Delay based Duplicate Transmission Avoid (DDA) Coordination Scheme for Opportunistic routing

Transcription

1 Delay based Duplcate Trasmsso Avod (DDA) Coordato Scheme for Opportustc routg Ng L, Studet Member IEEE, Jose-Fera Martez-Ortega, Vcete Heradez Daz Abstract-Sce the packet s trasmtted to a set of relayg odes opportustc routg strategy, so the trasmsso delay ad the duplcato trasmsso are serous. For reducg the trasmsso delay ad the duplcate trasmsso, ths paper, we propose the delay based duplcato trasmsso avod (DDA) coordato scheme for opportustc routg. I ths coordato scheme, the caddate relayg odes are dvded to dfferet fully coected relayg etworks, so the duplcate trasmsso s avoded. Moreover, we propose the relayg etwork recogto algorthm whch ca be used to judge whether the sub-etwork s fully coected or ot. The propertes of the relayg etworks are vestgated detal ths paper. Whe the fully coected relayg etworks are got, they wll be the basc uts the ext hop relayg etwork selecto. I ths paper, we prove that the packet delvery rato of the hgh prorty relayg odes the relayg etwork has greater effecto o the relayg delay tha that of the low prorty relayg odes. Accordg to ths cocluso, DDA, the relayg etworks whch the packet delvery ratos of the hgh prorty relayg odes are hgh have hgher prorty tha that of the low oe. Durg the ext hop relayg etwork selecto, the trasmsso delay, the etwork utlty, ad the packet delvery rato are take to accout. By these ovatos, the DDA ca mprove the etwork performace greatly tha that of ExOR ad SOAR. Idex Term-Opportustc routg, coordato scheme, trasmsso delay, duplcate trasmsso. I. INTRODUCTION I the past decades, the wreless sesor etworks (WSNs) have bee appled more ad more wdely, such as the wldlfe motorg [][2][3][4], the forest protecto [5][6][7], the smart grd [8][9][0][][2][3], the smart cty [4][5][6], etc. The WSNs chage our lfestyle may areas. Oe of the crtcal ssues of WSNs s the routg algorthm desg, whch guaratees relable ad effcet data trasmsso betwee the source ode ad the destato ode. The routg algorthms of WSNs have bee vestgated for a log tme ad may excellet algorthms have bee proposed to mprove the etwork performace. These algorthms ca be dvded to two categores: the determstc routg ad the opportustc routg [7]. I determstc routg, the source ode chooses oe of ts eghbors as the ext hop relayg ode based o optmal algorthms. The advatages of the determstc routg algorthm are that t s smple ad the duplcate trasmsso s slght. However, the determstc Ng L, Jose-Fera Martez-Ortega, ad Vecete Heradez Daz are wth the Uversdad Polteca de Madrd, Madrd, Spa. The research leadg to the preseted results has bee udertake wth the SWARMs Europea project (Smart ad Networkg Uderwater Robots Cooperato Meshes), uder Grat Agreemet SWARMs-ECSEL- 204-, partally supported by the ECSEL JU ad the Spash Mstry of Ecoomy ad Compettveess (Ref: PCIN C02-02). E-mal: {l.g, jf.martez, vcete.heradez}@upm.es. routg, the packet delvery rato betwee the seder ad the recever s low ad vares, whch cause frequet packet retrasmsso betwee seder ad recever. For solvg ths ssue, the authors [7] propose the cocept of opportustc routg. I opportustc routg, the seder seds the data packet to a set of eghbors to mprove the packet delvery rato. The opportustc routg ca mprove the packet delvery rato successfully; however, due to more tha oe eghbors receve the data packet from the seder, so durg the data packet relayg, the trasmsso delay ad the duplcate trasmsso are hgher tha that of the determstc routg strategy. The opportustc routg ca be dvded to two stages: ) the seder chooses the caddate relay odes ad prortzes these odes based o some performace metrcs (such as, the dstace to the destato ode, the ETX, the resdual eergy, etc); ths stage, the ode utlty, deoted as U, s calculated based o the performace metrcs; 2) the odes the caddate relayg set relay the data packet to the ext hop relayg odes based o the coordato schemes (such as the tme-based coordato scheme [7][8], the cotetobased coordato scheme [9][20][2], etc). I the prevous researches, the caddate relay odes selecto ad prortzato have bee vestgated detal [22]. The secod stage s mportat to the routg performace, sce the trasmsso delay ad the duplcate trasmsso are maly caused by ths stage. Because ths stage, whe the caddate relay odes receve the data packet, who s the frst oe to trasmt the data packet to the ext hop relayg odes ad how they otfy the other relayg odes that the data packet has bee relayed to the ext hop relayg odes are decded. There are four coordato schemes for the opportustc routg: coteto-based coordato, tme-based coordato, toke-based coordato [23][24], ad radom coordato [25]. I ths paper, we maly focus o the tmebased coordato scheme. The prcple of the tme-based coordato scheme has bee troduced detal [7], [8], ad [22]. The ma ssue wth the tmer-based soluto s that t s based o packet overhearg, thereby leadg to hgh duplcate trasmssos ad trasmsso delay [22]. These latter occur whe some caddates do ot overhear the selected relay s reply. Ths s the case especally sparse etworks, where caddate relays are placed further apart. I order to mtgate ths problem, oe possble soluto cossts removg some odes from the caddate relay set so that oly fully coected caddate relays are kept.

2 seder ode Sed packet to Caddate relays set Fg.. The caddate relayg etworks of opportustc routg. Ufortuately, the prevous researches, how to costruct ad judge the fully coected relayg etwork has ot be vestgated suffcetly. Moreover, as show Fg., to the odes the caddate relayg set, more tha oe fully coected relayg etworks ca be costructed; the topologes ad the odes these etworks are dfferet, such as the etwork (,2,3,7) ad etwork (4,5,8), etc. For the caddate relayg set show Fg., may dfferet relayg etworks ca be costructed; sce the odes ad topologes these relayg etworks are dfferet, so the propertes (such as the relayg delay, the packet delvery rato, etc) of these etworks are dfferet; for example, the packet delvery rato ad the relayg delay of etworks (,2,3,7) ad etwork (4,5,8) are dfferet. Therefore, how to evaluate the performace of these relayg etworks ad select the most approprate relayg etwork for the opportustc routg are also the ma cotets of ths paper. Moreover, for reducg the trasmsso delay, the ode whch the packet delvery rato s hgh should have hgh relayg prorty (ths wll be proved Secto IV). As the vewpots proposed [7] ad [26], the packet delver ratos of the odes the commucato lk from the source ode to the destato ode have dfferet effecto o the routg performace. For stace, the packet delvery rato of the ode at the ed of the lk have great effect o the eergy cosumpto ad trasmsso delay [26]; the ETX relates to all the packet delvery ratos of odes the commucato lk from the source ode to the destato ode [7]. I ths paper, we wll prove that the routg performace, such as the trasmsso delay, s also affected greatly by the frst ode s packet delvery rato the commucato lk. Therefore, ths paper, the effecto of the packet delvery ratos of the caddate relayg odes o the routg performace wll be vestgated detal. Motvated by these, we propose a ew tme-based coordato scheme, amed the delay based duplcate trasmsso avod (DDA) coordato scheme. I DDA, the odes the caddate relayg set are dvded to dfferet fully coected relayg etworks. Sce for the caddate relayg odes, more tha oe relayg etworks ca be costructed ad oly oe relayg etworks ca be chose as the fal relayg etwork, so the ma objectves of ths paper ca be summarzed as: ) how to recogze the fully coected relayg etworks that costructed by the caddate relayg odes; ad 2) how to chose the most sutable relayg etwork from these etworks. I DDA, the relayg etwork selecto takes the packet delvery rato betwee the 2 5 seder ad the relayg etworks, the trasmsso delay, ad the relayg prortes of odes the relayg etworks to accout to choose the most effectve relayg etwork. By these, the trasmsso delay ad duplcate trasmsso are reduced whle the effectve of the opportustc routg s kept. The ma cotrbutos of ths paper ca be summarzed as follows:. We defe the relayg etwork for the caddate relayg set; the relayg etworks are fully coected. Moreover, we also propose a algorthm to judge whch odes ca costruct a fully coected relayg etworks ad how may relayg etworks ca be costructed by the caddate relayg odes; to the best of our kowledge, ths s the frst algorthm that troduce the relayg etwork to the relayg odes selecto ad ca be used to judge whether the etwork s fully coected or ot; 2. We propose the calculato model of the oe-hop average relayg delay for the opportustc routg; 3. By vestgatg the relayg etworks, we propose the er-etwork propertes ad the -etwork propertes of the relayg etworks, whch ca be used the relayg etwork selecto; 4. Based o the trasmsso delay of the relayg etwork ad the packet delvery rato betwee the seder ad relayg etwork, we propose a relayg etwork selecto algorthm to choose the most sutable relayg etwork for data packet trasmsso; ths algorthm, ot oly the trasmsso delay ad the packet delver rato, but also the ode utlty ad the relayg prorty of ode are take to accout. The rest of ths paper s orgazed as follows: Secto II troduces the dfferet coordato schemes of opportustc routg; Secto III, the problems wll be solved ths paper are stated, the etwork model s troduced, ad the calculato model of etwork relayg delay ad packet delvery rato are proposed; Secto IV vestgates the propertes of the relayg etworks; Secto V, the relayg etwork based coordato scheme for the opportustc routg s proposed; Secto VI, the performace of the ew coordato scheme s compared wth the tradtoal oes; the Secto VII summares the work ths paper. II. RELATED WORKS The coordato scheme s used to fd the approprate caddate relayg odes for packet trasmsso. I the past decades, may coordato schemes for the opportustc routg algorthm have bee proposed. These coordato schemes ca select the best relayg ode whle currg the smallest cost ( terms of the relayg delay, the duplcated trasmsso, etc) ad ca be classfed to four ma classes: coteto-based coordato [9][20][2], tme-based coordato [7][8], toke-based coordato [23][24], ad radom coordato [25]. I the followg of ths secto, we wll troduce the algorthms relate to these four schemes brefly. I [7] ad [8], the tme-based coordato schemes are used. I [7], the cocept of opportustc routg s proposed. The source ode prortzes ad chooses the caddate relayg odes based o the values of odes estmated trasmsso cout (ETX) to the destato ode. The ode whch the ETX s small wll be set wth hgh prorty to relay the packet. Whe the source ode seds the packet, the relayg odes

3 relay the order whch they appear the forwardg lst, hghest prorty frst. Low prorty relayg odes drop the packet whe they receve the ACK from the hgh prorty relayg odes durg the watg tme; otherwse, relayg the packet. Smlar to [7], [8], the coordato scheme s the same as that troduce [7]; moreover, ths algorthm the watg tmer s set to 45ms. For reducg the trasmsso delay tme-based coordato schemes, some algorthms troduce the etwork codg to the routg algorthm, such as [27], [28], [29], ad [30]. The etwork codg mproves the etwork throughput ad reduces the overhead; however, the ssue of decdg whe ad how ofte to geerate coded packets s stll ot solved these researches [22]. The coteto-based coordato scheme s used [9], [20], ad [2]. I [9], the source ode sed RTF (Request to Forward) packet, the eghbors who receve ths RTF packet wll reply CTF (clear to forward) packet to the source ode. These CTF packets trasmsso s compettve wth each other. The eghbor whch the CTF packet s receved by the source ode wll be the ext hop relayg ode. The forwardg scheme used [20] s the smlar cotetobased scheme wth that used [9]. The coordato approach used [2] s dfferet wth that show [9] ad [20]. I [2], whe the caddate relayg odes receve the packet trasmtted from the source ode, they wll cotet the same trasmsso chael to relay the packet to the ext hop relayg odes; the caddate relayg ode whch competes to the commucato chael wll trasmt the packet to the ext hop relayg odes. I the toke-based coordato schemes, such as [23] ad [24], sce oly the ode whch holds the toke ca trasmt packets, so the duplcate trasmsso s reduced greatly. However, the toke-based coordato scheme, the cotrol cost s pretty hgh. Whe the source ode trasmts the packet to the caddate relayg odes, the relayg odes receve ad store the packet. The relayg ode s allowed to relay the packet oly t receves the tokes. The tokes clude the ackowledgemet formato ad are passed from hgh prorty relayg ode to low prorty ode. The caddate relayg odes receve the tokes ad ca oly trasmt the uackowledgemet packet. Smlar to the tme-based coordato scheme, the toke-based coordato scheme, the caddate relayg odes should also be fully coected. For reducg the watg delayg the above coordato schemes, [25], the authors propose the radom selecto coordato scheme. I ths scheme, each caddate relayg ode decdes whether to cotue forwardg the packet to the destato or ot probablstcally, so the relayg delay that caused by the watg tmer s reduced greatly. However, ths scheme, sce the caddate relayg odes decde whether forwardg or ot probablstcally, so the duplcato trasmsso s serous. III. NETWORK MODEL A. Network model I ths paper, two odes ca commucate wth each other drectly (wthout the help of the thrd ode) f ad oly f there s a b-drectoal commucato lk betwee these two odes. The b-drectoal commucato lk meas that the trasmsso rages of these two odes are all larger tha the dstace betwee these two odes. For stace, as show Fg. 2(a), ode s ad ode 7 ca commucate wth each other drectly whe s7 rs ad s7 r7, where s 7 s the Eucldea dstace betwee ode s ad ode 7, r s ad r 7 are the trasmsso rages of ode s ad ode 7, respectvely. The trasmsso rage of ode s s a crcle whch the cetre s ode s ad the radus s r s, deoted as Csr (, s). Ths ca be foud Fg. 2(a). (a) (b) (c) Fg. 2. The etwork model for opportustc routg: (a) the etwork of the caddate relayg odes; (b) the depedet sub-etworks of the orgal etwork; (c) the depedet sub-etworks of Fg. 2(b.) As show the Fg. 2(a), opportustc routg, whe the seder wats to sed data packet, frst, a set of eghbor odes are chose as the caddate relayg odes based o the performace metrcs (such as, ETX, dstace, etc), ad the seder relays the data packet to all the odes the caddate relayg set (the caddate relayg set s the set of all the caddate relayg odes). For stace, Fg. 2(a),, 2,3, 4, 5,6, 7,8. The etwork that costructed by the odes s deoted as GV, E, where V represets the set of odes ad E represets the set of b-drectoal commucato lks the etwork. Secod, the caddate relayg odes relay the data packet to the ext hop caddate relayg odes wth the same process as the seder. I ths paper, we maly cocetrate o the secod step. I the secod step, the caddate relayg odes eed to be fltered based o the requremets of the coordato schemes. For stace, the tme-based coordato scheme, the

4 relayg odes should be able to commucate drectly wth each other,.e. the etwork costructed by these odes should be fully coected. The fully coected etwork meas that betwee ay two odes ths etwork there exsts a bdrectoal commucato lk; otherwse, the etwork s ot fully coected. However, as show Fg. 2(a), the GV (, E) may ot the fully coected etwork. For stace, ode_3 ad ode_6 are ot coected drectly. The feasble approach s to keep the fully coected caddate relayg ode set ad remove the u-fully coected odes, where s the subset of. For stace, the odes, 2,3, 7, whch s show Fg. 2(b), are fully coected. To, there are may dfferet subsets, whch meas that to GV (, E ), there are may fully coected sub-etworks GV (, E ) ca be costructed by the odes. For example, the etworks are show Fg. 2(b) ad Fg. 2(c) are all the fully coected sub-etworks of Fg. 2(a). Sce these fully coected etworks are dfferet, so for vestgatg the dffereces betwee these etworks more clearly, some deftos are preseted as follows. I the fully coected etworks, there must have bdrectoal lks betwee ay two odes, so we ca smplfy the expresso of the fully coected etwork by oly showg the odes ths etwork; such as, for G((2,6,7),(26, 27,67)) whch s show Fg. 2(b.2), we ca smplfy the expresso as G(2,6,7). Sce the tme-based coordato scheme, the relayg etworks that costtuted by the caddate relayg odes should be fully coected, so we defe the relayg etwork as follows. Defto : The fully coected sub-etworks GV ( ) of GV ( ) are the relayg etworks of caddate relayg set. For stace, Fg. 2(a), G(2,6,7) s oe of the relayg etworks. Sce there are more tha oe relayg etworks ad the odes these relayg etworks are dfferet, such as the relayg etworks G(2,6,7) ad G(,2,3,7), so for dstgushg these etworks, we defe the etwork degree Defto 2. Defto 2: The degree of the relayg etwork s defed as the umber of odes the relayg etworks, deoted as d G. For stace, Fg. 2(b), the etwork degree of Fg. 2(b.) s 4. Notce the fact that the relayg etworks, the small degree relayg etworks may be the sub-etwork of the large degree relayg etworks (t s ot always true); so we defe the relevat ad rrelevat for the relayg etworks Defto 3. Defto 3: For ay two relayg etworks GV ( ) ad GV ( ), whch V V ad V V, f G( V V ) 2 2 s stll 2 2 the relayg etwork, the these two relayg etworks are relevat; otherwse, these two relayg etworks are rrelevat. Based o Defto 3, we ca gve the Defto 4 as follows. Defto 4: For the relayg etwork GV ( ), f there exst relayg etwork GV ( ) whch relevat wth GV (, the j ) GV ( ) s called s-etwork; otherwse, GV ( ) s called o- etwork. For stace, the G(,2,3,7) show Fg. 2(b) s a o- etwork; the G(,2,3) show Fg. 2(c) s a s-etwork of G(,2,3,7). The s-etwork ca be derved from the o-etwork. To each o-etwork, there are more tha oe s-etworks ca be derved from ths o-etwork; the degree of these s-etworks are smaller tha that of the o-etwork. For stace, the relayg etworks show Fg. 2(c) are all s-etworks that derved from the o-etwork show Fg. 2(b.). Moreover, sce the etwork degree of Fg. 2(b.) s 4, so the s-etworks that derved from Fg. 2(b.) wll be 2-degree ad 3-degree, respectvely. Note that f the etwork degree s -degree, the the algorthm wll be the same as the determstc routg, so ths paper, we do ot cosder the -degree etworks. The otatos used ths paper are lsted Table. TABLE THE NOTATIONS parameter meag the caddate relayg set wthout flterg the fal caddate relayg set after flterg V the set of odes. T watg tme tme-based opportustc routg DT G(,2,,) relayg delay of relayg etwork G(,2,,) P G,2,... packet delvery rato of relayg etwork G(,2,,) the packet delvery rato of the th prorty ode P DT the varato of DT G(,2,,) whe the packet delvery G,2,... rato of th prorty ode chages, j the dfferece of the DT DT G(,2,,) varato betwee G,2,... ay two relayg odes the ode utlty calculated the frst stage of U opportustc routg ETX oe-hop oe-hop ETX for each relayg odes U the ode utlty of the relayg odes whe takg the ETX oe-hop to accout eb the eghbor matrx of th ode D G(,2,,) the result of (0) of the relayg etwork G(,2,,) t G(,2,,) the ETX of the relayg etwork G(,2,,) DT etwork relayg delay whe takg t G(,2,,) to accout U G(,2,,) utlty of the relayg etwork G(,2,,) U utlty of the relayg etwork G(,2,,) whe G,2,..., takg t G(,2,,) to accout F U fal utlty of relayg etwork G(,2,,) relatve varace of parameter x v rx B. The calculato model of etwork relayg delay ad packet delvery rato For vestgatg the performace of the relayg etworks, ths secto, we wll troduce the calculato model of relayg delay ad packet delvery rato of the relayg etwork. For the tme-based coordato scheme, the relayg delay s maly caused by overhearg the hgh prorty ode s ACK message. For better uderstadg the relayg delay of the tme-based coordato scheme, the followg, we troduce the prcple of the tme-based coordato scheme detal. The prcple ca be foud Fg. 3.

5 Tme Slots Node Node 2 Node No ode receve packet 0 T 2T 3T 4T (-2)T (-)T T Recevg packet wth probablty P Recevg packet wth probablty (-P )*P 2 Recevg packet wth probablty Recevg packet wth probablty P : Recevg delay P P Fg. 3. The prcple of the tme-based coordato scheme As show Fg. 3, tme-based coordato scheme, the hgh prorty ode has hgh prorty to relay data packet to the ext hop relayg odes, the low prorty odes overhear the ACK messages from the hgh prorty odes. The ode prorty s determed based o the ode utlty U whch s calculated the frst stage of opportustc routg algorthm (the dfferet stages of opportustc routg s troduce Secto I). After the seder seds the data packet to the caddate relayg odes, the frst prorty ode wll check f t receves the data packet. If yes, ths ode wll be the ew seder mmedately ad broadcasts the ACK message to other caddate relayg odes; the caddate relayg odes whch receve ths message wll drop the data packet that receved from the seder. If the frst prorty ode fals to receve the data packet, the after tme T (whch s called the watg tme, [8], ths tme s set to 45ms), the secod prorty relayg ode begs the same process as the frst prorty ode. Ths process wll be repeated utl oe of the caddate relayg odes receves the data packet or oe of the ode receves the data packet. So the average oe-hop relayg delay after oe trasmsso try ca be calculated as: DT P () G,2,... P P T j where s the degree of the relayg etwork, s the prorty of each ode the relayg etwork, P s the packet delvery rato of the th prorty ode ad 0 < P <, T s the watg perod. The secod term () represets that oe of the ode receves the data packet trasmtted from the seder. Based o the average oe-hop relayg delay troduced (), we ca coclude that to the same relayg etwork, the etwork relayg delay wll be the smallest whe the ode prortes are determed based o the packet delvery rato of ode (ths ca be got easly from ()). The packet delver rato of the relayg etwork used ths paper s defed as the probablty that the data packet set by the seder ca be receved by at least oe ode. So the packet delvery rato of the relayg etwork G(,2, ) ca be calculated as [7]: P P. (2) G,2,... Note that P s dfferet wth P G(,2, ), sce P s the probablty that the th prorty ode ca receve the data packet from seder, ad P G(,2, ) s the probablty that the data packet set by the seder ca be receved by at least oe ode. From () ad (2), we ca coclude that eve the s-etworks ca be derved from the o-etworks, the relayg delay ad the etwork packet delvery ratos of these two kds of etworks are dfferet. I the ext secto, we wll vestgate the propertes of the relayg etworks detal. IV. PROPERTIES OF THE RELAYING NETWORK I ths secto, based o the calculato model of etwork relayg delay ad etwork packet delvery rato that proposed Secto III, we vestgate the propertes of the relayg etwork detal. The propertes are dvded to -etwork propertes ad ter-etwork propertes. These etwork propertes ca be used durg the relayg etwork selecto. I the opportustc routg, for determg the prortes of the caddate relayg odes, some dfferet performace metrcs are used based o dfferet applcato purposes. These metrcs ca be dvded to two dfferet categores: ) the packet delvery rato based metrcs, such as the ETX [7], the lk correlato [8], etc; ad 2) ot the packet delvery rato based metrcs, such as the dstace to the destato odes, the resdual eergy, the terferece, etc. The etwork relayg delay of these two dfferet routg algorthms have great dfferece, sce the etwork relayg delay s affected serously by the packet delvery rato of the caddate relayg odes ad ther relayg prortes, whch wll be proved the followg of ths secto. As show (), the etwork relayg delay wll be dfferet whe the ode prortes are dfferet to the same etwork; however, as show (2), to the same relayg etwork, the packet delvery rato of ths relayg etwork s the same eve the ode prortes are chaged. A. Iter-etwork propertes The ter-etwork propertes represet the propertes of the whole relayg etwork,.e. the relayg etwork s regarded as a etrety. Corollary : If the GVE, s a relayg etwork, the E VV /2; otherwse, E V V /2. Proof. See Appedx A. For each, whch the umber of caddate relayg odes s, the umber of relayg etworks (cludg the s- etworks ad the o-etworks) ca be calculated as: um c. (3) I (3), c s the umber of -degree relayg etworks. I ths paper, the -degree etwork has bee gored, sce the - degree etwork s equal to the determstc routg. B. I-etwork propertes I the relayg etworks, dfferet ode parameters, cludg the packet delvery rato ad the ode prorty, have dfferet effecto o the etwork performace. For vestgatg the effecto of the ode parameter (cludg the packet delvery rato ad the ode prorty) o the etwork performace, ths secto, we vestgate the -etwork propertes of the relayg etwork. Defto 5: To the relayg etwork G(,2, ), the effecto of P o the etwork relayg delay s defed as whe P chages whle the packet delvery ratos of the other odes keep costat, the varato of DT G(,2, ), deoted as DT G.,2,... 2

6 Accordg to the Defto 5 ad (), the DT G,2,... (where ad s the degree of the relayg etwork) ca be calculated as: DT,2,... G P P P P P T j P2 jpj Pj j 2 j 3 Pj PT, (4) j 3 Pj jpj Pj j j j Pj PT, j where P j represets the packet delvery rato of the jth relayg ode G(,2, ); s the degree of G(,2, ); P s the varato of the packet delvery rato P. Note that the j used (4) does ot the ode relayg prorty, t s the relayg prorty. For stace, f the relayg etwork s G(2,6,7), the the P, P 2, ad P 3 (4) represet P 2, P 6, ad P 7, respectvely. The coeffcet of each term (4) does ot chage for the same relayg etwork. Based o (4), we ca calculate the dfferece of the relayg delay varato betwee two adjacet relayg odes DT ad G,2,...,, DTG,2,... DT, whch s deoted as DT. The G,2,... G,2,... ca be calculated as follows:, DT DT DT G,2,... G,2,... G,2,... Pj P P P2 (5) j 2 P3 P 2P PT Based o (5), we ca get the dfferece of the relayg delay varato betwee ay two relayg odes, deoted as, j DT G, whch ca be calculated as:,2,... j, j k, k G,2,... DTG,2,... k DT Pj P (6) j j 2 P 2 P Pj 2P PT For stace, for the relayg etwork G(,2,3,7),,3 DT G(,2,3,7) represets the dfferece of the relayg delay 3 varato betwee DT G(,2,3,7) ad DT G(,2,3,7). Corollary 3: To the relayg etworks whch the prorty of the relayg odes are determed based o the packet delvery rato based metrcs, the hgher relayg prortes (.e. the packet delvery rato s hgh), the hgher effecto o the, j etwork relayg delay;.e. f > j, the DT G ; ad f,2,... 0, j, k (-j) > (-k), the DT DT. G,2,... G,2,... Proof. Ths ca be proved drectly by (4), (5), ad (6). The Corollary 3 demostrates that the packet delvery ratos of the hgh prorty relayg odes have greater effecto o the etwork performace tha that of the low prorty relayg odes. Based o (4) ad (5), we ca derve the Corollary 4 ad Corollary 5 as follows. Corollary 4: To the relayg etworks whch the relayg prortes of the caddate relayg odes are decded based o the packet delvery rato based metrcs, wth the creasg of the etwork degree, the effecto of the same P becomes more ad more serous, whch meas f > m, the, j, j DTG,2,... DTG,2,... m DT,2,... DT G G,2,... m ad. Proof. Ths ca be proved drectly by (4), (5), ad (6). For stace, based o Corollary 4, for the relayg,3 etworks G(,2,3) ad G(,2,3,7), the s smaller DT G(,2,3),3 tha DT G(,2,3,7) ad the DT G(,2,3) s smaller tha DT G(,2,3,7). Corollary 5: To the relayg etwork G(,2, ) whch the prortes of the caddate relayg odes are decded based o the packet delvery rato based metrcs, wth the decreasg of, the relayg prorty, f, the DT ad. DT G,2,... 0,2,... 0 G Proof. See Appedx B. The Corollary 5 demostrates that the effecto of the low prorty relayg ode o the etwork performace becomes smaller ad smaller whe the umber of ode the relayg etwork creases. For the relayg etworks whch the ode relayg prortes are ot decded based o the packet delvery rato relevat metrcs, the propertes are the same wth that of the relayg etworks whch the ode relayg prortes are decded based o the packet delvery rato. Before vestgatg the propertes of ths kd of relayg etwork, accordg to (5) ad (6), we propose Corollary 6 frst. Corollary 6: To the relayg etwork G(,2,,) whch the relayg prortes of the caddate relayg odes are ot decded based o the packet delvery rato based metrcs, f P, j < P j, the the codto that DT G 0 s show as,2,... follows: j 2 Pj Pk 2 P P, j k j j 2Pj Pk k (7) Proof. See Appedx C. As show (8), sce P ad P j are all smaller tha, so the (P j -P ) s smaller tha, too. So the (8) wll ot hold. The cocluso Corollary 6 meas that eve P < P j, the, j DT G,2, Moreover, the Corollary 6 also llustrates that ot oly the packet delvery rato but also the relayg prorty ca affect the etwork relayg delay. Based o Corollary 6, we ca coclude that to the relayg etworks whch the prortes of the caddate relayg odes are decded based o the packet delvery rato rrelevat metrcs, wth the decreasg of the relayg prorty, the effecto of the ode packet delvery rato o the etwork relayg delay decreases. Ths meas that the etwork whch the odes are prortzed based o the packet delvery

7 rato rrelevat metrcs, we ca get the same corollares as that show Corollary 3, Corollary 4, ad Corollary 5. Accordg to the propertes of the relayg etwork, the parameters of ode whch the relayg prorty s hgh, has greater effecto o the trasmsso delay tha that of the ode whch the prorty s low. So for reducg the trasmsso delay, the hgh prorty relayg odes should have hgher packet delvery ratos tha that of the low prorty relayg odes. Ths cocluso s smlar to the coclusos [7] ad [26]. I [26], the authors llustrate that the ode s packet delvery rato whch s at the ed of the commucato lk has great effect o the eergy cosumpto; the commucato lk whch ths packet delvery rato s low wll deterorate the routg performace greatly. The authors [7] use the ETX whch relates to all the packet delvery ratos the commucato lk to evaluate the effecto o the routg performace. I ths paper, we prove that the packet delvery rato of the hgh prorty relayg odes ca affect the trasmsso delay greatly. Sce for reducg the trasmsso delay, the hgh prorty relayg ode should have hgher packet delvery rato tha that of the low prorty relayg odes, however, ths s ot always hold the algorthms whch the ode prorty s ot determed based o the packet delvery rato based metrcs. I these algorthms, the hgh relayg prorty does ot mea small packet delvery rato. For stace, whe the performace metrc s resdual eergy, the ode whch has large resdual eergy may ot have hgher packet delvery rato tha the odes whch have small resdual eergy. Therefore, for reducg the relayg delay, oe approach s resettg the relayg prorty based o the packet delvery rato. However, ths wll deterorate the routg performace, because the ode whch the resdual eergy s large may have low relayg prorty that determed based o the packet delvery rato. So to these algorthms, for takg both the ode utlty that calculated the frst stage of opportustc routg ad the packet delvery rato to accout, the ode prorty eeds to be re-calculated. Assumg that the utlty of th caddate relayg ode whch calculated the frst stage of the opportustc routg s U (U does ot take the packet delvery rato to accout), ad the packet delvery rato of ths ode s P ; accordg to the defto of ETX [7], we defe the oe-hop ETX for each relayg odes, deoted as ETX oe-hop, as follows: ETX oehop = / P. Therefore, whe takg the packet delvery rato to cosderato, the utltes of the caddate relayg odes that calculated the frst stage of the opportustc routg wll deterorate; the lower of the packet delver rato, the more serous deterorato s. So the ew utlty whch has take the packet delvery rato to accout ca be calculated as: U U / ETX oe hop U P (8) The (8) demostrates that whe takg the packet delvery rato to accout, the utlty of relayg ode deduces to U from U. The ew prortes of the caddate relayg odes * wll be determed based o the value of U. A example ca be foud Table 2. As show Table 2, whe takg both the packet delvery rato ad the resdual eergy to accout, ode b has better performace tha ode a ad ode c. I Table 2, we ca fd that the hgh prorty ode determed by (8) has both hgh packet delvery rato ad resdual eergy. TABLE 2. AN EXAMPLE ode a b c d e resdual eergy (%) packet delvery rato (%) prorty decded by resdual eergy prorty decded by packet delvery rato prorty decded by (8) V. DELAY BASED DUPLICATE TRANSMISSION AVOID (DDA) COORIDNATION SCHEME I Secto III, we troduce the etwork model ad the calculato model of the etwork relayg delay ad etwork packet delvery rato; Secto IV, we vestgate the propertes of the relayg etwork, cludg the ter-etwork propertes ad -etwork propertes. I ths secto, based o the coclusos Secto III ad Secto IV, we propose the relayg etwork recogto algorthm (RNR) ad delay based duplcate trasmsso avod (DDA) coordato scheme. A. Relayg etwork recogto algorthm I Secto III, we troduce the defto of the relayg etwork, whch s the fully coected sub-etwork of GV (, E). The relayg etworks clude the s-etworks ad o-etworks; moreover, the s-etworks ca be derved form the o-etworks. However, how to judge whether the odes ca costruct a relayg etwork or ot has ot bee vestgated suffcetly. I ths secto, based o the cocluso Corollary, we propose a relayg etwork recogto algorthm (RNR) to estmate whether ay odes ca costtute a relayg etwork or ot ad dstgush the relayg etwork s s-etwork or o-etwork. Before troducg RNR, we frst defe the eghbor matrx for each caddate relayg ode. Assumg that there are m odes, for ode, the eghbor matrx ca be expressed as: 234 m (9) eb 000 I (9), f the ode j has b-drectoal commucato lk wth ode, the the jth value eb wll be ; otherwse, ths value wll be 0. I RNR, we regard that ode s a eghbor of tself. For estmatg the exstece of the relayg etwork, we defe a sum operator betwee ay two eghbor matrxes as follows. Defto 7: For two eghbor matrxes whch oly cota 0 ad, the + betwee two eghbor matrxes eb ad eb j s defed as: m (, j) j j k D eb eb eb k eb k. (0) where s the ad operator Boolea algebra. For stace, to the matrxes [ 0 0 ] ad [0 0 0], based o (0), the summary of these two matrxes wll be 2. Accordg to Defto 7, we ca estmate whether ay - degree etwork s the relayg etwork or ot. Corollary 7: For ay etwork GV, E whch the etwork degree s, f D, the the etwork s the relayg GVR, E etwork; otherwse, the etwork s ot the relayg etwork.

8 Proof. See Appedx D. Fg. 4. The eghbor matrxes of the caddate relayg odes Fg. 2(a) For stace, the eghbor matrxes of the caddate relayg odes Fg. 2(a) are show Fg. 4. As show Fg. 4, accordg to the Defto 7, D (,2,3) =4, whch s larger tha the etwork degree of G(,2,3), so based o the Corollary 7, we ca coclude that G(,2,3) s a relayg etwork. However, sce D (2,5,6) =, whch s smaller tha the etwork degree of G(2,5,6), so G(2,5,6) s ot a relayg etwork. The rest of the relayg etworks ca be gotte by the same process based o the coclusos of Defto 7 ad Corollary 7. Note that the relayg etworks gotte from Corollary 7 clude both the s-etworks ad the o-etworks. The Corollary 7 s oly the algorthm to estmate whether the etwork s a relayg etwork or ot; t ca ot dstgush the relayg etwork s s-etwork or o-etwork. Therefore, we propose the Corollary 8 whch ca be used to dstgush dfferet kds of relayg etworks. Corollary 8: For ay relayg etwork GV ( * ) whch the etwork degree s, f DGV (, the the etwork * ) GV ( * ) s a o-etwork; otherwse, f m, where m s the D GV ( * ) degree of GV ( * ), the GV ( * ) s a s-etwork, ad the degree of the o-etwork that GV ( * ) s derved from s ; moreover, based o (2), the umber of the relevat m-degree s-etwork s m c. Proof. See Appedx D. For stace, Fg. 4, D (,2,3) =4 ad the degree of G(,2,3) s 3, so G(,2,3) s s-etwork ad derved from a o-etwork whch the etwork degree s 4. Addtoally, the umber of 3- degree relevat s-etwork of G(,2,3) s 4. I Fg. 4, sce D (,2,3,7) =4 whch s equal to ts etwork degree, so the etwork G(,2,3,7) s a o-etwork. The relayg etwork recogto algorthm s show as follows. Algorthm : The Relayg Network Recogto (RNR) Algorthm. caddate relayg ode calculates the eghbor matrx eb ; 2. f DGV ( * ) GV ( * ) s the o-etwork; 3. f DGV ( m GV ( * ) * ) m m s the s-etwork; 4. f DGV GV ( * ) * s ot the relayg etwork. ( ) B. Delay based duplcate trasmsso avod (DDA) coordato scheme After the recogto of the relayg etwork, we eed to decde whch relayg etwork s the most approprate oe as the fal relayg etwork. The odes the selected relayg etwork wll be the fal relayg odes ad the other odes wll be deleted. As talked Secto I, for mprovg the performace of the opportustc routg, durg the relayg etwork selecto, the followg propertes of the relayg etwork should be met as much as possble: ) the relayg delay of the relayg etwork should be as small as possble; 2) the packet delvery rato of the relayg etwork should be as large as possble; 3) the etwork whch the ode utltes (.e. the utlty s calculated the frst stage of the opportustc routg) are hgh should be selected as much as possble for guarateeg hgh etwork performace. Therefore, the relayg etwork selecto, ot oly the etwork packet delvery rato ad the etwork relayg delay, but also the ode utltes the relayg etwork should be take to accout. Based o () ad (2), the etwork relayg delay ad etwork packet delvery rato ca be calculated, respectvely. Smlar to the Expect Trasmsso Cout (ETX) of relayg ode whch s defed [7], accordg to the etwork packet delvery rato, we defe the oe-hop ETX of the relayg etwork G(,2,,), whch ca be expressed as: t () G,2,... PG,2,... P where P s the packet delvery rato of ode the relayg etwork. Whe takes the etwork ETX to accout, the etwork relayg delay deterorates, so the etwork relayg delay whch takes the etwork ETX to accout ca be calculated as: DT DT t G,2,... G,2,... P P P T j P (2) Smlarly to the aalyss Secto III, durg the relayg etwork selecto, the relayg etwork whch has good performace o both the etwork relayg delay ad the ode utltes should have hgh prorty to be selected as fal relayg etwork. For evaluatg the effecto of the ode utltes o the etwork performace, we defe ad calculate the etwork utlty U G(,2, ) as follows. For the relayg etwork G(,2,,), cosderg the packet delvery ratos ad utltes of odes the relayg etwork, whch s calculated the frst stage of opportustc routg, the etwork utlty U G(,2, ) vares; ths ca be expressed (3): U, the probablty s P U 2, the probablty s PP 2 U (3) G,2,..., U, the probablty s PP 0, the probablty s P where U meas the utlty of th relayg odes that calculated the frst stage of opportustc routg (demostrate

9 Secto I). Therefore, for a relayg etwork whch the etwork degree s, the average etwork utlty ca be calculated as: U,2,..., UP U P G jp (4) 2 j The (4) s the average etwork utlty of etwork G(,2,,) o oe trasmsso try. Smlar to the etwork relayg delay, whe takg the etwork ETX whch calculated () to accout, ths utlty deterorates. Accordg to (2), the etwork utlty whch takes the etwork ETX to accout ca be calculated as: U U / t G,2,..., G,2,..., G,2,... UP U PjP P (5) 2 j Based o (2) ad (5), we ca fd that for each relayg etwork, two etwork parameters should be take to accout durg the relayg etwork selecto: () the etwork relayg delay DT whch takes the etwork ETX to accout ad (2) the etwork utlty U whch takes the ode G,2,..., utlty ad etwork ETX to accout. The selected relayg etwork should have hgh qualty performace o both of these two metrcs. I ths paper, for achevg ths purpose, we troduce the weght based optmal approach to the fal etwork utlty calculato, whch ca be expressed as: F U DT U (6) DT U G,2,..., where DT s the weght of DT, U s the weght of U G(,2,..., ). For the weght based algorthm, the frst mportat ssue s to determe the weghts for each performace metrcs. To the metrcs of the relayg etwork, there s a fact that the metrc (.e. DT ad U ) whch the varato rate s large has greater effecto o the etwork performace tha the metrc whch the varato rate s small. For stace, as the parameters show Table 3, sce the values of U betwee dfferet relayg etworks are smlar, so whch U G(,2,..., ) s chose as the fal relayg etwork has small effecto o the etwork performace. However, for dfferet relayg etworks, the values of DT are qute dfferet, so whch DT G(,2,..., ) s chose has great effecto o the etwork performace. Based o ths cocluso, oe of the feasble approaches s to use the varaces of DT G(,2,..., ) ad U G(,2,..., ) as the weghts (6). However, as show [3], f we use the values of DT ad U that calculated (2) ad (5), ad the varaces of DT G(,2,..., ) ad U (6) drectly, there may have problems. Because: ) the fal etwork utlty wll be maly decded by the metrc whch ts value s large; for stace, Table 2, sce the value of DT s much F larger tha U, so the value of U G(, 2,..., ) wll be maly decded by DT ; 2) the varace s affected serously by the value of the metrc, so t ca ot reflect the practcal varato rate of the metrc; for stace, as show Table 3, the varace of U s larger tha that of DT ; however, whe takg the values of the metrcs to accout, the varato rate of U s smaller tha that of DT G,2,..., fact. So whe we choose the ext hop relayg etwork, the DT should has greater effecto o the routg performace tha that of the U. Ths s because the G,2,..., varace s the absolute dfferece betwee dfferet parameters, so t s affected serously by the values of the parameters. Therefore, ths paper, for vestgatg the effecto of dfferet metrcs o the routg performace, we propose the relatve varace (rv) whch takes the average of the parameter to accout ad use the relatve varace as the weght show (6). TALBE 3. AN EXAMPLE etwork a b c varace rv U G,2,..., DT The relatve varace s defed as: 2 x x vrx (7) x where x represets DT ad U, x s the average G,2,..., of x, s the umber of relayg etworks. I the relatve varace, the value of (7) ca reflect the effecto of dfferet parameters o the routg performace accurately. Ths ca be foud Table 3. I Table 3, eve the varace of U s larger tha that of DT G,2,...,, the relatve varace of DT s larger tha that of U, whch s cosst wth G,2,..., the effecto of the metrc o the routg performace. For evaluatg the dfferece betwee the relatve varaces of these two metrcs, we defe the parameter resoluto rato as: vrdt / vru, vrdt vru, vrdt vru (8) vru / vrdt, vrdt vru From (8), we ca fd that, the larger s, the larger dfferece betwee the relatve varaces of these two parameters. For the etwork utlty calculated (6), wth the creasg of, the effecto of the metrc whch the relatve varace s large o the etwork utlty creases, ad the effecto of the parameter whch the varace s small decreases. Whe the s small, the effecto of these two parameters o the etwork utlty s smlar. For the frst ssue, f we use the values of metrcs drectly the etwork utlty calculato, the there wll have problems. For stace, as the metrcs show Table 3, sce the relatve varace of Metrc_ s smaller tha that of the Metrc_2, so accordg to the aalyss above, the etwork utlty should be affected maly by the Metrc_2; however, the fact s that the etwork utltes are decded maly by Metrc_,.e. the etwork whch the value of Metrc_ s the largest wll have the hghest etwork utlty. Accordg to the etwork utlty defed (6), the prortes of the etwork utltes are: etwork_c etwork_b etwork_a, whch s the same as the prortes of Metrc_. Ths s ot cosstet wth

10 the aalyss above. The reaso s that the value of Metrc_ s much larger tha that of the Metrc_2. Whe the dfferece betwee Metrc_ ad Metrc_2 s too large, t wll cover up the effecto of Metrc_2 o the relayg etwork selecto. For solvg ths ssue, [3], the authors map the dfferet order of magtudes parameters to the same order of magtude; ths paper, cosderg the fact that for each performace metrc, there has a order umber relates to each relayg etwork, so we troduce the order umber of the relayg etwork to the etwork utlty calculato. For stace, as the values of Metrc_2 show Table 4, the order umbers of the relayg etworks relate to Metrc_2 are: etwork_a, etwork_b 3, ad etwork_c 2, respectvely. The large order umber meas that the related metrc s value s large the relayg etwork, vce versa. So ths paper, the value of parameter show (6) wll be replaced by the order umber of each relayg etwork, whch ca be expressed as: where U v v F rdt DT ru UG,2,..., DT (9) s the order umber of G(,2,,) relates to DT, s the order umber of G(,2,,) relates to U. U G,2,..., The etwork utlty wll be decded by (9), whch ca be foud Table 4. I Table 4, the etwork utlty of etwork_b s larger tha that of etwork_c, whch s cosstet wth the aalyss above. I Table 4, we also preset the etwork utltes that calculated based o the algorthm proposed [3] whch s the weght based algorthm ad [34] whch s the fuzzy logc based algorthm. From Table 4, we ca fd that the prortes of the relayg etworks that calculated by (9) are the same as that calculated by [3] ad [34]. TABLE 4. AN EXAMPLE etwork a b c rv Metrc_ Order umber of Metrc_ 2 3 Metrc_ Order umber of Metrc_2 3 2 Utlty calculated by (6) Utlty calculated by (9) Utlty calculated by [3] Utlty calculated by [34] Based o (8) ad (9), we ca derve the property of ths algorthm as follows. The etwork utlty calculated by (9) relates to both the weght of the metrc ad the prorty of the relayg etwork. Assumg that there are two relayg etworks, for the etwork_, the order umber based o DT s ad the order umber based o U s j ; for the etwork_2, the order umbers relate to these two Metrcs are m ad k, respectvely. Let DT j, U m k,, ad vrdt vru, the we ca derve the property of ths algorthm as follows. Corollary 9. If U / DT, the utlty wll be decded maly by DT, ad f U / DT, the the utlty wll be decded maly by U; vce versa. Proof. See Appedx E. A example ca be foud Fg. 6. The values of the metrcs Fg. 6 are the same as that show Table 3. As show Fg. 6(a), for the etwork_2 ad etwork_3, sce DT ad U, so U / DT ; sce.32 U / DT, so Fg. 6(a), the etwork utlty wll be decded maly by the value of DT. Therefore, Fg. 6(a), the relayg prorty of etwork_2 s ad the prorty of etwork_3 s 2, whch s the same as the order of DT. However, as show Fg. 6(b), for etwork_2 ad etwork_3, sce U / DT 2 whch s larger tha, so the etwork utlty wll be decded maly by the value of U. Therefore, Fg. 6(b), the relayg prortes of etwork_2 ad etwork_3 are 2 ad, respectvely; ths s the same as the order of U. The relayg prortes of etwork_2 ad etwork_3 are opposte these two fgures. U 29, DT 0.27 U , R 3 U2 45, DT U 0.55, R U3 63, DT U , R2 (a) U 45, DT 0.27 U 0.307, R 3 U2 29, DT U , R 2 U3 63, DT U 0.525, R (b) Fg. 6. A example of the relayg etwork prortze ad selecto algorthm Whe the relayg etwork s selected by the algorthm troduced above, the odes the relayg etwork wll relay the data packet based o the relayg prorty that calculated Secto IV. The relayg s tme-based, whch has bee troduced [7], [8], ad [22] detaled; the watg tmer s set to 45ms, whch s the same as that show [8]. Whe the ode the relayg etwork relays the data packet to the ext hop relayg etwork, the processes are the same as that show above utl the data packet s receved by the destato ode. The process of the DDA ca be foud below. Algorthm 2: DDA coordato scheme. each relayg etwork calculated the etwork ETX based o (); 2. based o (2) ad (5), the etwork relayg delay DT ad etwork utlty U G,2,..., are calculated; 3. the source ode calculate the varaces of etwork relayg delay ad etwork utlty,.e. ad DT G (,2,..., ) U G,2,...,, respectvely; 4. applyg the Corollary 2, Corollary 3, ad Corollary 4 to preselect the relayg etwork; F 5. based o (9), the fal etwork utlty U s calculated; 6. the relayg etwork whch has hghest fal etwork utlty wll be chose as the relayg etwork. VI. SIMULATION AND DISCUSSION I ths secto, we wll evaluate the performace of DDA coordato scheme. We compare the performace of DDA wth ExOR [7] ad SOAR [8], respectvely. The varato parameters are the umber of odes ad the umber of CBR coectos. The umber of CBR coectos represets the traffc load of the etwork. The parameters of the smulato evromets are show Table 5.

11 TALBE 5. SIMULATION PARAMETERS smulato parameter value smulato area 2000m 2000m umber of vehcles 00, 50,, 300 trasmsso rage 250m chael data rate Mbps the traffc type Costat Bt Rate (CBR) umber of CBR coectos 20, 40,, 00 packet sze 52bytes beaco terval s maxmum packet queue legth 50 packets MAC layer IEEE 802.ll DCF smulato tool NS2 The algorthms used ths smulato are ExOR, SOAR, ad DDA. The troducto of ExOR ad SOAR ca be foud [7] ad [8], respectvely. The DDA s the algorthms that proposed ths paper, the detal of DDA ca be foud Secto IV ad Secto V. The performace matrxes used ths paper are the trasmsso delay, the packet delvery rato betwee seder ad the caddate set, ad the etwork throughput: () Ed-to- Ed Packet delvery rato: the packet delvery rato s defed as the rato of the umber of packets receved successfully by the destato ode to the umber of packets geerated by the source ode [26][32]; (2) Ed-to-Ed delay: the trasmsso delay of the data packet from the source ode to the destato ode; (3) Network throughput: the etwork throughput s the rato of the total umber of packets receved successfully by the destato ode to the umber of packets set by all the odes durg the smulato tme [33]. A. Performace uder dfferet etwork desty I ths secto, we evaluate the performace of DDA, SOAR, ad ExOR uder dfferet etwork desty,.e. the umber of odes the etwork vares. I ths smulato, the etwork load s costat, whch meas that the umber of the CBR coectos s set to 60. The results ca be foud Fg. 7, Fg. 8, ad Fg. 9. I Fg. 7, the average ed to ed delays of these three algorthms are preseted. I these three algorthms, wth the creasg of the umber of odes the etwork, the average ed to ed delay decreases both these three algorthms. The fewer odes the etwork, the larger decrease s. For stace, DDA, whe the umber of odes the etwork creases from 00 to 50, the delay decreases from 780ms to 602ms; however, whe the umber of odes creases from 250 to 300, the delay decreases from 520ms to 500ms. The smlar cocluso ca be foud SOAR ad ExOR. Ths ca be explaed as: whe the umber of ode creases, the probablty of etwork porto decreases, so the delay wll decrease whe the etwork desty creases; whe the etwork desty s large eough, the the probablty of etwork porto s qute low, so the decreasg of the trasmsso delay s slow. Moreover, for the same etwork desty, the ed to ed delay of DDA s much smaller tha that of the other two algorthms. Ths s because DDA, the relay odes are fully coected ad the relay etwork whch the delay s the small has hgh prorty to be chose, so the ed to ed delay DDA s the smallest these three algorthms. I Fg. 8, the packet delvery ratos of these three algorthms are llustrated. Wth the creasg of the etwork desty, the packet delvery ratos of these three algorthms crease; the packet delvery rato of DDA s the largest these three algorthms. Sce wth the creasg of the etwork desty, for the seder, more relayg odes ca be foud ts trasmsso rage, so accordg to the calculato (2), the etwork packet delvery rato wll crease. Sce DDA, the packet delvery rato s take to accout durg the relayg etwork selecto, so the packet delvery rato of DDA s the largest. I Fg. 8, whe the etwork desty s large eough, ths creasg becomes slowly; ths s due to whe the etwork desty s large eough, the umber of caddate relayg odes s large, so there always exts at least oe ode ca receve the data packet ad sed t to the destato ode, whch makes the creasg slow. The etwork throughputs of these three algorthms are preseted Fg. 9. From Fg. 9, we ca coclude that whe the etwork desty creases, the etwork throughput keeps costat approxmately; these values fluctuate a very small rage. For stace, the varato rage of DDA s 0.03 approxmately ad s about 0.02 SOAR. O oe had, whe the etwork desty s small, the packet delvery rato s small whch ca be foud Fg. 8, the the probablty of retrasmsso s hgh; however, the umber of hops to the destato s small whe the etwork desty s small, whch cotrbutes to the umber of cotrol packet reducto. O the other had, whe the etwork desty s large, the packet delvery rato creases; however, the average umber of hops to the destato ode creases, whch causes the umber of cotrol packets creasg. So the etwork throughput keeps stable these algorthms; moreover, the etwork throughput of DDA s the best these three algorthms. Average ed to ed delay (*00ms) DDA SOAR ExOR Number of odes Fg. 7. The average ed to ed delay uder dfferet etwork destes. Packet delvery rato (%) DDA SOAR ExOR Number of odes Fg. 8. The packet delvery rato uder dfferet etwork destes.