Performance Evaluation of WDM LAN s with Propagation Delay Constraint Analysis

Transcription

1 Pefomance Evaluaton of WD AN s wth Popagaton Dela Constant Analss IOANNI E. POUNOURAKI Depatment of Electcal & Compute Engneeng Natonal echncal Unvest of Athens Zogaphou, Athens GREECE Abstact: -In ths pape we stud the effect of ound tp popagaton dela n pefomance measues of Wavelength Dvson ultplexng (WD netwoks. Even though the mpact of popagaton dela s substantal n optcal netwoks behavo, most of the studes gnoe the effect of ths object n thoughput dela evaluaton. We assume a WD ocal Aea Netwok (AN whee the ound tp popagaton dela s less o equal to a data packet tansmsson tme. he poposed asnchonous tansmsson polc avod data channel collson. In the analss we take nto account the popagaton delas the effect of eceve collson fo a sstem wth fnte numbe of statons. Ke-Wods: - Wavelength Dvson ultplexng, ound tp popagaton dela, eceve collson, Elang- fomula, aveage ejecton pobablt.. Netwok Achtectue odel he sstem unde consdeaton as Fgue shows s a passve sta netwok. he sstem uses N + wavelengths, λ 0, λ,..., λ N, to seve a fnte numbe ( > N of statons. he sstem at wavelength λ 0 opeates as the contol channel whle the emanng N channels at wavelengths λ,..., λ N consttute the multchannel of data tansmsson sstem[-4]. hus the poposed netwok model can be descbed as a CC FR R stuctue. It has a common contol channel CC. means that each staton has a tunable tansmtte tuned at λ 0, λ,..., λn. he outcomng taffc fom a staton s connected to one nput of the passve sta couple. Addtonall, eve staton also uses a fxed tuned eceve FR fo the contol channel one tunable eceve to an of data channel λ,..., λ N ndcated b R. he ncomng taffc to a use staton s spltted nto N + wavelengths b a WDA spltte fom whch one of N wavelengths can be selected b the tunable eceve as Fgue ndcates. he tansmsson tme of a fxed sze contol packet s used as tme unt (contol slot the data packet tansmsson nomalzed n contol slot tme unts s ( > whch s called data slot. We assume the exstence of a common clock, obtaned b dstbutng a clock to all statons. he oundtp popagaton tme between an staton to the hub of the sta couple to an othe staton s assumed to be equal to R tme unts. he oundtp popagaton plas a ke ole n the pefomance evaluaton of the WDA potocols. ost of the studes consde data packet tansmsson tme s much geate than popagaton dela. Howeve n optcal netwoks, popagaton dela n most cases s hghe than data packet tansmsson tme. Fo example lets sa a netwok wth damete 2Km data packets wth sze 800 bts. In case of a channel wth capact 0 b/s 8 popagaton speed of 2 0, the popagaton dela s 0µsec whle the data tansmsson tme s 800µsec. In case of a wavelength wth capact of Gbt/sec the data tansmsson tme s 8µsec. he close elaton the small dffeence between popagaton dela data packet tansmsson tme s a ve mpotant facto n desgned multple access WD netwoks.

2 he poposed scheme belongs to the asnchonous tansmsson potocols n whch the data channels ae unslotted. Contol channel s consdeed to be slotted wth R + tme unts sze. he contol packet conssts of the tansmtte addess, the eceve addess the wavelength λ k as s shown n Fgue 2. he access method follows the "tell wat " polc n whch a data packet s tansmtted f onl f ts coespondng contol packet has successfull tansmtted. contol data packet b lstenng to the sta couple multchannel sstem snce t opeates as a boadcast medum. he packet of a backlogged staton must be etansmtted n some late tme slot accodng to etansmsson polc, wth possbl futhe such etansmssons untl successful ecepton. he poposed achtectue potocol acheves collsonless data packet tansmsson tackng the avalablt of data channels. We stud data collson due to destnaton staton contenton n pefomance measue evaluaton. Fgue 2. Data Contol packets stuctue. Fgue. Passve sta couple. oe ove each staton s equpped b a buffe wth capact of one data packet. If the buffe s empt the staton s sad to be fee, othewse, t s backlogged. If a staton s backlogged geneates a new packet, the packet s lost neve etuns. A staton wll hea the esult of a tansmsson of ts Analss We use the followng notatons: numbe of statons n the sstem; N numbe of data channels n the sstem; length of data packets n contol packet tansmsson tme unts; R ( R < the oundtp popagaton dela n the sstem; R + length of contol slot n contol packet tansmsson tme unts; G the aveage numbe of tansmtted contol packets pe contol slot tme on contol channel; c output ate of successful tansmtted contol packets; the aveage ate of successfull tansmtted d he speed the ange of tunable tansmttes set majo lmtatons affectng WD opeaton. In ou stud we ae not take nto account these lmtatons assumng neglgble tunng tmes ve lage tunable bwdths. data packets though one of the data channels pe data slot. d the aveage ate of successfull eceved data packets at destnaton though one of the data channels pe data slot. 2. Access mode A staton contnuousl montos the contol channel wth ts fxed tuned eceve. At the begnnng of each contol slot each staton knows the status of data channels (dle o bus. o the staton ecognzes the dle channels. In case of detecton of dle channels, the staton selects one of them oml, wats the begnnng of the next contol slot sends fst the contol 2

3 packet ove the contol channel, specfng the eseved channel numbe fo data tansmsson. At the end of the contol slot, namel R tme unts late, the staton hea the esult of ts tansmsson. In case of successful tansmsson on the contol channel, the staton mmedatel tansmts the coespondng data packet ove the chosen dle data channel wth avodance of data channel collson. If thee s unsuccessful tansmsson on the contol channel due to contol channel collson o thee s no dle data channels, the staton becomes backlogged defe ts tansmsson accodng to etansmsson polc. he nput nto the data channels sstem has one to one coespondence to the output of the contol channel. heefoe the netwok achtectue wth N data channels, wth constant mean aval ate of data packets, alwas an dle channel s ead fo tansmsson untl all data channels become bus. At ths pont the ncomng successful tansmssons ae ejected n a F -seve loss sstem. In ths taffc model the block pobablt of a data packet s P esults fom the well known Elang- fomula. he fxed data packets length gves constant sevce ate /. he Elang- fomula was deved fo Posson nput taffc. he nput nto data channels sstem has one to one coespondence to output fom the contol channel. We appoxmate the output ate of the successful tansmtted contol packets whch coesponds to the nput taffc ate of the accompanng data packets nto the data channels tansmsson sstem, wth Posson aval pocess [-3]. o obtanng closed fom expessons fo the stead state behavo, we can expess the output ate of successful tansmtted contol packets nomalzed n contol slots duaton tme unts as follows : Ge c ( R + he evaluaton of block pobablt s gven b P N n ( Ge R + ( Ge R + N N! n n! (2 We defne as thoughput the aveage ate of successfull tansmsson of data packets ove N- data channels sstem dung a data slot tme peod n stead state. Ge R + o we get d Ge N R + ( P ( P.2 Recepton mode (3 (4 In the ecevng mode, at the end of the contol slot, f a staton dentfes ts addess announced n a contol packet on a contol channel the coespondng data packet wll be tansmtted successfull. hen, mmedatel adjusts ts tunable eceve to the wavelength channel specfed n the contol packet fo data packet ecepton. Fgue 3. Vulneable peod. We sa that a tunable eceve of a staton Z s actve, f t s tuned ecevng a data packet fom a data channel λd (,..., N as Fgue 3 ndcates. It s possble the tunable eceve of staton Z to be actve at a tme nstant. o an successfull tansmtted data packet addessed to staton Z s ejected. hs phenomenon s called eceve collson [5-9]. We consde that at an pont n tme each staton s capable of tansmttng at a patcula wavelength λ d smultaneousl ecevng at a wavelength λ dr. We assume unfom dstbuton of 3

4 etansmssons. he om tme dela ntoduced between two consecutve etansmssons s unfoml dstbuted fom to K tme unts..3 Receve Collson he thoughput educton nduced b eceve collson s elated wth the possblt a eceve to be actve. hus we examne what wll happen f a data packet whch stats tansmsson at tme nstant t has as destnaton a staton Z who belongs to the set,2,. he tme nstant that a successful tansmtted data packet aves at ts destnaton s dffeent fom the othes, because the tansmsson stat tmes among two successve data packets ae ndependent ma dffe at least R + tme unts. It s obvous that f a successful data packet has stated tansmsson between t { ( R + } t ( R + wll have actvate the eceve of staton Z a eceve collson occus. In the opposte case, the Z staton tunable eceve wll be able to ead ts destnaton addess so the data packet s eceved coectl. hus the vulneable peod tme lasts ( R + tme unts. It s evdent that an othe successful data packet tansmsson, statng between t + ( R + t + { ( R + }, wll fnd the staton's Z eceve actve wll be aboted, causng eceve collson. In othe wods the collson wndow nteval s extendng fom t to t + { ( R + }. he pobablt that staton Z s destnaton of a data packet s / (fo sake of smplct of the analss, we assume that a staton ma sent packets to tself. We defne the followng events fo the vulneable tme peod tt { ( R + } p t : A, the successful tansmsson of a data packet, statng tansmsson n the th tme unt of the vulneable peod ove a gven data channel j {,2, N}., the data packet statng tansmsson n the th tme unt, whose coespondng contol packet has been tansmtted ove the contol channel at th ( R + tme unt, has as destnaton a gven staton, let's sa Z {,...,. akng nto account the ndependence of the of the A events fo each tme unt, we defne C, as the event that no one data packet has as destnaton the staton Z dung the vulneable peod. We nomalze the vulneable peod n contol slot tme peods as follows: If modulus ( R + equals to zeo then x R + x.else x x. the ntege pat of R + C I ( A I (5 We defne as P co, the pobablt of coectl ecepton of a data packet fom staton Z statng tansmsson at the gven tme nstant. hs pobablt s equvalent wth the pobablt P (C. Fom (5 we get, P co P( C [ G [ P( A I ] [ ] ( C e P( A I [ P( A P( / A ] ( P ] (6 We defne as thoughput pe staton n stead state, the facton of successfull data packets that ae eceved coectl at destnaton b a staton dung a data slot tme. G G e ( P [ e ( P ] R + (7 Usng appoxmatons n the above equaton, we take G G e ( P exp[ e ( P ] R + (8 et RC be the total sstem thoughput of the sstem, that s defned as the aveage numbe of the successful tansmssons of data packets at destnaton dung a data slot tme n stead state. 4

5 RC (9 Rc d N (0.4 Aveage Rejecton Pobablt We defne P ej as the aveage ejecton pobablt at destnaton, n stead state, the ato of the aveage numbe of data packets ejected at destnaton due to actve eceves, to aveage numbe of successfull tansmtted packets ove the multchannel sstem dung a data packet tansmsson tme, then P ej RC ( that the pobablt of success s the same on an t, n has a geometc dstbuton,.e. Q ( n F ( F n W the aveage numbe of tals fo successful tansmsson of a contol packet. o W E[ n] nq ( n / F G n ( P [ e ( E[ D] E[ D ] + E[ D R + + ( W ( D 2 3 Numecal Results w b e G ] + + 2R + (4 P ] ( R R R + (6 2 Dela Analss We assume unfom dstbuton of etansmssons. he om tme dela ntoduced between two consecutve etansmssons s unfoml dstbuted fom to K contol slot tme unts, wth aveage value gven b D b ( K + / 2. D the nteval between the geneaton tme of a data packet the tme of successful ecepton at destnaton. Data packet dela D, s composed fom thee pats as follows: D Dw + D R + (2 D w the watng tme fom the geneaton of a packet untl the begn of the next contol slot. D the dela fom the tansmsson of a data packet untl the begn of successful ecepton at the destnaton. F the pobablt of successful tansmsson of a data packet. Fom (7 we take G F e ( P [ e ( P ] (3 Q (n the pobablt of successful etansmsson of a packet afte n tals. Assumng Fgue 4. he thoughput pe data channel wthout wth eceve collson, vesus the offeed taffc chaactestcs fo R0,5,25 tme unts N0 data channels wth 00 tme unts 00 statons. he esults fom the analss ae llustated n the Fg. 4. It s obvous fom the fgue that as R nceases the thoughput pe data channel deceases. Especall fo R0 we take d (max Fo R5 we take d (max wth educton 37.2% fom the case of R0 fo R25 we take d (max 0.4 wth educton 87.69% fom the case of R % fom the case wth R5.. 5

6 4 Conclusons Ou analss poves that ound tp popagaton dela plas a ke ole n sngle-hop WD Passve sta technolog netwoks. he thoughput measue deteoates damatcall as data packet tansmsson tme s less than ound tp popagaton dela. Also destnaton conflcts educe an moe the pefomance measues n ths WD netwoks catego. Ou stud gves a fame fo the futue eseache fo a eal pefomance measues evaluaton unde the condtons of popagaton dela eceve collson phenomenon. Refeences: [] H. agak. Klenock, Output pocess n contenton packet boadcastng sstems, IEEE ans. Communc., vol.co-33, n., pp9-99, Nov 985 [2] N. ehava," Pefomance Potocol Impovements fo Ve Hgh -peed Optcal Fbe ocal Aea Netwoks Usng a Passve ta opolog ", J. ghtwave echnolog, vol.8, pp , Ap.990. [3].I. Habbab,.Kavehad, C.E.W. undbeg," Potocols fo Ve Hgh -peed Optcal Fbe ocal Aea Netwoks Usng a Passve ta opolog ",J. ghtwave echnolog, vol. -5,pp , Dec [4] J. u. Klenock, " A wavelength dvson multple access potocol fo hgh-speed local aea netwoks wth a passve sta topolog", Pefomance Eval., vol.6 pp , Nov [5] I. E. Pountouaks, " Pefomance Evaluaton wth Receve Collsons Analss n Ve Hgh- peed Optcal Fbe ocal Aea Netwoks usng Passve ta opolog ", J. ghtwave echnolog, vol.6, No.2 pp , Decembe 998. [6] I. E.Pountouaks, " A ultwavelength Contol Achtectue fo Electonc Pocessng ottleneck Reducton n WDA, ghtwave Netwoks", Compute Communcatons vol.2 Numbe 5-6, pp , eptembe 999. [7] I. E. Pountouaks " Wavelength Contol Potocols fo WD AN's wth Restcted Data Channel Collsons", Intenatonal Jounal of Communcaton stems, vol.3, Issue 4, pp , June [8] I.E.Pountouaks A ultwavelength Contol Achtectue fo Electonc Pocessng ottleneck Reducton In WDA ghtwave Netwoks Compute Communcatons vol. 22 Numbe 5, 6 eptembe 999 pp [9] Ioanns.E.Pountouaks: Desgn Potocol Analss fo Passve ta opolog of WD Netwok, cowave Optcal echnolog ettes John Wle & ons, td, vol.25 Numbe 3, a 2000 pp

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