World Scientific Research Journal (WSRJ) ISSN: A Algorithm for Location in Wireless Sensor Networks Based on Local

Transcription

1 World Scentfc Research Journal (WSRJ) ISSN: A Algorth for Locaton n Wreless Sensor Networks Based on Local Deand Level Hu Yang 1, a, Zhengsheng Dng 2, b 1 College of Scence, X an Unversty of Scence and Technology, X an , Chna 2 College of Geology and Envronent, X an Unversty of Scence and Technology, X an , Chna a yangh816@alyun.co, b dngzs@xust.edu.cn Abstract: A Crtcal proble n wreless sensor networks s localzaton whch deterne the geographcal locatons of sensors. Most exstng localzaton algorths were desgned to work well ether n networks of statc sensors or networks n whch all sensors are oble. In a wreless sensor network where ost sensors are wthout an effectve self-postonng functonalty, the geographc locaton proble of nodes was researched. In ths paper, a novel algorth for locaton proble n the optzaton of Wreless sensor networks (WSNs) was proposed. Wth the consderng of requreents, eergency response te and total syste cost, a dstrbuton of the dspatch ponts can be obtaned by the algorth. Usng the Gaussan convoluton, the local deands level can be obtaned and the dstrbuton based on covers and sorted deands s ore effcent. Nuercal exaples show that the proposed algorth can solve the locaton proble n the optzaton of eergency systes. Keywords: Wreless sensor networks, localzaton, square scalng, soft constrant, Gaussan convoluton 1. INTRODUCTION Wth the developent of technology, Wreless sensor network has attracted a lot of nterest n ndustry, agrculture and ltary fled due to the dversty of applcatons. It conssts of countless low cost sensor nodes that are capable of data gatherng, data processng and rado councaton. Sensor nodes ntegrated wth ebedded coputaton are randoly deployed pervasvely for collectng nforaton we are nterested n, such as teperature, hudty, lght and so on [1]. Then the collected essage s transtted to nternet through rado councatons. Data that s beyond the defned lt wll trgger the alar syste, so as to rend people to take easures approprate as soon as possble. Localzaton nforaton s 265

2 helpful for target trackng. So the accuracy of localzaton s essental for WSN envronents, for localzaton algorths that have a low level of accuracy provde useless nforaton. We consder deployng the sensor networks to fnsh the functon of Urban Eergency Systes. The econoy and the convenence are both portant and should be consdered together n the desgn process. Many ethods and odels have been appled to these scenaros [1, 2, 3]. Slar to the publcaton facltes, the locaton of eergency facltes requres well desgn. These facltes wll be used to eet the deands when the eergences happened. The losses of people s lves and property can be reduced. In response to the process of eergences, tely supply of eergency facltes/resources s the key to provng the effcency of eergency servce. Urban eergency systes ust eet the eergency requreents n a lted te, space and resource n order to axze the te effcency and nze the losses. Therefore, the optzaton of the eergency systes s help to prove the effcency and effectveness of eergency servce. Locaton-Allocaton Probles (LAP) of eergency systes are crucal proble n the optzaton of eergency systes [4, 5, 6, 7]. In fact, t s related wth the path probles and they affected each other and depended on each other. Wth the opnon of syste optzaton, t s necessary to research the Locaton-Routng Proble (LRP). Currently, any approaches have been conducted on LAP or LPN of general logstcs Systes [8, 9] whle very few has been conducted on LAP or LPN of eergency response systes. [10] studed the coordnate optzaton proble of aterals dstrbuton and nured transportaton n eergency rescue of natural dsasters. The locaton of teporary edcal ponts, assgnent of edcal staffs, dstrbuton of eergency supply and decson-akng of vehcle transport route are consdered. Then a deterned xed nteger network flow odel of ult-speces ateral has been establshed and solved by soe applcaton software. Ths paper dscusses the requreent of eergency servce, eergency servce te and total syste cost on each deand pont based on the wreless sensor networks (WSNs), and then ntroduces the Gaussan convoluton of urgent deands. A cover algorth s dscussed for the locaton proble. Based on t, a ore effcent dstrbuton of dspatchng nodes can be obtaned wth the consderng of sorted deands. The rest of the paper s organzed as follows: In Secton 2, we frst gve the locaton proble of eergency systes and a general optzaton proble s gven wth a fxed condton. The Gaussan convoluton s ntroduced n Secton 3 and an unsorted cover algorth wth fxed radus s gven n eergency systes. In Secton 4, wth the consderng of local deand level, a sorted cover algorth s proposed for the locaton proble and several nuercal exaples are presented. The conclusons are gven n the last secton. 2. RELATED WORKS The exstng research whch s known about localzaton n oble sensor networks s relatvely less and the research n stuatons where the sensors ay be statc or oble s uch ore less. 266

3 We survey soe relevant papers n ths secton, and refer the user to the surveys by Bachrach and Taylor [1] and by Savvdes et al. [2] for ore coprehensve lterature revews. [4] used receved sgnal strength (RSS) to estate dstances. Ward et al. [7] presented a range-based algorth reled on the Monte Carlo approach. Range-free localzaton: He et al. [12] proposed a range -free algorth called APIT n whch all possble rangles of the seeds are constructed. The locaton of a node s the center of ntersecton regon of all trangles. Sextant [11] proposed a dstrbuted algorth that uses Bezercurves for estatng the possble locatons of the nodes. The nodes estate ther locatons by usng the locaton nforaton of ther neghbors. Bergao and Mazz [3] presented a range-based algorth for oble sensor networks whch uses only two statc seeds that are located at a specfc locaton n the network and ther rado ranges cover the whole network. Recently, we proposed a range-free localzaton algorth [6] that works n both statc and oble networks. The prary proble assocated wth the algorth n [6] s that t cannot estate locatons well when the rado ranges of sensors are not perfect crcles. Tlak et al. studed how often a localzaton algorth should be appled n a oble sensor network. Ths nvolves a balance between energy and accuracy localzng usually wastes energy and localzng occasonally results n havng fusty locatons at ost of the te. 3. LOCATION PROBLEM After the occurrence of eergency servce requreents, the urban should quckly ake the approprate response and t can reflect the urban s eergency anageent capabltes. Manageent capacty s deterned by the aount of avalable eergency facltes and axu effectveness of these facltes [11]. Eergency anageent s reflected n early warnng, evacuaton, publc safety and protecton such as [12]. Therefore, effectve eergency anageent capabltes by anagng the qualty and scope of facltes and the effectve ablty play the ost effectve use of lted facltes. Eergency facltes should be prepared n soe selected dspatchng ponts, and f eergences servce requreents (such as extngush a fre, ask for a doctor, and so on) occur, anagers ust quckly select a eergency dspatch pont, and transport lted eergency facltes to deand ponts n a lted te as shown n Fgure 9. Proper locaton of eergency dspatch ponts wll greatly reduce transport costs, prove effcency of eergency facltes utlzaton and reduce the losses, called Locaton Proble (LP) of eergency syste. Assued that there are any servce requreents occurred n the past te. The deands dstrbutes on the ponts P ( x, y )( 1,2, n) n the urban. The deand aount on the ponts areq ( 1,2, n). Then the aount and the postons of the dstrbuted ponts should be deterned. Obvously, the desgn should satsfy the future requreents. In ters of the past requreents, we can suppose that future dstrbuton be the sae as past. If the nuber of eergency deployng nodes s fxed, t s convenent to establsh and solve the prograng 267

4 odel. Suppose the nuber of requred deployng nodes for the k, a total of canddate Eergency Dspatch Pont N ( x, y )( 1,2, ). The cost of unt faclty s transferred fro dspatchng nodes to requred ones whch s defned by C. The cost of unt faclty to be prepared on dstrbuted nodes are set to be D ( ). Wth the constrant condton of servce cost T on each requste node, then a relatve optzaton ssue can be bult as followng. n (1) n SIXV (,, ) ( CIV)+ ( DX I) st.. I {0,1} ( I X ) Q ( I C ) I X, 1,2 I C T, 1,2 n, 1,2. Where I denotes pont whether to adopt the dspatchng pont quantty of facltes on dspatchng pont dspatch pont N to deand pont P. N, X denotes the N, V s the aount of facltes derved fro (a) Ponts rando topology (b) Requreent dstrbuton Fgure 1. Ponts rando topology and orgnal deand dstrbuton. Above proble (1) can be solved f the nuber k of eergency dspatchng ponts s cohere wth supply tet. Otherwse there wll be no soluton. To avod ths unexpected stuaton, the nuber of dspatchng ponts should not be fxed and there are two coon solutons. The frst one s pre-establshes an addtonal optzaton proble to deterne the nuber of schedulng ponts, and then solved the above proble (1).The correspondng dynac 268

5 prograng odel wll be constructed. The frst one consder reasonably about the addtonal odel as the second one wll enhance the dffculty of solvng proble. Sequentally, t s urgent to obtan a ore reasonable soluton. As shown n Fgure GAUSSIAN CONVOLUTION AND LOCAL DEMAND LEVEL In order to deterne the nuber and locaton of dspatchng ponts, the Gaussan convoluton and local deand level was ntroduced. Convoluton f g of functon f and g can be denoted as followng [ f g]( x) f( t) g( tx) dt Where the functon g denote the kernel of convoluton to functon f. The convoluton can be used to construct a ore sooth functon. The result holds better propertes and t has been appled to varous practcal felds such as sgnal processng, age processng, nforaton theory, and so on. The orgnal dstrbuton of requreents are dsorder and rough, t can tell us few nforaton about the deand ntensty. So a new dstrbuton of requreents s expected and t should tell us ore about the deand ntensty or other portant nforaton whch are advantageous to solve the proble. For deternng the postons of dspatchng ponts, t s a coon consderng that to obtan the local average deand ntensty. And t s sure that there should be ore dspatchng ponts n the regon where holds hgher deand ntensty. Wth ths vew, the convoluton s ntroduced to get local average ntensty of orgnal dstrbuton of requreents. For a certan orgnal dstrbuton of deands, dfferent kernels lead to dfferent convoluton results, For exaple, the dsk kernel and ts convoluton result was shown n Fgure 2. (a) Dsk kernel (b) Convoluton result Fgure 2. Dsk kernel and the convoluton result 269

6 5. LOCATION ALGORITHM BASED ON LOCAL DEMAND LEVEL In ths secton, we wll frst proposed a cover algorth accordng to the local deand level. A set of crcles wth the radus d s coposed to a cover of the deand regon. Effcency and applcablty of algorth are llustrated by several nuercal results. The algorth s set as followng: Step1. Copute the local deand level through calculatng the convoluton of orgnal deands f ( x ) and Gaussan kernel kx; ( ) Step2. Sorted the deand ponts accordng the local deand level by descendng; Step3. Set a proper radus d accordng to the constrant condton of supply te; Step4. Generate a set of crcles coverng the deand regon as followng procedure accordng the sorted ponts. DO For the frst pont P n the sorted pont set PSET f t s not n anyone of the crcles then generate a new crcle wth the center P and erase t fro PSET WHILE PSET s not null 6. CONCLUSION In ths paper, we have proposed a cover algorth for locaton proble n urban eergency systes. We frst dscusses the requreent of eergency facltes, servce supply te and total syste cost n the syste, and then ntroduces the Gaussan convoluton of eergency deand dstrbutons. At last a sorted set of crcles wth radus d s generated to cover the deand regon/urban. Nuercal results show that the proposed ethod and algorth can solve the locaton proble for optzng the urban eergency syste. REFERENCES [1] Toregas C, Swan R, Revelle C, et al. The locaton of eergency servce facltes. Operatons Research, 1971, 19: [2] Vladr M, Charles R. The queung axal avalablty locaton proble: A odel for the stng of eergency vehcles. European Journal of Operatonal Research, 1996, 93: [3] AlyAdel A, WhteJohn A. Probablstc foraton of the eergency servce locaton proble. Journal of Operatonal Research Socety, 1978, 29(12): [4] Yang Feng, Lang Lang, B Gongbng and Du Shaofu. Select the Locaton of Multple Eergency Facltes accordng to Road Condtons: a DEA-based Research.Manageent Revew, 2008, 20(12):41-44, 60. [5] A. Haghan, S.C. Oh. Forulaton and soluton of a ult-coodty, ult-odal network flow odel for dsaster relef operatons. Transportaton Research Part A: Polcy 270

7 and Practce, 1996, 30(3): [6] Y. Arda. A two-stage stochastc prograng fraework for transportaton plannng n dsaster response. Journal of the Operatonal Research Socety, 2004, 55(1): [7] E. Eknc. Eergency logstcs plannng n natural dsasters. Annals of Operatons Research, 2004, 129(14): [8] H. Mn, V. Jayaraan, R. Srvastava. Cobned locaton-routng probles: A synthess and future research drectons. European Journal of Operatonal Research, 1998, 108(1): [9] G. Nagy, S. Salh. Locaton-routng ssues, odels and ethods. European Journal of Operatonal Research, 2007, 177(2): [10] W. Y. A dynac logstcs coordnaton odel for evacuaton and support n dsaster response actvtes. European Journal of Operatonal Research, 2007, 179(3): [11] G. Wllas, S. Batho, L. Russell. Respondng to urban crss - The eergency plannng response to the bobng of Manchester ctycentre. Ctes, 2000, 17(4): [12] J. Wlsona. The evoluton of eergency anageent and the advanceent towards a professon n the Unted States and Florda. Safety Scence, 2001, 39(12):