Ravine Streams: Persistent Data Streams in Disruptive Sensor Networks

Transcription

1 Ravine Streas: Persistent Data Streas in Disruptive Sensor Networks Mingsen Xu, Wen-Zhan Song Departent of Coputer Science, Georgia State University Atlanta, Georgia 333, USA Eail: Abstract Opportunistic network coding has been developed and applied in disruptive networks to provide optial data delivery. Though network coding syste utilizes coding opportunities aong ultiple paths, its application in data collection suffers fro a disconnected sink node and the liited storage space available for data cache. The state-of-the-art approach has studied preserving data persistence as an optiization proble under storage and energy constraints, without considering disruptive network dynaics during data redistribution. In this paper, we propose Ravine Streas () to axiize data preservation under the constraints of liited storage and probabilistic node failure throughout data redistribution. Our approach leverages adaptive power control to achieve ensured storage of each redistribution data. Meanwhile, in the course of data redistribution, distributed coding-based rebroadcast strategy not only reduces the data duplication, but also iproves the statistical property of sybol randoness. We show that the perforance of preserving data persistence of proposed is approxiately bounded by the optial solutions. The experiental evaluations deonstrate that increases data delivery ratio, consues even less counication energy with only coparable storage cost, when copared with existing data preserving algoriths. Index Ters Persistent Data Collection, Network Erasure Coding, Transission Power Control, Disruptive Sensor Network I. INTRODUCTION In a large-scale sensor network deployent, one of ajor reasons contributing to interittent connections and disruptive counication is sensor nodes failure. Note that the reasons for node failure have a quite broad range, which can be either power depletion, unable to route packet to destination or overflowed receiving and transitting buffer. Each node failure influences the data collection flow routed through it. In the worst case, sink node failure ipairs the entire network traffic. To preserve data persistence, data strea has to be rerouted to other paths or redistributed to other storage nodes if none active routes are found. Existing algoriths fro the literature studied this data preserving as an network flow optiization proble, like [] axiizes the iniu residue energy in the network for the next data redistribution to arise; [2] cobines iniizing data redistribution and retrieval cost into a single proble. Though optial solutions are devised under either energy or storage space constraints, ost of the previous works ignore the fact that node failures could happen in the course of data rerouting or redistribution. The deterined approach is not capable of scheduling data redistribution without the global knowledge of which part of nodes could fail in the iddle. Moreover, the data redistribution is conducted in the network of heterogeneous node failure probabilities. This fact iplies that data should ove towards ore reliable nodes with sufficient residue energy and storage space, such that higher data delivery rate can be achieved. In this paper, we propose Ravine Streas to preserve data strea persistence in disruptive sensor networks. Source data is initiated and delivered in its encode for by network erasure codes OnCode [2]. For data preservation, receiving nodes distributively ake the acceptance decision based on local failure probability and storage space. Note that here nodal failure probability has taken the residual energy into account and dynaically update across the process. Adaptive transission power control in ensures that data acceptance probability by neighbor nodes is expected at for each broadcasting under iniu transission power. With data packet recoding, the dispensable data content redundancy is constrained for ore energy efficiency. Moreover, we show that the delivery perforance of proposed is bounded by Optial solution: η = OPT ln( δ ) 2λ [ + ω() + 2ω(2) 2 ( 2) ]. In suary, this work has three contributions: () leverages probabilistic transission power control and network erasure recoding to preserve data throughout disruptive network connection. Additionally, the data redundancy is largely reduced, increasing algorith energy efficiency. (2) akes distributed probabilistic decision that directs redistribution data to ore reliable storage nodes, without global knowledge of density and node failure probabilities, soothing data collection traffic under disruptive connections. (3) Our analysis shows that the proposed algorith has bounded perforance copared with optial solution. The rest of the paper is organized as follows. In section II, we suarize and copare related works. Then we present the design and analysis of Ravine Streas protocol in section III. In section IV, we present experiental evaluation results. We conclude our work in section V. II. RELATED WORKS A. Data persistence without storage constraint GROWTH [3] ensures data reliability in a zeroconfiguration network with no storage constraints. Growth code evolves its code degree over tie. For each code degree,

2 2 it leads to a better decoding probability than LT codes when partial encoded packets are received. MORE [4], SlideOR [5] and [6] leverage rando linear coding to encode innovative received packets. All of the have better perforance than the ExOR [7], which is the opportunistic routing protocol without network coding. MORE encode sybols by rando linear coding, without needs of selecting next-hop forwarder list and iproving spatial usage in ultiple transissions. CCACK [8] uses a null-space based ACK to notify neighbor nodes about the reception of encoded packets. CCACK suppress redundant packets, which carry linearly dependent encoded sybols. Distributed LT Codes [9], [] decoposes original degree distribution into different probability distributions for sources only one-hop away fro data relay based on a two-branch relay odel. The degree deconvolution with selective XOR in forwarders theoretically yield a degree distribution close to D in the receiver. Xu et al. proposes ONEC [] to explore network erasure coding in disruptive sensor networks. ONEC leverages a strict structure, e.g. tree structure, to conduct recursive deconvolution of degree distribution. And opportunistic recoding is exploited to ensure ore sybols can seep through network to receiver. All the aforeentioned works do not consider storage constraint and the scenario of sink failure. Sink failure and O() storage space constraints can pose a big challenge to network coding based ethods, which erely encode and forward packets to sink, in either opportunistic or ACK-control anner.. Data persistence with storage and energy constraint Lin et al. [2] propose a LT codes based erasure coding for preserving data in a large-scale network. The key idea is to randoly walk data fro redistribution nodes to storage nodes to eulate the rando selection in LT coding. Multiple redundant rando walks are initiated by each of data which stop in a storage node with specific probability derived by its selected code degree. A optial redundancy factor for each data sybol is derived offline by linear prograing. In [3], Aly et al. suggest to construct LT codes without knowledge of axiu node degree. In [4], Aly et al. eploy rando walk based schee to distributively construct the Raptor Codes, which is of scalable decoding coplexity (+ɛ)n with respect to the network size and sybol size. [5] presents a packetcentric approach to ensure that degree distribution confor with final degree distribution. Every encoded packet is associated with a selected code degree. The packet collects and encodes the sybols fro passing nodes uniforly distributed in the network. The packets terinate once associated code degree is satisfied. The above ethods preserve data persistence in a robust anner by using network coding, however, they ignore the storage and energy constraints. Tang et al. [6] foralizes storage depletion induced data redistribution as the iniu cost flow proble, and devises a distributed data redistribution algorith (). [7] consider the energy and storage depletion to axiize data preservation tie. Valero et al. [2] forulates the proble as an optiization proble and use Linear Prograing to find the optial solution. A distributed algorith () is ipleented for in-network storage and later data retrieval. [8] proposes a probabilistic broadcasting based data redistribution schee. Their contribution is to derive a proper probability distribution for rebroadcasting packet. Hou et al. [] seeks to axiize the iniu reaining energy aong the nodes storing data ites. It presents a centralized greedy heuristic to approxiate the optial solution under certain conditions. The above optiization algoriths, though considering energy and storage constraint, ignore an iportant fact that disruptive condition ay happen in the course of data redistribution. The disruptive network seriously challenges data redistribution. Distinct fro the existing works, our contributions of are three fold: first, conducts probabilistic broadcasting with adaptive transission power to overcoe the disruptive connection during data redistribution. It has high energy efficiency and low essage redundancy. Second, insitu recoding can reduce data redundancy in sybol wise. Third, generalizes the energy and storage constraints to nodal utility, which includes failure probability and storage constraint. According to the nodal utility, data storage decision can be ade distributively. III. ALGORITHMS AND ANALYSIS Ravine Streas is an integrated set of distributed algoriths that protect data collection strea fro disruptive network nodes and connections. The data persistence preservation of is built upon the opportunistic in-network coding and delivery (OnCode) [2]. Data packets are initially encoded and transit by OnCode. When local storage space vanishes, redistributes excessive received data packets to ore reliable nodes to preserve data persistence. considers both heterogeneous failure probabilities (due to energy depletion or other factors) and storage constraints, and addresses the proble of disruptive connection during data redistribution. leverages network erasure coding in data redistribution, and deterines the rebroadcasting probability and transission power level according to nodal utilities. It is worth to ention that algoriths are probabilistic, adapting to the dynaic network conditions with iniu execution overhead. We describe the properties of an ideal data recode and redistribution algorith, which is referred to as OPT. As the optial benchark solution, OPT presents the following properties that our algorith design concerns. First, OPT does know how uch data can be accepted and how uch data needed to be redistributed if the node happens to be disruptive at a certain tie. Here, we define a node is disruptive as it can not forward any data towards sink, and data strea is disconnected hereafter. In other words, OPT deterines the data acceptance in an optial way so that the storage use are balanced across the network. Second, for a data redistribution in a tie range ahead, OPT can always find a deterined path fro disruptive node to destination storage node with stable counication link and ensured data delivery. And only

3 3 one copy of source data packet needs to be aintained inside network. In practice, it is unlikely to predict a stable counication link across ulti-hop connection in the disruptive network conditions, which eans the data redistribution is not guaranteed to be successful every tie. Thus, ultiple copies of data packet are necessary to reduce the risk of data loss. Under this condition, data redundancy needs to be reduced between ultiple survived data copies. Third, OPT can observe if the disruptive node is trapped in bad region or not, so as to adjust the appropriate radio transission power to assist the counication. In fact, without perfect knowledge ahead of tie, it consues considerable overhead to search different levels of transission powers until a proper power is found. adopts two integrated echaniss to tackle the unideal situations: Deterine Data Acceptance, Probabilistic Data Redistribution. is able to preserve data persistence in heterogeneous situations subject to node failure probability and storage constraints. The atheatical sybol and notations are described in Table I. Notation Ni Ui δ i C i C ax β α q i p τ TALE I NOTATION IN ALGORITHM Explanation A. Deterine Data Acceptance Neighbor set of node i under power level Nodal utility under TX power Failure probability of node i Free storage space on node i Maxiu storage space Syste paraeter for data acceptance Replaceent factor Probability of accepting incoing packet in node i Selection probability for power level Exponential index of power adjustent Due to the opportunistic nature of encoded network traffic, it is unlikely to predict the exact aount of incoing packet in a certain tie window. Therefore, when disruption occurs, there is hardly a deterined way to calculate the exact aount of data needed to be redistributed. The best approach is to ake this decision based on the dynaic available storage space in each node. adopts the reactive ethods to discern available storage in node i, defined as C i. We first look at an exaple of a data strea fro i j k, where node k becoes disconnected, aking node j not able to forward any incoing traffic. Node j stores data packets unsent in its own buffer. To preserve data persistence, node j has to redistribute the excessive data to other nodes for storage before its space is used up. If data packets are redistributed only when storage space is full, the network will experience a sudden and unexpected traffic burst. To avoid this draatic traffic change, adopts probabilistic ethod to pre-estiate the probability q j for each incoing packet. The probability q j indicates the probability with which node j accept the received packet. With this soothing technique, network traffic can reain relatively stable even under unforeseen disruptive conditions. The probability q j is deterined distributively, based on local ratio of nodal available storage space C j and axiu storage space C ax. With less available storage ratio, incoing packet will be less likely to be accepted. Moreover, each node i has a certain failure probability δ j due to either energy depletion or other external factors. Therefore, final data C acceptance probability is estiated against factors j C ax and δ j. We cobine these two factors by ultiplicative operation. q j = β U j = β ( δ j C j C ax ) () where U j represents the available nodal utility, and β is introduced by algorith to hold a tolerance guard, which is tunable. If node decides not to save the received packet, it will proceed to redistribute the packet to other nodes for storage.. Probabilistic Data Redistribution The reason of redistributing data packet following a probabilistic anner is two fold. First, having packets probabilistically broadcast consue significantly less counication cost for offloading data to other storage nodes than that of gossip flooding. Second, statistically such a probabilistic redistribution can itigate the risk of data loss despite the fact part of delivery paths ay fail in the course of redistribution. Two ain challenges arise in design. First is about how to ake data redistributed towards reliable storage nodes instead of nodes with higher failure probability. Due to heterogeneous node densities, rebroadcast essage can be heavily stored in nodes with denser vicinity but unreliable nodes. Data is unlikely to be redistributed to other nodes, which ight have better connection to sink node for collection purpose. integrates the adaptive power control to change the outcoe of data redistribution towards ore reliable nodes. Second challenge is to reduce data redundancy in redistribution. More redundant data packets broadcast in the network iplies ore energy are consued to achieve this process. Although energy cost for preserving data persistence is the extra overhead ust paid, this cost needs to be carefully conserved. Excessive waste of energy severely causes nodes to fail due to power depletion. Probabilistic data redistribution is articulated in Algorith, which describes the transission power control based rebroadcast and recoding based data redundancy constraining. When the node with decreasing storage space decides not to save the incoing packet, it starts to redistribute the data to other storage nodes with adaptively controlled transission power. In line 5 8 of Algorith, node i selects a certain power level for broadcasting, according to a posterior probability distribution of transission power, i.e. {p, p 2,..., p }. This power distribution is dynaically updated based on available storage space aong neighbor nodes. This rebroadcast is invoked when the essage is not accepted by the node. Since it is the source of data redistribution, there is no duplicate copy of this packet in the network yet.

4 4 Algorith Probabilistic Data Redistribution Input: Effective storage space C i, β, ax storage C ax, replaceent factor α, Power distribution {p, p 2,..., p } : Draw rando variable ρ fro range (, ) 2: Set q i = β U i = β ( δi Ci C ax ) 3: if ρ < q i then 4: Save this data packet to local storage 5: else 6: Node i select power level with probability p 7: Rebroadcast the data packet κ using selected transission power. 8: end if 9: Node j upon receiving a rebroadcast data packet κ : Draw rando variable ρ fro range (, ) : if ρ < q j then 2: Save the data packet to local storage flash 3: else 4: if Check coding distance(κ, S) > then 5: Select sybol S l with sallest distance with other sybols in storage 6: Replace S l with κ with probability α 7: if ISRECODALE(κ, S) == TRUE then 8: Recode κ by XORing sybols in storage 9: end if 2: Rebroadcast packet κ with probability ( α) 2: else 22: if ISRECODALE(κ, S) == TRUE then 23: Recode κ into κ by XORing sybols fro storage 24: end if 25: Rebroadcast new packet κ 26: end if 27: end if Then the rebroadcast packets are treated differently. When a rebroadcast packet arrives at a node with sufficient storage, the essage will be accepted and stored (line -3). In the other hand, when no sufficient storage is available, receiving node will operate recoding before it rebroadcast out the essage with a selected probability. In line 4, it exaines the code distance between received packet κ and encoded sybols in the storage space with the sae code degree. If there exists data of the sae degree which has different code sybols, the packet will replace the one with sallest coding distance fro other sybols with a probability α. The purpose of replaceent is to axiize the decoding probability, since the encoded sybol with iniu code distance contribute little to the decoding. In case that no sybol with the sae degree is found in the storage, algorith evaluates the opportunity that rebroadcast packet can be recoded by XOR operation with stored sybols to generate a new sybol. Note that the recoding does not change the code degree associated with the packet (line 23-25). Recoding the sae rebroadcast essage in different nodes can ix the essage randoly with diverse sybols, generating non-duplicate encoded data. Hence, it reduces the data redundancy in rebroadcast essages, avoiding wasting energy in broadcasting duplicate essages. Adaptive power control and constrained data redundancy are two ajor technical building blocks in the probabilistic data redistribution, which are described as follows. ) Adaptive Power Control: Without adjusting radio transission power, packets ay be trapped in low storage region. Adjusting transission power oves packet out to the nodes with ore sufficient and reliable storage space. The transission power adjustent procedure itself is probabilistic. An intuitive way for adjusting probability of transission power is to ake it proportional to the total available nodal utilities U j in node j: p = c U j (2) The above equation iplies that transission power that reach larger aount of U Pi j has a larger probability to be selected for data rebroadcast. However, there exists one drawback of directly using the proportional equation to deterine the probability of transission power. Applying this strategy, each node greedily selects the axiu power to rebroadcast throughout the process, leading to significant essage flooding and useless data redundancy, though the local data entrapent is relieved. Figure shows an exaple depicting this proble. In the figure, nodes fro A to G select their axiu power respectively, i.e. = 3, for it can reach nodes with ost nodal utilities. However, each node, like node F, receives 6 copies of rebroadcast essages, which are ostly duplication. Meanwhile, transission with power can consue quadratically ore energy than that of power. The energy efficiency can be enhanced by letting each node selects their transission power conservatively. Meanwhile, we still wish to preserve the data persistence, which eans that rebroadcast essage is stored by at least one storage node. Adaptive power control has been designed to achieve both of goals. U_A =. Fig.. A = =2 =3. C..2 D.3 F E G.2.3 Exaple of transission power control The probability of selecting transission power level is redistributed to be exponentially proportional to the total nodal utilities aong rebroadcasting node s neighbors. p = ( Ūj Ū j (Uj )) τ (3) j

5 5 where τ is the exponential syste paraeter tunable between and and Ū j is the average nodal utilities of node j and node j s neighbors, when power level is applied in node j s transission. When the su of nodal utilities equals to, the expected probability of storing the rebroadcast essage is. This ensures that the corresponding power level is selected to guarantee the data persistence. Rather than linear proportional relationship, the above equation has the power exponent τ (, ). With syste exponent τ, the power level p, under which the su of nodal utilities Uj is closest to, has highest probability in all power levels. The reasons of adding coefficients Ū j are two fold. First, the power level, which increases not only total nodal utilities but also the average values, should be given a higher probability in the power distribution. Second, p needs to approach to ore aggressively once the next power level leads to a larger average utility aount, so that cut-off power level ay appear saller. A saller cut-off power level indicates exponential energy conservation. In Equation 3, if the calculated p, then let p =. Notice that, in which p, is the cut-off power level in power probability distribution. Through probability noralization, it ensures that p equal to. The average nodal utility follows that: Ū j = /Ūj N j + U j In order to calculate the nodal utility suation and average value, node j needs to know its neighbors utilities. Thus, algorith adds two extra fields in each broadcasting packets: power level indicator and available nodal utility. Upon receiving rebroadcast essage, node j records both power level received and available nodal utility fro neighbor node. For instance, in Figure, before adaptive power control, node A choose power level based on Equation 2, so that a total nodal utility can reach or exceed. Since ( ) =.3 >, the ost likely power level for node A is = 3. We set τ =.4. With adaptive power control, when =, it gives p = (. 3).4 =.68. Set = 2, then p 2 = (.4..7).4 =. Thus, node A s cut-off power is reduced fro level 3 to level 2. Average TX Power Level Fig. 2. APC PC Node Density Average TX power level for data redistribution. Figure 2 shows the average TX power levels selected by Equation 2 (PC) and Equation 3 (APC) under different node densities respectively, within the TOSSIM [9] network siulator. Fro the results, it shows that adaptive power control (APC) reduces the power level by 6% on average copared with basic power control (PC). In addition, the saller deviation of power level aong nodes indicate that energy consuption of TX power is relatively ore balanced if executed by APC. Moreover, the value of power level decreases slowly in PC. The reason is that each node greedily selects its power level, so that storage space is consued faster than necessary, aking other nodes have to take higher transission power to discover ore storage nodes. 2) Data Redundancy Constrain: Adaptive power control (APC) reduces the energy consuption of rebroadcast as well as the total aount of rebroadcast data replication. However, redistribution packets consist of duplicate data due to the rebroadcasting process. Data content redundancy wastes counication energy as well as the storage space. Therefore, we further constrain the content redundancy of rebroadcast essage by conducting sybol recoding without ipairing the original code degree distribution. Recoding procedure is shown in Algorith 2. Recoding step takes as input the rebroadcast encoded packet S, a set X of both decoded sybols and encoded packets of degree less than 2 and regenerates a fresh encoded packet with the sae degree as d. This recoding step ixes the encoded sybol of rebroadcast packet with local sybols in storage, such that ultiple copies of broadcast packets can be stored with distinct encoding contents after their redistribution process. Algorith 2 Data Recoding Input: Received rebroadcast packet S, a set X of both decoded sybols and encoded packets of degree 2 Output: Recoded packet Y : for all s S do 2: 3: for all x X do 4: x, if{x s & freq(x) < freq()} 5: end for 6: if = then 7: Y S x 8: end if 9: end for The basic operation in network erasure coding is XOR, which is effective and of low coputation cost. It verifies the properties that swapping sybol only requires another XOR operation. For instance, a native sybol s in S can be replaced with s 2 if target pair (s s 2 ) is available, where s 2 is not contained in S. That is, (s... s ) (s s 2 ) = (s... s 2 ) = S. We denote this relationship as s s 2. Since there are ore than 5% encoded packet of degree equals to or less than 2 in LT Codes and Raptor Codes and the search for degree 2 packets are faster than higher degree packets, we ainly leverage those local packets with degree d 2 to recode rebroadcast packets. When ultiple target

6 6 pairs are found in the storage or can be generated fro native sybols, like (s s 3 ) and (s s 4 ), the sybol s i, with less appearance frequency is selected. Illustrated in Figure 3, conduction of sybol recoding constrains the data redundancy. In Figure 3, packet of {x + x2 + x3} is broadcast fro node C, and two duplicate copies are received by node A and respectively. There exist different groups of encoded sybols previously cached in node A and storage. For exaple, node A has 3 decoded native sybols x3, x4, x6 (degree ), which has different appearance frequency in the prior sybol recoding, shown in nuber arked in the right-top corner. According to line 4 in Algorith 2, node A selects {x2 + x5} to recode, because x5 satisfies x5 x2 and {x2 + x5} has the lower frequency than {x3} and {x4} as well. The recoded packets fro node A and becoe distinct and carry different native sybols. (2) (2) () x3 x4 x6 () x2+x5 () x7+x8+x9 x+x2+x3 Fig. 3. A + x2+x5 x+x2+x3 Rebroadcast Node x+x3+x5 Redistribution Node C x+x2+x3 Rebroadcast Node x+x2+x3 + x3+x4 x3+x4 () (2) x4+x5 () x8+x9 x+x2+x4 Illustration of sybol recoding in rebroadcast node. Although a successful decoding probability depends on the code degree distribution adopted during encoding, sybol recoding does increase the decoding probability. Fro LT encoding point of view, our data redundancy constrain approach builds stronger and ore reliable connections between left and right coponents in the Tanner Graph. Introducing ore connections between sybol and encoded packet prevent decoding fro early failure, in the case of encoded packet loss. Average Packet Redundancy Fig. 4. Recode norecode Node Density Data redundancy under various node densities. Figure 4 evaluates the data redundancy against different node densities. With our recoding on rebroadcast packet, the redundancy of data content has been reduced by at least 5%. With node deployent becoes denser the data redundancy with recoding can be further lowered to approach to, which eans that there is alost no identical rebroadcast essage on the network. In contrast, without recoding the data redundancy increases as the node density, because ore nodes are involved in packet rebroadcasting, causing ore duplicate packets in the network. C. Algorith Analysis preserves data when disruptive connection causes buffer to overflow. This data quality preservation layer is built upon opportunistic in-network coding-based (OnCode [2]) data delivery. The packets delivered in the network before redistribution are handled by OnCode protocol. The deliverable sybol size for unit tie span is based on the disruption probability distribution Π, shown in [2]. Lea : [2] Given a disruption probability distribution Π = {π w, π w2,..., π wn }, with π wi denoting the probability for discretized disruption probability w i, then by recursive hitting tie estiation, the deliverable sybol size = n i= i= n R i i= (+ɛ)λ = n /(+ɛ)λ i= L(i,sink) = /(+ɛ)λ k Nbr(i) P ik(t ik +L(k,sink)), where both P ik and T ik are n i= deterined by distribution Π. Hence, the perforance bound of OnCode is described as: Theore 2: [2] Given the size of sybol set as and degree distribution of Raptor Codes ω( ), the delivery ratio of OnCode is OPT/λ, where λ = + +4 ( e ɛ /δ) 2 ω() (+ɛ) (δ, ɛ (, ]), with a successful decoding probability of all sybols ( e ɛ ). [2] shows that OnCode provides a OPT/λ perforance bound. We continue to consider the optial solution of data preserving in the course of disruptive network connection: OPT. A stable path fro distribution node to storage node is always perceived in OPT for distributing data, and exact one copy of data distribution is sufficient for preserving persistence. Therefore, the storage cost for OPT is O(). For, adaptive power control in section III- ensures that in each broadcast the expected acceptance probability of distribution data in storage node approxiates, and adopts 2-hop rebroadcast to ake sure the event that storage nodes accept distributed data with probability equivalent to. We assue that there are available storage space for innovative data sybols. OPT can exactly leverages all of these space to store redistribution data for persistence. Then, the delivery ratio of is derived as follows. Theore 3: Given the size of source data set, and degree distribution of Raptor Codes ω( ), the final delivery ratio of : η = OPT ln( δ ) 2λ [ + ω() 2 + 2ω(2) ], where ( 2) λ = + +4 ( e ɛ /δ) 2 ω() (+ɛ) and δ, ɛ (, ], with a successful decoding probability of sybols ( e ɛ ). Proof: adopts 2-hop redistribution to ensure the acceptance of data, therefore only 2 can be accepted in storage nodes expectedly without recoding. In other words, the final delivery ratio of becoes λ 2. However, leverages recoding to eliinate data duplication, so that any 2 copies

7 7 are distinct fro each node when they are stored. Therefore, the final delivery ratio is deterined by the portion of data that can be recoded shown in Algorith. Only packets of degree and 2 are utilized in recoding. And we define the event A as that packets are recodable when there exists a sybol x in the packet that can find x y in the storage sybol set of either degree or 2. The probability of event A is ln( δ ) (ω() 2 +ω(2) ). If this event occurs, ( 2) the corresponding delivery ratio of is /λ, otherwise /2λ. Therefore, the final expected delivery ratio equals to: OPT ln( δ ) 2 2λ [ + ω() + 2ω(2) ( 2) ]. IV. PERFORMANCE EVALUATION In this section we present the perforance evaluation of on TOSSIM [9] siulation. The perforance of is copared against other existing data collection and redistribution algoriths fro the literature. The experiental results deonstrate that data delivery ratio under disruptive networks is substantially iproved by our algorith, with an efficient energy cost and oderate storage cost. Experiental setup and result analysis are discussed as follows. A. Experiental setup To illustrate the advantages of Ravine Streas in iproving data delivery ratio, hence enhancing data persistence over disruptive sensor networks, this work ipleents and copares with three other existing data collection and redistribution protocols: [2], [6] and. is proposed to optially solve the data redistribution proble under interittent network connection, i.e. iniizing the data redistribution and retrieval cost. is ipleented in a distributed anner by push-relabel network flow ethods. devises an index based potential field, which is used to deterine the aount of data redistributed to storage nodes. It shows the optiality of data redistribution without data retrieval cost. is a plain data collection protocol, without specific redistribution and coding strategy. Once node disruption happens, data is redistributed randoly to other storage nodes by broadcasting. The experient is carried out in square area with nodes randoly deployed. We test the algoriths in a network of size and 5 respectively, and the total storage space, nodal failure probability and nuber of data generators inside network vary to copare the perforances under different scenarios. Moreover, energy cost and flash storage cost are also evaluated aong different algoriths. For, the total power levels are set as 8, each of which can reach areas of different radii. Set nodal utility factor β =.9, and replaceent factor α =.5. We show the experiental results in the following sections.. Data persistence under disruptive networks For nuerical evaluation, we use data delivery ratio to represent data persistence. Data delivery ratio is defined as the ratio between the aount of data sent and the actual aount of data recovered by the destinations. Figure 5 shows the data delivery ratio for ultiple algoriths under variable total storage spaces. The average nodal failure probability is 2% and there are 5 and 2 data generators in network size of and 5 respectively. Each of data generators has kbps data rate. In Figure 5, y-axis denotes the percentage of data sent which can be preserved throughout the network disruption, with x-axis showing different total storage space in nodes. outperfors other algoriths for all cases of different storage spaces. Fro both of experients, the ratio of data persistence iproves along with the increasing storage space. For exaple, it can be observed that with increasing nodal storage space (.4Mbytes to.mbytes), the ratio of data persistence is significantly iproved by, increasing fro 5% to 93%, which is uch ore than the increents in other algoriths. Copared with the and, the application of network erasure coding in akes packet redistribution ore robust. Unlike the and, which does not has reliable data redistribution to storage node, adopts probabilistic broadcasting together with randoized recoding for data redistribution. Therefore, ore data packets are preserved even in the present of disruptive nodes and network conditions. Copared with the, eliinates the duplicate packet retransissions. The recoding of redistributed packet with innovative data in is beneficial for itigating the data content redundancy. Each packet carries different innovative sybols which contribute to the final decoding. Recoding not only reduces the data redundancy, but also prootes the randoness in ixing sybols. The network erasure coding based data delivery can axiize its coding gains when the sybol selection is pure rando across the entire source sybol set Storage Space (Mytes) Storage Space (Mytes) (a) Network Size (b) Network Size 5 Fig. 5. Data delivery ratio over different storage spaces (failure prob. = 2%). Figure 6 deonstrates the delivery ratio under different node failure probabilities. The storage space of each node is set to Mbytes. In the left figure, it shows that stills has the best perforance in ters of delivery ratio. More iportantly, when average nodal failure probability increases, the delivery ratio of only reduces by 3%, and still aintains above 6% delivery ratio under 9% failure probability. On the contrary, the delivery ratio of and fall below 2%, and has even less than 5% data delivery ratio. The right figure in Figure 6 deonstrates the sae trend. An essential reason is that algoriths other than fail to consider disruptive network condition during data distribution,

8 8 and hence algoriths are not able to adapt to interittent connection and disruptive counication link. For exaple, after redistribution node in deterines how any aount of data should be rerouted to the destination storage node, based on the potential index, redistribution nodes take it for granted that the redistribution data can reach or be stored in the destination. Unfortunately, it is not always true, especially in disruptive networks where the interittent connection can happen any tie during the entire data delivery. This experient anifests that disruptive counication poses a big challenge to existing data redistribution protocols Failure Probability Failure Probability (a) Network Size (b) Network Size 5 Fig. 6. Data delivery ratio over different failure probabilities (storage=myte). Figure 7 deonstrate the delivery ratio under different data generators in the network. With increasing nuber of data generator, the network traffic becoes heavier and preserving data persistence is hence ore challenging. The figure shows that when there are data generators in a network of 5 nodes, and can still preserve ore 5% data, with 45% data persistence for. However, the data delivery ratio of all three approaches drop significantly as the nuber of data generator increases fro to 35. In the worse case, all three data preserving algorith only anage to preserve less than 2% aount of innovative data. y coparison, it shows the advantages of, which retains a steady perforance of above 9% data persistence across different nuber of data generators. Efficient data duplication avoidance (by recoding) and essage redundancy reduction (by opportunistic rebroadcasting and adaptive power control) in play an iportant role in axiizing data delivery ratio. C. Storage cost We evaluate the storage cost for each of the algoriths in Figure 8. We observe that ethod consues ore storage space than others when nuber of data generator increases higher than. Under 35 data generators, there are only 6% storage space on average is available in each of nodes. This iplies that the uncontrolled rebroadcasting of results in uch redundant packets which requires uch ore storage space. Although consues less storage space than and in the network of light traffic, requires ore storage space as the network traffic becoes higher. This is because adopts the opportunistic rebroadcasting to accoodate the disruptive counication link which introduces oderate duplicate essages. and consue less storage space but introduce uch ore energy cost. Available Storage Ratio # of Data Generators Fig. 8. Available storage space ratio v.s. aount of data generators (storage=myte, failure prob. = 2%). D. Energy cost Energy cost is critical to the data preserving, since excessive energy consuption will increase the nodal failure probability due to energy depletion. Illustrated in Figure 6, all the algoriths experience a perforance degradation under higher failure probability. Therefore, energy conservation is not only for the sake of efficiency, but also for axiizing data persistence Percentage Power Select Frequency Selection Cuulative TX Power Level # of Data Generators Fig. 9. Transission Power Level Distribution. Fig. 7. Data delivery ratio v.s. aount of data generators (storage=myte, failure prob. = 2%). The energy cost increent is exponentially proportional to transission power level. Thus, we evaluate the experiental output of power level adaptation algorith in Figure 9. Figure

9 9 9 represents the transission power probability distribution according to Equation 3. The diaond-dotted curve is the cuulative probability of power selection. It shows that ore than 7% probability fall into power level 3 and 4, which are low-oderate power level for the radio. This results is consistent with the preliinary results fro Figure 2. It also depicts that adaptive power control can adapt to network dynaics, including neighbor node failure, node storage space changes and node density alteration, with sall transission power cost. Energy Consuption Rate Fig.. Optial Failure Probability Energy Consuption Rate (storage=myte). Figure deonstrates total energy consuption of different algoriths, noralized against the Optial solution. The optial solution is assued to establish a stable delivery path fro distribution node to storage node, which only consues iniu energy cost. In low failure probability, only expend 2.3 ties as Optial solution. It is due to that in probabilistic rebroadcasting is applied to accoodate the disruptive connection. Copared with Optial, ore redundant nodes are required to rebroadcast packets in the absence of global knowledge of node failure prediction. In the worse case, consues 3.5 ties as uch as Optial solution. Although adjusts its transission power for better expected coverage, its total energy consuption is 4% less than and. The packet retransission in those two approaches consue considerable energy when the path for data redistribution becoes interittent. randoly rebroadcasts the packet for redistribution, which is unaware of network dynaics, so that energy consuption of reains 5 ties as uch as the Optial solution. ut the data preserving perforance of is draatically influenced by failure probability as in Figure 6. V. CONCLUSION An integrated network coding based approach, Ravine Streas (), has been proposed in this work to achieve persistent data streas in disruptive wireless sensor networks. axiizes the probability that source sybols seep through ultiple disruptive paths, via probabilistic rebroadcasting with adaptive power control and recoding, preserving the persistence of data strea. The experiental results reveal that the delivery ratio of source sybols (data strea persistence) is iproved considerably with efficient energy cost and odest storage cost. REFERENCES [] X. Hou, Z. Supter, L. urson, X. Xue, and. Tang, Maxiizing Data Preservation in InterittentlyConnected Sensor Networks, in IEEE International Conference on Mobile Ad hoc and Sensor Systes, Oct. 22. [2] M. Valero, M. Xu, N. A. Mancuso, W.-Z. Song, and R. eyah, : A Sink Failure Resilient Approach for WSNs, in IEEE International Conference on Counications, Jun. 22. [3] A. Kara, V. Misra, J. Feldan, and D. 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