Cooperative Routing in Multi-Source Multi-Destination Multi-hop Wireless Networks

Transcription

1 oopertive Routing in Multi-Soure Multi-estintion Multi-hop Wireless Networks Jin Zhng Qin Zhng eprtment of omputer Siene n ngineering Hong Kong University of Siene n Tehnology, HongKong {zjzj, qinzh}@se.ust.hk strt In network supporting oopertive ommunition, the sener of trnsmission is no longer single noe, whih uses the onept of tritionl link to e reinvestigte. Thus, the routing sheme sing on the link onept shoul lso e reonsiere to truly exploit the potentil performne gin introue y oopertive ommunition. In this pper, we investigte the joint prolem of routing seletion in network lyer n ontention voine mong multiple links in M lyer for multi-hop wireless networks in oopertive ommunition wre network. To the est of our knowlege, it is the first work to investigte the prolem of oopertive ommunition wre routing in multi-soure multi-estintion multi-hop wireless networks. Severl importnt onepts, inluing virtul noe, virtul link n virtul link se ontention grph re introue. sing on those onepts, n optiml oopertive routing is hieve n istriute routing sheme is propose fter some prtil pproximtions. The simultion results show tht our sheme reues the totl trnsmission power ompring with non-oopertive routing n gretly inreses the network throughput ompring with single flow oopertive routings. I. INTROUTION In this pper, we investigte the joint prolem of routing seletion in network lyer n ontention voine mong multiple links in M lyer for multi-hop wireless networks in whih oopertive ommunition is exploite s effiient physil lyer tehnology. Multi-soure multi-estintion multiple flows re serve in suh networks, whih my use ontention mong ifferent flows. In wireless ho n mesh networks, routing is n importnt ftor ffeting the system performne. Numers of routing protools hve een propose to hieve optiml power onsumption or mximize the network throughput, whih re summrize in [1]. mong them, little routing sheme ever expliitly leverge n importnt property of the wireless mei, wireless rost vntge (W), whih ws first stuie in [2]. This physil lyer property signifintly hnges the route seletion prolem in network lyer. The prolem of fining the minimum energy multist n rost tree in wireless network is stuie in [2] n [3]. With the vntge of rost in wireless meium, oopertive ommunition is propose reently [4], whih llows severl noes oopertively trnsmit signls to estintion together. Reserhes hve shown tht oopertive ommunition n offer signifint performne enhnements in terms of inrese pity, improve trnsmission reliility, This reserh ws supporte in prt y Hong Kong RG RG 62247, the NS Overse Young Investigtor Grnt , the 863 Progrm uner Grnt No. 261Z228, n the Ntionl si Reserh Progrm of hin (973 Progrm) uner Grnt No sptil iversity n iversity-multiplexing treoff [8-11]. However, uner oopertive ommunition, the sener of t trnsmission will no longer e single noe, whih uses the onept of tritionl link to e reinvestigte [5]. Thus, the routing sheme, sing on the onept of link, shoul lso e reonsiere to truly exploit the potentil performne gin introue y oopertive ommunition. To the est of our knowlege, referene [6] is the first work isusse oopertive ommunition wre routing. In this work, the uthors investigte the energy effiient routing whih supports rost n oopertive ommunition. They nlyze the optiml routing seletion n propose heuristi lgorithm. However, s they ssume tht only one flow exists in the network, the intertions mong multiple neighoring flows hve not een isusse. s we know, the onurrent trnsmission of multiple links my use sptil ontention in relisti trnsmission, thus, new routing sheme whih n voi link ontention shoul e stuie. In this pper, we will onsier the network lyer routing prolem n M lyer ontention prolem jointly, to investigte the oopertive routing for multi-soure multiestintion multi-hop wireless network. The key ontriutions of this work re: 1) it is the first work to investigte the prolem of oopertive ommunition wre routing in multisoure multi-estintion multi-hop wireless networks; 2) the onept of virtul noe n virtul link is introue in this pper for the first time to tke the ple of tritionl link n noe, n they ppropritely reflet the ffetion to the upper lyers of using oopertive ommunition s physil lyer tehnique; 3) to voi ollision mong links of multiple flows in network, ontention reltionship is investigte. Moreover, to support oopertive ommunition in physil lyer, virtul link se ontention moel is given, sing on the moel, the optiml routing is selete; 4) finlly istriute routing lgorithm is presente. The rest of the pper is orgnize s follows: Setion II gives the motivtion of our reserh. Setion III formultes the nlyti moel of the oopertive routing uner multiple flows n solves tht prolem theoretilly. Then, the istriute lgorithm of the optiml routing is esrie in Setion IV. Setion V presents the simultion results. inlly, the pper is onlue in Setion VI. II. MOTIVTION In this setion, we give n exmple to show tht simple oopertive routing strtegy without onsiering the link ontention mong multiple flows i not work effiiently for multisoure multi-estintion wireless networks, thus my not hieve glol optimiztion routing /8/$ I 36

2 Trnsmission Rnge S1 1 2 ig. 1 () Trnsmit senrio otine y existing oopertive routing strtegy whih my use ollision 2 Trnsmission Rnge S1 ig. 1 () Possile trnsmit senrio whih n solve the ollision prolem s ig. 1 shows, there re two t flows trnsmitte simultneously in the network. Soure n estintion of flow 1 n flow 2 re S 1, 1, S 2 n 2 respetively. We ssume tht the interferene rnge equls to trnsmission rnge. Now, n S 1 re in the trnsmission rnge of eh other, using tritionl oopertive routing for single flows, for flow 1, S 1 will rost messge to n simultneously n then, they two will oopertively forwr messge to the next hop noe e.g. s ig. 1() shows. Thus, the routing is S 1 (,). Similrly, routing for flow 2 is S2(,). However, in suh senrio, trnsmission of flow 1 n flow 2 will interfere with eh other in noe, whih is unle to reeive t from two iniviul flows simultneously n eoe it orretly. Thus eme the ottlenek noe of the network. It n only trnsmit for flow 1 n flow 2 lterntely y time ivision. Thus, only hlf of s throughput n e given to flow 1 n the other hlf to flow 2, then, the per-flow-throughput uner multiple-flow senrio will erese y 5% ompre with single-flow senrio. However, onsiering the M lyer ontention, we shoul hoose link S1 n S2 to e the next hop inste of the oopertive routing of S1(,) n S2(,), s in ig. 1(). Uner the new routing, there will e no ontention in M lyer, thus higher throughput n e hieve. The ove exmple illustrtes tht existing oopertive routing strtegy, when use in the network with multiple flows, my use ollision n result in ottlenek noe, thus reue the overll system performne. Moreover, with the numer of flows inresing, the proility of ollision will inrese rmtilly, n performne will egre tstrophilly. Thus, we nee to investigte multi-flow oopertive routing to hieve resonle tre-off etween energy effiieny n ollision voine. In the following setions, prolem formultion will e given n optiml solution will e presente. III. PROLM ORMULTION To solve the oopertive routing prolem uner multisoure multi-estintion multi-hop wireless networks, we first S2 S2 1 rost Moe Virtul Link e=(,) Virtul Noe =(,) oopertive Moe Virtul Link f=(,) ig. 2 virtul noe n virtul link introue some new onept: virtul noe n virtul link on wre of the new hrteristi of oopertive ommunition. Then, sing on the new efinition of noe n link, link ost n pth ost is lulte. lso, to express the ontention reltionship of links in multiple flows, virtul link wre ontention grph is onstrute. fter the introution of virtul link n new efinition of P, L, virtul link se ontention grph, the originl prolem n e formulte s n optimiztion prolem whih intens to minimize power onsume uner ertin flow onstrint n ontention onstrint. y solving the prolem we re le to fin the optiml routing for the oopertive multi-soure multi-estintion network.. onept of Virtul Noe n Virtul Link oopertive ommunition rings gret hllenge for the upper lyer strtion n esign. It reks two ssumptions tht usully me on the lssil notion of link [5]: 1) physil lyer link n originte from only one trnsmitter; 2) onurrent trnsmissions of multiple trnsmitters re not llowe euse they result in interferene. To support the hnge oopertive ommunition rings, the onept of virtul noe is given to reple the funtion of multiple noes tht omplish funtion oopertively. Similrly virtul link is introue sing on virtul noe. In network supporting oopertive ommunition, there re three types of trnsmission: ) orinry moe: the informtion is trnsmitte y single noe n reeive y single noe ) rost moe: the informtion is trnsmitte y single noe n reeive y multiple noes; or ) oopertive moe, multiple noe simultneously sen the informtion to single reeiver. Unlike the orinry moe, uner rost moe n oopertive moe, multiple noes n ehve oopertively n simultneously s one single noe, thus, the onept of virtul noe is introue, severl noes tht simultneously reeive informtion y single trnsmission in rost moe or oopertively sening informtion to single reeiver in oopertive moe re lle virtul noe (e.g. virtul noe whih onsists noe n in ig. 2). Uner suh efinition, the tritionl link whih is onsiste y sener n reeiver is lso enlrge into virtul link, whih my soure in tritionl noe n estine in virtul noe uner rost moe (e.g. virtul link e=(,), whih work in rost moe in ig. 2), or soure in virtul noe n estine in tritionl noe uner oopertive moe (e.g. virtul link f=(,) whih work in oopertive moe in ig. 2).. Link ost ormultion To speify the ost for trnsmitting in ertin link, link ost (L) of link i, enote y L i, is efine to e the minimum power for trnsmitting from soure of the link, enote 37

3 y S i, to estintion of the link, enote y T i. oth S i n T i oul e virtul noe. L i is efine n lulte ifferently, oring to whih moe link i works on. 1. Tritionl moe, where S i =1, T i =1. S i ={s i }, T i ={t i }. 2. rost moe, where S i =1, T i =n>1. S i ={s i }, T i ={t 1, t 2,, t n }. 3. oopertive moe, where S i =n>1, T i =1. S i ={s 1, s 2,, s n }, T i ={t i }. The link ost formultion in eh trnsmission noe is efine s in [6] for the Point-to-Point Link, Point-to- Multipoint rost Link n Multipoint-to-Point oopertive Link respetively.. Pth ost ormultion esies link ost, pth ost (P) is introue n efine to e the minimum power neee to trnsmit t long pth from the reeiver noe of the urrent link to the estintion noe of the flow the link serves Pij = min Lk, P, s.. tsp = Ti, P = j (1) P k P In whih, P ij is the pth ost of link i for flow j, P is ny pth suh tht soure of P, enote y S P, equls to the trnsmitter of link i, enote y T i, n estintion of P, enote y P equls to the estintion of flow j, enote y j. To lulte P ij, virtul link se network onnetion grph GT=(V 1, 1 ) is onstrute sing on the originl network topology G=(V, ), to fin the optiml pth tht minimize pth ost of link i in flow j. In the new onnetion grph, if the reeiver of link i is virtul noe, enote y T i, V1 = V { T i } ; otherwise,v 1 =V. When oopertive ommunition is supporte, some new pth will emerge euse of the existene of virtul noe. Note tht only one en of link n e virtul noe, therefore, in the pth of flow, etween two virtul noes, there is t lest one tritionl noe etween them. Therefore, in the originl topology, some new eges re e 1 =. or noe pir (i,j), i, j V1, if there exits virtul noe k suh tht (i,k) n (k,j) oth re virtul links, (, i j). Weight of ege (i,j) is the power neee to trnsmit t from noe i to noe j vi virtul noe k. In the moifie new onnetion grph GT, using ijkstr lgorithms, shortest pth from noe T i to estintion of flow j j n e foun. The ost of the shortest pth is P ij. f:->(,) e:->(,) () Network topology e f r1 f r2 () Resoure llotion grph e () ontention grph ig. 3 ontention grph n resoure llotion grph. Generlize ontention Grph onstrution There re multiple flows in the network. To voi ontention mong multiple flows, ontention grph (G) is neee to esrie the ontention reltionship etween ny two links. In our network, tritionl G is generlize to support virtul noe n virtul link through the following moifitions. irst, verties in generlize G represent oth rel noes n virtul noes. Thus, new verties representing virtul noes shoul e e in tritionl ontention grph. s ig. 3() shown, vertexes representing virtul link e n f re e. Then, the ontention reltion etween virtul links shoul e reefine n new eges shoul e e orresponingly. Two virtul links on t interfere with eh other, if n only if they hve no ommon noes n ny two tritionl links seprtely ontine in the two virtul links o not interfere with eh other. Thus, two virtul links re ege either they ontin ommon tritionl noe or ertin tritionl link whih is ontine in one of the two virtul link onten with some ertin tritionl link whih is ontine in the other virtul link. In ig. 3(), virtul links e n f ontin the sme tritionl noe, thus they re ege in ig. 3(). or virtul link n tritionl link, there is no ege etween them, if n only if the former one oes not ontin ny one of the two noes in the ltter one n ny link ppere in the former one oes not onten with the ltter tritionl link. In ig. 3, link is ontine in link e thus they shoul e ege. Link e n link re ege euse the ltter one ontens with link whih is ontine in the former virtul link. or two links whih re oth tritionl links, it is the sme s tritionl ontention grph. sing on the ontention grph G=(V, ), the resoure onstrint grph GR=(V, ), whih ptures the vrious ontention regions in the network topology, n e onstrute. The resoure onstrint grph is essentilly iprtite grph with two sets of vertexes eing V n R, where V =V UR n R represents the set of resoure verties, one for eh ontention region. The ontention regions n e otine y ientifying the vrious mximl liques in the flow ontention grph. Thus in ig 3(), there re six vertexes representing link,,,,e,f n two vertexes r 1 n r 2 representing two mximl liques {,,,e,f} n {,,,e,f}, respetively. The eges in GR orrespon to links going from the set V to set R initing the memership of the tive links in the vrious ontention regions. or exmple, if ege ( i, j) '', then, i,j equls to 1, whih mens tht vertex i ( i V ' ) in the flow ontention grph to the ontention region j ( j R ), otherwise, i,j equls to. In ig. 3(), r 1 is ege to,,, e, f n r 2 is ege to,,, e, f.. Optimiztion Prolem ormultion We ssume tht the network support multi-soure multiestintion trnsmission, n there re totlly m flows. Thus, the ojetive is to hoose the mximum sum of eh flow s throughput uner the onstrint of ontention grph. The prolem n e formulte s the following optimiztion prolem. min ( L () t + P ())(, t I i j,), t t I(, i j,) t i, j i ij 38

4 s. t. I( i, j, t) = 1, j = 1,, m i S j k, ( t) I( i, j, t) 1 i, j ik, In whih I(i,j,t) equls to 1 when t time slot t, link i is selete to trnsmit t for flow j, else I(i,j,t) equls to. S j is the link set whose trnsmitter noe is the noe who reeive flow j t time slot t-1, in nother wor, it s potentil link set whih my e selete for flow j t time t. The ojetive of the optimiztion prolem is to minimize the sum of link ost n pth ost of the links selete t time t within two onstrints: 1) for eh flow, selet one link to trnsmit t ertin time slot, 2) the links selete for ifferent flows shoul not interfere with eh other. This optimiztion prolem hs liner ojetive funtion n liner onstrint funtions. Thus it n e solve y liner optimiztion lgorithms, suh s, simplex lgorithm. IV. ISTRIUT LGORITHM In previous setion, y solving the optimiztion prolem, optiml links whih is le to minimize the trnsmission power uner the onstrint of ontention reltionship is selete, thus, the optiml routing is forme step y step. However, it is hr to e iretly implemente in istriute mnner in the relisti systems, euse of the glol informtion neee in the lultion of P n G. Thus in this setion, we propose istriute lgorithm whih ims to pproh the optiml routing ut with some resonle n prtil pproximtions. irstly, link ost n pth ost for eh link is lulte in omprtively long time intervl sing on the perioilly upte network topology. or perio, eh noe oes physil-lyer proing using inrementl power level n rost the proing result. L n P re lulte sing on the proing informtion. It is ssume tht in the intervl of two proing, L n P is not hnge. Seonly, to voi flooing overhe, we introue lol ontention grph (LG), whih nee only two-hop trnsmission rnge informtion exhnge, to reple glol ontention grph. In [7], the uthors prove tht LG is suffiient for the ollision resolution. Moreover, we use n verge LG, inste of time-vrying LG. sing on the verge LG, using methoology introue in setion III., the generlize LG whih support oopertive ommunition is onstrute. Lstly, t eh time slot, the links whih potentilly hve informtion to e trnsmitte notify its neighor links of their potentil trnsmission. Thus, the glol soure set of eh flow is reple y the lol soure set of flows. When mking the routing eision, only the trnsmissions of two-hop-rnge flows re onsiere, inste of oing glol optimiztion. sing on the ove pproximtion, our istriute lgorithm is s follows. or eh link, L n P re lulte perioilly sing on the upte network topology. LG is onstrute y eh link vi two hop neighor informtion exhnge. If t one time slot, one noe reeive some pkets of flow, it will inform its two hop neighors tht the links soure t this noe will potentilly trnsmit some pkets in the next hop. t eh timeslot, if one link is soure t new e soure noe of flow, it onstrut LG, in whih eh vertex hs weight representing the totl ost whih is initite s. When the link reeive potentil trnsmission notifition of ertin link, it sets the weight of the orresponing link s the sum of L n P of tht link. It lso sets the weight of the potentil links of its own flow the sum of L n P of tht link. On the weighte LG, the mximl inepenent set (MIS) is lulte n the sum of noes weight in the MIS is lulte. hoose the MIS with the smllest weight sum, if the link is in the MIS, the link is selete to forwr the pkets of the flow. V. SIMULTION RSULT In this setion, we will show the performne evlution of the multi-flow oopertive routing we propose. We simulte networks of vrying numer of noes, N, ple rnomly within 1 meters 1 meters re. We rnomly hoose M pirs of noes, with eh pir to e the soure n estintion of flow respetively. It is ssume tht the mximum trnsmission rnge is 25 meters. Note tht only noes in eh other s trnsmission rnge n o oopertive ommunition. The rio trnsmission lose onstnt is ssume to e equl to 2 n hnnel gin invert to the 2, where is the istne etween soure n estintion. or eh plot shown, the results re verge over 1 rnomly generte network instnes. It is ssume tht virtul noe onsist t most two rel noes. We will ompre the energy svings n throughput gin of our routing lgorithm (Multi-low oopertive Routing-2) over non-oopertive routing to tht of the tritionl oopertive routing sheme PN-2 n propose in [6]. lso, noe ensities n totl flow numer is hnge to show the reltion etween performne improvement n ifferent network ftors. s ig. 4() shows, when numer of noes inreses, ver ge energy svings of three oopertive routing shemes ompring with non-oopertive sheme inrese. It is euse with more noes existing in ertin re, noe ensity inreses. Thus, the hne of fining suitle neighoring noe to o oopertive ommunition inreses. s result, more energy is sve. s we n see, when numer of noes equls to 6, s muh s 2% of totl trnsmission power n e sve y oopertive ommunition. Here, the numer of flows is set to e 3 y efult. The throughput gin of vrious oopertive routings ompring with non-oopertive routing is shown in ig. 4(). It is shown tht the throughput of N-2 n is 9% s muh s tht of non-oopertive routing. Tht is euse s oopertive ommunition is supporte, more noes involve in the trnsmission, thus, proility of ontention is inrese, whih uses lower throughput. However, using our multi-flow oopertive routing sheme, the throughput rmtilly inrese y 5%-15%. The throughput is inrese euse ontention of multiple flows is voie when hoosing the next hop noes, with the proility of ollision erese, the network throughput inrese rmtilly. However, the throughput gin is not hieve without ny ost. The energy svings of is less thn N-2 n s shown in ig. 4(). We me tre-off etween trnsmission power n network throughput. s result, y losing less thn 5% of energy sving, we hieve more thn 1% throughput gin ompring with single flow oopertive routings. In ig.5, energy svings n throughput gin of vrious routing shemes re stuie when numer of flows inrese. 39

5 verge nergy Svings N-2 numer of flows inresing, performne of oth nonoopertive routing n single flow oopertive routing will e egre rmtilly. ompring with them, MR, whih voi ollision suessfully, mnges to hieve muh etter throughput performne. When numer of flows equls to 5, throughput of MR n e 5 times s muh s tht of N-2 n, whih lso justify the importne of tking multiple flows into onsiertion when mking routing eisions ig. 4() vernge energy svings vs. numer of noes verge nergy Svings Throughput Gin N ig. 4() Throughput gin vs. numer of noes N Numer of lows ig. 5() vernge energy svings vs. numer of flows Throughput Gin N ig. 5() Throughput gin vs. numer of flows Here the totl numer of noes is set to e 5. With the numer of flows inresing, energy svings of MR ompring with non-oopertive routing is slightly erese, tht is euse, with more numer of flows simultneously trnsmitte, more links re ontening the sme wireless meium, proility of ollision inrese, to voi the ollision whih is muh more likely to e hppene, more ost on energy shoul e pi, thus, energy svings of MR is erese ompring with single flow oopertive routing shemes. lthough it is erese, it still sves s muh s 15% of energy. On the other hn, the throughput gin of MR inreses rmtilly with the numer of flows inresing, s shown in ig. 5(). euse of the inrese proility of ollision when VI. ONLUSION In this pper, we formulte the prolem of fining optimum oopertive routing uner multi-soure multi-estintion multi-hop wireless networks. We efine new onept virtul link n virtul noe to explore the hrteristi of rosting n oopertive ommunition. We onstrut virtul link se ontention grph to express the ontention reltionship of multiple links in multiple flows. We onvert routing eision into n optimiztion prolem uner our moel n solve it y liner optimiztion. Through some resonle n prtil pproximtions, istriute routing sheme is propose. The simultion results show tht our oopertive routing sheme n hieve 2% energy svings ompring with nonoopertive routing n rmtilly inrese network throughput y severl times ompring with tritionl single flow oopertive routing. The gret enefit is hieve y jointly onsiertion of routing in network lyer n ollision voine in M lyer over multiple flows. RRNS [1] M. Royer n.-k. Toh, review of urrent routing protools for ho moile wireless networks, I Mgzine on Personl ommunition, Vol.17, No.8, 1999, pp [2] J.. Wieselthier, G.. Nguyen,. phremies, lgorithms for energyeffiient multisting in ho wireless networks, Moile Networks n pplitions, vol. 6, numer 3, June, 21, pp [3] J.. Wieselthier, G.. Nguyen,. phremies, On the onstrution of energy-effiient rost n multist trees in wireless networks, INOOM', vol. 2, pp , Tel viv, Isrel [4]. Nosrtini, T.. Hunter n. Heyt, oopertive ommunition in wireless networks, I ommunitions Mgzine, vol. 42, no. 1, Otoer 24, pp [5]. Sglione,. Goekel, n J. N. Lnemn, oopertive ommunitions in Moile -Ho Networks: Rethinking the Link strtion, I Signl Proessing Mgzine, vol. 23, no. 5, pp , Sept. 26. [6] mir Khnni, Jinne ouni, ytn Moino, Lizhong Zheng, oopertive Routing in Stti Wireless Networks, I Trnstions on ommunitions, to pper, 28. [7] X. L. Hung n. ensou, On mx-min firness n sheuling in wireless ho networks: nlytil frmework n implementtion, in Pro. of M MOIHO 1, pp , Ot. 21. [8] T. M. over n... Gml, pity Theorems for the Rely hnnel, I Trns. Info. Theory, vol. 25, no. 5, Sept [9] J.N. Lnemn, oopertive iversity in Wireless Networks: lgorithms n rhitetures, Ph.. Thesis, Msshusetts Institute of Tehnology, ug. 22, mrige, M [1] J.N. Lnemn,.N.. Tse, G.W. Wornell, oopertive iversity in wireless networks: ffiient protools n outge ehvior, I Trnstions on Informtion Theory, vol. 5, issue 12, e. 24, pp [11] J.N. Lnemn, G.W. Wornell, istriute spe-time-oe protools for exploiting oopertive iversity in wireless networks, I Trnstions on Informtion Theory, vol. 49, issue 1, Ot