Alorg Universitet Cross-Lyer Optimiztion of Multipoint Messge Brodst in MANETs Nielsen, Jimmy Jessen; Grønæk, Lrs Jesper; Renier, Thiult Julien; Shwefel, Hns- Peter; Toftegrd, Thoms Pulished in: Wireless Communitions nd Networking Conferene, 29. IEEE WCNC 29 DOI (link to pulition from Pulisher):.9/WCNC.29.497654 Pulition dte: 29 Doument Version Peer reviewed version Link to pulition from Alorg University Cittion for pulished version (APA): Nielsen, J. J., Grønæk, L. J., Renier, T. J., Shwefel, H-P., & Toftegrd, T. (29). Cross-Lyer Optimiztion of Multipoint Messge Brodst in MANETs. In Wireless Communitions nd Networking Conferene, 29. IEEE WCNC 29 IEEE. DOI:.9/WCNC.29.497654 Generl rights Copyright nd morl rights for the pulitions mde essile in the puli portl re retined y the uthors nd/or other opyright owners nd it is ondition of essing pulitions tht users reognise nd ide y the legl requirements ssoited with these rights.? Users my downlod nd print one opy of ny pulition from the puli portl for the purpose of privte study or reserh.? You my not further distriute the mteril or use it for ny profit-mking tivity or ommeril gin? You my freely distriute the URL identifying the pulition in the puli portl? Tke down poliy If you elieve tht this doument rehes opyright plese ontt us t vn@u.u.dk providing detils, nd we will remove ess to the work immeditely nd investigte your lim. Downloded from vn.u.dk on: My, 27
Cross-Lyer Optimiztion of Multipoint Messge Brodst in MANETs Jimmy Nielsen, Jesper Grønæk, Thiult Renier Dept. of Eletroni Systems Alorg University, 922 Alorg, Denmrk {jjn,ljg,tr}@es.u.dk Hns-Peter Shwefel AAU nd ftw. 22 Wien, Austri hps@es.u.dk Thoms Toftegrd TietoEntor IP solutions 826 Viy J, Denmrk thoms.toftegrd@tietoentor.om Astrt Multipoint-to-multipoint messge rodst is demnding pplition senrio in d-ho networks. Adptive mngement of wireless resoures is neessry to support suh pplitions in sfety ritil ontext. In this work we study dpttion of trnsmission rte nd power to vrying densities of d-ho nodes. Our pproh is to onstrut ross-lyer model uilding on existing models for physil nd link lyers. To enle optimiztion in reltion to metris of end-to-end dely nd messge reeption proility model of flooding rodst is proposed s prt of the ross-lyer model. In simultion study we show tht dpttion of trnsmission power nd rte n e neessry to hieve dely requirements nd mximize messge reeption proility. Compred to simultion our ross-lyer model sed optimiztion pproh genertes slightly more onservtive prmeter settings. It is further shown how orrelted losses hve signifint impt on the roustness of the rodst tehnique. I. INTRODUCTION Adptive mngement of wireless resoures in d-ho senrios is neessry to utilize the shred medium resoures optimlly under vrying onditions used y moility nd wireless hnnel properties. One of the more demnding pplition senrios is multipoint-to-multipoint (mp-to-mp) rodst. In group of nodes, eh node hs messges to disseminte to ll other nodes while reeiving messges from ll other nodes s well. This is highly relevnt senrio in r-to-r ommunition, where messges ontin informtion out rod onditions nd rupt hnges in neighour r movement (e.g. emergeny rking)[]. The informtion is used to inrese trffi sfety nd improve trffi flow. Consisting of multiple soures periodilly sending nd forwrding messges, oviously, suh ommunition senrios hve potentil to use hevy ontention in the wireless medium whih my ffet sfety properties of the pplitions. To enle suh sfety ritil pplitions, under vrying onditions, we study distriuted pprohes to link dpttion in moile nodes in IEEE 82. sed vehiulr networks. Two signifint link dpttion prmeters re trnsmission power (tx power) nd trnsmission rte (tx rte). In d-ho networks, dpttion of suh prmeters to network onditions is minly trgeted t improving overll throughput nd dely while reduing power onsumption [2]. In unist settings, tx power ontrol is ommonly pplied to optimize single hop onnetions [3][4] s well s in routing nd topology ontrol [2][5] to ensure full nd relile network onnetivity while reduing ollision domins nd onserving energy. Power minimiztion hs lso een studied topi in rodst settings. In work of [6][7][8] pprohes re mde to minimize tx power of the individul nodes while mintining rodst overge t the ost of trnsmissions in more hops. This pproh yields redution in the numer of nodes in trnsmission rnge nd therey redution in redundny. It is however not thoroughly studied wht impt the minimum power ojetive hs on reliility when onsidering unrelile hnnels nd ses where ontention is high. A dominnt prt of other work in optimiztion of rodst performne fouses on effiient network lyer rodsting tehniques to redue numer of forwrding trnsmissions, endto-end dely nd to inrese overge [9][]. These tehniques re typilly sed on ssumptions of fixed trnsmission rnge nd rte. A relevnt option is to further improve the overll performne nd reliility of suh protools y lso onsidering dpttion of link nd physil lyer prmeters. In this work we study the potentil of ross-lyer optimiztion (CLO) of the mp-to-mp rodsting. We onsider possiilities of ontrolling lyer prmeters of tx power nd tx rte. In ontrst to dominnt prt of existing work our fous is not to redue power onsumption, whih is less ritil in vehiulr senrios thn in ttery-driven sensor network senrios. Insted our primry im is to optimize performne nd reliility metris of end-to-end messge delivery dely (D e2e ) nd suessful messge delivery proility (P smd ) in reltion to onstrints set y QoS requirements from n pplition. This requires to nlyze the following trdeoffs: I) High tx power inreses the ollision domin nd mount of redundnt nodes ut my redue end-to-end delys due to fewer hops to the network edge. II) High tx rte gives less ontention (nd dely), wheres employing more resilient modultion shemes (lower rtes) inreses trnsmission rnge without inresing the ollision domin. Our ross-lyer pproh is sed on n overll ross-lyer model inluding si rodst mehnism nd existing models of fst fding hnnels nd MAC. The pper is orgnized s follows: Setion II desries the model sed optimiztion pproh inluding the min rosslyer model nd sumodels sed on existing work. In setion III, the rodst model is introdued nd finlly in setion IV, optimiztion results re evluted in simultion study.
II. OPTIMIZATION APPROACH AND SYSTEM MODELS A streth of highwy represents the senrio in whih optiml settings for tx power nd tx rte re needed. We onsider stti snpshot of the reltive distnes etween rs where the width of the rod is onsidered insignifint nd the rs re in stright line. For sueeding rs, the sping is ssumed to e equl, s depited in fig.. The pplied optimiztion pproh tkes its strting point in rodst soure node (), whih rodsts messges within limited re (zone) defined y the pplition. It is ssumed tht in generl the node frthest from, the edge node, will experiene the worst end-to-end dely nd hs the highest risk of not reeiving messge. Thus, the optimiztion gol is defined to mximise P smd nd keep D e2e within requirements for the edge node. Figure. Brodst soure () Trnsmission pths Edge node n -2 n - n n n 2 n 3 n 4 n 5 Ntr Positions nd tx rnge (N tr /2) of rodsting nodes in highwy. In the following ross-lyer model is presented tht llows P smd nd D e2e to e evluted for the edge node, given tx power, tx rte nd node density. A. Cross-Lyer Model _freq (f) The ross-lyer model is uilt from su-models overing individul funtionlities in TCP/IP protool stk on top of IEEE 82. link nd physil lyers. These su-models re developed s individul modules, to llow extension of seleted model prts. The min model is presented in fig. 2. Grey oxes re su-models representing protool stk funtionlities, where the reminder re equtions of output metris nd intermedite vriles. In the following we in- pylod_size tx_rte tx_power density (σ) Input pylod_size tx_rte Figure 2. Nol Dtx Components of the overll optimiztion model. trodue the min prmeters nd equtions of the model. In order to mintin n eptle omputtionl omplexity, the vriles nd prmeters tht re pssed etween sumodels nd the output vriles re slrs. For rndom vriles the men vlues re used. Z o n e e d g e Output The proility of frme loss due to hnnel vritions, P herr, is given in the Chnnel Error eqution of fig. 2. P out is the outge proility whih desries the proility tht the signl power in reeiving node drops elow the reeive threshold leding to frme loss. Assuming independent it errors, the frme error proility for frme trnsmitted using the short premle option for IEEE 82. [] is: P fer = ( P edbpsk ) n pre ( P edqpsk ) n hdr ( P emod ) n frme () where P ex is the BER of the used trnsmission sheme for different prts of the frme trnsmission nd n X re the numer of its in the premle, heder nd MAC frme. Frme losses n lso e used y ollisions represented y the ollision proility P ol. Thus, the overll proility of loss of trnsmission P loss is given from the Aggregte Loss eqution, ssuming independene of P ol nd P herr. The output metri P smd is lulted from the rodst model whih is desried in Setion III. As input, the model needs P loss, the trnsmission rnge N tr nd the zone rnge. Given the node density, the trnsmission rnge is defined s the men mount of nodes rehed y trnsmission. We define the trnsmission rnge s the nodes where the proility of suessful reeption in free hnnel is.5. The end-to-end dely D e2e is defined in terms of the numer of hops H, nd the delys tht our t eh hop: D e2e = J fw (H ) + (D m + D tx + D q )H (2) In (2) the forwrding jitter J fw is the men of rndom dely, whih is dded to the sheduled trnsmission time in the flooding rodst sheme to redue the ollision proility when forwrding rodst (see [9]). The trnsmission dely D tx depends on the PHY mode nd the frme size nd n esily e otined from []. Deriving the MAC dely, D m, nd link lyer interfe queueing dely D q, however, requires more extensive modelling work to inlude influenes from ontention window size nd the numer of ontending nodes. In this work simple queueing sed model pproh hs een pplied to identify hnnel utiliztion nd sturtion points where D e2e inreses signifintly. This model is desried in setion II-C. In the following the individul sumodels re presented. B. PHY Model The PHY model must provide the proilities for vg. it error P er nd outge P out. These re depending on the hrteristis of the hnnel model. The wireless hnnel in the onsidered streth of highwy is hrterized y rurl environment. The hnnel model onsidered in this work is sed on the two-ry ground refletion model in onjuntion with Rien [2] fst fding model. In Rien hnnel, P er, n e derived from the vg. it error proility for n AWGN hnnel using eq. (6.5) in [3]. However, due to the omputtionl omplexity of P er for the CCK modultion shemes with tx rtes of 5.5 nd Mit/s, only the DBPSK nd DQPSK with tx rtes of nd 2 Mit/s, respetively, hve een implemented in the optimiztion model. The expression
used to lulte the it error proility for DBPSK hs een derived nlytilly nd is given in terms of the Rie ftor K nd the SNR E N in (3). P e = M 2 exp(k(m )), where M = ( + K) ( + K) + E N (3) The it error proility of PQPSK is otined numerilly. For Rien fding P out is otined s desried in eq. (6.46) [3]. The PHY model lso provides N ol, whih is the men numer of nodes tht will otin n SNR ove the usy sensing threshold [] in trnsmission. Notie tht N ol > N tr. C. MAC Model The MAC sumodel minly provides the ollision proility P ol nd the hnnel utiliztion ρ. ) Collision proility: The lultion of P ol is given from equtions (8),() nd (2) in [4], whih is sed on the ssumption tht ll nodes lwys hve pket redy for trnsmission. In the onsidered multipoint rodsting pplition this is not neessrily the se nd the outome of the model my therefore e too pessimisti in these ses. It must e noted tht we ssume stndrd IEEE 82. MAC ehviour where in the se of lyer 2 rodsts, fixed size ontention window is used. ) Chnnel utiliztion: In order to estlish si pproh for modelling D q we onsider single server queueing system where µ is the men rte t whih node gins ess to the medium, λ is omposed of the rrivl rte of rodsts from the pplition lyer nd forwrds from other nodes, nd ρ = λ µ is the hnnel utiliztion. We my otin λ = f ( + (N zone )P smd ), where f is the rodst frequeny, N zone is the numer of nodes in the zone, nd P smd is the proility tht rodst is reeived suessfully y node, whih is then le to forwrd the rodst. Further, the hievle medium ess rte for eh node is in the intervl 2 D tx N ol µ D tx N ol, where D tx is the trnsmission time of frme inluding DIFS, nd N ol is the numer of nodes within usy sensing rnge. The time used for derementing the ontention window ounter is omitted in µ s it is onsidered negligile ompred to D tx. The upper ound of µ results from the se when prllel trnsmissions (most likely leding to ollisions though) our in the onsidered one dimensionl topology. In the following we will onsider heuristi estimte 3 of µ = 2 D tx N ol, s it is in the middle of the intervl. III. FLOODING BROADCAST MODEL The studied network lyer rodst protool in this work is flooding rodst where every node forwrds eh reeived unique messge one. A high level of redundny mkes flooding rodst roust to losses ut lso greedy in the use of hnnel resoures. In existing work [9], flooding rodst is onsidered seline for omprison while its si priniples mke it useful in this initil model study. The outome of the flooding rodst model is metri of P smd for eh node sed on P s = ( P loss ) nd the men mount of nodes tht n reeive frme trnsmission. As sis for the model onstrution the following ssumptions hve een mde: (I) Equl trnsmission proility: The proility of suessful error-free reeption, P s, is onsidered to e the sme for ny node in the network. (II) Independent reeption proilities: P s is ssumed to e independent for eh node. (III) Time invrint P s during BC: P s is ssumed not to vry throughout the durtion of rodst. The flooding rodst model onsists of two prts. An nlytil model for fully onneted network nd n empiril model to inlude prtilly onneted networks. ) Fully onneted network model: In fully onneted network (FCN) it is ssumed tht ll nodes reeive trnsmission suessfully with proility P s. To derive P smd the pproh is to lulte the proility tht ll potentil pths from soure node to sink node will fil. For two node network this proility is oviously P f ( ) = P s. When introduing more nodes, other intermedite pths exist etween nd. M(i, j) is the proility tht these intermedite pths will fil; i is the mount of nodes tht hve reeived opy of the messge nd re redy to forwrd it. j is the mount of neighour nodes in set N (not inluding ) who hve not reeived the messge yet. Thus, for network onsisting of three nodes we hve: P smd = P f ( )M(, ) where M(, ) = [( P s ) + P s ( P s )] Figure 3 depits two exmples of how trnsmission n evolve in network of five nodes. In (α) only node reeives the first trnsmission. Susequently, the trnsmission ontinues vi nodes nd. M(, 2) is the proility tht the trnsmission from fils to reh diretly or vi nd. Notie, hs lredy sent opy of the messge nd does not trnsmit it further. In (β) two nodes hve reeived the first trnsmission nd M(2, ) expresses the proility tht trnsmissions from nd diretly nd vi will fil. In (5) M(, 3) is given from expressions of M(, 2) nd M(2, ). Figure 3. M(,3) tx-round = tx-round = 2 tx-round = 3 Legend Link: Ative link: Trnsmitting node: Depleted node: Empty node: M(,2) M(2,) M(,) (4) Two exmples of rodst progress in fully onneted network. M(, 3) = Ps ( P s ) 3 + + 2 P P 2 s ( P s ) 3 M(2, ) + s ( P s ) 3 M(, 2) 3 P 3 s ( P s ) 3 (5)
Reognising the reursive elements of (5), n expression for M(i, j) n e defined for ny i, j N: for i =, j > M(i, j) = for i >, j =, i, j N g(i, j) otherwise g(i, j) = j ( ) j ( P s ) q [ ( P s ) i] q q q= (6) [( P s ) i] j q M(q, j q) Finlly from (7) P smd n e lulted for ny numer of nodes in FCN tht orresponds to the ssumptions initilly presented in this setion. P smd = P f ( )M(, j) = ( P s )M(, j) where j = numer of nodes in N (7) A simultion of flooding rodst in n FCN hs een implemented in MATLAB in ompline with ssumptions I- III. A omprison of the results from simultion to the model verifies tht the model urtely provides P smd for vrying P s nd node size of the FCN. d) Prtilly onneted network model: The FCN model must e extended to over more relisti settings of prtilly onneted networks (PCN) where not ll nodes re in reh of eh other. The se of PCN is inresingly omplex to model in similr mnner s in the fully onneted se. First of ll the proility P smd hs to e estlished individully for eh node. In ddition, rodst n evolve in mny different wys. As n exmple, fig. depits rodst for trnsmission rdius of 2 nodes. Essentilly, messge my propgte in either diretion in reltion to the soure. As result lrge mount of trnsmission pths exist etween ny two nodes. Ext nlysis s onduted in the FCN model, thus, eomes intrtle. The lterntive option onsidered for the PCN model is to introdue n empiril pproh. The empiril model is prtilly sed on the FCN model nd simultion. The messge reeption onditions in the re round the soure node,, within rdius of N tr /2 hve good resemlne to the FCN model. Thus, the FCN model is useful pproximtion of P smd to this rnge of nodes, whih is denoted the neighourhood. To inlude ehviour outside the neighourhood MAT- LAB sed simultion model of the rodst mehnism hs een implemented. The simultion evlutes trnsmissions in rounds similr to fig. 3 to otin P smd for individul nodes. ne the onditions for the simultion re firly si little effort is required to generte results with high smple ount for permuttions of trnsmission rnge nd P s. To represent results from simultion in ompt form the progress of P smd outside the neighourhood hs een fitted to polynomil funtion of third degree, P smd = f(x), x = [,..., N] where N is the zone edge node. As result only four prmeters need to e stored for eh permuttion of R nd P s mking it suitle for implementtion with limited requirements for storge. The PCN model hs een implemented in n ns-2 environment with the simple MAC omponent dpted to inlude loss ehviour orresponding to the ssumptions I-III (ontrollle P s ). The omprison etween simultion nd model is depited in fig. 4, whih shows very good orreltion etween the model nd simultion results. The empiril model is generted with step size in P s of.. The model hs een reted from n ssumption tht the streth of nodes is infinitely long. In relisti setting node lose to the edge of network will hve fewer forwrding neighours resulting in little lower P smd thn the model predits s seen in fig. 4. P smd.5 mple MAC simultion, P s =., density=/ [nodes/m] neighorhood (tx rnge = 6m) 5.542 dbm (3m).8672 dbm (6m) 5.328 dbm (m) 7.45 dbm (3m) 3 2 2 3 node Figure 4. Brodst model (lines) vs. simple MAC simultion (mrkers). The rodst model ssumptions hve een revisited from initil results otined from detiled ns-2 simultion environment, s desried in setion IV. It hs een seen tht (I) seems to e resonle ssumption for most nodes. Also, s density nd trnsmission requirements of nodes do not hnge signifintly during rodst, ssumption (III) lso seems vlid. In mny ses P loss is influened y ollisions mening tht mny losses, in ontrst to ssumption (II), re orrelted. This impt of this is nlysed nd disussed further in the following setion. IV. RESULTS AND DISCUSSION This setion presents omprison of output from the rosslyer model nd referene dt sed on simultion runs from detiled ns-2 simultion setup. Extensions [5] hve een dded to ns-2 v. 2.29 for orret IEEE 82. MAC ehviour nd it-error proilities in Rien hnnel. A senrio is studied where nodes re pled in equidistnt lotions s shown in fig. t streth of m. Brodsts re evluted from n node t 5 m to the two edge nodes within zone rnge of 3 m. The rodst messge size is 3 ytes nd pplition requirements re D e2e = 6 ms nd P smd = 99 %. Further detils of the simultion environment n e found in [6]. Model nd simultion results re ompred for different onfigurtions in terms of density (σ) nd rodst frequeny (f ) for different settings of tx rte nd tx power. We will use the nottion (tx rte, σ, f ) to for eh onsidered se in whih we vry the tx power. For simpliity, tx powers re in the following onverted to pproximted tx rnges using two-ry PHY model. The simultion is for prtil resons
evluted t orse resolution while more evlution points re used for the model. In the following we initilly study the effets of vrying tx power for single se, nd seondly we evlute the overll performne of the optimiztion sheme for seletion of ses. Fig. 5 (A) depits omprison for simultion nd model of P s nd P smd for vrying tx power t fixed density nodes m σ = 3. In generl P s dereses s tx power is inresed due to n inresing mount of ollisions. The model estimte is little lower thn the simultion. This is likely n effet of the simplifying ssumptions used to otin P ol. For inresing tx power, P smd lso inreses s more nodes re rehed y trnsmission. The inresed roustness from more nodes, in the onsidered se, lso mens tht nerly onstnt level of P smd is otined despite the derese in P s. For the model P smd onverges to, wheres, the simultion P smd onverges to.6. The min use of this differene is found in ssumption (II). Tht is, in ontrst to independent reeption proilities in the model, mny losses re orrelted due to ollisions in relity. As result there is signifint risk of multiple nodes simultneously filing to reeive trnsmission. The onvergene point of P smd therefore primrily depends on the proility tht the initil rodst from the node is not reeived suessfully y ny neighor nodes. This is likely to our in the presene of orrelted ollisions. If n rodst is reeived y just few nodes, the redundny of flooding prtilly ensures overge. This vulnerility of the initil rodst mkes the flooding rodst sheme less roust thn the model suggests. Despite this differene, the model nd simultion results hve interesting similrities. T. I ontins rnges of optiml P mod smd D e2e [ms] Proility.8.6.4.2 (A) Delivery nd trnsmission proilities, whih we for the m. P smd m. P s Model P smd Model P s (B) Chnnel utiliztion nd end to end dely 2 5.8 m. D e2e.6.4 5 Model ρ.2 5 5 2 25 3 Trnsmission rnge [m] Figure 5. Model vs. simultion for vrying tx rnges for σ = nodes 3 m model define s the rnge of points tht re within. of the mximum Psmd mod, nd for the simultion s the men vlues tht overlp the onfidene ounds of the mximum men Psmd sim. The vlues typeset in old denote the points tht re onsidered the optiml hoies, when only onsidering the P smd. For oth the model nd simultion it n e seen tht when ontention is low (σ < nodes 2 m ), the optiml rnge extends to Utiliztion ( ρ) the longest tx rnges of 3 m, wheres in the high ontention ses (σ = nodes 2 m ), P smd drops efore rehing rnges of 3 m. In these ses, the ddition of nodes for longer trnsmission rnges does not ompenste the orresponding drop in P s. From the simultion results we further see tht exept for the ses (, 4, ) nd (2, 2, ), the rnge of optiml points overs wide rnge. This suggests, s indited in fig. 5 (A), tht within some rnge of the highest vlues of P smd, the sensitivity to vrition of tx power is low. The simultion results in t. I further show tht in Setting Model multion tx rte, σ, f opt [m] Psmd mod opt [m] Psmd sim (, 4, ) > 7.998 3.7(±.8) (2, 4, ) > 7.998 5,3.88(±.6) (2, 3, ) > 6.9969..3.65(±.) (2, 2, 5) 5..27.992 7..2.6(±.8) (, 2, ) 5..27.992, 2.2(±.8) (2, 2, ) 5..27.992 5.44(±.) Tle I TX RANGE FOR OPTIMAL P SMD FOR SIMULATION AND MODEL. low ontention ses, higher tx rte generlly leds to higher P smd. This n e explined y the ft tht hidden nodes hve less time to use ollisions with shorter frme trnsmission time. A similr effet is not seen in the model s the MAC sumodel does not onsider hidden nodes to derive P ol. In the following we evlute the hnnel utiliztion model. However, sine the P smd model does not tke orrelted ollisions into ount, we ompenste our model nd use λ = f ( + (N zone )P smd P ol ). Fig. 5 (B) shows how De2e sim inreses due to n inresing level of ontention s tx power inreses. In this se, the De2e sim < 6 ms requirement is exeeded in the intervl 5 2 m where the network sturtes, using queue instility. The hnnel utiliztion model estimtes the sturtion point (ρ ) t 9 m. Revisiting the disussion regrding hidden nodes in setion II-C, the results show tht the onsidered estimte of µ seems resonle. Fig. 6 show optiml tx power nd tul P smd nd D e2e for ll ses, onsidering 3 tx power seletion shemes. defult is fixed defult setting of 6 mw used in the PRISM 82. hipset, lso modelled in ns-2. Using this sheme, the D sim e2e < 6 ms requirement is exeeded in most ses exept when ontention is low in (2,4,). Clerly, this fixed defult tx power is unsuitle for the onsidered mp-to-mp rodst. Turning ttention to optimiztion options, two shemes re onsidered: model uses the presented models for estimting P smd nd ρ, nd simultion is sed on P smd nd D e2e from simultion results lone. In terms of optimiztion, we first onsider the tx rte in reltion to the trdeoff II etween lower ontention nd higher roustness mentioned in se. I. The results for (x, 4, ) nd (x, 2, ) lerly show tht inresing tx rte leds to improved P smd, wheres lower tx rte, i.e. more roust modultion sheme, is not enefiil. This is onsequene of ollisions nd not fding eing the min use of losses.
Fousing the nlysis on optimiztion of tx power, we first study the seline results hieved from simultion in fig. 6. The optiml tx power vries etween pproximtely mw, whih lerly shows the need for tx power dpttion to ensure mximistion of P smd within the dely requirements. To estlish the pilities of the ross-lyer model to provide optiml results, we onsider the results for model. In ll ses exept (, 4, ), the otined P smd vlues re similr for model nd simultion nd D e2e is well elow the limit in ll ses. Overll, this shows tht the proposed model is in most ses suited for determining tx power settings tht led to prtilly optiml P smd. The exeption here is (, 4, ) where lower P smd is otined due to the hnnel utiliztion model eing slightly onservtive. Interesting is lso the se (2, 2, 5), where similr P smd vlues re otined for very different tx powers. In the simultion result in t. I, the optiml rnge spns from 7 2 m, mening tht the seletion of tx power within this rnge minly influenes D e2e, whih is lso ler from fig. 6. Considering the results in t. I, we see tht the optiml rnge of the simultion results, exept (, 4, ) nd (2, 2, ), inlude the 5 m tx rnge. This indites tht simple optimiztion sheme hving defult tx rnge of 5 m omined with hnnel utiliztion model to prevent sturtion, would yield eptle results in most ses. However, model improvements nd further studies of ses for other tx rtes nd densities re needed to determine if P smd model does give signifint enefit. Finlly, this spet should e onsidered for other rodsting shemes tht re needed nywy in order to stisfy the P smd requirements. P tx [mw] D e2e [ms] p smd [] 2.8.6.4.2 >5... 2 5 5 (,4,) (,2,) (2,4,) (2,3,) (2,2,) (2,2,5) (,2,) (,4,) (,2,) (2,4,) (2,3,) (2,2,) (2,2,5) (,2,) (,4,) (,2,) (2,4,) (2,3,) (2,2,) (2,2,5) (,2,) Figure 6. Tx power, P smd nd D e2e for different onfigurtions. Brs represent: defult (lk), model (drk gry), model+simultion (light gry), nd simultion (white). Notie: No Mit support in model. s V. CONCLUSION AND FUTURE WORK This work hs onsidered model-sed ross-lyer optimiztion of PHY lyer prmeters tx rte nd tx power to redue end-to-end dely nd inrese the suessful messge reeption proility in rodst setup. It is shown tht tx power dpttion is needed to redue ontention for vrying densities ut my hve less signifine in low ontention senrios. Our proposed flooding rodst model ssumes independent losses, however, it is shown tht orrelted losses due to ollisions impt messge reeption proilities gretly; even in low ontention senrios. Finlly, heuristi hnnel utiliztion model for estimting network sturtion hs een proposed. Altogether, our studies hve shown good orreltion etween results of ns-2 sed simultions nd the ross-lyer model. Clerly, flooding rodst is simple ut ineffiient rodsting sheme. In prtie, other rodsting shemes, e.g. AHBP [9] should e onsidered in future work. Also, in the onsidered ses, simultion nd model results hve indited tht good hoie of trnsmission rnge is 5 m. Additionl work is needed to determine if this result n e generlized, prtiulrly in reltion to other rodsting shemes. Aknowledgments: This reserh ws prtilly supported y ftw. nd the EU IST FP6 projet HIDENETS nd the EU IST FP7 projet WHERE. REFERENCES [] M. Rdimirsh nd et l., D.: Use se senrios nd preliminry referene model. http://www.hidenets.u.dk/: HIghly DEpendle ipsed NETworks nd Servies HIDENETS, 26. [2] M. Krunz nd A. Lee, Trnsmission power ontrol in wireless d ho networks: hllenges, solutions nd open issues, Network, IEEE, vol. 8, no. 5, pp. 8 4, 24. [3] L. Wng, K. Yen, J. Hung, A. Chen, nd C. 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