Reducing Information Gathering Latency through Mobile Aerial Sensor Network

Transcription

1 Reducing Infomation Gatheing Latency though Mobile Aeial Senso Netwok Zhaoquan Gu, Qiang-Sheng Hua, Yuexuan Wang and Fancis C.M. Lau Institute fo Theoetical Compute Science, Institute fo Intedisciplinay Infomation Sciences, Tsinghua Univesity, Beijing, , P.R. China epatment of Compute Science, The Univesity of Hong Kong, Hong Kong, P.R. China Abstact Gatheing infomation in a sensing field of inteest is a fundamental task in wieless senso netwoks. Cuent methods eithe use multihop fowading to the sink via stationay nodes o use mobile sinks to tavese the sensing field. The multihop fowading method intinsically has the enegy hole poblem and the mobile sinks method has a lage gatheing latency due to its low mobility velocity. In addition, all the mobile sinks methods assume unlimited powe supply and memoy which is unealistic in pactice. In this pape, we popose a new appoach fo infomation gatheing though a Mobile Aeial Senso Netwok (MASN We adopt the Hive-one model [5] whee a centalized station (Hive) esponsible fo seving and echaging Mico-Aeial Vehicle (MAV) senso nodes (ones) is stategically placed in the sensing field. We then face the challenges of how to contol the mobility of each MAV and devising intefeence-fee scheduling fo wieless tansmissions that can substantially educe the latency. We pesent a family of algoithms with constant memoy to educe both gatheing latency, which is the duation fom dispatching the MAVs to the moment when all the sensed infomation ae gatheed at the cental station, and infomation latency, which is the duation fom when some infomation is sensed to when it is eceived by the station. We also conside how to extend the single Hive to multiple Hives fo monitoing an abitaily lage aea. Extensive simulation esults cooboate ou theoetical analysis. Index Tems Mico-Aeial Vehicle, Infomation Gatheing, Senso Netwoks, Gatheing Latency, Infomation Latency. I. INTROUCTION Wieless senso netwoks have been widely used in envionmental monitoing, uban suveillance, disaste ecovey, industial sensing and contol, etc. [7], [15], [18]. Thei pimay task is to gathe cucial infomation of the sensing field fo subsequent decisions to be made such as whee pests o diseases exist in cops o in ode to povide a bid s eye view of the envionment fo disaste ecovey. Taditional methods fo infomation gatheing begin with deploying a lage numbe of stationay sensos andomly o unifomly in the taget field. Two appoaches of data gatheing ae widely applied. One is though the wieless senso netwok. In this appoach, all infomation will be fowaded hop by hop to the sink node. Howeve, this kind of multi-hop fowading method may suffe fom the enegy hole poblem [19] whee the nodes nea the sink will deplete thei powe moe quickly than the nodes fa away. Thus the senso netwok may become disconnected afte being deployed fo some length of time. The othe appoach utilizes mobile elements [8], [20], in which the land-based mobile sinks will tavese each sensing field to collect the needed infomation. This appoach, howeve, suffes fom the following poblems. Fist, the gatheing latency, i.e., the time fo gatheing all the infomation, may be lage as the mobility velocity is much smalle than the netwok tansmission speed. The polonged gatheing time may affect significantly subsequent decisions to be made using the gatheed infomation. Second, since the mobile sink will tavese each sensing field to collect the field s infomation, it has to have a lage enough enegy supply and memoy space; fo a elatively lage field, this assumption will limit the method s applicability in pactice. In this pape, we popose infomation gatheing though a Mobile Aeial Senso Netwok (MASN) based on the Hive- one model [5]. MASN compises a swam of Mico-Aeial Vehicles (MAVs), each of which caies a senso and can fly to specific egions fo sensing. In the Hive-one model, the Hive is a centalized station which is suitably placed in the sensing field fo echaging the MAVs batteies and deciding how to dispatch the MAVs (ones) to pefom specific tasks. This model is attactive fo two easons. Fist, it is moe convenient to deploy since the Hive can decide each MAV s flying tack and it can fly to a egion without the need fo deploying the stationay senso nodes in advance. Second, the MAV sensos (ones) wheneve necessay can fly back to the Hive to be echaged, which avoids the enegy hole poblem. Although attactive, the MASN method faces some tough challenges. Actuation dominates the enegy budget of each MAV, leaving the bae minimum fo sensing, contol and communication. Such a limit calls fo a moe efined mobility contol fo educing enegy consumption. In addition, in ode to educe the infomation gatheing latency, this kind of mobility contol needs to be jointly consideed with the design of intefeence-fee wieless tansmission scheduling. Fo example, should the MAV fly to anothe sensing field to gathe new infomation o stay in the cuent sensing field acting as the elay node fo tansmitting infomation fom the othe MAV nodes needs pecise coodination. The contibution of this pape is as follows: Fist of all, to ovecome the dawbacks of the two fequently used methods fo infomation gatheing, i.e., the multihop-fowading method via the stationay wieless senso netwok and the mobile sinks method, we intoduce the Hive-one model which not only can avoid the enegy hole poblem, but also educe the infomation gatheing latency with only constant /13/$ IEEE 656

2 memoy. In paticula, fo the case whee thee is only one MAV (one), we pesent a geedy algoithm which yields a constant appoximation atio. Fo the case whee thee ae enough MAVs to cove the entie monitoed aea, we pesent constant appoximation algoithms unde both gaph based and physical (SINR) intefeence models. Finally, fo the case whee thee is only a small numbe of MAVs, we popose anothe appoach with a slightly inceased gatheing latency at the cost of uncoveed boundaies of the monitoed aea. Moeove, we extend this appoach to the multiple Hives scenaio in ode to monito a much lage aea. The emainde of the pape is oganized as follows. The next section gives the elated wok. Peliminaies ae povided in Section III. A geedy constant appoximate algoithm is descibed in Section IV fo the case of only one MAV. When thee ae many MAVs to cove the monitoed aea, we pesent how to jointly contol the MAV mobilities and design intefeence-fee wieless tansmission schedules fo educing both gatheing and infomation latencies in Section V. We analyze the case whee thee is only a small numbe of MAVs and conside the multiple Hives scenaio fo monitoing an abitaily lage aea in Section VI. We conclude the pape with some futue wok suggestions in Section VII. II. RELATE WORK Infomation gatheing is a fundamental task in wieless senso netwoks. Many algoithms have been poposed in the past decades. Geneally speaking, thee ae two categoies of wok in this aea. The fist uses stationay wieless senso netwoks whee the geneated data will be fowaded to the sink node hop by hop. We call this method the multi-hop fowading method. The othe categoy uses mobile elements (sinks) to tavese each sensing field in the monitoed aea fo infomation collection. We biefly suvey each of the two methods. A well known shotcoming of the multi-hop fowading method is that it has the notoious enegy hole poblem in which the senso nodes nea the sink will deplete thei powe much quickly than the nodes that ae fa away. This phenomenon significantly educes the wieless senso netwok s lifetime. A numbe of methods have been poposed to mitigate the enegy hole effect, such as using non-unifom node distibutions [19]. Aiming at minimizing the gatheing latency, ominating Tee is poposed in [16] and [17] unde the physical intefeence model and fo a multi-channel multihop netwok, espectively. [4] deives the uppe and constuctive lowe bounds fo data collection capacity theoetically in abitay netwoks and analyzes the lowe bounds fo both the potocol intefeence model and the geneal gaph model. Moeove, degee-constained spanning tees and capacitated minimal spanning tees ae poposed to show the impovements, and the impacts of diffeent intefeence models ae also consideed; howeve, all these methods did not conside how to eliminate the enegy hole. Although the mobile elements methods [6] could avoid the enegy hole, as mentioned ealie, they implicitly assume unlimited powe and memoy in the mobile elements, which makes them impactical when the monitoed aea is elatively lage. In this line of wok, thee kinds of mobilities have been studied: andom mobility [13], pedictable mobility [3] and contolled mobility [8]. [13] initiated this topic by poposing a thee-tie achitectue fo spase senso netwoks, whee the mobile entities, efeed to as ata Mobile Ubiquitous LAN Extensions (MULEs), move aound in the netwok to collect infomation fom senso nodes and dop off the data to wied access points. [3] models the infomation gatheing pocess as a queuing system with pedictable mobility whee andom aivals model andomness in the spatial distibution of senso nodes. Powe consumption of the netwok is quantified with the success analysis of infomation collection. [8] adopts contolled mobility and fomulates the collection pocess as the Taveling Salesman Poblem with Neighbohoods (TSPN A combine-skip-substitute (css) scheme is poposed to educe the tou length and data gatheing time with mobile elements, which is the best known heuistic algoithm. Instead of mobile sinks, mobile sensos ae consideed in [10] fo impoving the the netwok coveage. Seveal systems ae designed aound the notion of dispatching mobile sensos to geneate and gathe infomation. TiopsNet is an example fo pipeline monitoing [9] and it can cove the sensing aea with fewe sensos while maintaining a high data collection ate with a stable netwok topology. Along with the development of mobile sensing systems, Micoaeial Vehicles (MAVs) has become an emeging topic at the foefont of systems eseach. In [12], MAVs ae used in disaste management applications by poviding a bid s view of the envionment. Flight data exchanges can happen between MAVs and one majo concen is how to place the sensing points in ode to monito the entie aea as efficiently as possible. [5] poposed the Kama system based on the Hive-one model in cop monitoing which collects flowe infomation fo seaching fo pests and diseases. MAVs ae dispatched fom a station in the field and move aound the sensing field to sense and bing back infomation. A pollen task will be activated when flowes in bloom ae being detected. Howeve, the Kama system suffes fom lage gatheing latency and the infomation of blooming flowes may not each the station quickly enough due to the slow mobility velocity. Thus, we popose infomation gatheing though a Mobile Aeial Senso Netwok (MASN) consisting of all the MAVs in the sensing field (monitoed aea) fo educing infomation gatheing latency while poviding the station with the cucial sensed infomation as quickly as possible. III. PRELIMINARIES A. Hive-one Model The Hive-one Model is intoduced in [5] whee a centalized station (Hive) is placed in the monitoed aea to seve the MAVs (ones), in paticula to echage thei batteies. Table I gives some notations used in this model. Geneally speaking, f T f, > and P is much smalle than the flying powe consumption. 657

3 Notations N T f f P TABLE I NOTATIONS IN HIVE-RONE MOEL Meaning Numbe of MAVs The maximum time fo flying The maximum distance a MAV can fly The sensing adius of each MAV The flying speed of each MAV The netwok tansmission speed Maximum powe fo each tansmission B. Intefeence Models Thee ae two commonly adopted intefeence models: the gaph based model [1] and the physical model [11]. The gaph based model assumes the netwok consists of two gaphs: connectivity gaph G C and intefeence gaph G I. A node v can eceive fom u successfully if it is connected with u in G C but not with any othe simultaneous tansmitting nodes in G I. Hop distance model and potocol model ae two specific gaph based intefeence models. The h-hop distance model assumes that if the hop distance of two links is less than h hops, then they cannot be scheduled in the same timeslot [14]. Note that potocols mainly assume h =2. The potocol model assumes the tansmission ange and the intefeence ange vay with signal powe. Two nodes ae connected in G C (G I ) if thei distance is no moe than the tansmission (intefeence) ange. Typically, we assume the maximum tansmission ange is R T and the intefeence ange R I vaies with R T (R I R T The physical model is moe pactical compaed with gaph based models. The classic one is the signal-to-intefeenceplus-noise atio (SINR) model which is based on the study of fading channel models. The enegy of a signal fades with the distance to the powe of the path-loss exponent α. Ifthe signal stength eceived ove the intefeing stength of all othe tansmittes plus the backgound noise I b is above some theshold β, the ecipient can decode the signal successfully. Moe pecisely, it can be fomulized as: P u /d(u, v) α I b + w S\{u} P w/d(w, v) α β (1) whee d( ) means the Euclidean distance and S is the set of simultaneous tansmittes. C. Poblem efinition In this pape, we fist conside the case of only one Hive, as poposed in [5], and a bounded aea fo infomation gatheing F = isk(c, ) whee c is the cente and is the adius satisfying = f 2 in the wost case; we extend this to abitaily lage monitoing aea in Section VI. The Hive has thee opeations: ispatch(mav i,p i,t d (i)): ispatch MAV i to the sensing point P i at time t d (i); Receive(m i ): Receive infomation m i and ecod the eceive time as t (m i ); Rechage(MAV i ): Rechage MAV i when it is back to the Hive; The opeations of each MAV ae as follows: Fly(P s,p d ): Fly fom point P s to P d with speed ; Land(P i ): Land at point P d and thee opeations ae available: GI(m i ): Geneate Infomation of the sensed aea F i = isk(p i,) (such as taking a photo of its sensed aea) and assume m i costs one unit of memoy; SI(m i,mav j ): Send Infomation m i to node MAV j ; RI(m j ): Receive Infomation fom some othe MAV node; Back: Fly back to the station fo echaging and may cay some infomation to the station at the same time. When the Hive pefoms ispatch n times, a sequence of n sensing points {P 1,P 2,,P n } is geneated. Fo each sensing point P i, suppose MAV i aives thee at time t a (i) and geneates infomation at t g (m i Fo the sake of bevity, we omit the sensing delay and t g (m i )=t a (i We assume these points can fully cove the sensing field F if F i=1,,n F i. Ou goals ae to educe: Gatheing Latency: T G =max i t (m i ) denotes the last infomation aival time; Infomation Latency: T I =max i {t (m i ) t g (m i )} is the longest delay fo some infomation geneated to be collected at the station. T G is an impotant measue epesenting the time to gathe all infomation. Low gatheing latency implies high efficiency. Infomation latency is also impotant in pactical applications because low infomation latency can facilitate subsequent tasks. Fo example, as shown in [5], if a MAV detects a blossomed flowe, the Hive will aange a one to pollen the flowe as quickly as possible. IV. SINGLE MAV GATHERING Conside the simplest case whee only one MAV is available to fly back and foth fo infomation sensing and gatheing. This is quite simila to the mobile sink method, but as mentioned ealie, an MAV has only limited powe and memoy which means that it cannot visit each sensing field within one flight without echaging. Since the MAV has to each at least 2 points fom simple aea calculation, if only one unit of 2 memoy is allowed and it has to each evey point, then this would tun out to be a coveage poblem. Thus, we assume the MAV can fly to diffeent points to gathe infomation with moe memoy on boad. The velocity will decease when the MAV pefoms the Land(P i ) opeation and incease to again when it Fly to anothe point. Thus, it cannot fly the maximum distance f. Supposing the time fom Land to Fly is t d, denote the distance delay as d t d 2.Ifk diffeent points ae eached fo sensing, the maximum fly distance is f = f k d. 658

4 ρ Fig. 1. Schedule to cove all points within the angle δ Fig. 2. Gatheing Latency compaisons: = 3000m, ρ (1/2, 1) Theoem 1: The lowe bounds fo Single MAV Gatheing ae: T G =Ω( 2 ) and T I =Ω( Poof: In ode to cove all maginal points, the lagest angle is γ = 4 acsin /2 when the MAV is actually at the 2π magin and sensing a disk of adius. Thus at least π π 2 acsin /2 γ = flights ae needed. Each flight costs at least time eaching the magin and at least time when it caies back the infomation. Thus T G 2π2 and T I, concluding the theoem. We popose a geedy algoithm to cove the aea within a cetain angle. In Fig. 1, the distance of evey two consecutive disks centes is Δ=2ρ,ρ (1/2, 1 Obviously, the aea 1 ρ2 within the angle δ = 2 acsin 2 1 ρ 2 can be coveed. We label all centes along the adius as c 1,c 2,,c Δ and these points will be eached geedily fo infomation gatheing. Algoithm 1 Geedy Infomation Gatheing fo Single MAV 1: Δ=2ρ,ρ (1/2, 1); a =2Δ+ d ; π 2: fo ound = 1 to do 1 ρ 2 3: i =1, k i = 2 a ; 4: while k i 1 do 5: 6: i = k i d, p i = i Δ ; Fly(H, c pi ), Land(c pi ) and GI(m(c pi )); 7: fo j =1to k i 1 do 8: Fly(c pi j+1,c pi j), Land(c pi j) and geneate infomation GI(m(c pi j)); 9: end fo 10: Back fo echage and exchange infomation; 11: i = i +1, k i = k i 1 d a ; 12: end while 13: end fo In Alg. 1, k i means the numbe of points to each fo sensing duing the i-th flight in each ound. The main idea is the MAV eaches the fathest cente c,i and then flies to the neaby k i 1 centes fo sensing along its way back to the Hive. Since each ound can cove the whole aea within δ = 2 1 ρ 2 π, 1 ρ 2 ounds ae enough to gathe the sensing field s infomation. The elations between k i and d ae fomulated as: k 1 d +2k 1 Δ = 2 i 1 k i d +2k i Δ = 2( k j Δ) j=1 Thus all centes along the adius can be coveed geedily. The numbe of flights in each ound is the smallest value i such that k i = 2 a ( d a ) i < 1: d is compaable with ( d =Θ()); let i = c log whee c is an appopiate constant, k i < 1 can be satisfied; thus all infomation can be gatheed with log - appoximation when compaed with the lowe bound in Theoem 1. d = o(), ( d 2Δ+ d ) i =(1 2Δ 2Δ+ d ) i 1 2Δ 2Δ+ d i; we can find a constant c such that 1 2Δ 2Δ+ d c < a 2 implies constant appoximation to the lowe bound. Theoem 2: Algoithm 1 can gathe all infomation within T G = O(log 2 ) when d =Θ() and T G = O( 2 ) when d = o(); T I =Θ( We simulate this algoithm with diffeent d values and evaluate the gatheing latency vaying with ρ (1/2, 1 In Fig. 2 ( = 3000m, =2m/s, =20m), when d becomes lage, the gatheing latency inceases unde the same ρ value. Fo each d, the latency inceases as ρ gows. In Fig. 3, when d is small (such as d =0.001 o d =0.1), the gatheing latency will not incease too much as compaed with the ough lowe bound as shown. In pactice, d will not be compaable to the sensing ange. Fo simplicity, we omit the impact of d in the following when the MAV can fly to moe than one point fo sensing. Coollay 1: If we only utilize the mobility to sense and gathe infomation with no wieless tansmission, T I =Ω( Remak 4.1: The memoy needed in Alg. 1 is O( Howeve, the lowe bound in Theoem 1 will not change even if we have unlimited memoy, which is constained by the limited enegy. Remak 4.2: In view of the apid development of battey echaging techniques, we do not take the echaging time into consideation in ou algoithm design. Nevetheless, the geedy 659

5 Fig. 3. Gatheing Latency compaisons: ρ =0.6, [200, 2000] Fig. 4. Spatial ecomposition of the space algoithm also yields a constant appoximation atio when the echaging time fo each MAV is the same when d = o( the distance to the Hive (dis j (c, H)) satisfies: 2 j dis j(c, H) j (2) Poof: Conside the tiangle in Region 1 (c.f. Fig. 4), the length of the edges is equal to l = j due to the distance of two consecutive hexagon centes being the same. The lagest distance fom the Hive to the opposite edge is d max = l and the shotest one is the line fom the Hive to the foot point with d min = l sin π 3 = 2 j. Thus, 2 j dis j(c, H) j. We bound the numbe of hexagons (N h ) needed to cove F by: Lemma 5.2: 2 N 2 h Poof: Each hexagon can be coveed by a disk of adius and the aea of the sensing field is π 2,soN h π2 π = hexagons ae necessay. As in Fig. 4, thee ae at most j max = /2 = 2 layes fom the distance elation in Lemma 5.1. j-th laye has 6j hexagons, thus N h j max i=1 6j = B. Laye by Laye Gatheing We assume the numbe of MAVs is enough to cove all the hexagons, which means N N h. We pesent the Laye by Laye Gatheing Algoithm based on the following notations: h(i, j, k): The i-th egion, j-th laye, k-th hexagon (clockwise); (1 i 6, 1 j 2, 1 k j) Ch(i, j, k): The cente point of h(i, j, k); h(i, j, k): The distance fom Ch(i, j, k) to the Hive; Ph(i, j, k): The paent senso node fo the MAV dispatched to Ch(i, j, k); Th(i, j, k): The time delay to invoke tansmission schedule afte the aival; The ispatching Schedule at the Hive is pesented in Alg. 2(c is a constant in Line 3, to be defined late fo diffeent intefeence models V. MASN REUCES THE LATENCY We have bounded the infomation latency as Ω( ) when no communication exists between the MAVs. The flight velocity is about 1 to 5 metes pe second, which is extemely slow as compaed with the wieless tansmission speed. We popose the MASN method fo infomation gatheing to educe both gatheing latency and infomation latency. A. Spatial ecomposition The field F can be coveed by egula hexagons with adius as in Fig. 4 (the Hive is in the cente ivide these hexagons into six egions with left side open and ight side closed, as shown, and assume they ae placed laye by laye. Take the j-th laye in Region 1 as an example, thee ae j hexagons and the distance between two consecutive hexagon cente is. Lemma 5.1: Fo each hexagon cente c in the j-th laye, Algoithm 2 ispatching Schedule at the Hive 1: δ f =,δ t =, T =0; 2: fo j =1to 2 do 3: t i =max{0,cjδ t δ f /6}; 4: fo i =1to 6 do 5: t(i, j) = j +(i 1) δf 6 ; 6: fo k =1to j do 7: if h(i, j, k) then 8: t dp = t(i, j) h(i,j,k) ; 9: 10: Ph(i, j, k) =MAV(i, j 1, 2 k 2 1); Th(i, j, k) =T +(i 1)t i ; 11: ispatch(mav(i, j, k),ch(i, j, k),t dp ); 12: end if 13: end fo 14: end fo 15: T = T +6t i ; 16: end fo 660

6 Algoithm 3 MAV Opeations ispatch(mav,ch(i,j,k),t dp ): 1: When time = t 2: Fly(H, Ch(i, j, k)); 3: When time = t + h(i,j,k) 4: Land(Ch(i, j, k)) and GI(m(i, j, k)); 5: if Th(i, j, k)+cjδ t </ then 6: Invoke Hop elay Schedule; 7: else 8: Back fo caying infomation to the Hive; 9: end if On RI(m): 1: SI(m, P h(i, j, k)) accoding to the Hop elay Schedule; Fig. 6. Hop elay in Potocol Model Fig. 5. Topology fo j-th laye Infomation Gatheing The opeations at MAV(i, j, k) is pesented in Alg. 3: The main idea of the schedule at the Hive is dispatching j MAVs to j-th laye of each Region and contol them to aive at the same time. (The aiving times fo two consecutive egions diffe by δ f /6.) We assume the sensed infomation by j MAVs can be gatheed in cjδ t time and t i denotes the delay when the next egion MAVs should begin tansmitting. (t i =0means the sensed infomation is gatheed by the Hive befoe the next egion s MAVs aive.) The topology is constucted as in Fig. 5 and we pesent the Hop elay Schedule (c.f. Alg. 4) to gathe j pieces of infomation fom the same laye in cjδ t time unde diffeent intefeence models. 1) Hop istance Model: Suppose any two nodes within h-hops will intefee with each othe. Algoithm 4 Hop elay Schedule 1: =1, δ t = ; 2: fo k =1to j do 3: MAV(i, j, k) executes SI(m, P h(i, j, k)) at time δ t ; 4: = + h +1; 5: end fo 6: When The MAV i eceives m 7: Execute SI(m, P h(i)) afte δ t ; Lemma 5.3: The Hop elay Schedule can gathe the infomation fom j-th laye in (h +2)jδ t time. Poof: We can egad the scheduling opeates in ounds whee each ound takes δ t time. Fom the delay defined Line 4 in Alg. 4, the j pieces of infomation will begin tansmitting in ound 1,h+2, 2(h +1)+1,, (j 1)(h +1)+1. The time used fo tansmitting fo 1 hop is exactly δ t, and thus when each piece of infomation is delayed fo h +1 ounds, the hop distance of any two consecutive tansmissions will be at least h and they can tansmit successfully unde the hop distance model. So we can gathe all the infomation in (j 1) (h +1)+1+j (h +2)j ounds and the time is bounded by (h +2)jδ t. 2) Potocol Model: The Potocol Model is moe complicated. Without loss of geneality, suppose R T and we can adjust the powe such that the equality is satisfied (if R T <, econstuct the decomposition such that the hexagon adius equals RT 3 The coesponding intefeence ange R I R T =. enote R I = ɛr T, whee ɛ is a constant and ɛ 1. Lemma 5.4: The infomation fom the j MAVs of the same egion can be gatheed at the Hive in (ɛ +3)jδ t time. Poof: Modify the hop delay in Alg. 4 based on following calculation: Suppose we delay each infomation piece by d hops. Conside two consecutive infomation m 1 and m 2. If they shae a common paent in the topology, d = ɛ +2 can make the tansmissions of m 1 and m 2 successful duing fowading to the Hive. If they have two diffeent paents as in Fig. 6 (the only case fom the topology), hop delay should be lage enough such that TI > R I. Fom the Cosine theoem: AT 2 + AI 2 2AT AI cos 2π 3 = TI2 Plug in AI =2, then AT =(ɛ 1) is enough to satisfy TI > R I. Thus, adding the fist thee hop delays, if each infomation piece is delayed by d = ɛ +2 hops, the coectness of Alg. 4 is guaanteed. Thus, the last piece of infomation can be gatheed in (j 1) (ɛ +2)+1+j (ɛ +3)j ounds which implies all infomation can be gatheed in (ɛ +3)jδ t time. 661

7 3) The SINR Model: Based on the topology constucted, all link lengths ae l =. The maximum powe used in one tansmission slot is P and the backgound intefeence is I b. efine R m =( P βi b ) 1 α be the maximum tansmission ange when no othe MAVs ae tansmitting simultaneously. Geneally R m >and define λ =1+( β(16ζ(α 1)+8ζ(α) 6) 1 ( l /R m) ) 1 α α. Lemma 5.5: If the eceiving ends of a set of links have mutual distances geate than λ l, they can be scheduled simultaneously. Poof: Let S be the set of links. Pick (u, v) S; divide all othe links into sets S 1,S 2,,S such that S i = {(u,v ) S iλ l d(v, v ) (i+1)λ l }. S 1 18 and S i 8(2i+1) fom [2]. Thus, d(u,v) d(v, v ) d(u,v ) iλ l l i(λ 1) l. The intefeence caused by othe tansmittes is I t = = (u,v ) S\{(u,v)} i=1 P d(u,v) α P d(u,v) α (u,v ) S i P S i (i(λ 1) l ) α i=1 P β R α m α l R α m α l P βr, and we have P/α m α l I b +I t Plug in I b = β, and so the lemma follows. Based on Lemma 5.5, the SINR Model can be tansfomed to the Potocol Model whee R I = λ l. Thus these infomation can be gatheed to the Hive in (λ +3)jδ t time. Remak 5.1: The constant c in Line 3 of Alg. 4 is detemined by the intefeence models: c = h +2 in the h-hop istance Model, c = ɛ+3 in the Potocol Model and c = λ+3 in the SINR Model. Theoem 3: When vt =Ω( ), all infomation can be gatheed though the MASN with T G =Θ( ) and infomation latency T I =Θ( ) unde both gaph based models and the SINR model. Poof: Fom the ispatching Schedule in Alg. 2, all infomation can be gatheed in j max + c j max δ f (3) =Θ( ) time while the infomation latency is c j max =Θ( ) whee c is a constant based on the intefeence model chosen. Remak 5.2: The lowe bound to gathe j pieces of infomation is jδ t, and thus Alg. 4 achieves constant appoximation when compaed with the lowe bound. In addition, one unit of memoy is enough to buffe the infomation duing the scheduling pocess. Remak 5.3: Afte the infomation fom the j-th laye is gatheed at the Hive, j 2 1 MAVs (in each egion) can fly back fom the topology constucted, which impoves the efficiency when pefoming some othe tasks at the same time. Table II compaes the poposed algoithm, the mobile sinks method (fly back and foth fo gatheing) and the ough lowe TABLE II COMPARISON OF T G AN T I Methods T G T I 2 3 Laye by Laye Gatheing c 2 Mobile Sinks Method MASN Lowe Bound + bound though the MASN when ( vt =Ω( ) We simulate the thee methods in Fig. 7 whee = m/s fo geneal wieless tansmissions. The esults show that ou algoithm achieves lowe gatheing latency when compaed with the mobile sinks method, and the infomation latency is educed substantially which is a constant appoximation with espect to the lowe bound though MASN. If we extend this algoithm to some othe applications such as undewate senso netwoks whee acoustic waves may be used, we get some inteesting esult. We simulate the case when = 340m/s in Fig. 8. The esult shows that both gatheing latency and infomation latency will incease as the sensing adius gows. Infomation latency will convege to the mobile sinks method and gatheing latency will be slightly lage when the sensing adius is lage enough due to the time delay fo dispatching. In geneal, we claim ou algoithm can achieve both low gatheing latency and low infomation latency though the MASN. VI. FEWER MAVS, LARGER FIEL? The algoithm descibed in the pevious section can achieve both low gatheing latency and low infomation latency. Howeve, the numbe of MAVs used is as lage as N h =Θ( 2 2 ) and the sensing field is limited by the maximum distance the MAV can each. In this section, we extend the Hive-one model to sense an abitaily lage field with a small numbe of MAVs. Given a sensing field F whee the diamete is much lage than a single Hive s sensing adius, multiple Hives (cental stations) need to be placed in F. We descibe the Contolled Path Gatheing algoithm fo each Hive whee only 2 =Θ( ) N h MAVs ae used. The sequential fowading is based on the h Hop istance model and we give an example fo illustation in Fig. 10. Lemma 6.1: The sequential fowading method can gathe the N l layes of infomation in (h +1)N l ounds whee each ound takes time δ t =. Poof: Each MAV in the j-th laye will tansmit N l j pieces of infomation fom highe layes, and any messages tansmitted in the same ound have hop distance no less than h. Thus all N l infomation can be gatheed in (h +1)(N l 1) + 1 (h +1)N l ounds and the time fo each ound is δ t =. Moeove, one unit of memoy is enough fo each MAV to buffe the infomation and we can tansfom the potocol model and the SINR model to the hop distance model with 662

8 (a) Gatheing Latency when = m/s (b) Infomation Latency when = m/s Fig. 7. Latency Compaisons when = m/s, =1.5m/s (a) Gatheing Latency when = 340m/s (b) Infomation Latency when = 340m/s Fig. 8. Latency Compaisons when = 340m/s, =1.5m/s Algoithm 5 Contolled Path Gatheing S1. Fo one egion, dispatch N l = MAVs to the centes on the adius L 1 as Fig. 9; S2. Gathe infomation fom N l layes by invoking Sequential Fowading; S3. MAV in the highest laye ( ) goes back as the dotted line, othes Fly to the highe laye cente by one hop as the aow in Fig. 9; a new MAV is dispatched along adius L 2 with a black point; S4. Repeat S2 and S3 until all MAVs ae on the adius L 2 ; Sequential Fowading: 1: fo MAV in the j-th laye do 2: =j,δ t = ; 3: fo time = j to N l do 4: SI(m, P h(mav)) at -th ound (afte δ t time) ; 5: = +(h +1); 6: end fo 7: end fo a constant facto diffeence. So Lemma 6.1 follows fo both gaph based models and the physical model (the SINR model enote Hex(H, ) as the hexagon whee H is the cente Fig. 9. Contolled Path Gatheing and the adius is. Theoem 4: Alg. 5 can gathe all infomation fom Hex(H, ) within T G =Θ( + 2 ) and has low infomation latency T I =Θ( Poof: Alg. 5 takes loops to gathe the infomation of each egion in Hex(H, ) and the fist loop will cost 663

9 Hives, it will be inteesting to see whethe we can design efficient distibuted algoithms, such as fo dispatching the MAVs (ones) and scheduling the wieless tansmissions between MAVs, with guaanteed low gatheing and infomation latencies. Fig. 10. Sequential Fowading fo 7 layes when h = 2 time fo flying, while only δ f = time will be used duing the othe two consecutive loops. Fom Lemma 6.1, we can gathe the infomation duing each loop in (h +1)N l δ t + = + (h+1)2 vt =Θ( + 2 ) time. Refe to the 6 egions, all infomation can be gatheed within T G =Θ( + 2 Moeove, any infomation can aive the Hive in (h + 1)N l ounds whee each ound takes time, and thus the infomation latency is T I =(h+1)n l δ t =(h+1) =Θ( Any space can be fully coveed by hexagons with the same adius. Simila to Fig. 4, an abitaily lage field F can be coveed by Hex(H 1,),Hex(H 2,),,Hex(H n,) such that F i=1,2,,n H i, whee each Hive uses only Θ( ) MAVs to gathe infomation with a slight incease in gatheing latency when is lage. Thus, we can monito an abitaily lage aea by placing multiple Hives and each Hive has Θ( ) MAVs. VII. CONCLUSION In this pape, we discuss how to gathe infomation though a Mobile Aeial Senso Netwok (MASN) based on the Hive-one model. This method can ovecome the enegy hole poblem which can easily occu in stationay wieless senso netwoks, and can educe both the gatheing latency and the infomation latency substantially as compaed with the mobile sinks method. In addition, We pesent a geedy constant appoximation algoithm fo the single MAV case, which is simila to the mobile sinks method but with limited enegy and bounded memoy. Fo the case whee thee ae enough MAVs (Θ( 2 )) to cove the entie monitoed aea, 2 unde thee fequently used intefeence models, i.e., the hop distance model, the potocol model and the SINR model, we popose the Laye by Laye Gatheing Algoithm though the MASN. This algoithm can achieve both low gatheing latency and low infomation latency while using only one unit of memoy to buffe infomation duing tansmission scheduling. Fo the case whee thee ae only a small numbe of MAVs (Θ( )), we descibe an appoach with only a slight incease in gatheing latency and extend the single Hive to multiple Hives in ode to monito an abitaily lage aea. Ou extensive simulation esults clealy indicate that ou methods can indeed achieve low infomation and gatheing latencies while using only one unit of memoy. Note that all ou poposed algoithms ae centalized algoithms since we use the Hive-one model whee the Hive is a cental station. In the futue, when we conside multiple VIII. ACKNOWLEGMENTS The authos thank Pof. Thomas Mosciboda fo pointing us to efeence [5]. 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