heurstc sngle-copy routng schemes. The routes formed from the predcaton asssted sngle-copy routng schemes share the same features wth the routes dscovered n. In the followng, we frst present the generc scheme of PASR, and then descrbe how to nstantate PASR to construct two specfc protocols for underwater sensor networks wth dfferent moblty patterns How PASR works? Hstorcal nformaton If the moblty pattern s stable for a long tme, the hstory can tell the future. Wdely used hstorcal nformaton ncludes: Recent trajectory: the geographc locatons just vsted. Average contact duraton: the average duraton of a contact. 2 Fg. 5. Runtme comparson of ILP and. 1

9 1144 Z. Guo et al. / Ad Hoc Networks 11 (213) Average nter-contact duraton: the average duraton between two contacts. A contact coupled wth the next nter-contact nterval s called a perod. Last contact tme: the last tme two nodes contacted. Contact frequency (or contact probablty): the average contact frequency wth another node or a landmark. Not all the above nformaton s avalable n a network or related to the moblty pattern. captures what hstorcal nformaton predcts the future wth current moblty model Gudance from The followng propertes of routes and node contacts, whch are closely related to the underlyng moblty model, can be captured by : Geographc preference: ths s defned as the common feature of geographc locatons that the greedy routes prefer. It s useful n geographc-related networks where nodes prefer certan geographc areas, or n landmark-based networks where nodes vst some landmarks frequently. Contact perodcty: ths descrbes whether any par of nodes have perodc contacts. Two nodes may have strct/weak contact perod wth fxed/varable contact and nter-contact duratons. Ths perodcty may not last for the whole network lfetme. Inter-contact tme dstrbuton: e.g., unform or exponental dstrbuton. It can be obtaned through curve fttng. Contact probablty: the contact probablty wth another node or one landmark n a certan tme nterval Predct the future After characterzes the moblty pattern, t suggests what hstorcal nformaton can be used for predcton. If the gudance exhbts geographc preference, a node can use t to determne whether to forward packets to a neghbor or not. For example, f the current neghbor wll travel to a locaton whch s preferred n wth hgh probablty, then t s qualfed to be the next relay. If moblty shows contact perodcty, we can utlze the average contact duraton and average nter-contact duraton to estmate the future perods usng lnear predcton, and utlze the last contact tme to estmate the next contact tme wth hgh accuracy. If the nter-contact tme follows some well-known dstrbuton, then the last contact tme can be used to predct whether a node s approachng or departng away from another node. Several models have been exploted n [2]. If a node contacts another node or landmark wth a certan probablty, the future contacts may be modeled as a sem-markov process as descrbed n [7]. In summary, connects hstory and future through proper nformaton selecton and predcton. Hence, effcent PASR can be nstantated followng ths procedure Instantatng PASR We next descrbe how to nstantate PASR for dfferent moblty models. For llustraton, we consder three models n an underwater sensor network. Ths network conssts of 3 layers and 15 nodes n each layer (n addton, the surface layer has one snk n the mddle). Each layer covers a 8 m 8 m square area and the dstance between two adjacent layers s 4 m. Each node has a buffer of 1 packets, a transmsson range of 5 m and a transmsson rate of 5 packets per second. The power capacty vares from 3 to 3 transmssons, and the slot duraton s 1 s. We examne UWSNs wth three moblty patterns UWSN n regular currents The frst moblty model we nvestgate assumes all nodes n the network float wth the regular currents followng Eq. (1) wth k 4 = k 5 =. We frst obtan gudance about the underlyng moblty pattern from, then propose a PASR protocol accordngly Gudance from. Snce our network conssts of three layers whch can be treated as three geographc areas and nodes move wth regular currents, we focus on two propertes: geographc preference and contact perodcty. The geographc preference n ths network means nodes n whch layer are preferred. Results from show that most nodes hghly prefer forwardng packets to an upper layer node drectly even when havng prevous contacts wth many nodes n the same and lower layers. Thus we obtan the frst gudance: an upper layer node s more preferred than other layer nodes. The contact perodcty for a par of nodes s declared f a certan contact perod repeats more than four tmes wthn 15 slots. We fnd that more than 8% of pars observe perodcty. Ths leads to the second gudance: nodes pars have perodc contacts. We should note that only ndcates perodcty, the perod duratons for dfferent pars are dfferent. Ths perodc contact property domnates the feasblty and accuracy of future contact predcton and the length of predcton wndow Protocol followng. Based on the detaled depcton of the network moblty and the gudance obtaned above, we propose a specfc PASR for ths network, energy effcent hstory predcton asssted routng (). Ths scheme ncludes two essental operatons: predcton and per-contact forwardng decson. Both predcton and forwardng decson at a node u are bult based on an predcton vector (PV), donated as E u,as shown n Fg. 6. PV s a vector of tuples (, v, Dv) to predct the potental contacts n the followng T slots (T s the length of predcton wndow) and estmate delay to the snk. In each tuple, s the predcton slot, v s the best potental relay n ths slot and Dv s the estmated delay through ths relay v to the snk. For example, a tuple (5, v 1, 2) means that the current node u expects to contact the node v 1 at the 5 slots later wth an estmated delay of 2 slots through ths node v 1. In addton to E u, node u also mantans an ndvdual PV (PV) E v u for each neghbor node v t met recently. E u s updated from all PVs t

10 Z. Guo et al. / Ad Hoc Networks 11 (213) node u E u v D v v 1 v 2 D Dv 1 v2 v j D v j E v1 v2 u Eu E v j u Fg. 6. PV and entres n node u. node u E u v D v v 1 v 2 v j Dv 1 D v 2 E E v1 v2 u u D v j E v j u node v 1 E v1 V' D v ' Fg. 7. The predcton update procedure for node u wth node v 1. mantans. For a tme slot t n the predcton wndow, the entry n E u s selected from entres at the correspondng slot n all PVs wth the mnmum estmated delay. As llustrated n Fg. 6, the node u expects to contact nodes v 1 and v j at 5 slots later, and the estmated delay s 2 slots f forwardng a packet to v 1 or 3 slots f forwardng a packet to v j. Thus, E u can choose the tuple (5, v 1, 2) from v 1 as ts entry at tme slot t. The PV E u s passvely updated every tme an PV s updated. Fg. 7 represents the update procedure when u contacts ts neghbor v 1 (u and v 1 are n the communcaton range of each other) at a tme slot. Durng the communcaton, v 1 wll upload ts predcton vector E v1 to u, whch s used by u to update the correspondng entry E v 1 u wth the predcted future contacts between them. The update procedure s as follows: node u frst clears all tuples n E v 1 u and predcts the future contacts wth ths node v 1 n the followng T slots. Snce ndcates weak perodcty n ths network, we choose the prevous two perods (two contact duratons and two nter-contact duratons) to estmate the future perods usng lnear predcton. For each predcted contact tme slot t, u wll fnd the smallest estmated delay D v n E v1 after t, then update the correspondng D v1 as D v for the tme slot t n E v 1 u. Ths tuple then becomes (t, v 1, D v ), whch means node u can forward packets to node v at tme slot t and expect the delay of D v. Once D v1 s updated, node u wll check the correspondng tem wth tme slot t n E u : f the current estmated delay n ths slot s larger than D v1, then ths tuple wll be updated as (t, v 1,D v1 ). PVs are exchanged only when they are updated, and can be pggybacked to the HELLO message at the begnnng of each slot. Therefore, the update s not frequent owng to the sparse connectvty n DTNs. Per-contact forwardng decsons are made based on the PV and the gudance from every tme a node encounters a neghbor. Snce results from ndcate that few nodes forward packets to a lower layer, we only allow forwardng to nodes n the upper or the same layer for smplcty. We take node u to llustrate the decson. When u can communcate wth v, t searches the expected delay Dv through v from E v u and the mnmum expected delay D v through the predcted best relay v from E u. Then node u makes postve forwardng decsons to v under two condtons: (1) D v 2½D v ; D v þ d 1 Þ and (2) D v 2½D v þ d 1 ; D v þ d 2 Š and node v s n the upper layer. The parameters d 1 and d 2 are called predcton error tolerances. These tolerances, whose values are small wth accurate predctons or large otherwse, are used to compensate the predcton error UWSN n currents wth randomness The second moblty model we explot nvolves random movements by followng Eq. (1) wth non-zero k 4 and k 5. The randomness smulates the mpact from envronment, whch may lead to estmaton errors and predcton errors n real systems. We notce that PASR can tolerate these

11 1146 Z. Guo et al. / Ad Hoc Networks 11 (213) Delvery rato Delvery rato Power capacty (a) (a) Delvery rato. rato. Average delay (s) Average delay (s) (b) (b) Average delay. Average energy consumpton Average energy consumpton Power Power capacty capacty (c) (c) Average energy. Fg. 8. Performance comparson of varous routng schemes n UWSN wth regular currents. Combned performance Lfetme (s) Fg. 9. Combned performance n UWSN wth regular currents. Fg. 1. Lfetme n UWSN wth regular currents. errors to some extent snce just captures the general propertes of the majorty of nodes, who exhbt smlar moblty patterns. In ths settng we use wth larger d 1 and d 2, and demonstrate ts performance n Secton UWSN n rregular currents The last moblty model ncorporates rregular currents whch wll sgnfcantly change the underlyng moblty pattern. Through ths settng, we can evaluate whether dscovers ths change and reacts correspondngly. We assume that nodes n the frst two layers wll be affected by an rregular water current, whch drfts nodes away from the center of the network area. The nodes affected swtch between the regular current and rregular current every 1 s. To provde connectvty to the snk, one node s anchored n the mddle of the frst two layers, whch are not affected by the rregular current. After executng under ths moblty, we fnd that, affected by the rregular current, most nodes n the bottom layer route packets to the center area through nodes n the same layer to take advantages of anchor nodes. We also notce that only the nodes n the same layer have contact perodcty. Thus we obtan the followng two gudance from : (1) a node n the same layer s preferred and (2) only predct for nodes n the same layer. Therefore, we modfy to obtan a new predcton asssted sngle-copy routng scheme, named, accordng to the new gudance. In, we adopt the technques and operatons n, but only predct future contacts for nodes n the same layer n the predcton update phase, and prefer nodes n the same layer n the forwardng decson phase. 6. Performance evaluaton In ths secton, we evaluate the performance of the nstantated PASR protocols for the UWSN descrbed earler. In ths network, nodes n the bottom layer randomly generate 3 packets from the 5th second wth the total generaton rate of one packet per second. In each moblty model, we compare nstantated PASR wth the followng schemes: : serves as the lower-bound. : energy effcent predcton asssted routng. It dffers from by precse predctons usng the determnstc terms n Eq. (1). Ths s an dealzed scheme for UWSN snce we do not know the precse moblty model n practce. s executed n the frst two moblty models, and we show that performs as well as although t only uses hstorcal nformaton.

12 Z. Guo et al. / Ad Hoc Networks 11 (213) Delvery rato (a) Delvery rato. Average delay (s) (b) Average delay. Average energy consumpton (c) Average energy. Fg. 11. Performance comparson of varous routng schemes n UWSN wth regular currents and randomness. Frst Contact (): The sngle-copy routng by forwardng packets to the frst node encountered wthout any predcton [5,18]. If multple nodes are contacted at the same tme, one n the upper layer s preferred. : a floodng scheme [4]. To save energy, we allow epdemc ACK to be broadcasted through the network, whch s used to delete useless copes. To compare performance, we adopt the followng metrcs: Delvery rato: the rato of packets delvered. Average delay: the average delay for all delvered packets. Average energy consumpton: the average number of transmssons needed to successfully delver a packet. Energy consumpton Delay Delvery rato, Combned performance: defned as used as a comprehensve performance measurement [8]. The smaller the value, the better performance s. Lfetme: the tme when the frst node des owng to power exhauston after packets generaton UWSN n regular currents We frst compare varous routng schemes n Fg. 8. When the network resources change from loosely to strngently constraned, t s not surprsng to see that the delvery rato of drops rapdly to.3 when the power capacty s 3. Ths s because uses too much energy durng the floodng as shown n Fg. 8c and exhausts sensors quckly. Ths ndcates that s not sutable for resource constraned networks. Meanwhle, performs better than wth hgher delvery rato, but t degrades quckly especally from the power capacty 1 to 3 snce the amless forwardng not only delays the packets, but also wastes energy. provdes the best results under all crtera. Wth the gudance from, the performance of both and approaches the results of. It s nterestng to notce that only causes a slghtly hgher delay than snce ts predcton based on hstorcal nformaton s not as precse as. Fg. 9 shows the comprehensve performance comparson consderng all crtera. We clearly observe that the proposed PASR protocols are close to and outperform others sgnfcantly. Ths confrms that leads to effcent PASR. We also plot the network lfetme under dfferent routng schemes n Fg. 1. We can see that sngle-copy schemes sgnfcantly extend the network lfetme wth much fewer energy consumpton compared to, and almost overlap wth the result from. We beleve that the lfetme of mult-copy schemes fall nto the between. It confrms that sngle-copy routng scheme wth proper predcton s more energy effcent n resource constraned networks UWSN n currents wth randomness We now examne the performance under a non-determnstc moblty pattern wth randomness by settng non-zero k 4 and k 5 n Eq. (1). We assume both k 4 and k 5 follow unform dstrbutons n the nterval [ c, c] and vary c from.1 m/s to 1 m/s. Each node has the buffer sze of 1 packets and the power capacty of 1 transmssons. stll uses the determnstc terms n Eq. (1) for predcton. Fg. 11 shows the performance comparson of dfferent schemes n UWSN wth regular currents and randomness. The results are smlar to that n regular currents wthout randomness, and the conclusons are stll vald even the current movement s not determnstc. Fg. 12 exhbts Combned performance Randomness Fg. 12. Combned performance n UWSN wth regular currents and randomness.

13 1148 Z. Guo et al. / Ad Hoc Networks 11 (213) Delvery rato (a) Delvery rato. 5 Combned performance (b) Combned performance. 5 Fg. 13. Performance comparson of varous routng schemes n UWSN wth rregular movements. the comprehensve performance of varous schemes under dfferent levels of randomness. We can see that PASR outperforms and and PASR can tolerate large randomness: ts performance only slghtly degrades when ncreasng the amount of randomness UWSN n rregular currents We now explore the performance under mpact from rregular currents as shown n Fg. 13. We observe that s no longer sutable for ths network and s even no better than (whch uses no predctons). Ths ndcates that napproprate predcton may sgnfcantly degrade the performance. The modfed performs much better and approaches. Therefore, we conclude that captures the propertes of dfferent moblty models and provdes correspondng gudance for nstantatng predcton asssted sngle-copy routng schemes. 7. Conclusons and future work In ths paper, we present a generc scheme predcton asssted sngle-copy routng (PASR) for UWSNs. We frst propose aggressve chronologcal projected graph (). It s a greedy algorthm that provdes results close to optmal and characterzes the propertes of the underlyng moblty pattern. We then desgn onlne heurstc protocols by choosng approprate hstorcal nformaton and forwardng crtera based on the gudance from. We nvestgate an UWSN wth varous moblty patterns and randomness usng two nstantated predcton asssted sngle-copy routng schemes, and. Smulaton shows that captures the propertes of varous moblty patterns and provdes correspondng gudance, and the nstantated routng schemes outperform others. As future work, we would lke to pursue the followng drectons: (1) we plan to explore the performance wth dfferent slot ntervals, predcton wndow and predcton technques and (2) we wll extend PASR to other DTNs wth dfferent network structures and moblty models. References [1] K. Fall, A delay-tolerant network archtecture for challenged nternets, n: Proc. of SIGCOMM, Karlsruhe, Germany, 23. [2] Z. Zhang, Routng n ntermttently connected moble ad hoc networks and delay tolerant networks: overvew and challenges, IEEE Communcatons Surveys and Tutorals 8 (1) (26). [3] R.J. D Souza, J. Jose, Routng approaches n delay tolerant networks: a survey, Internatonal Journal of Computer Applcatons 1 (17) (21) [4] A. Vahdat, D. Becker, Routng for Partally Connected Ad Hoc Networks, Tech. Rep., Duke Unversty, Aprl 2. [5] S. Jan, K. Fall, R. Patra, Routng n a delay tolerant network, n: Proc. of SIGCOMM, Portland, Oregon, USA, 24. [6] C. Lu, J. Wu, An optmal probablstc forwardng protocol delay tolerant networks, n: Proc. of ACM MOBIHOC, New Orleans, LA, USA, 29. [7] Q. Yuan, I. Carde, J. Wu, Predct and relay: an effcent routng n dsrupton-tolerant networks, n: Proc. of ACM MOBIHOC, New Orleans, LA, USA, 29. [8] S.C. Nelson, M. Bakht, R. Kravets, A.F. Harrs, Encounter based routng n DTNs, ACM SIGMOBILE Moble Computng and Communcatons Revew 25 (1) (29). [9] T. Spyropoulos, A. Jndal, K. Psouns, An analytcal study of fundamental moblty propertes for encounter-based protocols, Internatonal Journal of Autonomous and Adaptve Communcatons Systems 1 (1) (28). [1] W. Hsu, T. Spyropoulos, K. Psouns, A. Helmy, Modelng tme-varant user moblty n wreless moble networks, n: Proc. of IEEE INFOCOM, Anchorage, Alaska, USA, 27. [11] X. Zhang, J. Kurose, B.N. Levne, D. Towsley, H. Zhang, Study of a busbased dsrupton-tolerant network: moblty modelng and mpact on routng, n: Proc. of ACM MOBICOM, Montréal, Québec, Canada, 27. [12] J. Leguay, T. Fredman, V. Conan, Evaluatng moblty pattern space routng for DTNs, n: Proc. of IEEE INFOCOM, Barcelona, Span, 26. [13] T. Hossmann, T. Spyropoulos, F. Legendre, Know thy neghbor: towards optmal mappng of contacts to socal graphs for DTN routng, n: Proc. of IEEE INFOCOM, 21, pp [14] A. Mtbaa, M. May, C. Dot, M. Ammar, Peoplerank: socal opportunstc forwardng, n: Proc. of IEEE INFOCOM, 21, pp [15] A. Lndgren, A. Dora, O. Schelén, Probablstc routng n ntermttently connected networks, ACM SIGMOBILE Moble Computng and Communcatons Revew 7 (3) (23). [16] C. Lee, D. Chang, Y. Shm, N. Cho, T. Kwon, Y. Cho, Regonal token based routng for DTNs, n: Proc. of ICOIN, Chang Ma, Thaland, 29. [17] H. Dubos-Ferrere, M. Grossglauser, M. Vetterl, Age matters: effcent route dscovery n moble ad hoc networks usng encounter ages, n: Proc. of the ACM MOBIHOC, Annapols, Maryland, USA, 23.

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Mascolo, Adaptve routng for ntermttently connected moble ad hoc networks, n: Proc. of IEEE WoWMoM, Washngton, DC, USA, 25, pp [42] Z. Zhou, J.-H. Cu, A. Bagtzoglou, Scalable localzaton wth moblty predcton for underwater sensor networks, n: Proc. of IEEE INFOCOM 28, Mn-Conference, Phoenx, Arzona, USA, 28. [43] S.P. Beerens, H. Rddernkhof, J. Zmmerman, An analytcal study of chaotc strrng n tdal areas, Chaos, Soltons and Fractals (1994). [44] L. Ford, D. Fulkerson, Flows n Networks, Prnceton Unversty Press, [45] D. Bertsmas, J.N. Tstskls, Introducton to Lnear Optmzaton, Athena Scentfc, Zheng Guo s currently a Professor of X an Unversty of Posts and Telecommuncatons, X an, Chna. He receved hs bachelor degree n Electronc Engneerng from Unversty of Scence and Technology of Chna (USTC) n 25, and Ph.D. degree n Computer Scence and Engneerng from Unversty of Connectcut n 21. Hs research nterests are network codng, channel codng, routng and delay/dsrupton tolerant network n the area of Underwater Sensor Network (UWSN). Bng Wang s currently an Assocate Professor of the Computer Scence & Engneerng Department at the Unversty of Connectcut. She receved her B.S. degree n Computer Scence from Nanjng Unversty of Scence & Technology, Chna n 1994, and M.S. degree n Computer Engneerng from Insttute of Computng Technology, Chnese Academy of Scences n She then receved M.S. degrees n Computer Scence and Appled Mathematcs, and a Ph.D. n Computer Scence from the Unversty of Massachusetts, Amherst n 2, 24, and 25 respectvely. Her research nterests are n Computer Networks, Multmeda, and Dstrbuted Systems. She receved NSF CAREER award n 28. Jun-Hong Cu receved her B.S. degree n Computer Scence from Jln Unversty, Chna n 1995, her M.S. degree n Computer Engneerng from Chnese Academy of Scences n 1998, and her Ph.D. degree n Computer Scence from UCLA n 23. Currently, she s an Assocate Professor n the Computer Scence and Engneerng Department at Unversty of Connectcut (UConn). She also serves as the Assstant Dean for Graduate Studes and Dversty of School of Engneerng at UConn. Her research nterests cover the desgn, modellng, and performance evaluaton of networks and dstrbuted systems. Currently, her research manly focuses on algorthm, protocol and system desgn and development n underwater sensor networks, autonomous underwater vehcle (AUV) networks, and dstrbuted cyberaquatc systems. She has also been conductng actve research on smart health and smart transportaton systems. At UConn, she leads UbNet (Ubqutous Networkng) Lab and UWSN (UnderWater Sensor Network) Lab. See for her recent projects and publcatons. She s actvely nvolved n the communty as an organzer, a TPC member, and a revewer for numerous conferences and journals. She now serves as an Assocate Edtor for Elsever Ad Hoc Networks. She co-founded the frst ACM Internatonal Workshop on UnderWater Networks (WUWNet 6), and she s now servng as the WUWNet steerng commttee char. She receved 27 NSF CAREER Award and 28 ONR Young Investgator Award. She also receved the Unted Technologes Corporaton (UTC) Professorshp n Engneerng Innovaton award at UConn n 28 and UCLA Engneerng Dstngushed Young Alumnus Award n 21.