Modeling of Wireless Networks as Queuing System

Transcription

1 Procng of h Wor Congr on Engnrng an Comr Scnc 3 Vo II WCECS Ocor 3 San rancco USA Mong of Wr Nwor a Qng Sm L.Mrhava Mmr IAENG G. Ggnahv M. Kna Arac Th ar rn h of ca Erang ron mo n wr nwor an mo comng. W monra ha h Erang fam rov mor f n mong ha onna fam whch on ha on aramr. In racca aon h Erang fam rov mor f n fng a ron o ra aa ha h onna fam rov. Th Erang ron ao f n qng ana ca of raonh o h onna ron. To monra h aca of h Erang ron w conr qng mo rrn a wr chann whr h nrarrva m wn far hav h Erang Dron. In Trm Erang ron nrarrva m wn far roac aroach qng mo. I. INTRODUCTION An accra maon of nwor rformanc va for h cc of a nwor of an n. Nwor whhr voc or aa ar gn aron man ffrn vara. Two of h mo moran facor ha o n o conr n nwor gn ar rvc an co. Srvc na for mananng comr afacon. Co awa a facor n mananng rofa. On wa ha o can facor n om of h rvc an co mn n nwor gn o om crc aon. Ao o a arg n h cc of a nwor n on h vomn of ffcv congon conro chnq ha aow for oma aon of a nwor' caac. Prformanc mong ncar for cng h of congon conro oc o mmn. Prformanc mo n rn rqr vr accra raffc mo ha hav h a o car h aca characrc of h aca raffc on h nwor. Th gn of ro an ra nwor an nwor rvc comng ncrang ffc n oa' wor. Th on ah o achv h goa o vo a a nranng of h raffc characrc of h nwor. Managng rformanc of nwor nvov omng h wa nwor fncon n an ffor o mam caac Mancr rcv Ma 6 3 rv Jn 4 3. Th wor wa or n ar Ivan Javahhv T Sa Unvr Goc LLC an Gorgan Tchnca Unvr. L. G. Mrhava wh h Comr Scnc Darmn Ivan Javahhv T Sa Unvr Aoca rofor Inrm Char of Tchnca Informac. Snor Engnr Cor Nwor Oraon Goc LLC. Mmr IAENG. Mmr IEEE. Mmr UK Soc for Mong an Smaon. hon: ma: a.mrhava@.g. G. N. Ggnahv wh h Comr Scnc Darmn Ivan Javahhv T Sa Unvr Inv Lcrr hon: ma: g.ggnahv@gma.com. M. G. Kna wh h Comr Engnrng Darmn Aoca rofor hon: ma: m.na@g.g ISN: ISSN: Prn ISSN: Onn mnm anc an offr hgh ra rgar of anwh avaa an occrrnc of far. Nwor rformanc managmn con of a marng mong annng an omng nwor o nr ha h carr raffc wh h caac an ra ha c h acaon ng h nwor or rqr n a arcar cnaro. Nwor ar of ffrn an can cagor a on vra facor. Howvr h facor ha affc h rformanc of h ffrn nwor ar mor or h am. If h nrng raffc mo o no ffcn car h characrc of h aca raffc h r ma h nr-maon or ovr-maon of h rformanc of h nwor. Th wo oa mar h gn of h nwor. Traffc Mo ar hnc a cor comonn of an h rformanc vaaon of nwor an h n o vr accra. Dnng on h of nwor an h characrc of h raffc on h nwor a raffc mo can chon for mong h raffc. II. TRAIC MODELS AND ERLANG DISTRIUTION Sca Erang Dron n f w o mong ac nrarrva m for a nmr of raon. Th fr h fac ha Th Erang ron a conno roa ron wh w aca rmar o raon o h onna an Gamma ron. Th onna fncon a rc crang fncon of. Th man ha afr an arrva ha occrr h amon of wang m n h n arrva mor o ma han arg. To gn mong w fn Т a f ngh of ac. Sm raffc con of ng arrva of cr n ac. Th n of raffc can r mahmaca a a Pon Proc. Pon roc can cr a a Conng Proc or Inr-Arrva Tm IAT Proc. W ao am ha T h ngh of h mag n h nmr of ac n h mag w fn o a nmr of ha n h Erang ron of far.. hr h chm of far arrva accorng o whch h far m go hrogh ha ag for h aca w arrv Dron fncon D of ac ngh wh a ccc chc rnanc CRC whr n fncon an =Т/n oc ngh r- h nmr of aow ron of ranmng a oc G- Dron fncon of rcovr m - h ron nn of ach ha.. h raon of m nrva wn qn momn of occrrnc of far foow h Erang Dron gvn : A! WCECS 3

2 Procng of h Wor Congr on Engnrng an Comr Scnc 3 Vo II WCECS Ocor 3 San rancco USA Or a o fn Dron ncon of ranfr m of f ngh mag nng on nmr of h ac nc n an nmr of hr rranmon for a gvn nwor characrc. r n.4. r n G.4.3 W no Ф T h roa ha h mag ranfr of f ngh of T conng of n ac ach of ngh of arng from -h oc w com n a m han nr h conon ha: a h = momn aa chann DCH n K ha accorng o far an -h ar [ б ] of -h oc ha n ranfrr who oron An am wa ma o ranfr h -h oc who oron m. fnon: T T nr = nr > r n W no ФT h D of h roa of ranfr ~ m of f ngh mag T=n б an Df of ranom ngh mag hn w hav h foowng noaon: ~ whr r D o ranfr m of f ngh mag of Th mo mnon aov can cr h foowng m of qaon: T.4. n r = ISN: ISSN: Prn ISSN: Onn / whr - -fo convoon an T L am Ф Ф > r n Th onar conon hav h form: n n r Z n Ingrang h roc of h roa of vn accorng o an mmng h roa of ncoma vn w oan.4.. Ung h Laac Tranform n.4. w oan: WCECS 3

3 = б -= =. Z Z Dnong : W oan: K or.4.4 Movng on o ffrna qaon..4 w oan:.4.5 n r - monoonc an conno fncon accorng o n h rang nr W a h Laac ranform o.4.. or h ro fr of a = =. W rwr.4. a foow: ] [ an changng h orr of ngraon n h con mmr w g: Ang h Laac-S w g: If w no: Th w hav: [ w w w C C ].4.7 whr C h aca of convrgnc of h mror ngra whch n h oman of anac of nr h ngra gn fncon or w c c w w W w c c W W w.4.8 Procng of h Wor Congr on Engnrng an Comr Scnc 3 Vo II WCECS Ocor 3 San rancco USA ISN: ISSN: Prn ISSN: Onn WCECS 3

4 Procng of h Wor Congr on Engnrng an Comr Scnc 3 Vo II WCECS Ocor 3 San rancco USA Ang h Laac-S o..3 w oan: r.4.9 g n.4.8 an.4.9 conn [-rr] =r - qaon a nmr of nnown qa o r ~ Ф [ n ]. h mho of con w caca.4.8: w w / w w w whr / w w.4. w / -h ro of h qaon. w а W =- To mf frhr cacaon w nroc a nw vara = - -m rmanng h n of h oc ranfr. ng nw vara mnon aov n h qaon an.4. hn h hav h foowng form ang no accon ha: ~ W hav: ~ ~ ~ ~ Ф. ~ Ф..4. w w / w w / w w w ~ r.4. g.4.3 Ang h Laac ranform of h argmn rcv oraor к и.4.3 w oan: ~ ~.4.4 r n ~ = / w w w w w w w.4.4 r w / w ~ r / g n Hr ~ ~ ~ ~ ~ ~ ~.4.6 ISN: ISSN: Prn ISSN: Onn WCECS 3

5 Procng of h Wor Congr on Engnrng an Comr Scnc 3 Vo II WCECS Ocor 3 San rancco USA A a r of oon of agrac qaon an ang no accon.4.7 w fn ~ n r. Dfnng h rvr convron ~ an afr ng n = = w rmn h va of Ф. L ov h qaon.4.4 ccv on arng from =- =-... -m= m=- hn w hav:.4.8 L caca h foowng qaon an.4.8 w gv an am for h whr = r= n= = Ф =. ~ ~ S. S S n accoranc wh.4.8 ~ g ~ w w w w w w w w w w w w w w w w c c S ~ ~ c S S = w w w w w Smar o: A T D T A T E T S A T T S Conona man qa o: ' S S S Sovng h r of h qaon w fna oan: M Ф S K S Ф S K [gm] S K Ф S { - S S [gm]fm} K Ф S [fm] S ' = SФ S =M S ' = Ф - [- S S S fm]fm ' = SФ S =- [-]- S {[ в ]- - f}m[f]m ' = SФ S =- - fm S fm где а=/ - б[/ - б- = б с=/- - б[/ - б- б = - б- б =/[- - б] f=- - б = - б M=[ - бас]/[- - бg f] III. CONCLUSION In h ar w nvga qng mo rrn a wr m whr m nrva wn far ar Erang r. W rn om avanag of h Erang mo w roo for mo mong. W how h gnra of ch mo whch can o mo no on nrarrava m wn nghorng far ao ohr m vara n wr nwor an mo comng m. ISN: ISSN: Prn ISSN: Onn WCECS 3

6 Procng of h Wor Congr on Engnrng an Comr Scnc 3 Vo II WCECS Ocor 3 San rancco USA REERENCES [] La Mrhava Mahmaca Mo of Prcon of Ra of Wr Commncaon Nwor. Camrg Un Kngom - Ar 3. UKSm-AMSS 5 h Inrnaona Confrnc on Comr Mong an Smaon. IEEE ranacon [] W. Jon an D. Jong. Ca amon conro for cma mo commncaon m orng mma rvc. IEEE Tran. on Wr Commncaon 4: [3] J. I. Sanch. rco an J. Joron. Inr-arrva m ron for chann arrva n car hon. In Procng of h 5h In. Worho on Mo Mma Comm. MoMc 98. Ocor -3 rn Grman Khan LTE for 4G Mo roaan: Ar Inrfac Tchnoog an Prformanc Camrg Unvr Pr Nw Yor 9. [4] S. Parva E. Dahman J. Sö an P. mng 3G Evoon: HSPA an LTE for Mo roaan Evr Phr Scon Eon 8. [5] J. C. Ino M. Wrch an M. R TCP Prformanc an mong of LTE H-ARQ n rocng of h Inrnaona ITG Worho on Smar Annna WSA 9 rn Grman 9. [6]. Ln S. Mohan an A. Nor Qng ror chann agnmn rag for hanoff an na acc for a PCS nwor IEEE Tranacon on Vhcar Tchnoog [7] Y. ang an I. Chamac Traffc ana an mo mong for PCS nwor IEEE Tranacon on Commncaon 477 J [8] R. E. Ha an C. T. Ca Trann gna roagaon n o oroc ama Ror USA Camrg R. La. Camrg MA R. ARCRL II 994 vo.. [9] G. ogga P. Camara an N. D ono. Traffc ana of hrarchca car commncaon nwor. IEEE Tran. Vh. Tchnoog 54: [] Sama haachara Har Mohan Ga an Sra Kar. Traffc mo an rformanc ana of car mo m for gnra r hanoff raffc an namc chann aocaon. IEEE Tran. Vh. Tchnoog 576: [] Y. Iraq an R. oaa. Hanoff an ca rong roa n wr car nwor. In Procng of Inrnaona Confrnc on Wr Nwor Commncaon an Mo Comng WIRELESSCOM 5 ag 9 3 Ma Hawa USA Jn 5. [] D. Macman. Traffc mong an ana for car mo nwor. In Procng of 3h ITC 9 ag ISN: ISSN: Prn ISSN: Onn WCECS 3