A Packet Buffer Evaluation Method Exploiting Queueing Theory for Wireless Sensor Networks

Transcription

1 DOI: /CSIS Q A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks T Qu 1,2, Ln Fng 2, Fng Xa 1*, Guow Wu 1, and Yu Zhou 1 1 School of Softwar, Dalan Unvrsty of Tchnology, Dalan, Chna qut@dlut.du.cn; f.xa@.org 2 School of Innovaton Exprmnt, Dalan Unvrsty of Tchnology, Dalan, Chna fngln@dlut.du.cn Abstract. In larg-scal wrlss snsor ntworks (WSNs), whn th consumpton of hardwar s lmtd, how to maxmz th prformanc has bcom th rsarch focus for mprovng transmsson qualty of srvc (QoS) of WSNs n rcnt yars. Ths papr prsnts a nw valuaton mthod for packt buffr capacty of nods usng quung ntwork modl, whos packt buffr capacty s analyzd for ach typ nod, whn t s n th bst workng condton. In ordr to valuat congston stuaton n th quung ntwork, and to gt ral ffctv arrval rats and transmsson rats n th modl, holdng nods wr addd n th quung ntwork modl, and quvalnt quung ntwork modl s xpandd. W stablsh an M/M/1/N typ quung ntwork modl wth holdng nods for WSNs and dsgn approxmat tratv algorthms. Exprmntal rsults show that th modl s consstnt wth th ral data. Kywords: wrlss snsor ntworks, quung ntwork modl, blockng, packt buffr capacty, nod utlzaton. 1. Introducton Wrlss snsor ntworks (WSNs) ar succssfully appld n ntllgnt transportaton, montorng nvronmnt, locaton and othr flds. Thy consst of tny snsng dvcs that hav lmtd possssng and computaton capablts, and can collaborat ral-tm montorng, snsng, collctng ntwork dstrbuton of th varous nvronmnts wthn th rgon or montorng obct nformaton [1,2,3]. WSNs of dstrbuton rgons ar composd of snk nods [4,5,6], transmsson nods and boundary nods [7]. Th prformanc of ach typ nod wll affct th ovrall ntwork prformanc n WSNs. Throughput and utlzaton [8,9,10] of th nods n th lftm [11,12] ar th man valuaton prformanc ndcators of WSNs. Th * Corrspondng author

2 T Qu, Ln Fng, Fng Xa, Guow Wu, and Yu Zhou packt buffr capacty of nods s an mportant factor n utlzaton of ntwork nods [13]. If a nod of WSNs s blockd, and packt buffr st too small, th ntr ntwork data transmsson and procssng ffcncy s not hgh. Thrfor, whn th consumpton of hardwar s lmtd, how to optmz th nod packt buffr sz and maxmz th prformanc for WSNs has bcom a rsarch focus for mprovng th Qualty of Srvc (QoS) of WSNs transmsson n rcnt yars. In ths papr, w consdr that packt buffr capacty corrsponds to th lngth of th watng quu n th stablshd lmtd capacty of th quung ntwork modl. Whn th lngth of th watng quu rachs th maxmum, th nod s blockd n th quung ntwork modl. Thrfor, a typcal WSN s modld by M/M/1/N typ quung ntwork modl. Th mthod of modlng basd on topology of nods n WSNs and prformanc analyss of th packts buffr capacty hav bn proposd. Accordng to th topology of WSNs and opratonal charactrstcs, arrval, transfrrng and lavng rlatonshps of transmsson nods, boundary nods and snk nod ar analyzd, and data flow balanc quatons ar obtand. In ordr to valuat th congston stuaton n th quung ntwork, and gt ral ffctv arrval rats and transmsson rats n th modl, holdng nods wr addd n th quung ntwork modl and quvalnt quung ntwork modl s xpandd. By analyzng th quung modl wth blockng probablty, to obtan th prformanc ndx of systm whn t s n stady stat, approxmat tratv algorthms ar dsgnd. Th prformanc paramtrs of nods modl n th WSNs ar calculatd usng lmtd traton tms. Th optmal valus for packts buffr szs sttngs ar obtand for transmsson nods, boundary nods and snk nods. Th rmandr of ths papr s organzd as follows. Th rlatd work and problm statmnt ar ntroducd n Scton 2 and Scton 3. Scton 4 dscrbs th modlng of WSN and analyss. Scton 4.1 dscrbs th modlng mthod of usng opn quung ntwork modl for WSNs; th balanc quatons of data flow ar stablshd. In Scton 4.2, th quvalnt quung ntwork modl s obtand, that holdng nods ar addd n th may b blockng nods. Th modl paramtrs of blockng probablty of data packts, th arrval rat and nod transfr rat, all ar analyzd n Scton 4.3 usng th quvalnt quung modl. Scton 5 dsgns tratv approxmaton algorthms for total arrval rat of nods and ffctv arrval rat and transfr rat of nods wth blockng probablty. Scton 6 gvs th numrcal calculaton and analyss of xprmntal rsults. Th prformanc paramtrs of WSN nods ar calculatd usng tratv algorthms gvn n Scton 5. Accordng to th rlatonshp curvs btwn utlzaton and buffr sz, th packts sz of th optmal buffr sttngs ar obtand for transmsson nods, boundary nods and snk nod, rspctvly. Th corrctnss of modlng and analyss mthod s vrfd by xprmntal data of th WSNs. Scton 7 contans th concluson and futur work ComSIS Vol. 8, No. 4, Spcal Issu, Octobr 2011

3 A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks 2. Rlatd Work Whn th hardwar has bn mplmntd, t s dffcult to adust th nod's hardwar rsourcs n accordanc wth spcfc nds. Thrfor, rsarchrs hav proposd th nd for larg-scal WSN nods modlng mthod [14]. Through prformanc valuaton of pr-sttng nods, optmal paramtrs of allocaton for th hardwar nods ar obtand. Th currnt modlng mthod basd on Ptr nts [15,16,17] s sutabl for macromodlng, but t s not a spcfc modlng tchnqu for larg-scal WSNs. Quung ntwork s an ffctv systm-lvl modlng mthod, whch s wdly usd n th modlng and prformanc analyss of computng and communcaton systms [18,19]. It has many advantags that nclud a hghly abstract and rch thory for modlng. In rcnt yars, rsarchs hav mad som progrss on analyzng and mprovng ntwork prformanc n th applcaton of fnt capacty quung ntworks. Bsnk t al. [20] modld random accss mult-hops wrlss ntworks as opn G/G/1 quung ntworks and usd dffuson approxmaton n ordr to valuat closd form xprssons for th avrag nd-to-nd dlay. In [21,22], Kouvatsos and Awan dscrbd th prorts and blockng mchansms wth opn-loop quung ntwork prformanc analyss, and quung ntwork paramtrs on th approxmaton and rror stmats. Özdmra t al. [23] prsntd two Markov chan quung modls wth M/G/1/K quus, whch hav bn dvlopd to obtan closd-form solutons for packts dlay and packts throughput dstrbutons n a ral-tm wrlss communcaton nvronmnt usng IEEE DCF. Mann t al. [24] dvlopd a quung modl for analyzng rsourc rplcaton stratgs n WSNs, whch can b usd to mnmz thr th total transmsson rat of th ntwork or to nsur that th proporton of qury falurs dos not xcd a prdtrmnd thrshold. In [20], Lhr t al. ntroducd nhancmnts to th standard of xtndd quung ntwork modls, whch allow th modlng and th smulaton of ntr-procss communcaton and hghlght th bnfts grantd by thr nhancd EQN approach. Howvr, ths rsarchs don t addrss th packt buffr capacty of nods and how to st th buffr sz to drv th optmal prformanc of th nods n WSNs. 3. Problm Statmnt Data packts ar transmttd and procssd n collaboraton by th snk nods, transmsson nods and boundary nods. For a larg scal WSN, a quung ntwork modl can b usd to analyz ts prformanc [25, 26]. But how to confgur rsourcs to fnd th bst valu hardwar usng trnds of changng th paramtrs of prformanc s an mportant rfrnc for nod dsgn. Th dfnton of th thrshold of nod buffr capacty s gvn blow: Dfnton 1. Whn th quung ntwork systm s stabl, nod s hardwar buffr capacty ust accommodat th maxmum lngth of th quu ComSIS Vol. 8, No. 4, Spcal Issu, Octobr

4 T Qu, Ln Fng, Fng Xa, Guow Wu, and Yu Zhou to b procssd. Buffr sz valu at th momnt s calld th nod thrshold, dnotd by N T Snk Nod Transmsson Nod Boundary Nod (a) A typcal topology of WSN o 2 o 3 o (b) Rlatonshp of arrval and lavng btwn th nods Fg. 1. Topology and nod transfr of th WSN. In WSNs, for any nod buffr sz, w mak th followng dscusson: () If N NT, nod quu lngth wll nvr b procssd ovr th buffr capacty whn a systm s n a stady stat. Thrfor, th packts that hav not bn tmly procssng data wll b placd n th packt buffr. Nwly arrvd packts wll not caus th blockng nod srvr. () If N NT, whn th packt buffr of nod s full, th lnk paths that nclud th nods ar blockd, and lad to th procssng ffcncy of th whol WSN down. On th othr hand, whn th lnk path s blockd, all th nods ar n an actv stat n th lnk path. Thrfor, nrgy consumpton of th nod s largr, and ndvdual nods ar nvaldatd du to nrgy xhauston. Fgur 1(a) shows a typcal topology of WSN, whch s composd of snk nod 1, transmsson nods 2 and 3, and boundary nod 4. Accordng to th modlng mthod of opn quung ntwork, t dscrbs th transmsson 1030 ComSIS Vol. 8, No. 4, Spcal Issu, Octobr 2011

5 A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks rlatonshp btwn th nod quus as shown n Fgur 1(b), whr o s th ndpndnt xtrnal Posson arrval rat of nod and s th lavng rat aftr th compltd srvc of nod. (Not: Boundary nod dos o not nclud ). In practc, th task contnt of snk nods, transmsson nods and boundary nods s dffrnt. Thrfor, ts consumpton of hardwar rsourcs wll b dffrnt. For xampl, n Fgur 1(b), th arrval rat of snk nod 1 packts s th maxmum. Thrfor, fndng a way to proprly valuat ts prformanc bcoms vry mportant. That s, how to st th packt buffr capacty of wrlss snsor nods, n ordr that ach nod has th hghst spd of data procssng and throughput. Thus, th bst paramtrs btwn th utlzaton of nod and consumpton of hardwar buffr capacty wll b found. In ordr to facltat th analyss of quung ntwork modl for WSNs, som symbols ar dfnd n Tabl 1. Tabl 1. Dfnton of symbols Symbol Dscrpton,, k, d Nod No. n th quung ntwork. M Total numbr of paths n th quung ntwork. N Sz of packt buffr capacty Arrval rat of nod. Srvc rat of nod. Utlzaton of nod. p Stady-stat probablty of arrval nod. o p Lavng probablty from nod. p Probablty of from nod to nod. S Stat of nod. T Montorng cycl of -th tms n WSN. A Aggrgat of all th holdng nods. pb Blockng probablty from nod to nod. pb Indpndnt xtrnal Posson arrval blockng probablty of nod. pb Total arrval blockng probablty of nod. a 4. Opn Quung Ntwork Analyss for WSN Modl In ths scton, w dscrb th modlng mthod of usng opn quung ntwork modl for WSNs and th balanc quatons of data flow ar stablshd. In ordr to analyz blockng of th quung ntwork modl, holdng nods wr addd n th may b blockng nods, and th quvalnt ComSIS Vol. 8, No. 4, Spcal Issu, Octobr

6 T Qu, Ln Fng, Fng Xa, Guow Wu, and Yu Zhou quung ntwork modl s obtand. Thrfor, analyss of th blockng quung ntwork s possbl Opn Quung Ntwork A typcal opn quung ntwork composd of WSN s consstnt wth a flow balanc quaton. Accordng to th thorm for flow balanc quaton [25,27], w can gv Corollary 1 and Corollary 2 for any WSN. Corollary 1. For th transmsson nod, arrval nod and lavng nod n th quung ntwork of WSN, th numbr of all possbl packts lavng th nod quals that of th arrval numbr n th stat. m1 d o k pk pf p 1 f (1) Proof: Usng rducto ad absurdum, suppos th numbr of packts ntrng th nod s not qual to th numbr of packts lavng th nod, thn accordng to th flow balanc quaton, thr must b packts wth probablty 0 p n th slf-loop. Ths s n contradcton wth th fact that transfr nod, arrval nod and lavng nod srvc s th ordr of on-way srvcs n WSNs. Thrfor, th Corollary 1 s stablshd. Corollary 2. For th snk nod n th quung ntwork of a WSN, th sum of th arrval packt and slf-loop packt quals that of th sum of th lavng packt for nod n th stat. m1 d o k pk p pf p 1 f (2) Proof: For th snk nod n th quung ntwork of a WSN, data transmsson btwn nods rqurs a vry hgh accuracy. Whn th data packts valdaton s not corrct, w should hav r-transmsson procssd untl th corrct calbraton data s rcvd. Thrfor, th phnomnon of slf-loop appars n th nod. Incrasd th numbr of arrvng packt s quvalnt to p. Thrfor, w can gt th sum of arrval packt as quaton (3). m1 k pk p 1 (3) Accordng to flow balanc quaton [25,27], w can dduc that th flow balanc quaton (2) s stablshd. Th Nods ar usd n nvronmntal montorng and control n WSNs, du to factors such as lmtd powr consumpton, whch ar not always n runnng stat [28,29,30]. Th stats of nods n WSNs ar altrnatng btwn 1032 ComSIS Vol. 8, No. 4, Spcal Issu, Octobr 2011

7 A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks montorng and slpng, as a prms n mtng th rqurd montorng condtons. Swtchng btwn stats of nods s shown n Fgur 2. T T +1 Slpng Montorng Slpng Montorng Slpng Fg. 2. Swtchng btwn stats of nods. Nxt, w gv th dfnton of th longst montorng cycl of nod. Dfnton 2. For all nods n WSNs, th wak-up from a slpng stat nto th montorng stat, and thn ntry nto anothr slp xprncd by far th longst tm s known as th longst montorng cycl of WSN nods. m T max{ T1, T2,..., T,..., TN } (4) In WSNs, ach nod has a packt capacty. If th packt buffr sz s st too larg, would b a wast of rsourcs. Convrsly, f th data packt buffr sz s st too lttl, block of systm wll b ncrasd. W gv th thorms for packt quu lngth of snk nods and transmsson nods. P λ λ k k μ k P k λ k λ μ Fg. 3. Transmsson rlaton of packt quu for snk nod. Thorm 1. For any snk nod n WSNs, packt quu lngth of snk nod s L, thn th followng rlatonshp s obtand. m L (5) m1 m k pk (1 p ) m 1 T Transmsson rlaton of packt quu for snk nod n WSNs s shown n Fgur 3. W gv th proof of Thorm 1 blow. Proof: For snk nod n WSNs, accordng to Corollary 2, th data packts arrval rat s obtand by quaton (6). m1 k pk p 1 (6) In th tm prod, th arrval numbr s X m T X gvn by quaton (7). (7) ComSIS Vol. 8, No. 4, Spcal Issu, Octobr

8 T Qu, Ln Fng, Fng Xa, Guow Wu, and Yu Zhou At ths tm, th srvc rat s. Th numbr of th data packts s Y gvn by Equaton (8) aftr complton of th srvc. m T Y (8) m Thrfor, packts quu lngth of nod s L, whch s th dffrnc btwn th numbr of ffctv arrval and lavng, and mnus th numbr of packts bng procssd. m L X Y 1 (9) Puttng Equatons (6), (7), and (8) nto Equaton (9) wll rsult n Equaton (5). Thrfor, Thorm 1 s provd. Thorm 2. For any transmsson nod n WSNs, f packts quu lngth of transmsson nod s L, thn th followng rlaton s obtand. m m1 m k pk m 1 T L (10) Proof of Thorm 2 s rlatvly smpl, usng Corollary 1, and wth rfrnc to th proof of Thorm Equvalnt Quung Ntwork Modl Th packt buffr sz should b consstnt wth th lngth of th quu n th quung modl of WSNs. Whn th quu lngth rachs th maxmum, th packt strams ar stoppd, rsultng n quung ntwork bng blockd [31,32]. Whn a data packt transfrs from on quu to anothr quu and f th path s full, th packt wll b blockd n by th ust compltd srvc n th quu. Thn th blockd nod cannot handl any othr data packts untl th dstnaton nod srvcs, whr thr s a fr packt buffr bfor thy can lft th blockng. Ths stuaton s calld Transfr Blockng. Transfr blockng maks th ntrnal arrval procss and srvc procss of nod complcatd. Th blockng rul s that blockng should occur aftr srvc. Thrfor, th quu wll not b cachd, only watng on th lnk path. Som rsarchrs [33,34,35,36] hav dscussd about thnkng of addng holdng nods n th quung ntworks, that adds th magnary lmtlss capacty nods, whch may occur on th blockng path n th nfnt quung ntworks. Th basc da s to rmov th blockng srvr, that s unblockd and sav t n th holdng nods. As shown n Fgur 1, th quung ntwork modl for th topology of WSN s xpandd to nclud holdng nods. Equvalnt quung ntwork modls ar shown n Fgur 4. M/M/1/ -typ quus ar addd holdng nods. (Not: Whn addd to holdng nods, assumng that th orgnal nod dos not xst, blockng s stablshd.) 1034 ComSIS Vol. 8, No. 4, Spcal Issu, Octobr 2011

9 A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks Intrvals btwn th arrval tm accord wth th xponntal dstrbuton. Thus, w calculat th ral ffctv arrval rat nods, and ts prformanc valuaton s possbl. h2 2 h23 h21 h32 h12 ho1 h3 3 h31 1 h1 h34 h14 h43 h41 h4 4 h13 Fg. 4. Quung ntwork modl wth holdng nods Quung Modl Analyss wth Blockng Probablty Whn th holdng nods ar addd n quung ntwork, th packts that dd not rcv tmly srvcs ar stord n th quu of holdng nods, as watng for an mpty targt nod. Total ffctv arrval rat s qual to th xtrnal arrval rat and th ntrnal arrval rat of nods 1 2,,..., A aftr consdrng blockng nods. Thn, th quung ntwork modl wth blockng probablty s shown n Fgur 5. Blow w dscuss flow balanc of arrval and lavng data packts n th quung ntwork modl. 1 pb (1 pb ) 1 1 A 1 pb 1 (1 pb ) A A pb Q (1 h 1 h h A ) A pb (a) Quung ntwork modl wth multpl arrval nods 1 A pb 1 pb A pb (1 pb ) 1 (1 (1 1 pb ) A pb Fg. 5. Quung ntwork modl wth blockng probablty. A ) h a a pb (1 pb ) (b) Equvalnt quung ntwork modl Fgur 5(a) shows that multpl arrval nods ar blockd n nod, and Fgur 5(b) shows an quvalnt modl of Fgur 5(a). a ComSIS Vol. 8, No. 4, Spcal Issu, Octobr

10 T Qu, Ln Fng, Fng Xa, Guow Wu, and Yu Zhou Thrfor, th xtrnal ffctv arrval rat of nod s obtand as n Equaton (11). (1 pb ) (11) Th ffctv data packts stram from nod to nod as shown n Equaton (12). p 1 pb ) (12) ( Lt b th ffctv ntrnal arrval rat of nod, whch s qual to th sum of ffctv ntrnal arrval rat from ndpndnt ntrnal nods 1 2,,..., A. (13) A Total ffctv arrval rat wth probablty Equaton (14). a pb of nod s obtand by a (1 pb ) (14) Accordng to Corollary 1 and Corollary 2, w can obtan a flow balanc quaton of quung ntwork wth blockng. (15) Equaton (16) s drvd from applyng quatons (11) (12) (13) (14) nto Equaton (15). a (1 pb ) (1 pb ) p(1 pb ) (16) In ordr to obtan th ffctv arrval rat of nod, th calculatons of blockng probablty pb, pb and pb ar ndd. Th thr blockng a A probablts ar calculatd, th spcfc drvaton s shown as n [37]. Now w can dtrmn th prformanc paramtrs of ach typ nod accordng to th conncton btwn nods. In ths papr, w us th approxmat calculaton. Frst, th ntal valus of blockng probablts ar gvn, thn th algorthm prforms n a lmtd traton tms. Whn th ffctv arrval rat and dpartur rat tnds to rach qulbrum, th tratv algorthm s fnshd ComSIS Vol. 8, No. 4, Spcal Issu, Octobr 2011

11 A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks 5. Total Arrval Rat of Nods and Approxmat Algorthm Blockd nods ar rlasd by addng holdng nods of nfnt capacty n th quung ntwork modl. Procssng tm of blockd nod s th blockd tm, and thus w can dscrb arrval and srvc procss of nods n th quvalnt quung ntwork modl. In a lot of practcal applcaton and ngnrng xprmnts, w found that whn WSN nod communcaton ntrs nto a stabl stat, th avrag arrval rat of nod tnds to b a constant valu. W dsgnd an tratv mthod, such as shown n Algorthm 1. W st ntal valus to th ntwork status, and thn gradually rvsd th last tm arrval rat by our tratv mthod. In th nd, a systm was approachng to rach qulbrum. Th rducton algorthm s as follows. Algorthm 1 Bgn Stp 1. Accordng to transton probablty, ach nod conncton n th quung ntwork modl s obtand. Extrnal arrval rat ( s th numbr of nods) s dtrmnd. Stp 2. Intalz n nods wth th total arrval rat 0 (1 Stp 3. For quu n quung ntwork, calculat th arrval rat of nod : Stp 3.1. If nod s a transmsson nod or boundary nod, m 1 p 1 (17) go to Stp 3.3. Othrws, t s xcutd ordrly. Stp 3.2. nod s snk nod, m1 1 k pk p 1 (18) Stp 3.3. Th outputtng rat of nod s calculatd by Corollary 1 and Corollary 2. Go to Stp 3.1, untl th dffrnc of th ntrnal arrval rat for two computng (bfor and aftr) s lss than a crtan valu (rror lmt of our calculatons s 10-4 ). Stp 4. Aftr calculatng th arrval rat of all nods, f th dffrnc of th ntrnal arrval rat for two computng valus s lss than a valu (10-4 ), go to Stp 5. Othrws, us nstad, and go to Stp 3.1, contnu by 1 0 m). ComSIS Vol. 8, No. 4, Spcal Issu, Octobr

12 T Qu, Ln Fng, Fng Xa, Guow Wu, and Yu Zhou tratv calculaton. Stp 5. Rturn th total arrval rat End n of ach nod. Th tm complxty of Algorthm 1 s O(n*m), whr m s th numbr of quung ntwork nods and n s th numbr of tratv algorthms. Th total arrval rat of ach nod was obtand by Algorthm 1, but t s not th ffctv arrval rat, bcaus th blockng probablty of th nods s not consdrd. Nxt w wll hav th numrcal rsults of Algorthm 1 as th ntal valu of Algorthm 2, and thn solv th blockng probablty and systm prformanc ndcators. Th rducton Algorthm 2 s as follows. Th calculaton of Algorthm 2 manly focusd on th loop n Stps 3 to 6 of th cycl. Th tm complxty of Algorthm 2 s O(n*m*N), whr N s th packt buffr sz of nod. Whn th tratv algorthm convrgs, th WSN prformanc paramtrs ar outputtd. Accordng to that w can prdct th actual opraton of WSNs. Thus, th hardwar dsgn for th WSN nod s gudd by th prformanc paramtrs. Algorthm 2 Bgn Stp 1. Th quvalnt quung ntwork modl s xpandd by addng holdng nods n wrlss snsor quung ntworks. Th total arrval rat of Algorthm 1 s th ntal nput valu of Algorthm 2 for ach nod. Stp 2. Blockng probablts of ach nod ar ntalzd, and mans and varancs of ntrnal arrval tm ar calculatd. Stp 3. Calculat th utlzaton and stady-stat probablty of th nods, whr n {1,2,..., N }, that mans th numbr of data packt buffr of ach nod. Whn th systm rachs a stady stat, w assum that th probablty of quu n stat n s p( n ), whch s obtand by: n (1 ) p( n ) (19) N 1 1 whr. Spcfc drvatons of Equaton (19) can b found n [38,39]. Accordng to Jackson thorm [30], th status of nod and th status of all othr nods ar ndpndnt. Thus, w can gt th stadystat probablts of any nod n th lnk path. Stp 4. Calculat th blockng probablts. Stp 5. Corrct mans of th arrval tm ntrval and varanc of nods 1038 ComSIS Vol. 8, No. 4, Spcal Issu, Octobr 2011

13 A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks usng blockng probablts. Stp 6. If th dffrnc of th ntrnal arrval rat for two computng (bfor and aftr) s lss than a crtan valu (rror lmt of our calculatons s 10-4 ), thn go to Stp 7. Othrws go to Stp 3 followd by tratv calculaton. Stp 7. Rturn to th nod utlzatons wth a blockng whn systm s stabl. End 6. Numrcal Calculaton and Exprmntal Rsults Accordng to th prcdng analyss, w studd a WSN topology for tmpratur montorng. Th prformanc paramtrs of WSN nods ar calculatd usng th tratv algorthm proposd n Scton 5. By sttng dffrnt packt buffr capacty szs of nods, th rlatonshp curvs btwn utlzaton ( ) and data packt buffr sz ( N ) for transmsson nods, boundary nods and snk nod ar obtand. In ordr to ratonally allocat rsourcs, th maxmum utlzatons of nods ar nsurd wthn lmtd rsourcs. Accordng to th rlatonshp curvs btwn utlzaton ( ) and data packt buffr sz ( N ), th valus of packt buffr capacty sz for transmsson nods, boundary nods and snk nods ar st A WSN Topology W hav dsgnd th WSNs for tmpratur montorng. Its typcal topology s shown n Fgur 6. It conssts of many clustrs, ach of whch comprss a mxd structur from th rng and star ntwork topologs. Informaton btwn clustrs s communcatd by snk nods. From th WSN w can conclud that all th clustrs can b dvdd nto two catgors. () Boundary clustr: It s locatd n th boundars of th ntwork by th clustr nods, transfr nods and boundary nods; Clustr 1 s shown n Fgur 6. () Intrnal clustr: t s locatd wthn th ntwork only by th snk nods and transfr nods. Clustr 2 s shown n Fgur 6. Accordng to th packts statstcs n th ngnrng practc, amount of tasks for transmsson nod s th sam n th boundary and ntrnal clustrs. Thrfor, w studd Clustr 1, n whch prformanc of ntrnal nods wll b analyzd. Clustr 1 s comprsd of snk nod 1, transmsson nods 1 4, and boundary nods 5 6. Rng structur s comprsd of nods 1 6, and nod 7 s n th cntr of th othr sx noduls that shows a smlar star, whch s wth 6 nods to communcat. In practcal ngnrng n applcatons, how to st th buffr ComSIS Vol. 8, No. 4, Spcal Issu, Octobr

14 T Qu, Ln Fng, Fng Xa, Guow Wu, and Yu Zhou sz to obtan th optmal prformanc of th nods for hardwar dsgn of WSNs s a practcal applcaton problm that nds to b solvd. Clustr2 2 3 Clustr Boundary Fg. 6. A WSN topology for tmpratur montorng Nod Transton Probablts and Total Arrval Rat Th nod transton probablts for th topology of Fgur 6 ar obtand from packt statstcs n th ngnrng practc of WSNs for tmpratur montorng. Thus th transton probablty matrx s as follows P (20) In th dstrbutd tmpratur acquston procss, for ach snsor nod placd n dffrnt postons, th amount of transmttd data s dffrnt. For xampl, nod 1, nod 2, nod 3 and nod 4 ar transmsson nods wthn th WSN. Thus, th xtrnal arrval rats of th nods ar sam. Nod 5 and nod 6 ar th boundary nods (do not allow othr nods from outsd). Nod 7 s th snk nod. Th xtrnal arrval rats of ths nods ar dffrnt ComSIS Vol. 8, No. 4, Spcal Issu, Octobr 2011

15 A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks Tabl 2. Arrval rat for ach nod n th tm Nod numbr Extrnal arrval rats (p/s) m T Total arrval Rats (p/s) Accordng to th nput of th xtrnal arrval rats, th total arrval rat of nod can b calculatd usng Algorthm 1, as shown n Tabl Evaluaton for Packt Buffr Capacty of Nods In WSNs, packt buffr capacty of nods sttngs that affcts th ffcncy of th whol ntwork systm s an mportant factor. If packt buffr capacty s too small t wll caus srous blockng to som lnk paths of th systm, and lad to a low ffcncy of data procssng and transmsson. If packt buffr capacty s too larg, t wll tak up too much of th hardwar rsourcs, rsultng n an ncrasd cost of th hardwar nod. And th nrgy consumpton wll ncras, causng a lnk falur to ndvdual nods du to nrgy dplton. Thrfor, w dsgn hardwar nods that mak th data packt buffr capacty to rach th optmal sttngs. Othr nput paramtrs of quung ntwork modl for wrlss snsor ar shown n Tabl 3, whr CA s th ndpndnt xtrnal Posson arrval Varanc of nod, s th srvc rat of nod, CS s th srvc varanc of nod and N s th sz of packt buffr capacty whch rangs from 1 to 30. Tabl 3. Input paramtrs for modl CA CS N ~ ~ ~ ~ ~ ~ ~30 ComSIS Vol. 8, No. 4, Spcal Issu, Octobr

16 Nod utlzaton T Qu, Ln Fng, Fng Xa, Guow Wu, and Yu Zhou Accordng to of th approxmat tratv Algorthm 2 n Scton 5, packt buffr sz ( N ) and nod utlzaton ( ) ar calculatd Packt buffr sz Nod1 Nod2 Nod3 Nod4 Fg. 7. Rlatonshp curvs btwn utlzaton and buffr sz for transmsson nods. Th rlatonshp curvs btwn utlzaton and packt buffr sz for transmsson nods ar shown n Fgur 7. In WSNs for tmpratur montorng, nod 1, nod 2, nod 3 and nod 4 ar th transmsson nods, n whch th man functon of th ntwork s to collct data and transfr t to othr nods. Wth th ncras of packt buffr sz, ncrasd spd of nod 1 s th fastst, ncrasd spd of nod 4 has slowd down compars to othr thr nods. Whn th packt buffr szs ar ncrasd to N 1 N 4 14, curvs for nods 1 and 4 concd. Nxt, wth th ncras of packt buffr sz, th curvs n almost horzontal axs tnd to bcom paralll. At ths tm, f w ncras th packt buffr szs, utlzaton for nods wll not hav any mpact. Ths pont can b st as th valu of packt buffr sz thn th nod utlzaton s optmal. From pont of vw for th layout of th WSNs, nods 1 and 4 ar adacnt to th boundary nods, transmsson rats of data packts ar almost th sam. Thrfor, whn th systm rachs qulbrum, packt buffr szs n us bcom th sam. Th curvs btwn utlzaton and packt buffr sz for nods 2 and 3 ar n concdnc n fgur 8. Whn th packt buffr szs ar ncrasd to N 2 N3 11, th curvs n almost horzontal axs tnd to bcom paralll. At ths tm, f w ncras th packt buffr szs, utlzaton for nods wll not hav any mpact. Ths pont can b st as th valu of packt buffr sz thn th nod utlzaton s optmal. From th pont of vw of th layout of th WSNs, nods 2 and 3 ar ntrnal nods of th WSN, transmsson rats of data packts ar almost th sam. Thrfor, th rlatonshp curvs btwn utlzaton and buffr sz for boundary nods ar th sam ComSIS Vol. 8, No. 4, Spcal Issu, Octobr 2011

17 Nod utlzaton Nod utlzaton A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks Packt buffr sz Nod5 Nod6 Fg. 8. Rlatonshp curvs btwn utlzaton and buffr sz for boundary nods. Th rlatonshp curvs btwn utlzaton and packt buffr sz for boundary nods ar shown n Fgur 8. Wth th ncras of packt buffr sz, bgnnng curvs ar rlatvly stp. Th ncrasd spd of curv for nod 5 s th fastst; th ncrasd spd of curv for nod 6 has slowd down compard to curv for nod 5. Accordng to ths stuaton, w can spculat that, whn nod 5 s st to a smallr packt buffr sz, a mor srous blockng occurrd n th lnk paths for th nod, rsultng n rlatvly low nod utlzaton. Whn th packt buffr szs ncrasd to N 5 N6 13, curvs for nods 5 and 6 ar concdnc. And followng th ncras of packt buffr sz, th curvs n almost horzontal axs tnd to bcom paralll. At ths tm, f w ncras th packt buffr szs, utlzaton for nods wll not hav any mpact. If ths pont can b st as th valu of packt buffr sz, thn th nod utlzaton s optmal. From th pont of vw of th layout of th WSNs, nods 5 and 6 ar locatd on th outsd of th WSN, and thy ar boundary nods. Th transmsson rats of data packts ar almost th sam. Thrfor, whn th systm rachs qulbrum, th packt buffr szs n us ar th sam Packt buffr sz Fg. 9. Rlatonshp curvs btwn utlzaton and buffr sz for snk nod. Nod7 ComSIS Vol. 8, No. 4, Spcal Issu, Octobr

18 Arrval rat T Qu, Ln Fng, Fng Xa, Guow Wu, and Yu Zhou For snk nod 7, on th on hand, t s rsponsbl for collctng th dat packts of adacnt transmsson nods and boundary nods. On th othr hand, nformaton btwn clustrs s communcatd, and a partal data procssng s compltd by snk nod. Th rlatonshp curvs btwn utlzaton and packt buffr sz for snk nod ar shown n Fgur 9. Wth th ncras of packt buffr sz, bgnnng curvs ar rlatvly stp. As pr ths stuaton, w can spculat that, whn snk nod 7 s st to a smallr packt buffr sz, ts utlzaton s rlatvly low. Aftr th packt buffr szs ar ncrasd to N 7 19, and followng ths, th curvs n almost horzontal axs tnd towards paralll. At ths tm, f w ncras th packt buffr szs, utlzaton for nods wll not hav any mpact. If ths pont can b st as th valu of packt buffr sz, thn th nod utlzaton s optmal Comparson of Exprmntal Data and Modl Calculaton Data Accordng to th sz of th nods through th analyss of packt buffr sz n Scton 6.3, th xprmntal nvronmnt was dsgnd. Th packt buffr szs for transmsson nods ar st as N1 N 4 14, N2 N 3 11, rspctvly. Th packt buffr szs for boundary nods ar st as N N, rspctvly. Th packt buffr sz for snk nod s st as N Th smulaton nvronmnt usng NS2 softwar combnd wth random arrval drvd th algorthm [39]. Th xprmntal smulaton for arrval rat of nod wth holdng nods was carrd out. Fgur 10 shows th comparson of nods btwn th ffctv arrval rats dal calculatd valu of th nfnt capacty calculatd valus wth "holdng nods" of lmtd capacty masurmnt valus of th xprmntal data Nod numbr Fg. 10. Comparson of th data rsults ComSIS Vol. 8, No. 4, Spcal Issu, Octobr 2011

19 A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks In Fgur 10, th arrval rats of th thr stuatons ar dscrbd: () Assumng quung ntwork modl for wrlss snsor works n an dal stat, th blockng probablts { pb, a pb, pb } always qual 0, whch s calld th dal calculatd valu of th nfnt capacty nods. () Quung ntwork modl for wrlss snsor mantand by addng a fnt numbr of nods (basd on th valus obtand n Scton 6.3), consdrng th gvn blockng probablts { pb, a pb, pb }, th valus of th ffctv arrval rat ar calculatd, ths ar calld th calculatd valus wth holdng nods of lmtd capacty. () Exprmntal nvronmnt s cratd and random functon for arrval rat s dsgnd. Thrfor, th actual arrval rats ar obtand by statstcal calculaton, ths ar calld th masurmnt valus of th xprmntal data. Fgur 10 clarly dscrbs th comparson of data among th thr stuatons. W can s that rrors btwn th dal calculatd valu of th nfnt capacty nods and th calculatd valus wth holdng nods of lmtd capacty ar vry small, th maxmum rror bng 6.12%. Ths provs that by addng fnt holdng nods to a quung ntwork modl, and obtand quvalnt quung ntwork modl can rplac th nfnt capacty modl for prformanc analyss. Th maxmum rror btwn th masurmnt valus of th xprmntal data and th calculatd valus wth holdng nods of lmtd capacty s 9.56%. As n th modl calculaton rror s lss than 10%, almost consstnt ndcators for quvalnt quung ntwork modl can b obtand wth th actual opraton of th WSN. 7. Conclusons In alluson to dffr transmsson nods, boundary nods and th snk nod n WSNs, thr procssng data and th task capacty ar dffrnt. And thus, bfor dsgnng th hardwar for nods, an valuaton of packt buffr szs s crtcal for th bst prformanc. Basd on ths problm, w proposd an opn quung ntwork mod wth M/M/1/N quus for modlng WSNs. In ordr to valuat congston stuaton n th quung ntwork, and gt ral ffctv arrval rats and transfr rats n th modl, holdng nods wr addd n th quung ntwork modl and an quvalnt quung ntwork modl s xpandd. Th arrval rats whn systm rachs a stady stat n WSNs ar obtand usng approxmat tratv algorthm. Th obtand stady-stat paramtrs wll b ntrd nto wth th blockng quung ntwork modl. Blockng probablty and systm prformanc ndcators of ach nod ar calculatd usng approxmat tratv algorthm for blockng probablty. Th dal calculatd valu of th nfnt capacty nods, th calculatd valus wth holdng nods of lmtd capacty and th masurmnt valus of th xprmntal data ar compard. Th consstncy s vrfd for calculatd rsults of modl and xprmntal data n WSNs. Th rsults show that th mthod, whch s usd to analyz nod prformanc and nsur that packt buffr szs ar of rasonabl confguraton usng quung ntwork ComSIS Vol. 8, No. 4, Spcal Issu, Octobr

20 T Qu, Ln Fng, Fng Xa, Guow Wu, and Yu Zhou modl, provds a thortcal bass for dsgn of hgh cost-ffctv hardwar nods for modlng larg-scal WSNs. Ths work has mportant gudng sgnfcanc for hardwar dsgn and prformanc valuaton of WSNs systm. Ths papr prsnts a modlng for only a sngl-srvr modl n WSN and a mthod for calculatng th packt buffr capacty sz of nods. Howvr, th snk nod rqurs a hghr prformanc. Rcntly, thr has bn convrgnc of multpl procssor nods that can b usd for M/M/m/N quus, whch ar also mult-srvr quus. In addton, for larg-scal WSNs, f th clustrs ar st to b th prorty, t wll ffctvly mprov th prformanc of WSNs. Ths wll b our follow-up rsarch. Acknowldgmnt. Ths work was supportd n part by Natural Scnc Foundaton of Chna undr Grant No , and , Program for Nw Cntury Excllnt Talnts n Unvrsty (NCET ), th Fundamntal Rsarch Funds for th Cntral Unvrsts, and th SRF for ROCS, SEM. 8. Rfrncs 1. Onur, E., Ersoy, C., Dlç, H., Akarun, L.: Survllanc wth wrlss snsor ntworks n obstructon: Brach paths as watrshd contours. Computr Ntworks, Vol. 54, No. 3, (2010) 2. Lasassmh, S., M., Conrad, J., M.: Tm synchronzaton n wrlss snsor ntworks: A survy. Confrnc Procdngs-IEEE SouthastCon 2010: Enrgzng Our Futur, , Concord. (2010) 3. Son, J., H., L, J., S., So, S., W.: Topologcal ky hrarchy for nrgy-ffcnt group ky managmnt n wrlss snsor ntworks. Wrlss Prsonal Communcatons, Vol. 52, No. 2, (2010) 4. Yck, J., Mukhr, B., Ghosal, D.: Wrlss snsor ntwork survy. Computr Ntworks, Vol. 52, No. 12, (2008) 5. Akyldz, I., F., Su, W., Sankarasubramanam, Y., Cayrc, E.: A survy on snsor ntworks, IEEE Communcatons Magazn, Vol. 40, No. 8, (2002) 6. Alnabls, S., H., Almasad, H., M., Kamal, A., E.: Optmzd snk moblty for nrgy and dlay ffcnt data collcton n FWSNs. 15th IEEE Symposum on Computrs and Communcatons, , Rccon. (2010) 7. Shu, J., P., Sahoo, P., K., Su, C., H., Hu, W., K.: Effcnt path plannng and data gathrng protocols for th wrlss snsor ntwork. Computr Communcatons, Vol. 33, No. 3, (2010) 8. Gao, S., Zhang, H., Song, T., Wang, Y.: Ntwork lftm and throughput maxmzaton n wrlss snsor ntworks wth a path-constrand mobl snk Intrnatonal Confrnc on Communcatons and Mobl Computng, , Shnzhn. (2010) 9. Eun, D., Y., Wang, X.: Achvng 100% throughput n TCP/AQM undr aggrssv packts markng wth small buffr. IEEE/ACM Transactons on Ntworkng, Vol. 16, No. 4, (2008) 10. Srdharan, A., Krshnamachar, B.: Maxmzng ntwork utlzaton wth max-mn farnss n wrlss snsor ntworks. Wrlss Ntworks, Vol. 15, No. 5, (2009) 1046 ComSIS Vol. 8, No. 4, Spcal Issu, Octobr 2011

21 A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks 11. Vupputur, S, Rahur, K., K., Murthy, C., S., R.: Usng mobl data collctors to mprov ntwork lftm of wrlss snsor ntworks wth rlablty constrants. Journal of Paralll and Dstrbutd Computng, Vol. 70, No. 7, (2010) 12. Han, J., Cho, S., Park, T.: Maxmzng lftm of clustr-tr ZgB ntworks undr nd-to-nd dadln constrants. IEEE Communcatons Lttrs, Vol. 14, No. 3, , (2010) 13. Subramanan, R. Fkr, F.: Uncast throughput analyss of fnt-buffr spars mobl ntworks usng Markov chans. 46th Annual Allrton Confrnc on Communcaton, Control, and Computng, , Montcllo. (2008) 14. L, G., H., Zhu, C., M., L, X.: Applcaton of Chaos thory and Wavlt to Modlng th Traffc of Wrlss Snsor Ntworks Intrnatonal Confrnc on Bomdcal Engnrng and Computr Scnc, 1-4, Wuhan, (2010) 15. Eschkh, M., Barkaou, K.: Opportunstc MAC layr dsgn wth Stochastc Ptr Nts for multmda ad hoc ntworks. Concurrncy Computaton Practc and Exprnc, Vol. 22, No. 10, (2010) 16. Moon, C. Chung, W.: Dsgn of navgaton bhavors and th slcton framwork wth gnralzd stochastc ptr nts toward dpndabl navgaton of a mobl robot IEEE Intrnatonal Confrnc on Robotcs and Automaton, Anchorag. (2010) 17. Sharf, A., Zhu, Y.: Enrgy modlng of procssors n wrlss snsor ntworks basd on ptr nts. 37th Intrnatonal Confrnc on Paralll Procssng Workshops, , Portland. (2008) 18. Strln, J., C., Bark, B., Bckr, J., Jonas, V.: Analyss of quung ntworks wth blockng usng a nw aggrgaton tchnqu. Annals of Opratons Rsarch, No. 79, (1998) 19. Lhr, A., W., Buchnrdr, K., J.: Smulatng ntr-procss communcaton wth Extndd Quung Ntworks. Smulaton Modllng Practc and Thory, Vol. 18, No. 8, (2010) 20. Bsnk, N., Abouzd, A., A.: Quung Ntwork Modls for Dlay Analyss of Multhop Wrlss Ad Hoc Ntworks. Ad Hoc Ntworks, Vol. 7, No. 1, (2009) 21. Kouvatsos, D., Awan, I.: Entropy maxmsaton and opn quung ntworks wth prorts and blockng. Prformanc Evaluaton, Vol. 51, No. 2-4, (2003) 22. Awan, I.: Analyss of multpl-thrshold quus for congston control of htrognous traffc strams. Smulaton Modllng Practc and Thory, Vol. 14, No. 6, (2006) 23. Özdmra, M., McDonald, A., B.: On th prformanc of ad hoc wrlss LANs: A practcal quung thortc modl. Prformanc Evaluaton, Vol. 63, No. 11, (2006) 24. Mann, C., R., Baldwn, R., O., Kharoufh, J., P., Mullns, B., E.: A quung approach to optmal rsourc rplcaton n wrlss snsor ntworks. Prformanc Evaluaton, Vol. 65, No. 10, (2008) 25. Qu, T., Wang, L., Fng, L., Shu, L.: A nw modlng mthod for vctor procssor ppln usng quung ntwork. 5th Intrnatonal ICST Confrnc on Communcatons and Ntworkng, 1-6, Bng. (2010) 26. Qu, T., Xa, F., Ln, F., Wu, G., Jn, B.: Quung thory-basd path dlay analyss of wrlss snsor ntworks. Advancs n Elctrcal and Computr Engnrng, Vol. 11, No. 2, 3-8. (2011) 27. Bouchr, R., J., Dk, N., M.: Quung Ntworks: A Fundamntal Approach. Sprngr, 1st Edton. (2010) ComSIS Vol. 8, No. 4, Spcal Issu, Octobr

22 T Qu, Ln Fng, Fng Xa, Guow Wu, and Yu Zhou 28. Chassrn, C., F., Gartto, M.: An Analytcal Modl for Wrlss Snsor Ntworks wth Slpng Nods. IEEE Transactons on Mobl Computng, Vol. 5, No. 12, (2006) 29. Paul, S., Nand, S., Sngh, I.: A dynamc balancd-nrgy slp schdulng schm n htrognous wrlss snsor ntwork. Procdngs of th th Intrnatonal Confrnc on Ntworks, 1-6, Nw Dlh. (2008) 30. Raymond, D. R., Marchany, R., C., Brownfld, M., I., Mdkff, S., F.: Effcts of Dnal-of-Slp Attacks on Wrlss Snsor Ntwork MAC Protocols. IEEE Transactons on Vhcular Tchnology, Vol. 58, No. 1, (2009) 31. Almda, D., D., Kllrt, P.: Analytcal quung ntwork modl for flxbl manufacturng systms wth a dscrt handlng dvc and transfr blockngs. Intrnatonal Journal of Flxbl Manufacturng Systms, Vol. 12, No. 1, (2000) 32. Osoro, C., Brlar, M.: An analytc fnt capacty quung ntwork modl capturng th propagaton of congston and blockng. Europan Journal of Opratonal Rsarch, Vol. 196, No. 3, (2009) 33. Krbach, L., Smth, J., M.: Asymptotc bhavor of th xpanson mthod for opn fnt quung ntworks. Computrs and Opratons Rsarch, Vol. 15, No. 2, (1988) 34. Tahlraman, H., Manunath, D., Bos, S., K.: Approxmat analyss of opn ntwork of GE/GE/m/N quus wth transfr blockng. Procdngs of th th Intrnatonal Symposum on Modlng, Analyss and Smulaton of Computr and Tlcommuncaton Systms, , Maryland. (1999) 35. Brandwan, A., Bgn, T.: Hghr-ordr dstrbutonal proprts n closd quung ntworks. Prformanc Evaluaton, Vol. 66, No. 11, (2009) 36. Andransyah, R., Wonsl, T., V., Cruz, F., R., B., Duczmal, L.: Prformanc optmzaton of opn zro-buffr mult-srvr quung ntworks. Computrs and Opratons Rsarch, Vol. 37, No. 8, (2010) 37. Kouvatsos, D.: Maxmum ntropy analyss of quung ntwork modls. Lctur Nots n Computr Scnc, Prformanc Evaluaton of Computr and Communcaton Systms, Vol. 729, (1993) 38. Lfbvr, M.: Quung Thory, Appld Stochastc Procsss. Unvrstxt, Sprngr, (2007) 39. Ross, S., M.: Introducton to Probablty Modls, 10th Edton, Acadmc Prss. (2009) T Qu s a Lcturr and Ph. D. canddat n computr scnc at Dalan Unvrsty of Tchnology, Chna. Hs rsarch ntrsts covr mbddd hgh prformanc computng, wrlss snsor ntworks and systms modlng. Ln Fng s a Profssor n School of Innovaton Exprmnt, Dalan Unvrsty of Tchnology, Chna. Hs rsarch ntrsts covr dat mnng, wrlss snsor ntworks and Intrnt of Thngs. Fng Xa s an Assocat Profssor and Ph.D Suprvsor n School of Softwar, Dalan Unvrsty of Tchnology, Chna. H s th (Gust) Edtor of svral ntrnatonal ournals. H srvs as Gnral Char, PC Char, Workshop Char, Publcty Char, or PC Mmbr of a numbr of confrncs. Dr. Xa has authord/co-authord on book and ovr 100 paprs. Hs 1048 ComSIS Vol. 8, No. 4, Spcal Issu, Octobr 2011

23 A Packt Buffr Evaluaton Mthod Explotng Quung Thory for Wrlss Snsor Ntworks rsarch ntrsts nclud cybr-physcal systms, mobl and socal computng, and ntllgnt systms. H s a mmbr of IEEE and ACM. Guow Wu rcvd B.E. and Ph.D. dgrs from Harbn Engnrng Unvrsty, Chna, n 1996 and 2003, rspctvly. H was a Rsarch Fllow at INSA of Lyon, Franc, from Sptmbr 2008 to March H has bn an Assocat Profssor n School of Softwar, Dalan Unvrsty of Tchnology, Chna, snc Dr. Wu has authord thr books and ovr 20 scntfc paprs. Hs rsarch ntrsts nclud mbddd ral-tm systm, cybr-physcal systms, and wrlss snsor ntworks. Yu Zhou rcvd B.E. dgr from Dalan Unvrsty of Tchnology, Chna. Currntly h s a Mastr studnt n School of Softwar, Dalan Unvrsty of Tchnology. Hs rsarch ntrst covrs wrlss snsor ntworks and Intrnt of Thngs. Rcvd: Fbruary 27, 2011; Accptd: Aprl 25, ComSIS Vol. 8, No. 4, Spcal Issu, Octobr

24