Mobility Control with Local Views of Neighborhood in Mobile Networks

Transcription

1 Moblty Control wth Local Vews of Neghborhood n Moble Networks Zhen Jang Je W Robert Klne Dept. of Compter Scence Dept. of Compter Sc. and Eng. Dept. of Compter Scence West Chester Unversty Florda Atlantc Unversty West Chester Unversty West Chester, PA 98 Boca Raton, FL West Chester, PA 98 Abstract Recent work n moble ad hoc networks, smply MANETs, has drawn attenton to the moblty capablty of each node. In [], t s proved that the optmal postons of the relay nodes along a sngle actve flow mst le entrely on the lne between the sorce and destnaton wth each node spaced evenly along sch a lne. Based on ths, we propose two dstrbted schemes to control the relay nodes n MANETs to approach ther optmal postons n the local relatve coordnate system, one sng one-hop neghborhood and the other sng two-hop neghborhood. Unlke the one presented n [] sng only one-hop neghborhood, or methods have no oscllaton problem and wll converge more qckly. To redce the overhead n synchronzaton, otdated neghborhood (laggng by one rond of nformaton exchange and pdate) s sed n or two-hop neghborhood based approach. The smlaton reslts shows the sbstantal mprovement on the speed of achevng the optmal confgraton and the total movng dstance of nodes. Keywords: Moble ad hoc networks (MANETs), dstrbted algorthm, moblty control, neghbor nformaton (neghborhood). Introdcton Recent research work has drawn attenton to the control schemes n MANETs n order to acheve optmal confgraton n data flows for mprovng commncaton performance. In [], the optmal confgraton of a sngle actve flow s establshed and then a complete dstrbted teratve scheme s proposed to move each node toward ts optmal poston. Smply, n a synchronos rond based system, at each rond, every node s reqred to compte the average of ts two neghbors and then move to that new poston. The work was spported n part by NSF grants ANI 886, CCR 9966, CNS 76, CNS, and EIA 86. Contact E- mal: zjang@wcpa.ed. As we wll dscss later n ths paper, the rond-off error [] may case the oscllaton problem. In [], nstead of reachng the expected target poston, the node only moves toward that pont. The movement s damped and wll not sffer from large oscllaton. Bt the oscllaton problem s not solved completely. Indeed, the dampng slows down the convergence and cases delay n achevng optmal confgraton. Ths wll decrease the effectveness of sch moblty control n some real tme applcatons sch as target trackng systems [, 6, 8], n whch the trackng data mst be transferred qckly enogh to catch p wth the movng target. Ths, provdng a practcal scheme whch can form a stable data flow qckly whle keepng the relay nodes at or close to ther optmal postons s becomng ncreasngly mportant. In ths paper, we focs on a way to collect and dstrbte the locaton nformaton, whch s dscovered n the GPSfree postonng algorthm [], so that the above averagng algorthm sng sch nformaton can converge qckly to be sed n data transmsson. The challenge s twofold. Frst, the nformaton mst be accrate enogh to represent the exact confgraton. The effect of the rond-off error, whch may case oscllaton n the mplementaton, mst be consdered. Second, the collecton and dstrbton process mst be practcal and energy effcent. In other words, t mst be smple, have no complex comptaton, and mst not reqre any costly nformaton, whch demands expensve eqpment or a lot of mltcastng/broadcastng. A short smmary of or approach follows. Frst, n the averagng process sng -hop neghborhood [], the mnmm movng dstance per rond, M DP R, as a certan parameter for each node deployed, s ntrodced to avod the oscllaton cased by rond-off error. Instead of sng the dampng process, a node wll reach ts target poston mmedately. However, t wll be moved only f the dstance from the crrent poston to the target poston s larger than ths M DP R. Then, by sng -hop neghborhood, the above averagng process can converge more qckly and each node has less movement. To redce the overhead n synchronzaton, the se of otdated -hop neghborhood, also called

2 nconsstent neghborhood, s dscssed. Or smlaton reslts show the sbstantal mprovement of or control schemes on the nmber of ronds needed n the convergng process n the synchronos rond based system (.e., the speed of achevng optmal confgraton) and the correspondng total movng dstance of nodes. The remander of the paper s organzed as follows: Secton ntrodces some necessary notons and prelmnares, ncldng the related control schemes and the problems n ther mplementaton. Or control schemes n the local relatve coordnate system are presented n Sectons. Secton shows the smlaton reslts. Secton concldes ths paper and provdes deas for ftre research. Prelmnary We assme that all the nodes have the same commncaton range. The nodes nsde the commncaton range are called neghbors and two neghborng nodes are drectly connected. To send the data n an effcent way, the power spent at each node s determned by ts physcal dstance to the target neghbor, whch s called transmsson range. Ths, a network can be represented by a smple ndrected graph G = (V, E), where V s a set of vertces (nodes) and E s a set of ndrected edges. An ndrected edge (, v) denotes the connecton between two neghborng nodes and v. The neghbor set N() of node s defned as {w (w, ) E or (, w) E}. Or moblty control algorthm s orthogonal to the rotng dscovery protocol. Each node has the locaton (x, y ), smply denoted by L(). L() L(v) s the dstance between two nodes and v. L () denotes the target locaton of n ts movement. L (v) s the locaton of node v n the relatve coordnate system at node. Specfcally, L () = (, ). We assme that a path from the sorce s to the destnaton d has been dscovered sng a rotng protocol, e.g., a greedy rotng protocol or one of the ad hoc rotng protocols. We label the nodes from the sorce to the destnaton,,..., n. We call node the sorce, node n the destnaton, and nodes,..., n relay nodes. For each relay node, we have, + N( ). Ths, any nformaton of can be shared wth and + by the nformaton exchange among neghborng nodes. To smplfy the dscsson, we descrbe the schemes n synchronos rond based system. All the schemes presented n ths paper can be extended easly to an asynchronos rond based system; however, to make or schemes clear, we do not prse the relaxaton. After each relay node knows ts poston, the optmal confgraton of relay nodes for a sngle actve flow s establshed n [] as follows: Assme that the energy cost fncton s a non-decreasng convex fncton. Then the optmal postons of the relay nodes mst le entrely on the lne be- Algorthm (MCD): Moblty control at each relay node [].. Exchange L( ) wth and +.. Receve L( ) and L( + ). Set L () = L( )+L( +).. Set dampng factor g (, ], move toward L( ) + g (L ( ) L( )). tween s and d. Frthermore, the relay nodes mst be evenly spaced along the lne. A nform dstrbted algorthm that allows the relay nodes to move to ther optmal poston s also ntrodced n [] (see n Algorthm ). The key ngredent of ths algorthm s the smple averagng step. Note that althogh a relay node comptes the average of ts two neghbors, the node only moves toward ths pont, nstead of reachng t n one rond. In other words, the movement s damped. Sch an algorthm s denoted as MCD. [] also clamed that MCD wll converge and eventally evenly dstrbte all the relay nodes on the lne between s and d. However, n the fnal convergng stage, t only reqres a node to move a very short dstance. Becase of the rond-off error, sch a dstance cannot be expressed precsely n most compter langages sch as C and wll case napproprate rond-n or rond-ot. For example, a -hops path contans nodes s(9.,. ), (86., 9. 6), (8. 9, 6. 9), (7. 7,. 8), (69., 8. 6), and d(6. 7,. 9), where XX. Y Y stands for the coordnate vale begnnng wth XX as nteger part and endng wth Y Y n ts decmal part. In the frst rond, node s expected to move to (86., 9. 6). However, the target locaton of comes ot as (86., 9. 6) becase a rond-off error occrs. Respectvely,,, and wll move to (8. 9, 6. 96), (7. 7,. 7), and (69. 6, 8. 6). In the next rond, all the nodes wll bonce back to the postons n the prevos rond; that s, an oscllaton occrs. Accordng to or smlaton reslts, the oscllaton wll occr n most cases (> 7%) when g s fxed and set to. Or smlaton reslts also show that when g s randomly generated, the percentage of achevng stablzaton can be mproved bt the problem cannot be solved completely. Moblty Control n the Local Relatve Coordnate System In ths secton, we rewrte the -hop neghborhood based control scheme n [] n the local relatve coordnate system

3 Algorthm (M C): -hop neghborhood based moblty control at relay node, sbject to MDP R.. Set L ( ) = (, ) and bld the local coordnate system.. Apply the procedre n [] to obtan {L (v) v N( )} n the local coordnate system, whch only needs one rond nformaton exchange.. Get L ( ) and L ( + ). L ( ) = L ( )+L ( +).. If L ( ) (, ) > MDP R, move to L (). and solve ts oscllaton problem by ntrodcng the constrant of MDP R on moblty of each node. Then, to move the nodes closer to ther optmal postons and more qckly, a control scheme based on -hop neghborhood s presented. To redce the extra overhead n synchronzaton, the se of nconsstent vew of neghborhood s ntrodced n ths control scheme.. -hop neghborhood based control At each relay node, the locaton of neghbors and + n the relatve coordnate system of, L ( ) and L ( + ), can be determned n the postonng algorthm n [] n only one rond of nformaton exchange. Sch an algorthm does not rely on GPS (Global Postonng System) and only ses the dstances between the nodes to bld the relatve coordnate system n whch the nodes postons are compted. Then, we can apply the averagng algorthm n [] to estmate the target locaton of,.e., L ( ) = L ( )+L (+). Wthot dampng, node wll reach the new poston n or scheme before the next rond starts. As we dscssed n Secton, cased by the rond-off error, the relay nodes may oscllate between two consectve postons bt wthn a small range. To prevent the node from fallng nto nstoppable movement and wastng energy on sch oscllaton, the oscllaton range s set as the threshold called Mnmm Movng Dstance per Rond, MDP R. A relay node wll move only f the dstance from the crrent poston to the target poston s larger than ths MDP R. Ths s sffcent to avod oscllaton whle keepng the nodes close to ther optmal postons. The oscllaton range reles on the dfference between the calclated approxmaton of a nmber and ts exact mathematcal vale. Accordng to the table n [], t can be set as. (>. to cover all cases). The detaled process can be seen n Algorthm, whch s denoted as MC. s() d() movng drecton commncaton lnk crrent locaton new locaton Fgre. Illstraton of the averagng algorthm sng -hop neghborhood. After applyng MC, the relay nodes may not locate exactly at ther optmal postons de to the se of MDP R. However, we wll show n the smlaton reslts n the next secton that sch a gap s very small and can be gnored. Actally, the exstence of sch a gap can be accepted as the tradeoff cost for achevng a stable path qckly. It s noted that a relay node n MC wll move exactly lke the one n MCD when g =. When the MDP R blocks ts movement, the other nodes wll move lke those n MCD n an asynchronos rond based system. De to the se of MDP R, the nodes n MC wll stop to move before they reach the fnal convergng stage n M CD; that s, each node wll reach ts stable stats earler. Ths, the propertes of MCD dscssed n [], sch as the connecton of all the relay nodes, stll hold n MC.. -hop neghborhood based control By sng -hop neghborhood, the above averagng process can converge faster. It s noted that the collecton of sch nformaton reqres the extra overhead of synchronzaton. In a more effcent way, each node apples the postonng algorthm only once at the begnnng of network constrcton and then ses only one rond of nformaton exchange at each rond to pdate the poston record reactvely when the movement occrs. When two neghborng relay nodes share not only ther pdated locatons bt also the recorded locatons of all ther neghbors, a relay node can collect the locaton nformaton of all ts -hop neghbors from the correspondng -hop neghbors. In ths way, a sgnfcant amont of postonng comptaton and commncaton for neghborhood collecton can be saved whle the -hop neghborhood based averagng algorthm can stll be appled. It s noted that the -hop neghborhood collected at that -hop neghbor n the prevos rond may not represent the exact poston n the crrent rond. Ths, the -hop neghborhood collected n ths way s nconsstent. However, as we show n smlaton reslts n the next secton, the averagng algorthm sng sch nconsstent nformaton can stll have better performance than M C. The detaled process s shown n Algorthm, whch s denoted as MC. In MC, the pdate of locaton of a -hop neghbor node

4 Algorthm (MC): Inconsstent -hop neghborhood based moblty control at a relay node, sbject to MDP R.. Send L ( ), L ( + ), and the poston change of node n the prevos rond L ( ) to both and +.. Receve nformaton from and + and pdate ther records at : L ( ) = L ( ) + L ( ) and L ( + ) = L ( + ) + L + ( + ).. Determne the -hop neghborhood f any: L ( ) = L ( ) + L ( ) and L ( + ) = L + ( + ) + L ( + ).. L ( ) = L ( )+L (+). Otherwse, only -hop neghborhood s avalable and L ( ) = L ( )+L (+).. If L ( ) (, ) > MDP R, move to L ( ) and save the poston change for pdates at neghbors n the next rond. 6. Rebld the relatve coordnate system of and pdate each poston record accordng to the new poston of orgn pont. L ( ) (a) L ( ) L ( ) L ( ) (b) L ( ) crrent poston prevos poston movement n the prevos rond In MC, the locaton of -hop neghbors can be collected precsely. However, the collecton of -hop neghborhood s laggng by one rond n MC. Ths, the averagng process n M C wll converge n an asynchronos way. Fgre shows a sample of the convergence n a 6- hop data flow n MC. The relay nodes n MC were not sed n any data flow before, dd not move n the prevos rond, and have the consstent locaton nformaton at ts - hop neghbors n the frst rond (see n Fgre (c)). After that, each relay node wll move vacllatngly to approach ts optmal poston (see n Fgre (e)). Smlaton Fgre. Illstraton of nformaton collecton n MC. (a) Informaton at before the nformaton exchange. (b) Neghborhood collected at after nformaton exchange. s trggered by recevng the correspondng poston change n the prevos rond. For a node and ts -hop neghbor v, when v moves from (, ) to L v(v) n ts local system, the new poston n the relatve coordnate system of can be descrbed as L (v) = L (v)+l v (v) (see and n Fgre ). At node, after ths pdate for v, the locaton of another -hop relay neghbor of v,.e., the -hop neghbor of, say node w, can be determned by ths L (v) and ts locaton at neghbor v, whch has been pdated after the movement of v n the prevos rond (see,, and n Fgre ). Therefore, we have L (w) = L v (w) + L (v). It s noted that the pdate only occrs at relay nodes becase only they can move. In ths secton, we verfy the mprovement of or new schemes on speed and cost of convergng from a smlator. In a synchronos rond based system, the speed of achevng stablzaton s measred by the nmber of ronds needed for convergence. The cost of moblty control schemes prmarly comes from the energy consmed n node movement whch s determned by the dstance a node moves. The smlaton s condcted to test the nmber of ronds needed and the total dstance the nodes move n flows wth dfferent length from -hops to -hops n MC and MC. The transmsson range of each relay node eventally acheved n dfferent schemes s also tested to measre the ablty of each scheme to acheve optmal confgraton. The rads of commncaton range s set to be meters for each node [7]. All the nodes are deployed randomly. After the deployment, we randomly pck the sorce node s. From s, for each node selected, we randomly pck ts scceedng node (along the path) from ts neghbors. In ths way, the worst case n each rotng protocol can be generated and tested n or smlator. Then, we apply MC

5 rond rond rond rond rond rond 6 v w rond rond + (a) rond rond v w rond L (v)= (L()+L(w))/ L (v)=l(v) rond + s() d(6) rond s() d(6) rond s() d(6) rond rond rond rond 7 (b) (c) (d) (e) Fgre. (a) Informaton collecton at node v n rond. (b) Unchanged locaton n ronds. (c) Rond n MC. (d) Rond n MC. (e) Rond 7 n MC. MC MC MC MC MC MC Nmber of ronds Nmber of ronds Movng dstance (meters) (a) (b) (c) 6.. MC MC MC (x.e-) MC (x.e-) MC (x.e-) MC (x.e-) Movng dstance (meters) 8 6 relatve error.. relatve error (d) 6 8 (e) 6 8 (f) Fgre. Expermental reslts when MDP R =.. (a) Average nmber of ronds. (b) Maxmm nmber of ronds. (c) Average movng dstance of a node. (d) Maxmm movng dstance of a node. (e) Average relatve error of the acheved confgraton on transmsson range to the optmal one. (f) Maxmm relatve error.

6 and MC on those flows and compare the reslts n the followng fgres. It s noted that a flow wth -hops s the least case n whch we can apply MC and we wll probably never see any flow longer than -hops n an applcaton system wth a -meter commncaton range. We make the followng observatons from the comparson shown n these fgres.. Wth -hop neghborhood, even wth nconsstent nformaton, each node n MC needs fewer ronds to become stable (seen n Fgre (a) and (b)) and makes more accrate movement (seen n Fgre (c) and (d)) than the one does n MC.. The smlaton reslts show that M C and M C can move the relay nodes close to optmal postons; that s, the relatve errors are all less than. when MDP R =., althogh the MDP R prevents them from reachng ther expected target postons. Wth more accrate nformaton, M C can move nodes closer to optmal postons than MC does (see n Fgre (e) and (f)).. MCD presented n [] has oscllaton n more than 7% of flows. Both MC and MC are proved to converge wthn a certan nmber of ronds n smlaton. They are oscllaton-free and can perform better than MCD. MC s extended drectly from MCD by ntrodcng the constrant of M DP R. The convergence of MC and ts performance shown n Fgre prove the effectveness of ths M DP R. Conclson In ths paper, we ntrodce the MDP R n the mplementaton of averagng algorthm so that oscllaton cased by rond-off error can be avoded. New moblty controls sng -hop neghborhood, nconsstent wth the exact poston, are proposed. The process to collect and dstrbte each knd of locaton nformaton s also presented. In each control scheme, the connecton of relay nodes s garanteed. A smlaton s developed to test the performance and the cost of each control scheme and prove the mprovement of or schemes on achevng optmal confgraton n a data flow. In or ftre work, we wll apply or reslts to create a new rotng process so that when the nodes move and form dynamc networks, not only can the connected path be constrcted bt also the data can be transmtted n an energy effcent way. Also, the moblty control wll be extended for mltple flows as the connectvty constrants are consdered n MC and MC. References [] [] error. [] S. Capkn, M. Hamd, and J. Hbax. GPS-free postonng n moble ad hoc networks. Proc. of the th Annal Hawa Internatonal Conference on System Scences., pp [] A. Cerpa, J. Elson, M. Hamlton, J. Zhao, D. Estrn, and L. Grod. Habtat montorng: Applcaton drver for wreless commncatons technology. Proc. of ACM SIGCOMM Workshop on Data Commncatons n Latn Amerca and The Carbbean Costa Rca., pp. -. [] D. Goldenberg, J. Ln, A. Morse, B. Rosen, and Y. Yang. Towards moblty as a network control prmtve. Proc. of the th ACM nternatonal symposm on Moble Ad Hoc Networkng and Comptng (Mobhoc ). May, pp [6] R. Gpta and S. Das. Trackng movng targets n a smart sensor network. Proc. of the 8 th IEEE Vehclar Technology Conference (VTC ). Vol., Oct., pp. -9. [7] D. Tan and N. Georganas. A coverage-preservng node schedlng scheme for large wreless sensor networks. Proc. of the st ACM Workshop on Wreless Sensor Networks and Applcatons.. [8] F. Zhao, J. Shn, and J. Rech. Informaton-drven dynamc sensor colaboraton for trackng applcatons. IEEE Sgnal Processng Mag. Vol. 9,, pp