Halmstad University PostPrint


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1 Halmstad Unvrsty PostPrnt Explotng tm and frquncy dvrsty n IEEE ndustral ntworks for nhancd rlablty and throughput Krstna Kunrt, Magnus Jonsson and Elsabth Uhlmann N.B.: Whn ctng ths work, ct th orgnal artcl IEEE. Prsonal us of ths matral s prmttd. Howvr, prmsson to rprnt/rpublsh ths matral for advrtsng or promotonal purposs or for cratng nw collctv works for rsal or rdstrbuton to srvrs or lsts, or to rus any copyrghtd componnt of ths work n othr works must b obtand from th IEEE. Kunrt K, Jonsson M, Uhlmann E. Explotng tm and frquncy dvrsty n IEEE ndustral ntworks for nhancd rlablty and throughput. In: 2010 IEEE Confrnc on Emrgng Tchnologs and Factory Automaton (ETFA). Pscataway, NJ: IEEE; p IEEE Confrnc on Emrgng Tchnologs and Factory Automaton (ETFA), DOI: /ETFA Copyrght: IEEE PostPrnt avalabl at: Halmstad Unvrsty DVA
2 Kunrt, K., M. Jonsson, and E. Uhlmann, Explotng tm and frquncy dvrsty n IEEE ndustral ntworks for nhancd rlablty and throughput, Proc. 15th IEEE Intrnatonal Confrnc on Emrgng Tchnologs and Factory Automaton (ETFA 2010), Blbao, Span, Spt , Explotng Tm and Frquncy Dvrsty n IEEE Industral Ntworks for Enhancd Rlablty and Throughput Krstna Kunrt, Magnus Jonsson, and Elsabth Uhlmann CERES Cntr for Rsarch on Embddd Systms Halmstad Unvrsty, Box 823, SE Halmstad, Swdn {krstna.kunrt; magnus.jonsson; Abstract Industral ntworks basd on IEEE ar spradng, vn though th jont rqurmnt on prdctablty and rlablty from ndustral applcatons s hard to fulfl n wrlss ntworks, and th data rat of IEEE s rathr low. Wth th goal of provdng raltm guarants, wth ncrasd rlablty and throughput, w propos two multchannl ntwork archtcturs basd on IEEE wth prdctabl mdum accss, raltm analyss admsson control and transport layr rtransmssons. W valuat th archtcturs n trms of rlablty, utlzaton, dlay, complxty, scalablty and nrgy ffcncy. Th valuatons show that throughput and rlablty can b nhancd through rdundancy and concurrncy n th frquncy doman. 1. Introducton Industral applcatons ar charactrzd by concurrnt dmands on both rlablty and prdctablty. Rlablty s dfnd as th ablty to provd a low packt rror rat whras prdctablty s ablty to mt strct raltm dadlns. Th choc of wrlss ntworks as th undrlyng communcaton mdum maks t spcally challngng to fulfl ths communcaton rqurmnts. Du to advantagous nrgy savng tchnqus, IEEE [1] has bcom an ntrstng choc for wrlss snsor ntworks n ndustral contxts,.g., th ndustral standards WrlssHART [2] and ISA100.11a [3]. WrlssHART nabls prdctablty by placng a tmslottd mdum accss control (MAC) schm on top of IEEE , but lacks flxblty prvntng ffcnt us of rtransmssons for ncrasd rlablty. In arlr work [4] w dvlopd a thortcal framwork for rlabl raltm traffc whr rlablty was ncrasd through rtransmssons, whl stll guarantng raltm dlay bounds. Ths framwork was appld to an IEEE basd snglhop ntwork n [5]. Howvr, usng rtransmssons rducs th data rat, an alrady lmtd rsourc n IEEE Our goal n ths papr s to ncras th ffctv bandwdth wth IEEE by ntroducng dvrsty not only n th tm doman through rtransmssons, but also n th frquncy doman usng multchannl com /10/$ IEEE muncaton. Amng towards a multchannl mastrslav ntwork, two dffrnt ntwork archtcturs wth dffrnt snglhop star topologs ar consdrd. Th most straghtforward dsgn choc s to qup ach nod wth svral IEEE transcvrs fxd to dffrnt frquncy channls. In ordr not to ovrlap wth frquncs n IEEE b basd ntworks, four frquncy channls ar avalabl [1]. Th numbr of slavs n th ntwork s assumd to b hghr than th numbr of frquncy channls F, but dos not hav to b. Th scond ntwork archtctur uss on transcvr at ach slav, but tunabl ovr all F frquncs. Th ffctv bandwdth s ncrasd through th us of multpl frquncy channls, whl stll kpng th advantagous nrgy savng bhavour of IEEE , whch ncluds a synchronzd slp phas for all nods n th ntwork. Th frst dsgn choc s mor costly n trms of hardwar and nrgy consumpton, but s lkly to provd hghr rlablty and ncrasd throughput as compard to a tradtonal snglchannl IEEE ntwork. Th scond dsgn choc s lss costly n trms of hardwar, but tunng to dffrnt frquncs rducs th ntwork ffcncy vn f t provds ncrasd robustnss through frquncy dvrsty. W nvstgat th prformanc of th proposd archtcturs n trms of rlablty, prdctablty, bandwdth utlzaton, dlay, scalablty, hardwar cost, softwar complxty and nrgy ffcncy. 2. Rlatd works A ntwork basd on IEEE has two dffrnt mods: baconnabld wth slottd Carrr Sns Multpl Accss, Collson Avodanc (CSMA/CA) MAC and nonbaconnabld wth unslottd CSMA/CA. Whl th formr s avalabl only for ntworks wth a logcal star topology, th lattr s ntndd for logcal msh topologs. As our work assums a logcal star topology, only th baconnabld mod s consdrd. Th lngth of th bacon ntrval (TBI) s dfnd as th ntrval from whn on bacon transmsson starts untl t starts agan. Ths ntrval can thn b furthr dvdd nto th suprfram (TSF) and th slpng phas (Tslp). Th suprfram contans a contnton accss prod (CAP), whch can optonally b followd by a contnton fr prod (CFP) whr guarantd tm slots (GTS) can b ddcatd to spcfc nods n th ntwork through
3 rsrvatons mad durng th CAP. Snc channl accss dlays cannot b upprboundd (du to random backoff tms n th CAP or falur to rsrv a GTS n th CFP), hard dadln guarants cannot b nforcd wth plan IEEE Pror work n raltm communcatons typcally provds only statstcal prformanc guarants,.g. [6] whch targts mprovmnt of avrag dlay. Othr rlatd work nabls raltm traffc n IEEE ntworks wthout altrng th standard,.g., [7][8]. Howvr, vn though mprovmnts n trms of latncy and rlablty for tmcrtcal mssags hav bn achvd, avrag prformanc rathr than worst cas s typcally valuatd. [9] supports dadln guarants and uss rtransmssons for ncrasd rlablty, but mrly for traffc wth xactly on transmsson pr suprfram. Our approach has no such lmtatons, but nstad lts th numbr of rtransmssons allowd n th systm b rgulatd by an offln raltm schdulablty analyss. W thrby ncras rlablty wthout jopardzng dadln guarants alrady gvn to ordnary transmssons. Th bandwdth utlzaton pnalty nablng th mprovmnt s rasonabl, but th low data rat s lmtng th applcablty. To compnsat for ths, w ntroduc a multchannl IEEE ntwork wth prdctabl mastrslav mdum accss and transport layr rtransmssons. A prdctabl MAC mthod provds an uppr bound on th channl accss dlay whch s ncssary for raltm communcatons so that schdulng mthods lk arlst dadln frst (EDF) can b nforcd. Not, howvr, that a prdctabl MAC mthod dos not guarant rror fr transmsson. Earlr fforts of multchannl protocols nclud both dstrbutd and cntralzd MAC protocols for wrlss adhoc and snsor ntworks [10][12]. Howvr, vn f multpl frquncs xsts, thy ar not usd concurrntly, but mrly altrnatvly and non of th rvwd protocols can provd prdctabl mdum accss. [13] prsnts a multchannl MAC protocol for gnral wrlss ntworks, but dos not nclud rtransmssons, whl th schdulng mchansm prsntd n [14] dos not consdr communcaton rrors. Exampls of multchannl MAC protocols for IEEE ,.g. [15] and [16], do not consdr raltm guarants or rlablty. 3. Systm Modl To modl a typcal wrlss ndustral ntwork, th numbr of communcatng nods s chosn to b rasonably low,.., n th ordr of tnths of nods. All slav nods ar placd wthn transmsson rang of a mastr nod whch acts as th cntral controllr. Du to th lmtd sz of th ntwork, th propagaton dlay btwn th mastr and any of th slavs s approxmatly qual. Basng our framwork on IEEE , w nclud a slp cycl and assum a data rat of 250 kbps. Wth ndustral applcatons n mnd, w choos a data traffc modl wth short packts and prodc bdrctonal traffc btwn th mastr nod and ts slavs. As n [4], w modl th traffc as flows, dfnd by th paramtrs: sndng nod (S ), rcvng nod (R ), prod (P ), mssag lngth (C ), and dadln (D ). Ths flows ar dnotd raltm channls (RTCs) τ = {S, R, P, C, D }, whr = 1, 2. Each flow s ndpndnt of all othr flows, nablng th xstnc of svral flows btwn th mastr and any slav. To modl traffc typcal for ndustral applcatons, whch.g. collct data from snsors or dstrbut control data to actuators, ach flow s assumd to thr orgnat or trmnat at th mastr nod. D rfrs to th transport layr dadln as our rtransmsson schm provds ndtond rlablty at th transport layr. Th lnk layr rtransmssons n th standard ar thrfor not ndd and hnc swtchd off, as possbl wth.g. th IEEE complant ChpCon CC2420 transcvr [17]. Rtransmsson raltm channls, RRTCs, ar ntroducd nto th ntwork, modlld as traffc flows and dfnd by th sam paramtrs as ordnary traffc flows τ r,j = {S r,j, R r,j, P r,j, C r,j, D r,j }. Thr prod s th mnmum mandatory ntrval btwn two actvatons of a crtan RRTC. Ths ntrval s dfnd at th dsgn stag of th ntwork, thrby provdng an uppr bound on th bandwdth usd for rtransmssons. Th dadln of th RRTC dnots th maxmum tm that on rtransmsson s allowd to tak. To catr for rtransmssons, th transport layr dadln n ach RTC s dvdd nto an ordnary (D ord, ) and a rtransmsson dadln (D rtr, ), whr D ord, D rtr, = D. All packts contan a prfct CRC chcksum to dtrmn whn a rtransmsson s ndd. 4. Evaluaton Crtra To valuat th proposd multchannl ntwork archtcturs, th followng mtrcs ar usd: Rlablty Snc th admsson control basd on raltm analyss nsurs that only RTCs for whch a dadln guarant can b provdd ar allowd nto th ntwork, th dadln mss rato du to lat packt arrval s always zro. Nvrthlss, dadln msss du to mssag rrors can stll occur, makng th mssag rror rat (MER) an mportant prformanc masur. Howvr, rlablty s not only ncrasd through th tmdvrsty and data rdundancy provdd by rtransmssons but also through frquncy and hardwar rdundancy ntroducd by multpl transcvrs, all contrbutng to ncrasd ntwork robustnss and rlablty. Bandwdth utlzaton capablty Th capablty of utlzng as much of th avalabl bandwdth as possbl dpnds on th flxblty of channl allocaton and th dgr of concurrncy that can b achvd,.., how wll th frquncy dvrsty s xplotd. A hghr numbr of concurrnt channls avalabl at a nod may lad to ncrasd bandwdth and lowr dlay f proprly xplotd. Dlay Th worst cas dlay dpnds on th archtctur and th rsultng blockng bhavour of packts to and from a nod. Howvr, also avrag dlay and th dlay jttr ar of ntrst. Dlay also conncts to concurrncy. Scalablty Th ntwork can b lmtd by svral factors. Hr w consdr th rlaton btwn th numbr of slav nods, frquncs and transcvrs pr nod.
4 Hardwar and softwar complxty smply ndcats th stmatd hardwar cost pr nod n trms of numbr of transcvrs and th rlatv complxty of th channl allocaton algorthm (at runtm), takng nto account th numbr of concurrnt frquncy channls pr nod. Enrgy usag s assumng a smpl rlaton btwn th numbr of transcvrs pr nod and ts nrgy usag. 5. Ntwork Archtcturs To xtnd th snglchannl framwork prsntd n [5] to a multchannl wrlss ntwork, w qup, n th frst archtctur, ach nod wth F transcvrs fxd to F dffrnt frquncy channls. Th scond multchannl ntwork archtctur qups th mastr nod wth F fxd transcvrs, assumng t to b mor powrful and lss rsourc rstrctd than th slav nods, but only on transcvr pr slav, tunabl ovr all F frquncs Basln: Snglchannl ntwork As a startng pont for th multchannl protocols w tak th snglchannl protocol ntroducd n [5]. Th MAC mchansm n [5] s an xtnson of th IEEE MAC protocol wth a pollng mchansm provdng prdctabl channl accss and th ablty to schdul traffc accordng to EDF. Th mastr has accss to all traffc spcfcatons at startup and sorts all packts to slavs (or pollng mssags askng for packts from slavs) accordng to EDF. Th mastr thn thr snds a pollng packt to a slav and wats for a rspons (a data packt) or t snds tslf a data packt to a slctd slav and awats an acknowldgmnt (ACK). If th mastr dos not rcv an ACK (or a data packt) bfor a tmout corrspondng to th transmsson of th data and ACK packts (or poll and data packts) and som procssng and propagaton dlays th pollng or data packt s savd untl ts ordnary or rtransmsson dadln has lapsd. Whn th (ordnary or rtransmsson) dadln of th whol mssag has xprd, th mastr knows th xact numbr of packts n ths mssag that hav to b rtransmttd. In cas mor rtransmsson attmpts ar allowd and a rtransmsson channl s avalabl, th ncssary rtransmssons ar schduld. Th numbr and frquncy of rtransmssons allowd n th systm s rgulatd by th offln raltm schdulablty analyss Multchannl I: F fxd transcvrs Th avalablty of F concurrnt frquncy channls to accss all nods at any gvn tm nabls dffrnt organzatonal approachs. Ethr w can allow nformaton dssmnaton va all frquncs or hav on ddcatd control or rtransmsson frquncy channl, whl th rmanng F 1 channls ar usd for data dssmnaton. Altrnatvly, w can us som of th channls for dlayconstrand raltm traffc and th rmanng for bst ffort data traffc. Wth approprat schdulng, w can guarant concurrnt transmsson of at most F packts,.. a pur EDF handlng of th F packts wth th arlst dadlns. All schms nabl dvrson of traffc to anothr frquncy, avodng unncssarly hgh packt loss n th prsnc of hgh ntrfrnc at on partcular frquncy channl. Whn choosng to not allocat a spcal control frquncy, th mastr can schdul whch nformaton that should b snt on ach frquncy at ach tm nstanc. Th bacon, snt out prodcally by th undrlyng IEEE protocol, can b broadcastd on all frquncs so that all slavs rcv t on all frquncs. Basd on th addrss fld n th packt hadr th slavs assss th rlvanc of ach packt thmslvs. As th mastr polls ach slav, and has global knowldg of th schdulng, no mdum accss collsons du to svral nods tryng to us th sam frquncy occurs. In fact, th pollng procdur happns on all frquncs concurrntly. Th absnc of an xpctd data packt or ACK from a partcular slav at th nd of a mssag dadln lads th mastr to chck th avalablty of rtransmsson channls unlss th mssng packt has alrady rachd th maxmum numbr of allowd rtransmssons and schduls rtransmssons n xactly th sam mannr as an ordnary transmsson. Altrnatvly, on of th frquncy channls could b allocatd for control traffc only. Th control channl would b carryng pollng mssags askng for data packts from th slavs, to b transmttd on anothr frquncy. Ths lavs F 1 frquncs for actual data traffc, both ordnary transmssons and rtransmssons, allowng F 1 concurrntly transmttd data packts, to and from th mastr. Data packts transmttd by th mastr do not nd to b announcd on th control channl as slavs ar lstnng on all frquncs anyway, and thrfor ar rady to rcv. Howvr, th followng ACK nds to us a dsgnatd data channl, as slavs do not hav accss to th control channl. Ntwork wd pollng nformaton can b broadcastd ovr th control frquncy n paralll wth th ordnary data traffc ovr th rmanng frquncs. Howvr, as th control channl s usd xclusvly for pollng traffc, t may not b suffcntly utlzd. Th sam holds tru for a varant whr rtransmssons us a ddcatd frquncy channl. Furthr, systm vulnrablty s ncrasd by groupng pollng packts or rtransmssons onto on sngl frquncy. Consquntly, th altrnatv wth a ddcatd control frquncy s not tratd furthr hr Multchannl II: on tunabl slav transcvr In ths archtctur, th slavs hav on transcvr ach, tunabl ovr F dffrnt frquncs, whl th mastr has F transcvrs, ach on fxd to a sngl frquncy. Snc a slav only can b rachd through on frquncy at a tm, th mastr has to consdr traffc flow dpndncs whn allocatng th frquncs and only on RTC havng a partcular nod as ts dstnaton can b allocatd concurrntly. Ths also rsults n a maxmum of on packt that can b guarantd EDF tratmnt. Th fwr concurrnt frquncs pr slav, th hardr t s for th mastr to us th bandwdth ffcntly and xplot th frquncy dvrsty, as dpndncs amongst th dffrnt raltm traffc channls com nto play. Gvn th raltm constrant, th packt wth th shortst dadln s allocatd frst, but
5 th rmanng F 1 frquncs can only carry packts to or from slavs not nvolvd n anothr transmsson. A packt wth th scond arlst dadln nvolvng th sam slav cannot b schduld concurrntly. Th mastr thrfor gos through th EDF quu, dntfyng th F 1 packts wth arlst dadlns, but prtanng to ndvdual slavs. Whn havng dntfd whch (at most) F packts, ncludng rtransmsson packts, ar to b snt durng th nxt tm nstanc, th mastr broadcasts ths nformaton on all frquncs. Nxt, all slavs tun thr transcvrs to th rspctv allottd frquncy channl and th data transfr taks plac n paralll. W nd to tun for ach packt (rathr than for ach mssag or ach flow) to catr for packts or rtransmssons wth arlr dadlns ntrng th quu. Th rason for havng tunabl transcvrs, rathr than on ddcatd frquncy, for ach slav s that th ntwork s lkly to contan mor slavs than avalabl frquncy channls. Tunng, howvr, ntroducs addtonal dlay, frstly whn th slavs, aftr havng procssd th control nformaton, tun to th frquncy on whch thy ar supposd to transmt or rcv nxt. Scondly, th ACK for packts snt from th mastr to slavs nds to b transmttd bfor th nxt control mssag can b broadcastd, prolongng th prod of control mssags. For slow dvcs th tunng tm btwn two frquncy channls can b as long as th transmsson tm for on packt [16], whch mans that th possbl bandwdth utlzaton s dcrasd substantally. Howvr, progrss n hardwar dvlopmnt wll nabl fast tunng dvcs, dcrasng ths dsadvantag n th futur, and thus ths archtctur rprsnts an ntrstng altrnatv. 6. Tmng dtals and analyss A tmng analyss for a snglchannl IEEE ntwork was conductd n [5], but adaptatons ar ncssary for t to b applcabl also to multpl channls Tmng paramtrs Rcall that th suprfram ncluds both th actual bacon and th CAP. Bacon transmsson tm and CAP lngth ar dnotd as T bacon and T CAP, rspctvly. W assum that no GTSs ar usd as thy ar nthr ncssary nor suffcnt to guarant an uppr dlay bound. Not all of th CAP can b usd for transmssons as ach packt transmsson has to b fnshd bfor th start of th slpng phas. Hnc, th actual (usabl) lngth of th CAP s rducd by th maxmum tm t taks to snd on packt (T tmout ). Thrfor, T CAP can b calculatd as: TCAP TBI Tslp Tbacon Ttmout =. (1) As dscrbd blow, th valu of T tmout s dffrnt for dffrnt archtcturs, as th MAC protocol s adaptd accordngly. To account for th slpng phas w ntroduc th concpt of xprncd bt rat (r ), whch s a scald down bt rat as compard to th ral rat r. Th scalng factor dpnds on th lngth of tm provdd for communcatons,.. T CAP, n comparson to th lngth of th whol bacon ntrval, as: TCAP r = r. (2) TBI Th xprncd transmsson tm of data (T data ), pollng (T poll ) and ACK (T ACK ) packts scals accordngly. For multchannl cas I, r s th combnd bt rat of all channls,.., F tms th bt rat of on frquncy Snglchannl cas T tmout n th snglchannl cas s calculatd by takng nto consdraton th followng squnc of tm ntrvals. Th mastr starts by procssng th packt bfor transmsson (T procm ), followd by th actual transmsson (T poll or T data ) and propagaton tm (T prop ). Upon arrval th packt s procssd by th slav, and n cas t s a data packt, a CRC chck s don (T procs or T procs_crc ). Thraftr, th slav transmts a rspons (T packt or T ACK ), rsultng n anothr propagaton dlay. Th mastr procsss th packt and, n cas t s a data packt, dos a CRC chck (T procm or T procm_crc ). Takng nto consdraton th possblty of dlay propagaton varatons or nxact synchronzaton btwn mastr and slavs, a short tm margn (T margn ) s addd as a safty margn btwn th tm whn th mastr xpcts a packt and ts actual tm of arrval. Th quatons from [5] ar rpatd hr for convnnc: Ttmout _ poll, = TprocM Tpoll Tprop TprocS (3) Tdata, Tprop TprocM _ CRC Tmargn, Ttmout _ data, = TprocM Tdata, Tprop (4) TprocS _ CRC TACK Tprop TprocM Tmargn. Eq.(3) matchs th cas of th mastr pollng for a data packt from a slav. Eq.(4) assums a data packt snt by th mastr whch thn awats an ACK from a slav Multchannl I Havng F fxd transcvrs n all nods rsults n xactly th sam chan of vnts as for th sngl channl cas, so q.(3) and (4) ar drctly applcabl Multchannl II Wth a tunabl transcvr at th slavs and F fxd transcvrs at th mastr, furthr dlays hav to b consdrd. Th mastr starts by procssng th packts to b snt and thn broadcasts a control packt on all frquncs. Consdrng th frquncy lmtatons, th control packt concrns a maxmum of four frquncs, upprboundng th packt lngth. Aftr th transmsson tm and propagaton dlay of th control packt, th slavs procss th rcvd packt and thn tun thr transcvrs to th rspctv frquncy ndcatd n th control packt, ntroducng tunng dlay (T tun ). W thn hav to dffrntat btwn two cass: traffc flows from th slav to th mastr and vc vrsa. For th frst cas, th slav smply snds th rqustd data packt to th mastr on th ndcatd channl, rsultng n transmsson and propagaton dlay, procssng and CRC chckng dlay at th mastr, and an addtonal tm margn as statd n For th scond cas of traffc flows orgnatng at th mastr, th mastr wats for th slav to tun and thn snds a data packt. Th slav procsss th rcvd packt and conducts a CRC
6 chck, bfor t answrs wth an ACK, whch thn s procssd by th mastr. Evn hr th tm margn s addd. In ths archtctur, th xtra pollng packt ntroducd also for data packts snt from th mastr to th slav rsults n addtonal transmsson and propagaton dlay, procssng tm, plus tunng tm: Ttmout _ poll, = TprocM Tpoll Tprop TprocS (5) Ttun Tdata, Tprop TprocM _ CRC Tmargn. Ttmout _ data, = TprocM Tpoll Tprop TprocS Ttun Tdata, (6) Tprop TprocS _ CRC TACK Tprop TprocM Tmargn. Hr (5) dfns th tmout valu for traffc flows from slav to mastr and (6) vc vrsa Tmng analyss Th dadln D of an RTC τ s dvdd nto an ordnary dadln D ord, and a rtransmsson dadln D rtr,. Ths holds tru for all consdrd archtcturs. To b abl to us th dadln paramtr n th raltm analyss provdd blow, th dadln has to b shortnd furthr, such that t corrsponds to th latst possbl pont n tm whn th packt must hav lft th sndr n ordr to arrv n tm at ts dstnaton. Ths paramtr s calld maxmum quung dlay (d ord,, d rtr, ) and can b calculatd by subtractng from th gvn dadln a numbr of constants consttutng a worst cas stuaton. Th worst cas watng tm for a packt wth th hghst dadln occurs whn t arrvs to th EDF quu just as a packt wth a longr dadln has startd sndng, and thraftr, whn that packt s transmsson procss has ndd, th rmanng tm untl th ntwork ntrs th slp mod s not suffcnt to accommodat a packt transmsson. As a rsult, a hgh prorty packt has to wat two tmouts, on for ach cas statd abov, plus th followng slp phas and bacon transmsson. Thrfor d ord, for traffc flows from mastr to slav (M S) and (S M) ar: d = ordm S D ord, T slp T bacon Ttmout _ data, (7) max { Ttmout _ poll,, Ttmout _ data, }, d = ords M D ord, T slp T bacon Ttmout _ poll, (8) max { Ttmout _ poll,, Ttmout _ data, }. As RRTCs ar schduld as rgular RTCs, th sam adaptaton of dadln to maxmum quung dlay has to b mad. Th dadln of th RRTC s a systm paramtr and s rlatd to D rtr as follows. Th systm spcfs a maxmum numbr of rtransmsson attmpts (N attmpt ) ncssary to mt th rlablty dmands of th applcaton. Ths N attmpt attmpts hav to b fnshd bfor D rtr xprs, mplyng a prrtransmsson dadln (D r ). Assumng qual dadln parttonng w hav Drtr Dr = (9) Nattmpt To guarant th dadlns for ach of thos rtransmsson attmpts, w st th dadln of ach RRTC to D r. Isolatng th quung dlay for rtransmssons s agan don by subtractng th worst cas stuaton paramtrs and dffrs btwn M S and S M packts as: d = D T T T max { Ttmout _ poll,, Ttmout _ data, } d = D T T T max T, T rtrm S r slp bacon tmout _ data, rtrs M r slp bacon tmout _ poll, { tmout _ poll, tmout _ data, } (10) (11) Th quung dadln s calculatd n ths way for both th snglchannl and multchannl cas II, usng th approprat tmout ntrvals. Howvr, for th multchannl archtctur I, w hav to consdr th fact that th total bt rat s F tms th bt rat of on frquncy. Ths can lad to a fault n th calculaton whr th transmsson tm of a packt suddnly s only 1 / F tms as long as n ralty. Evn f th ntwork can snd F tms as many packts as wth on frquncy, ach packt tslf s nvr snt fastr than th actual bt rat pr frquncy. Thrfor w hav to subtract a furthr constant from th dadln whch s th actual tmout ntrval of on packt mnus th wrongly prcvd tmout ntrval of 1 / F tms th actual tmout. Ths rsults n a spcfc quung dlay for th multchannl cas I of: d = ordm S D ord, T slp T bacon Ttmout _ data, 1 (12) max { Ttmout _ poll,, Ttmout _ data, } 1 Ttmout _ data, F d = ords M D ord, T slp T bacon Ttmout _ poll, 1 (13) max { Ttmout _ poll,, Ttmout _ data, } 1 Ttmout _ poll, F 6.3. Raltm schdulng analyss Th raltm analyss usd n our arlr work s basd on EDF schdulng of prodc raltm tasks on a unprocssor [18], and ncluds both a chck of th utlzaton and of th workload mposd on th procssor by th schduld tasks. Ths analyss orgnally assumd fully prmptv tasks, but has bn adaptd for communcaton [19] whr prmpton s only possbl aftr th complt transmsson of on packt,.., onc a packt has startd to b snt, t cannot b stoppd n ordr to snd a hghr prorty packt. Thrfor th blockng tm of on packt has bn ntroducd nto th calculaton of th quung dadln of a packt. Th raltm analyss s usd ach tm a nw RTC rqusts accss to th ntwork, to dcd f ts ncluson s possbl wthout jopardzng any dadln guarants alrady gvn, whl also guarantng th dadln of th nw RTC. Th utlzaton chck smply tsts f th admttd RTCs and RRTCs ar not usng mor bandwdth than avalabl. For a snglchannl ntwork th condton s smply that th utlzaton U must not b gratr than 1. In multchannl cas I, th utlzaton must not b gratr than F du to th concurrncy of th F frquncs. Bcaus of th slpng phas, ths constrants only hold tru f w calculat U usng th xprncd bt rat: V T W tmout _ poll, N Ttmout _ data, N U = 1 P 1 P = = (14) X Y T tmout _ rtr _ poll, T tmout _ rtr _ data,, = 1 P r, = 1 P r,
7 whr T = T T T T tmout _ poll, procm poll prop procs T T T T data, prop procm _ CRC margn, T = T T T tmout _ data, procm data, prop T T T T T procs _ CRC ACK prop procm margn. (15) (16) Th tmout paramtrs for th rtransmssons ar solly ntroducd to ncras clarty and ar dfnd as T tmout_rtr_poll, = T tmout_poll, and T tmout_rtr_data, = T tmout_data,. N ndcats th numbr of packts pr mssag for RTC. As rtransmssons ar don pr packt, ths paramtr s assumd to b qual to on for all RRTCs and s thrfor omttd from th quaton. V and W ndcat th numbr of S M and M S RTCs, rspctvly, and X and Y th numbr of S M and M S RRTCs, rspctvly. As th tmout calculaton dffrd for th multchannl ntwork wth on tunabl transcvr at ach slav, th propr xprncd tmout ntrval s: Ttmout _ poll, = TprocM Tpoll Tprop TprocS (17) T T T T T tun data, prop procm _ CRC margn tmout _ data, = procm poll prop procs tun data, Tprop TprocS _ CRC TACK Tprop TprocM Tmargn T T T T T T T (18) Part two of th raltm analyss chcks th workload mposd on th ntwork by th traffc channls. It s dfnd by th workload functon h(t) whch s th sum of all transmsson tms of all mssags by all RTCs and RRTCs, ncludng thos mssag nstancs wth an absolut dadln bfor tm t. Tm t starts wth zro at th bgnnng of th hyprprod (hp),.., th nstanc n tm whn all RTC prods start smultanously. Th hp nds whn all prods bgn smultanously agan. Th rason for choosng ths startng pont s that to provd raltm guarants, w hav to analys th worst cas workload, snc th data traffc thn wll xprnc th worst dlay. Th smultanous start of all prods has bn provn to b th worst cas n [20][22], whr also th workload functon s usd to tst th fasblty of task sts. Th h(t) functon s gvn as t d ords M, h() t = 1 ( Ttmout _ poll, N ) [ 1, V], P T, dords M, t [ 1, X], r, d t rtrs M, 1 t d ( Ttmout _ data, N ) ordm S, [ 1, W], P T, dordm S, t t d 1 P rtrs M, T t d tmout _ rtr _ poll, rtrm S, 1 Ttmout _ rtr _ data,. [ 1, Y], P r, drtrm S, t (19) whr th frst two trms gv th workload of th ordnary traffc flows (S M and M S), and th last two trms th workload of th rtransmsson channls (S M and M S). Dpndng on f w calculat th workload of th snglchannl cas or th multchannl cass, only th tmout paramtr wll vary. Only multchannl cas II uss a dffrnt tmout ntrval, whl multchannl cas I and th snglchannl cas hav an dntcal tmout valu. Furthr, th quung dlay calculatons dffr and wll thus also nflunc th rsult of th workload functon. Whn tstng fasblty, th constrant h(t) t, t, has to b mt. In multchannl cas I, howvr, th concurrncy of frquncs lads to th constrant of h(t) F t, t. In [23], th computatonal complxty of ths tsts was rducd and a suffcnt subst of ponts n tm at whch th functon has to b chckd was provdd. 7. Prformanc valuaton W valuatd th two proposd multchannl ntwork archtcturs and compard thm to th rsults for th snglchannl ntwork n [5]. To valuat th rlablty n trms of MER and th bandwdth utlzaton capablty, w hav mplmntd a smulator n MatLab. Th rfrnc ntwork has a logcal star topology wth on mastr nod and 10 slav nods. A maxmum transmsson rang of 100 m was assumd, ladng to a propagaton dlay of 0.3 μs. Th undrlyng IEEE protocol s n bacon mod usng a bt rat of 250 kbps. A bacon fram lngth of ms was assumd to kp th sam paramtrs as n our arlr work for th sak of comparablty. Slpng phass corrspondng to 50% and 75% of bacon ntrval tm wr smulatd,.., th suprfram lngth was and ms, rspctvly. For tunabl transcvrs a tunng dlay of 131 μs was chosn basd on rsults from [24]. Th numbr of concurrnt frquncs, F, was st to four. W assum a bursty rror bhavour modlld by a typcal twostat Markov modl (GlbrtEllot). Th two stats hav a bt rror rat of 102 and 104 rspctvly, th stat changng probablts ar 0.5 and 0.99, and th stat hold tms qual on tmout tm. Th packt rror rat s thn gvn by P = 1 (1 P b ) C, whr P b s th bt rror probablty and C th packt lngth n bts. For smplcty, w assum an rrorfr fdback channl. To nsur statstcal sgnfcanc, smulatons hav bn run untl at last 10 mssag rrors wr xprncd, gvn th lowst rror probablty. Consdrng a typcal ndustral applcaton, th packt lngth s 120 bts for data, ACK, and pollng packts, gudd by th mnmum packt sz possbl n th standard. Th smulatd traffc flows, wth a known prod, dadln and mssag lngth, blong to on of two traffc classs spcfd n Tabl I. Th choc of traffc class s randomzd wth a unform dstrbuton, as s th choc of sourc and dstnaton nods for ach flow, but always ncludng th mastr nod as on of ths. Tabl I also shows th paramtrs of th rtransmssons channls. Smulatons hav bn run for 2, 4, and 8 rtransmsson channls, but du to spac lmtatons only rsults for 8 rtransmsson channls ar shown n th fgurs. For all packts th maxmum numbr of rtransmsson attmpts pr packt (N attmpt ) was fxd to two.
8 TABLE I: Traffc spcfcaton Traffc class No1 No 2 Ordnary traffc P (ms) D (ms) C (bts) Rtransmssons RRTC P r (ms) D r (ms) C r (bts) No N attmpt = 2 M = 2 or 4 or 8 Rlablty Th MER s dtrmnd through smulatons, but th total rlablty also ncluds hardwar rdundancy and th amount of rdundancy n th frquncy doman. Whn valuatng th MER through smulatons only accptd RTCs ar ncludd. As shown n Fg. 1, th MER for th cas wthout any rtransmssons s 101 for all archtcturs. Ths s xpctd as th MER only dpnds on th GlbrtEllot modl and th mssag lngth. For all archtcturs th hghst mprovmnt n MER was achvd wth 8 RRTCs (th rsults for 2 and 4 RRTCs wr btwn thos for 0 and 8 RRTCs). Th hghst MER mprovmnt by rtransmssons was xprncd for low numbrs of rqustd RTCs, qut ndpndnt of archtctur. Ths can b xpland by th fact that for a rlatvly small numbr of RTCs, th dmand for RRTCs s lowr and thrfor a hghr prcntag of rqustd rtransmssons can actually b grantd. Th dcras n MER btwn on and 20 RTCs can b attrbutd to th fact that bfor all th avalabl RRTCs can b usd, a crtan numbr of rqusts for rtransmssons s ndd, whch n turn rqurs a crtan numbr of RTCs. If th RRTCs ar not usd, th MER cannot b mprovd. Th rason why th curvs dffr btwn archtcturs for larg numbrs of rqustd RTCs s that th multchannl archtctur I could accpt consdrably mor RTCs, whl th numbr of rtransmsson channls was kpt constant, ladng to a lowr prcntag of grantd rtransmssons. Not also that multchannl archtctur II rqurs an xtra control packt to schdul concurrnt transmssons. Each xtra packt may ncras th MER and mak th protocol mor vulnrabl to channl nos. Incrasng th slpng phas to 75% of th bacon ntrval dd not affct th MER and thrfor th fgurs ar omttd. Consdrng rlablty n trms of hardwar and frquncy rdundancy, multchannl archtctur I s obvously th supror soluton. It has svral rdundant transcvrs and s concurrntly usng all avalabl frquncs. Consdrng th hardwar aspct, th snglchannl and multchannl archtctur II ar quvalnt, but th us of tunabl transcvrs provds hghr frquncy rdundancy for th multchannl approach. Evn f th possbl traffc channl ntrdpndncs mak t hard to us th frquncy doman ffcntly, th ablty to tun th transcvr stll provds frquncy dvrsty. Bandwdth utlzaton capablty Utlzng as much as possbl of th avalabl bandwdth dmands a hgh dgr of concurrncy. As mntond abov, multchannl ntwork I has th hghst dgr of concurrncy and can thrfor asly utlz th complt bandwdth offrd by ach avalabl frquncy. Obvously, snglchannl ntworks do not hav th possblty of concurrncy, but may utlz all of th avalabl bandwdth on th on avalabl frquncy. Multchannl ntwork II can b found n btwn ths two cass. It utlzs on of th frquncs wll, but whthr th rmanng frquncs ar usd ffcntly dpnds on traffc channl ntrdpndncs. In our analyss, w consdrd th ntwork utlzaton for th thr archtcturs both wth and wthout rtransmssons. Th graphs shown n Fg. 2 show th utlzaton of th actv part of th bacon ntrval and nclud only th utlzaton by ordnary traffc flows n ordr to dntfy th utlzaton pnalty ntroducd by th rtransmsson channls. Th calculaton of utlzaton also ncluds th acknowldgmnt and pollng packts rqurd to transmt th data packts. Consdrng Fg. 2 t bcoms obvous that th multpl transcvr cas s supror to th othr two cass n trms of bandwdth utlzaton capablty. Wthout rtransmssons, multchannl archtctur I saturats at a utlzaton of about 3.9 usng four concurrnt transcvrs. Th othr two ntworks saturat at a utlzaton just blow 1, whr multchannl cas II falls vn blow th snglchannl cas. Th rason for ths s th pnalty ntroducd by th tunng dlay, ladng to a lowr numbr of RTCs that can b schduld. Furthrmor, th xstnc of th addtonal control packt n th MAC protocol for multchannl cas II lads to an arlr saturaton of th ntwork as compard to th snglchannl or th othr multchannl cas. Whn ntroducng rtransmssons nto th systm, th utlzaton by ordnary traffc channls drops for all archtcturs. Multchannl ntwork I drops to around 2.5, whl th othr two cass drop to about 0.6, th tunabl cas stll bng lowr than th snglchannl on. Th man rason for ths consdrabl rducton s not th bandwdth utlzaton by th rtransmsson channls, whch s rathr small compard to th magntud of th pnalty. Instad all traffc flows bcom mor dffcult to schdul du to th shortnng of th dadln (from D to D ord, ) to catr for rtransmssons. Th sam pnalty was also vsbl for 2 and 4 rtransmsson channls (not shown n ths papr) wth hardly any dffrnc btwn th 2, 4 and 8 RRTCs cass. Whn consdrng a longr slp phas, th utlzaton for th multpl transcvr cas I wth rtransmssons fll to around 2.25, whl th two othr cass dcrasd to about 0.5. Th fgurs ar omttd du to spac lmtatons. Although ths rsults look vry favourabl towards th multpl transcvr cas, on has to tak nto consdraton crtan practcal constrants. W assum that multpl transcvrs locatd on on nod ar placd far nough apart to functon proprly wthout ntrfrng wth ach othr. Howvr, on small nods ths mght not always b possbl, n whch cas sndng and rcvng at th sam tm s problmatc. Ths mpls that traffc on th multpl transcvr archtctur cas I nds to b schduld such that thr all transcvrs on a slav
9 MER MER: 50% slp, 2 rtransmsson attmpts No rtransmssons, fxd multchannl M=8, fxd multchannl No rtransmssons, tunabl multchannl M=8, tunabl multchannl No rtransmssons, snglchannl M=8, snglchannl Numbr of rqustd channls Fgur 1. Mssag rror rat rcv concurrntly or all transmt concurrntly. Ths ntroducs smlar traffc dpndncs as prsnt n th tunabl archtctur. From th schdulng pont of vw ths dos not pos a problm, howvr, th analyss would suffr from th sam pssmsm as n th tunabl cas, dcrasng th utlzaton by guarantd raltm traffc to mrly on. Bandwdth not usd by guarantd raltm traffc can b usd by soft raltm and bstffort traffc. Introducng ths knd of traffc nto th ntwork would crtanly ncras th utlzaton, spcally for th tunabl transcvr cas, whr th pssmsm n th analyss s th gratst and thrfor th unusd bandwdth th hghst. Dlay Th worst cas dlay s hghst n th tunabl ntwork du to th ntroducton of th tunng dlay and th addtonal control packt, makng th tmout valu longr. Howvr, whn studyng th avrag dlay, our smulatons hav confrmd that t s ndpndnt of th archtctur, as t s mor dpndnt on th maxmum numbr of rtransmssons pr packt and th numbr of rtransmssons ncssary for a succssful transmsson,.., t s connctd to th MER. Both for th snglchannl ntwork and multchannl ntwork I, traffc ntrdpndncs ar rrlvant, but, whn ntroducng tunng, two packts can only b schduld for concurrnt transmssons f thy prtan to mutually ndpndnt traffc channls,.., f nthr sourc nor dstnaton contan th sam slav. Th traffc flow ntrdpndncs rndr th worst cas dlay for multchannl ntwork II dntcal to that of a snglchannl ntwork. Scalablty Th amount of hardwar ncssary for multchannl cas I mpls that t scals poorly, as for ach frquncy, on addtonal transcvr s ncssary at ach nod. Th tunabl cas has no such ssus wth scalablty and th mor nods thr ar n th ntwork, th lss lkly thy mght b to block ach othr. So, vn f th guarantd utlzaton s not ncrasd, th utlzaton by nonguarantskng traffc s lkly to Utlzaton Utlzaton: 50% slp, 2 rtransmsson attmpts No rtransmssons, fxd multchannl M=8, fxd multchannl No rtransmssons, tunabl multchannl M=8, tunabl multchannl No rtransmssons, snglchannl M=8, snglchannl Numbr of rqustd channls Fgur 2. Bandwdth utlzaton ncras. Th snglchannl cas has no such ssus. Th scalablty s also connctd to th utlzaton through th numbr of accptd RTCs, n whch cas th multpl transcvr archtctur cas I s supror. Hardwar and Softwar Complxty Obvously, th multchannl archtctur I suffrs th hardst from hardwar costs, whl th tunabl and snglchannl cas ar qually good solutons from that prspctv. Th snglchannl archtctur has th channl allocaton algorthm wth th lowst complxty. Multpl transcvrs at ach nod can b schduld n paralll wthout th nd to consdr whch packt to schdul ovr whch frquncy, so ths mplmntaton s also qut smpl. Th most complx cas occurs whn traffc ntrdpndncs can ntrfr wth pur EDF schdulng and thrfor th tunabl archtctur rsults n th most complx channl allocaton algorthm. Enrgy usag Although th dtald analyss of nrgy consumpton s out of th scop of ths papr, w argu that a hghr numbr of transcvrs, as n multchannl cas I, lads to a hghr nrgy usag, whl a sngl fxd transcvr s th bst soluton from an nrgy prspctv. Th tunng of transcvrs mpls addtonal nrgy consumpton n multchannl ntwork II. Summary W can conclud that non of th proposd archtcturs s bst for all consdrd prformanc mtrcs. An approprat archtctur should thus b slctd basd on th data traffc modl, th constrants on hardwar, softwar and nrgy, as wll as th rqurd utlzaton, throughput and rlablty. Whl multchannl I s supror n bandwdth utlzaton capablty and rlablty, t suffrs wth rspct to hardwar costs, scalablty and nrgy usag. On th othr hand, ths ar aras n whch th tunabl archtctur mplmntaton has ts advantags. Hardwar costs and nrgy usag ar kpt low and scalablty s not a problm. Howvr, th low bandwdth utlzaton capablty s th rsult of low concurrncy at ach nod, snc frquncy dvrsty only xsts on a ntwork wd lvl, not a prnod lvl.
10 8. Concluson W prsntd and valuatd two multchannl ntwork archtcturs basd on IEEE for ndustral ntworks. Usng a snglchannl ntwork as a basln, w addd dvrsty n th tm and frquncy domans to ncras rlablty and guarantd throughput n ndustral ntworks whl kpng th advantagous nrgy savng proprts of th undrlyng IEEE standard. Th two dscrbd ntwork archtcturs ar usng thr F fxd transcvrs on all nods or tunabl slav transcvrs. Through EDF pollng and raltm analyss admsson control, w addd prdctablty to th ntwork, ndd to support hard raltm traffc n ndustral applcatons. Th archtcturs wr valuatd n trms of rlablty, utlzaton, dlay, complxty, scalablty and nrgy ffcncy. Th rsults show that nthr of th dscrbd multchannl altrnatvs ranks hgh for all valuatd paramtrs. An approprat archtctur should thus b slctd basd on th ndustral applcaton n quston. Th opton wth svral slav transcvrs provds a hgh lvl of srvc through concurrncy n th frquncy doman and hardwar rdundancy, whras th opton wth tunabl slav transcvrs may ncras guarantd throughput for crtan data traffc modls whl havng low hardwar costs, good scalablty and low nrgy usag. Rfrncs [1] IEEE Standard (2006) Part 15.4: Wrlss mdum accss control (MAC) and physcal layr (PHY) spcfcatons for LowRat Wrlss Prsonal Ara Ntworks (LRWPANs), IEEE Standard for Informaton Tchn., IEEESA Standards Board, [2] [3] [4] M. Jonsson and K. Kunrt, Towards Rlabl Wrlss Industral Communcaton wth RalTm Guarants, IEEE Transactons on Industral Informatcs, vol. 5, no. 4, pp , Nov [5] K. Kunrt, E. Uhlmann, and M. Jonsson, Prdctabl raltm communcatons wth mprovd rlablty for IEEE basd ndustral ntworks, n Proc. 8th IEEE Intrnatonal Workshop on Factory Communcaton Systms (WFCS 10), Nancy, Franc, May [6] S. Pjhan, M. Schwartz, and D. Anastassou, Error control usng rtransmsson schms n multcast transport protocols for raltm mda, IEEE/ACM Transactons on Ntworkng, vol. 4, no. 3, pp , [7] A. Koubâa, M. Alvs, B. Nfz, and Y.Q. Song, Improvng th IEEE slottd CSMA/CA MAC for tmcrtcal vnts n wrlss snsor ntworks, n Proc. Workshop on RalTm Ntworks (RTN 06), Drsdn, Grmany, July [8] F. Shu, Prformanc valuaton of th IEEE CSMACA protocol wth QoS dffrntaton, n Proc. Intrnatonal Confrnc on Intllgnt Snsors, Snsor Ntworks and Informaton Procssng (ISSNIP 08), Sydny, Australa, Dc. 2008, pp [9] J. Francomm, G. Mrcr, and T. Val, A smpl mthod for guarantd dadln of prodc mssags n clustr clls for control automaton applcatons, n Proc. IEEE Confrnc on Emrgng Tchnologs and Factory Automaton (ETFA '06), Pragu, Czch Rpublc, Spt. 2006, pp [10] J. Mo, H.S.W. So, and J. Walrand, Comparson of Multchannl MAC Protocols, IEEE Transactons on Mobl Computng, vol. 7, no. 1, Jan 2008, pp [11] M. Wang, L. C, P. Zhan, and Y. Xu, Multchannl MAC protocols n wrlss ad hoc and snsor ntworks, n Proc. ISECS Intrnatonal Colloquum on Computng, Communcaton, Control, and Managmnt (CCCM '08), Guangzhou, Chna, Aug. 2008, pp [12] S.C. Lo, Dsgn of multchannl MAC protocols for wrlss ad hoc ntworks, Intrnatonal Journal of Ntwork Managmnt, vol. 19, no. 5, Spt. 2009, pp [13] B. Andrsson, N. Prra, and E. Tovar Prlmnary Dscusson on Globally Prortzd Mdum Accss for MultChannl Wrlss Systms, n Proc. 6th Intrnatonal Workshop on RalTm Ntworks (RTN 07), Psa, Italy, July [14] A. Rangnkar and K.M. Svalngam, QoS Awar Mult Channl Schdulng for IEEE Ntworks, Mobl Ntworks and Applcatons, vol. 11, no. 1, pp , Fb [15] P.G. Namboothr and K.M. Svalngam, Prformanc of a multchannl MAC protocol basd on IEEE Rado, IEEE 34th Confrnc on Local Computr Ntworks (LCN 09), Zurch, Swtzrland, Oct [16] H.K. L, D. Hnrksson, and T. Abdlzahr, A Practcal MultChannl Mda Accss Control Protocol for Wrlss Snsor Ntworks, Intrnatonal Confrnc on Informaton Procssng n Snsor Ntworks (IPSN '08), St. Lous, MO, USA, Apr. 2008, pp [17] Chpcon, 2.4 GHz IEEE /ZgBrady RF Transcvr, Chpcon Products Txas Instrumnts [18] C.L. Lu and J.W. Layland, Schdulng algorthms for multprogrammng n a hardraltm nvronmnt, Journal of th ACM, vol. 20, no. 1, pp , Jan [19] H. Hoang and M. Jonsson, Swtchd raltm Ethrnt n ndustral applcatons  dadln parttonng, n Proc. Th 9th AsaPacfc Confrnc on Communcatons (APCC 03), Pnang, Malaysa, Spt. 2003, vol. 1, pp [20] M. Spur, Analyss of dadln schduld raltm systms, Tchn. Rp. No. 2772, INRIA, Franc, [21] S.K. Baruah, A.K. Mok, and L.E. Rosr, Prmptvly schdulng hardraltm sporadc tasks on on procssor, n Proc. 11th RalTm Systms Symposum (RTSS 90), Lak Buna Vsta, FL, USA, Dc. 1990, pp [22] S.K. Baruah, L.E. Rosr, and R.R. Howll, Algorthms and complxty concrnng th prmptv schdulng of prodc, raltm tasks on on procssor, RalTm Systms, vol. 2, no. 4, pp , Nov [23] J.A. Stankovc, M. Spur, K. Ramamrtham, and G.C. Buttazzo, Dadln schdulng for raltm systms  EDF and rlatd algorthms, Kluwr Acadmc Publshrs, Boston, MA, USA, [24] T. Vogt, F. Östrlnd, and A. Dunkls, Improvng Snsor Ntwork Robustnss wth MultChannl Convrgcast, n Proc. 2nd ERCIM Workshop on Moblty, Tampr, Fnland, May 2008.
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