Patrolling Mechanisms for Disconnected Targets in Wireless Mobile Data Mules Networks

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1 20 Internatonal Conerence on arallel rocessn atrolln Mechansms or Dsconnected Tarets n Wreless Moble Data Mules Networs Chh-Yun Chan, Chh-Yu Ln, Cehn-Yu Hseh, and Y-Jun Ho Taman Unverst, Tae, Tawan cchan@mal.tu.edu.tw, {cln, avnson83, jho}@wreless.cs.tu.edu.tw Abstract Ths aer consders the taret atrolln roblem whch ass a set o moble data mules to ecentl atrol a set o ven tarets. Snce the tme nterval (also reerred to vstn nterval) or consecutvel vstn to each taret relects the montorn qualt o ths taret, the oal o ths research s to mnmze the maxmal vstn nterval. Ths aer rstl rooses a basc alorthm, called Basc (B-TCT), whch ams at constructn an ecent atrolln route or a number o ven data mules such that the vstn ntervals o all taret onts can be mnmzed. For the scenaro contann wehted taret onts, a Wehted-TCT (W-TCT) alorthm s urther roosed to sats the demand that tarets wth hher wehts have hher data collecton requences. B consdern the ener constrant o each data mule, ths aer addtonall rooses a RW-TCT alorthm whch treats ener rechare staton as a wehted taret and arranes the data mules vstn the rechare staton beore exhaustn ther eneres. erormance stud demonstrates that the roosed alorthms outerorm exstn aroaches n terms o vstn ntervals o the ven tarets and lenth o atrolln ath. Kewords taret coverae; WMSNs; data collecton; wehted taret I. INTRODUCTION Taret coverae roblem s one o the mortant ssues n Wreless Sensor Networs (WSNs). In lterature, man exstn aroaches have been roosed to coe wth the taret coverae roblem. Stud [] emlos an nteer lnear rorammn soluton to acheve the taret coverae urose. In stud [2], the roosed alorthm adots ds and sector coverae models to determne the node denst requred or the montorn reon. Stud [3] ams at lacn the mnmal number o sensors so that each taret can be covered b the laced sensor nodes. In studes [], [2], and [3], the roosed alorthms all need to delo a number o statc sensors over the montorn reon to mantan the networ connectvt. However, n the outdoor envronment, taret onts ma be dstrbuted over several dsconnected areas. Delon a lare number o statc sensors or the urose o networ connectvt ma result n sncant hardware and mantenance costs. A easble soluton s usn the moble Data Mules (DMs) to vst all taret onts erodcall and then collect the data bac to the sn node wthn a ven tme constrant. Studes [4] and [5] roose some heurstcs or the DM to construct a atrolln route so that the DM can vst all tarets alon the route. However, the do not balance the vstn ntervals. Furthermore, the treat that all tarets have the same weht value. Thereore, an mortant taret wll be montored as requent as the unmortant tarets. In addton to the abovementoned two roblems, studes [4] and [5] also do not tae nto consderaton the rechare roblem. As a result, the DMs mht exhaust ther ener durn executn the atrolln tas. Ths aer consders the taret atrolln roblem whch ass a set o moble DMs to ecentl atrol a set o ven tarets. Each DM wll start rom the sn node to vst all tarets alon the constructed atrolln route and then o bac to the sn node. It s well nown that constructn the shortest atrolln ath s a Eucldean Traveln Salesman roblem (ETS) [6]. In act, the roblem consdered n ths aer s more comlcated than the tradtonal ETS roblem because that each taret has a weht value to ndcate ts mortance. A taret wth a hher weht value should be vsted more requentl wthn a certan tme erod. Instead o handln the ETS roblem, ths aer ams to construct the atrolln ath whch vsts each wehted taret wth a arecate requenc. Intall, the B-TCT alorthm whch consders the ntal locatons o all DMs s roosed or the DMs to construct an ecent atrolln route, such that the vstn ntervals o all taret onts can be mnmzed. For the scenaro wth derent wehted tarets, the W-TCT alorthm s urther roosed or satsn the requrement that the tarets wth hher weht values wll have hher data collecton requences. B consdern the ener constrant o each DM, ths aer addtonall rooses a RW-TCT alorthm whch treats ener rechare staton as a wehted taret and arranes the DMs vstn the rechare staton beore exhaustn ther eneres. The remann art o ths aer s oranzed as ollows. Sectons II, III, and IV resent the detals o B-TCT, W-TCT, and RW-TCT alorthms, resectvel. Secton V examnes the erormance o the roosed alorthms aanst exstn studes. Fnall, a concluson o the roosed alorthms s drawn. II. BASIC TCT (B-TCT) ALGORITHM 2. Networ Envronment and Assumtons Ths aer assumes that some taret onts are dstrbuted over several dsconnected areas n the montorn reon. The networ connectvt s acheved b the moblt o DMs. Let M = { m n} and G = { h} denote the sets o the DMs and tarets, resectvel. Fure ves an examle o 0 tarets and 4 DMs. The sn node s also treated as a taret ont, whch should be vsted b DMs. Each DM nows the values o n and h whch reresent the numbers o DMs and tarets, resectvel. In addton, each DM s aware o all tarets and ts own / $ IEEE DOI 0.09/IC

2 locaton normaton. The movn seeds o all DMs are also dentcal. 3 2 b 4 Sn b b 8 b Taret ont ont atrolln route route Start Start Brea ont ont Data mule Fure. The constructed atrolln ath =( ) = (, 0, 9, 8, 7, 6,, 4, 3, 2, ). 2.2 The B-TCT Alorthm The roosed B-TCT alorthm manl conssts o two hases. In the rst hase, all DMs ndvduall construct the same atrolln ath. We notce that the consdered roblem n ths aer s derent rom the tradtonal ETS roblem snce each taret has a weht value, reresentn the requred vstn requenc wthn a certan tme erod. In the second hase, each DM erorms the locaton ntalzaton tas and then atrols the tarets alon the constructed atrolln ath. A. ath Constructon Intall, snce all DMs are aware o the locaton normaton o all tarets, thereore, based on a convex hull concet roosed n [5], the are able to emlo the same ath constructon rules and olces to ndvduall construct the same Hamltonan Crcut, whch s a ccle assn throuh each taret exactl once and returnn to the started taret, rom the same startn taret. Let = ( h + ) denote the constructed atrolln crcut, where denotes the -th vsted taret n ath n the counterclocwse drecton. Note that = h + because s a ccle. As shown n F., the constructed atrolln ath startn rom the sn node (also treated as a taret) s ( ) and the atrolln sequence s (, 0, 9, 8, 7, 6,, 4, 3, 2, ). B. atrolln Strate Each DM wll treat the most north taret ont as the rst start ont to artton the ath nto n equal-lenth sements, as shown n F.. The end onts o each arttoned sement are called start onts. Ater calculatn all start onts, each DM erorms the locaton ntalzaton tas. Each o them moves to the closest start ont. I there are more than one DMs stan at the same start ont, the DM wth hher remann ener wll move to next start ont alon the constructed ath. The above oeratons wll reeatedl be executed untl each start ont exactl has one DM. Let and M veloct denote the lenth o ath and the movn veloct o a DM, resectvel. III. WEIGHTED TCT (W-TCT) ALGORITHM Ths secton urther resents a dstrbuted W-TCT alorthm to sats the requrement that the taret wth a hher weht value has a hher data collecton requenc. The roosed W-TCT alorthm manl conssts o two hases. In the rst hase, all DMs ndvduall construct the same wehted atrolln ath (W). Then, each o them atrols alon the constructed W to vst all the tarets. The ollown denes derent tes o tarets whch have derent weht values. Denton : NT and VI Let w denote the weht value o taret. I w s equal to one, the taret ont s called Normal Taret ont (NT). Otherwse, the taret s called Ver Imortant ont (VI). 3. ath Constructon In ths hase, the man dea behnd our desn s to construct a W whch contans w derent ccles ntersectn at the VI such that the VI wll be vsted b a DM w tmes n each comlete ath traversal. For the ease o resentaton, the ollown ves some dentons o notatons C, W, and. Denton 2: Ccle C Let C = ( 0 q) denote the -th ccle whch asses throuh the VI, where w reresents the -th vsted taret ont startn rom VI b a DM movn alon the C n the counterclocwse drecton. Note that 0 = q = because C s a ccle. For examle, as shown n F. 2, taret 4 s a VI wth weht value w 4 =2. There are two ccles (,,..., ) (,,,,,, ) (,,..., ) (,,,,, ) C = = and C = = ntersectn at VI 4. Snce the atrolln ath contans two ccles, the VI 4 wll be vsted twce when a DM atrols the whole atrolln ath. 2 3 Sn Node C 4 0 w 4 = C VI NT atrolln route Fure 2. ath = ( 2) s a W because that t satses Denton 3. Denton 3: Wehted atrolln ath (W) h The ath = ( = w + ) s sad to be a Wehted atrolln ath (W) the ollown two crtera are satsed. () For each, there are exactl w ccles ntersectn at taret. (2) ath tsel s a ccle. 94

3 Note that denotes the -th vsted taret b a DM movn alon the ath n the counterclocwse drecton. Denton 4: Vstn Interval Let len denote the lenth o the -th ccle whch asses throuh VI. Let v denote the veloct o a DM. The -th vstn nterval or VI can be measured b len = v A. Snle-VI roblem The basc dea or constructn a W or snle-vi roblem s descrbed below. Intall, all DMs ndvduall construct the same Hamltonan Crcut [5] = ( h+ ) whch asses throuh each taret and then returns to the started taret. Wthout loss o eneralt, let the -th taret n Hamltonan Crcut be the VI. The ccle creaton rocess wll then be reeatedl executed b each DM untl the number o created ccles, whch ntersect at the VI, s equal to ts weht value w. The ollown ntroduces the ccle creaton rocess e + Fure 3. The ccle constructon rocess The ccle creaton rocess conssts o two tass: ede selecton and ccle constructon. Frstl, as shown n F. 3, a brea edes e = + whch connects taret onts + n the ath s selected. Heren, the two tarets + are reerred as brea onts. Then, the ccle constructon tas wll remove the ede e and connect the two brea onts + to VI = ndvduall. As a result, there are two ccles (,,...,, + ) (,,...,,..., + ) C = and C = 2 ntersectn at VI. Smlarl, the ccle constructon tas wll be reeatedl executed untl there are w ccles ntersectn at the VI. Fnall, the W wll ass throuh the VI exactl w tmes whle the other NT tarets are vsted exactl once. The olc o selectn the brea edes determnes the total lenth o W and each lenth o newl ormed ccles. Let taret = s a VI n the constructed Hamltonan Crcut. The ollown rooses two olces or selectn brea edes: () Shortest-Lenth olc and (2) Balancn-Lenth olc. () Shortest-Lenth olc The Shortest-Lenth olc s to select the brea ede e = + whch mnmzes the total lenth o W. The edes + whch sats Ex. () wll be selected to orm a newl ccle untl the w ccles are ormed, where notaton j j + denotes the lenth o +. j j mn[( + ) - ] () h + + (2) Balancn-Lenth olc The Balancn-Lenth olc ams to balance the lenth o each ccle or VI = so that the vstn ntervals or can be as smlar as ossble. Let L av = / w. The selected w ccles should sats Ex. (2) such that the maxmal lenth o the created ccles can aroach to the value o L av. As a result, the lenths o w ccles wll be smlar. w av mn ( C L ) (2) = B. Multle-VI roblem Ths subsecton consders that there are multle VIs exsted n the montorn reon. Accordn to the weht value, each VI s assned wth a rort value. The VI wth hher rort wll be executed the ccle constructon rocess b each DM ror to the other tarets. Heren, we notce that the VI wth hher weht value should select more brea edes to create more ccles and thereore have a hher rort. For ths reason, the rort o VI s set b = w. Fure 4 dects the rocedure o constructn W. As shown n lne 2, the same Hamltonan Crcut whch asses throuh each taret s ntall constructed b all DMs ndvduall. Then, the taret wth hher weht value wll have a hher rort to erorm the ccle constructon rocess. In lne 4, the DM nds out the taret wth the larest weht value. Ater that, n lnes 5-9, the DM constructs the ccles ntersectn at the taret accordn to ts weht value. I Shortest-Lenth olc s aled, the DM erorms the oeratons ven n lnes 6-2. Otherwse, t erorms the oeratons ven n lnes 3-9. Fnall, the W can be constructed b all DM ndvduall, as shown n lne 2. Alorthm: W Constructon Inut: A set o taret onts G={, 2, h } where h s the number o tarets. Outut: W. For each DM do 2. Hamltonan _CcleConstruct(); 3. ; 4. w max ( w) ; 5. Swtch(BreanEdeolc){ 95

4 6. Case :/* ShortestLentholc */ 7. or x to (w -) then 8. Fure out the edes and + whch sats the Ex. (), where h ; 0. + ;. + ; + 2. end or 3. Case 2: /* BalancnLentholc */ 4. or x to (w -) then 5. Fure out the ccle C whch sats the Ex. (2), where w ; 7. + ; 8. + ; + 9. end or 20. end For 2. Return Fure 4. The rocedure o constructn W. 3.2 atrolln Strate Ater constructn the W, n ths hase, each DM executes the locaton ntalzaton tas as roosed n B-TCT. Snce each VI s ntersected b w ccles, all DMs should have the same atrolln rules to determne the traversal order or these ccles when the arrved at each VI. It s because that two DMs have derent traversal orders or the VI, the vstn ntervals o VI wll result n sncant derence. Let w S denote the set o tarets whch are connected to n the W. The ollown rooses the atrolln rule. atrolln Rule. When a DM arrves at a VI rom taret j, t selects a taret S w, whch has mnmal ncluded anle wth the ormer route j to n the counterclocwse drecton, as ts next vstn taret. 2 3 Sn Node VI NT atrolln route Brean ede Fure 5. An examle o aln the roosed atrolln rule. As shown n F. 5, when the DM moves rom taret to VI 4, t selects taret 3 as ts next vstn taret snce has mnmal anle θ n the counterclocwse drecton. Smlarl, when the DM moves rom taret 9 to VI 4, t wll select 8 as ts next vstn taret. As a result, the constructed W wll be (, 0, 9, 4, 8, 7, 6,, 4, 3, 2, ). IV. W-TCT WITH RECHARGE (RW-TCT) ALGORITHM Snce batter s the ener source o DMs, extendn the DMs letme b vstn the rechare staton s needed. Ths secton urther rooses a RW-TCT alorthm whch taes ener rechare nto consderaton. The basc concet o RW-TCT s to treat the rechare staton as a NT and all the tarets are treated as VIs. The RW-TCT manl conssts o two hases: ath Constructon hase and atrolln hase. In the rst hase, each DM ndvduall constructs one ath or atrolln tarets and another ath or rechare. The second hase manl atrols the tarets alon one o the constructed two aths. 4. ath Constructon In ths hase, each DM ams to construct two aths: the eneral atrolln ath and the rechare atrolln ath. The oeratons or constructn the wehted atrolln ath (W) are smlar wth those dened n W-TCT whch constructs a W accordn to the tarets wehts. In addton, the DM wll construct a wehted rechare ath (WR) whch asses throuh all tarets lus the rechare staton. In case that the remann ener o DM s above a threshold, the DM sml atrols alon the W to vst all tarets. Otherwse, the DM atrols alon the WR to acheve the both uroses o taret atrolln and rechare. Denton 5: Wehted Rechare ath (WR) The ath = ( h w + 2) s sad to be a = Wehted Rechare ath (WR) the ollown three crtera are all satsed. () For each, there are exactl w ccles ntersectn at taret. (2) ath tsel s a ccle. (3) Recharn staton R. Note that denotes the -th vsted taret n ath n the counterclocwse drecton. The detals o constructn a WR are descrbed below. Each DM rstl selects a brea ede e = that satses Ex. (3) or mnmzn the lenth + o WR. The two end onts wll then be + ndvduall connected to the rechare staton R to orm new edes R + R. As a result, the WR asses throuh all taret onts and the rechare staton. R + + R + mn h (3) 4.2 atrolln Strate In ths hase, each DM determnes ts traversal ath rom one o the constructed aths and. Let M Ener denote the ntal ener o a DM. Let denote the 96

5 lenth o ath. Let c m and c s denote the ener consumtons or a DM movn or a unt dstance and or collectn snle taret s data, resectvel. Let h denote the number o tarets. Each DM wll ntall evaluate the atrolln rounds r b aln Equ. (4). The atrolln round r reresents that the DM s able to atrol all tarets r tmes alon the beore ts ener exhauston. r = M Ener ( c ) + ( ) m h cs Ths also means that each DM should atrol alon WR ever r rounds. I the DM has atrolled alon the W r- tmes, t wll atrol alon the WR n the next round or recharn ts ener. Fure 6 dects the rocedure desned or constructn the WR. As shown n lne 2, each DM constructs the WR based on the constructed W. To mnmze the lenth o WR, as shown n lnes 3-6, the DM selects an arecate brea ede accordn to Ex. (3). Fnall, the WR can be constructed b connectn the brea onts to the rechare staton R, as shown n lne 8. Alorthm: WR Constructon Inut: A set o taret ont s G={, 2,, h }, where h s the number o tarets. Outut: WR. or each DM do 2. W-TCT_RouteConstruct(); 3. Fure out the edes R + R whch sats the Ex. (3), where h. 4. ; R ; R ; 7. end or 8. Return Fure 6. rocedure o constructn WR V. ERFORMANCE EVALUATION Ths secton examnes the erormance o the develoed B-TCT, W-TCT and RW-TCT alorthms n terms o vstn nterval, standard devaton o vstn nterval, and ener ecenc o DM. The roosed alorthms are comared wth revous studes [4] and [5] whch are reerred to as Random, Swee, and CHB. The Random aroach randoml selects the non-vsted taret as ts next destnaton whle the Swee aroach ntall dvdes the DMs nto several rous and then each DM ndvduall atrols the tarets o one rou. The CHB aroach constructs an ecent Hamltonan Crcut and then all DMs vsts each taret alone the constructed Hamltonan Crcut. However, the CHB aroach does not consder the stuatons o the scenaro wth derent wehted tarets and the rechare roblem. 5. Smulaton Model (4) The veloct o each DM s set at 2 m/s whle the sensn rane and communcaton rane o each DM are set at 0 and 20 meters, resectvel. The ener consumtons or data collectn rom a taret and or movn a unt dstance are J/s and J/m, resectvel. The networ sze s 800m 800m and the locatons o tarets are randoml dstrbuted over the montorn reon. Each smulaton result s obtaned rom the averae results o 20 smulatons. 5.2 erormance Stud Fure 7 comares the roosed TCT wth Random, Swee and CHB mechansms n terms o Data Collecton Dela Tme (DCDT). In the Random method, each DM selects taret randoml and thus the DCDT sncantl chanes. In CHB, each DM ollows the same atrolln ath and thereore the DCDT vbrates erodcall. In Swee, some DMs move alon lon atrolln ath whle the other DMs move alon short atrolln ath. As a result, the DCDT also vbrates erodcall. Aln the roosed TCT alorthm, all DMs ntall move to the arecate locatons and then atrol the tarets alon the same Hamltonan ath. Hence, all ars o consecutve DMs have same dstance. Thus, ts DCDT ees a constant value. Data Collecton Dela Tme (sec) Randam Swee CHB TCT Vsted Tme Fure 7. Comarson o the Random, CHB, Swee, and TCT n terms o DCDT. Let SD denote the Standard Devaton o the ever two vstn ntervals or a snle taret. A small value o SD ndcates that the vstn ntervals o are smlar and thus the data collecton requenc s stable. The SD s ormulated as n SD = ( t - t) n = Fure 8 comares the TCT and CHB n terms o SD b varn the numbers o DMs and taret onts. Aln the CHB to construct the atrolln ath, the value o SD s ncreased wth the number o DMs. It s because that the sement lenths between ever two consecutve tarets are sncantl derent. I the number o DMs s ncreased, the total lenth o the constructed atrolln ath s also ncreased, resultn n lare derences o SD. On the contrar, the SD o the roosed TCT alwas ees zero. 2 97

6 The SD o taret ont (sec) Number o Taret TCT CHB Number o Data Mule Fure 8. Comarson o the CHB and TCT n terms o SD or varous number o tarets and data mules. Fures 9 and 0 dect the erormance o the roosed W-TCT alorthm when VIs are exsted n the networ envronment. Fure 9 comares the DCDT o the Shortest-Lenth olc and Balancn-Lenth olc b varn the number and wehts o VI. The DCDT s ncreased wth the number or weht o VI n both Shortest-Lenth olc and Balancn-Lenth olc. However, snce the ath lenth constructed b the Shortest-Lenth olc s alwas smaller than that constructed b Balancn-Lenth olc, the Shortest-Lenth olc has smaller DCDT. The The averae SDT DCDT o taret o taret ont (sec) (sec) Number o VI Shortest olc Balance olc Wehted Value Fure 9. Comarson o the Shortest-Lenth olc and Balancn-Lenth olc n terms o DCDT or varous number and weht o VI. Fure 0 comares the SD o the two roosed olces. The SD s sncantl ncreased wth the number and weht o VI n the Shortest-Lenth olc. On the other hand, the lenths o ccles constructed b aln Balancn-Lenth olc are smlar and thus the data collecton requences are also smlar. As a result, the SD o Balancn-Lenth olc ncreased slhtl wth the number and weht o VI. Thereore, the mact o derent number and weht o VI on Balancn -Lenth olc s small. Fure 0. Comarson o the Shortest-Lenth olc and Balancn-Lenth olc n terms o SD or varous number and weht o VI. VI. CONCLUSIONS Ths aer rooses a B-TCT alorthm amn at constructn an ecent atrolln ath alon whch all DMs can atrol each taret wth stable vstn ntervals. A W-TCT alorthm s urther roosed to sats the VI taret whch has a hher weht than the other tarets and s requred to be vsted more requentl n each run. B consdern the ener constrant o each DM, ths aer addtonall rooses a RW-TCT alorthm that treats ener rechare staton as a wehted taret and arranes all DMs vstn the rechare staton beore exhaustn ther eneres. erormance stud demonstrates that the roosed alorthms outerorm exstn aroaches n terms o vstn ntervals [4][5]. REFERENCES [] K. Charabart, S. Ienar, H. Q, and E. Cho, Grd Coverae or Survellance and Taret Locaton n Dstrbuted Sensor Networs, IEEE Transactons on Comuters, vol. 5, no. 2, , December [2] W. Wan, V. Srnvasan, B. Wan, and K. C. Chua, Coverae or Taret Localzaton n Wreless Sensor Networs, IEEE Transactons on Wreless Communcatons, vol. 7, no. 2, , Februar [3] G. J. Fan, F. Lan, and S. Y. Jn, An Ecent Aroach or ont Coverae roblem o Sensor Networ, IEEE ISECS, [4] W. Chen, M. L, K. Lu, Y. Lu, X. L, X. Lao, Swee Coverae wth Moble Sensors, IEEE IDS, [5] F. J. Wu, C. F. Huan, and Y. C. Tsen, Data Gathern b Moble Mules n a Satall Searated Wreless Sensor Networ, MDM, March [6] R. C. Larson and A. R. Odon, Urban Oeratons Research, rentce-hall, 98. The averae SD o taret ont (sec) Shortest olc Balance olc Number o VI Wehted Value 98