A method for calculating the productivity of cable communications networks

Transcription

1 IOP Cofrc Sris: Marials Scic ad Eiri PAPER OPEN ACCESS A mhod for calculai h produciviy of cabl commuicaios works o ci his aricl: S N Shuliki al 6 IOP Cof. Sr.: Mar. Sci. E. Rlad co - Prformac Compariso of BPL EhrLoop ad SHDSL choloy prformac o isi pilo cabl circuis udr h prsc of iducd vola Y X Ch H S O L C Lai al. - Smicoducor lasrs: from homojucios o quaum dos P G Elisv Viw h aricl oli for updas ad hacms. his co was dowloadd from IP addrss o //8 a 9:8

2 MEACS5 IOP Publishi IOP Cof. Sris: Marials Scic ad Eiri (6) doi:.88/ x/// A mhod for calculai h produciviy of cabl commuicaios works S N Shuliki M S Shulikia S S Maryi D V Vioradova ad M E Zavorodyaya omsk Polychic Uivrsiy Lia av. omsk 65 Russia Gaprom rasa omsk 9 Fru av. omsk 69 Russia omsk Sa Uivrsiy 6 Lia av. omsk 65 Russia hupy@pu.ru Absrac. A probabilisic-mahmaical isrum was usd o dvlop a mhod for calculai h produciviy of a cabl li. h ffc of dviaio of facors from daa of rcordi dvics was drmid wh idifyi radom sram characrisics. h dvlopd mhod was usd o prform prdiciv calculaio of h produciviy of h modr cabl commuicaio li.. Iroducio O of h dcis visibl i h mos rc ad modr dvlopms of commuicaio works is a cha i rms of a rasmissio srucur. h raffic has bcom mulimdia-basd i lar works. hy ar characrid as works wih a o-uiform iformaio sram whr h mphasis has b shifd owards h us of various work applicaios. h icrasd cos of crai ad buildi h sysm islf cssias a improvm of h acual qualiy of h dsi soluios paricularly h accuracy of h chal hrouhpu drmii h auaio facor ad ohr produciviy characrisics [ ]. O of h possibl approachs o h simaio of hs ssial dsi idicaors is probabilisic modlli wih h sysms bi rprsd as a s of rsourcs usd o by o. h validiy of probabilisic modlli of rsuls usi h waii-li hory ad ohr mhods is hihly dpd o h coformiy of h modls uilisd o h ral sysms. Nwork quipm dsirs ad dvloprs d o ahr daa abou h bhaviour of works of various scals archicur ad cofiuraio as wll as abou hir qualiaiv characrisics. hrfor such modlli aids ar rquird o accou for all h spcific faurs of h work opraio bu also o allow dfii iiial iformaio ad lasly o obai rliabl work characrisics [].. h pricipl of commuicaio li produciviy modlli I ral cabl commuicaio sysms h kow ad im-ivaria paramrs ar hos ha characri srvic faciliis. h isiy of icomi/ouoi srams ypically varis ovr im ad hs variaios ar of radom aur. Howvr i is clar ha h cabl sysm opraio is dircly dpd o h isiy of icomi srams or calls: h hihr h isiy of icomi srams h havir h srvic mod which rquirs for isac cocio of addiioal srvic faciliis. I viw of his a impora ask is o sima h paramrs of v srams a a arbirary poi i im basd o obsrvaio of his sram. Co from his work may b usd udr h rms of h Craiv Commos Aribuio. licc. Ay furhr disribuio of his work mus maiai aribuio o h auhor(s) ad h il of h work joural ciaio ad DOI. Publishd udr licc by IOP Publishi Ld

3 MEACS5 IOP Publishi IOP Cof. Sris: Marials Scic ad Eiri (6) doi:.88/ x/// Basd o hir radomss h srams of vs wih im-dpd isiy ca b dividd io which is a coiuous radom wo yps. h firs o compriss h srams wih isiy ( ) procss. h scod yp icluds oly srams havi isiy ( ) as a picwis-cosa procss wih a fii umbr of sas ( ). h rasiio of procss ( ) from o sa o aohr occurs a radom pois i im wih h sram of vs bhavi as saioary isiy flow i duri hos im irvals wh procss ( ) is i sa i. Such srams ar h mos ypical for ral works. hs picwis-saioary srams of vs ca b dividd io hr caoris: ) sychroous wic sochasic srams of vs srams wih h isiy for which sa rasiio occurs oly a radom pois i im ha ar h moms of vs occurrc; ) asychroous wic sochasic srams of vs srams wih h isiy for which sa rasiio dos o dpd o h moms wh h vs occur; ) half-sychroous wic sochasic srams of vs srams whr for o s of sas i is ha is ru ad for h rs of h sas i is ha is ru. aki io accou all h abov-sad rquirms for h cosrucio of h modl his papr suss rsarchi h problm of simai h paramrs of asychroous srams of vs wih isiy ( ) bi a picwis-cosa Markovia procss ha aks wo valus{ } of h alrai sram of vs wih h vs bi parially obsrvabl. h parial obsrvabiliy is du o h formaio of a so-calld dad im schm implyi ha a v occurrc i h alrai sram is accompaid by a fid priod of im (a dad im priod) duri which o ohr vs ca b obsrvd. O of h major disori facors wh drmii h characrisics of radom srams is h dad im of rcordi dvics. Dad im i his rspc is h priod wh a rcordd v is bi procssd whil ay ohr v rd io h sysm ipu duri his priod is los. I viw of his h d o sima h paramrs (characrisics) of h ral sram of vs rcivd a h sysm ipu ariss. h amou ad h characr of dad im of crai dvics dpd o umrous facors. A a firs approimaio i ca b assumd ha his priod lass for crai (fid) im. All rcordi dvics wih a suffici dr of approimaio ca b sparad io wo roups. h firs roup compriss dvics wih o-di dad im which is idpd of h rcip of ohr vs i h ra of is acio. No-di dad im is somims calld firs us dad im ad corrspodi rcordi dvics ar calld cours or yp I rcordrs. Dvics wih di dad im (yp II rcordrs) blo o h scod roup. I his cas dad im mrs afr ay v obaid a h sysm ipu rardlss of i bi rcordd or o. I rms of daa rasmissio lis dad im ca b rprsd by disurbacs failurs i.. ay ffcs o h work opraio. Sic hs ffcs ar also of radom aur rcordrs of h II yp wih di dad im will b usd for his sudy. L us cosidr a saioary sram of vs wih isiy ha is obsrvd oly a crai im irvals ad has wo sas ad. If h corol procss is i sa h sram ca b obsrvd. Bu if i is i sa h sram cao b obsrvd. h lhs of saioary scios wihi h corol procss ar disribud accordi o poial law [5] F ( ) = p( ) or F ( ) = p( ) whr ad ar isiis of h corol procss rasiio from sa o sa ad vic vrsa rspcivly. hus h corol procss iducs a alrai sram of vs. h alrai sram of vs i is ur is also parially uobsrvd. Wh a v occurs i his sram hr coms a crai im of duraio (dad im) wihi which ohr vs cao b obsrvd. hrfor oly h alrai sram v ha coms afr h d of h las priod of o-obsrvabiliy will b obsrvd. h occurri siuaio is show i Fiur whr h hachi is h idicaio of dad im ad ar h corol procss sas; curr im ad { } moms of v occurrc i h sram udr obsrvaio.

4 Fiur. A schm of h alrai sram. h obsrvaios { } a h fial im irval ar rquird o cosruc h simaio of oriial sram isiy h simaio of isiis for h corol procss sa rasiio (i.. o cosruc simas of paramrs for h alrai sram of vs) as wll as h simaio of dad im duraio. Assumi ha { } is h im irval bw ihbouri vs i h sram udr obsrvaio four saisical simas - sampli moms - ca b cosrucd: = = i k i k C = k. hrafr h quaios for drmii paramrs simaios { } will b formulad as follows: ( ) k k M = C = k. By solvi h probabilisic modl si quaios ar obaid for drmii rasmissio paramrs simaios [6]: ( ) ( ) ( ) [ ] ( ) ( ) [ ] ( ) ( ) = M ) ( ( ) ( ) () ( ) ( ) [ ] = M ( ) ( ) ( ) [ ] () Oriial sram of vs Corol procss Alrai sram of vs Schm of dad im formaio Obsrvd sram of vs oal dad im MEACS5 IOP Publishi IOP Cof. Sris: Marials Scic ad Eiri (6) doi:.88/ x///

5 ( ) = 6 M ( ) [ ] 6 [ ] () ( ) = 5 5 M ( ) ( ) [ ] [ ] [ ] [ ] IV () ( ) = ( ) =. (5) h sysm of h quaios is drmid by formulas ( 5) which mak i possibl o sima h paramrs of sysm rasmissio a ay poi i im. his sysm coais si quaios cocri si ukows{ }. h obaid sysm has oly a umrical soluio. h adquacy of h proposd compuaioal mhod was vrifid wih a spcific daa rasmissio sysm of JSC RIC Russia-Ialia Compay of lpho Isallaio ha provids various commuicaio srvics o h ciy of Mhdurchsk Kmrovo rio such as: ciy lphoy wir commuicaios radio-accss a mulipurpos dupl pay lpho work Ir IPlphoy addiioal srvics basd o illcual works c.. Calculaio of daa rasmissio work produciviy h oriial sram for h JSC RIC daa rasmissio sysm was a asychroous sram of vs wih isiy ( ) a picwis-cosa procss wih parially obsrvabl vs. his sudy amis carfully a par of h sysm comprisi a daa sourc (a o-uiform sram of vs) commuaor swichs ad ha wr usd for masuri isiy ( ) ad various sis (rsidial-accommodaio spacs producio plas c.). h dpdcs wr masurd o a worki day duri pak im from o p.m. wh h maimum load i h daa rasmissio work ca b obsrvd. h saisical prim o simai h ukow paramrs of h obsrvd sram of vs was basd o simulaio modlli of h amid sram of vs wih paramrs { } a a fid irval of obsrvaios ( ) assumi ha a som poi i im a v occurs i h oriial sram. h saioariy priods wihi h corol procss wr rad accordi o h ask dfiiio. If h v occurrd a h im poi wh h corol procss was i sa ad h im poi fll io h o-obsrvabiliy priod h h v was o rcordd as a v of h sram udr obsrvaio. If h v occurrd afr h dad im was ovr h h v was MEACS5 IOP Publishi IOP Cof. Sris: Marials Scic ad Eiri (6) doi:.88/ x///

6 MEACS5 IOP Publishi IOP Cof. Sris: Marials Scic ad Eiri (6) doi:.88/ x/// rcordd as a v of h sram udr obsrvaio. h saisical prim o simai ukow paramrs { } for h iv ask cosisd i cosruci h simaios wih cofidc irvals ad looks as follows: ) h alrai sram modl wih dad im is implmd ad i forms sampl { } of obsrvaios wih radom valu (a im irval bw ihbouri vs i h sram udr obsrvaio); ) saisical simas С С С C ar accumulad; ) i ordr o drmi h simaios of alrai sram paramrs { } a sysm of quaios is formd usi formulas ( 5) wih his sysm of quaios bi solvd by a umrical mhod; ar drmid; ) simaios { } N N 5) avra valus of simaios = i ad disprsio D( ) = ( i ) ar N i= N i= formd which is followd by h calculaio of cofidc irvals basd upo h obaid saisical daa [6]; 6) work load facor ρ is calculad. A imiaio prim was coducd o drmi paramrs { } udr his procdur. abl summaris h isiy valus obaid hrouh calculai h alrai sram of vs i h schm wih di dad im for commuaor swichs ad. Nwork chals abl Isiis of daa rasmissio hrouh commuaor swichs ad. Commuaor swich Commuaor swich rasmid o h srvr Mbps Rcivd from h srvr Mbps rasmid o h srvr Mbps Rcivd from h srvr Mbps Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ h dvlopd modl adquacy is vrifid by formi cofidc irvals basd upo h obaid saisical daa. o his d l us calcula h avra of simaios ad disprsio. L us abula h obaid umrical disprsio daa for commuaor swichs ad i abl. hrfor h cofidc irval of daa umrical calculaio obaid from commuaor swich 5 is qual o whil ha obaid from commuaor swich is.6. h obaid valus of cofidc irvals mak i possibl o cofirm h adquacy of h cosrucd modl. 5

7 MEACS5 IOP Publishi IOP Cof. Sris: Marials Scic ad Eiri (6) doi:.88/ x/// abl h simaio of disprsio for commuaor swichs ad. Nwork chals Commuaor swich Commuaor swich icomi ouoi icomi ouoi Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Isiy simaio h sp was o drmi h load facor. Assumi ha maimum isiy ma of h amid li is Mbps h load facor i our cas is h raio bw h isiy obaid hrouh calculai h alrai sram of vs i h schm wih di dad im ad h maimum load facor: ρ = whr ' is h isiy obaid hrouh calculai h alrai sram of vs i h schm wih di dad im; ma is maimum isiy of iformaio sram rasmissio wihi h work. h obaid daa ar summarid i abl. Nwork chals ma abl h load facor for commuaor swichs ad. Commuaor swich Commuaor swich icomi ouoi icomi ouoi Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/ Gi/

8 MEACS5 IOP Publishi IOP Cof. Sris: Marials Scic ad Eiri (6) doi:.88/ x/// Havi calculad h li produciviy a prdiciv calculaio of his commuicaio li produciviy was prformd. o his d i was cssary o calcula h maimum daa rasmissio ra wihi h work so ha hr would b o ovrload of srvici faciliis o losss of rasmid ad rcivd daa calls as wll as o sur ha h srvic ad calls procssi im would o lad o srvr ovrload. I ohr words h formulad ask was rducd i ordr o fid a maimum accpabl work load facor followd by h calculaio of opimal isiy for his work. L us ak a maimum accpabl li load facor as ρ = Kowi h load facor h maimum possibl rasmissio ra qual o Gbps ad aki io accou h umbr of chals l us calcula h accpabl rasmissio ra for ach chal. By applyi h dvlopd probabilisic-mahmaical isrum i was foud ha cosidri h maimum accpabl load facor ad iori dad im h maimum ra is wihi h ra of Mbps. Howvr aki io accou dad im ad sad rquirms h daa rasmissio isiy wihi h work ca fall bw 9 ad Mbps.. Coclusio. I ordr o calcula h commuicaio work wih a o-uiform sram of iformaio w hav cosrucd a modl ha was usd as a basis for prformi h ask of simai a asychroous sram wih parially obsrvabl vs of various isiis which is a picwiscosa procss.. I has b sablishd ha o of h major disori facors wh drmii h characrisics of radom srams is h dad im of daa rcordi dvics. Upo h v occurrc i h sram hr coms a crai im of fid duraio wihi which ohr vs cao b obsrvd i.. dad im is h priod wh a rcordd v is bi procssd whil ay ohr v rd io h sysm ipu duri his priod is los.. h isiy obaid hrouh calculaio by a probabilisic-mahmaical mhod ad h daa rasmissio isiy i h amid ral commuicaio work is wo ims hihr ha h isi o i.. h commuicaio li is uloadd. his coclusio srvs as a rcommdaio o a possibl daa rasmissio ra icras ad hc h improvm of h commuicaio sysm produciviy as a whol. Rfrcs [] Shmalko A Commuicaio Bulli [] Spaov A 7 Archicur of compuaio sysms ad daa-procssi works (Moscow: Sroyida) p. 9 [] Grodv I ad Vrik S 988 Commuicaio lis Radio ad Commuicaio (Moscow) p 5 [] Kooov A 8 Sudy ad dvlopm of mhods for capaciy facors of compui machis works wih o-uiform raffic hsis for Cadida of Scics (Orbur) p. [5] Vsl E 969 h hory of probabiliy (Moscow: Nauka) p [6] Zavorodyaya M Esimaio of dad im duraio ad paramrs of alrai sram of vs hsis for Cadida of Scics (omsk) p. 7