ICN 00 Prorty Queung wth Fnte Buffer Sze and Randomzed Push-out Mechansm Vladmr Zaborovsy, Oleg Zayats, Vladmr Muluha Polytechncal Unversty, Sant-Petersburg, Russa Arl 4, 00
Content I. Introducton II. III. IV. Comuter Networ as the Prorty Queung: Throughut vs. Delay Factors Mathematcal And Structural Model of the Comuter Networ as the Prorty Queung Results of Model-based Analyss and Future Develoment V. Concluson
I. Performance Measure Characterstcs at Dfferent Layers From the very begnnng the usage of the mechansm of statstcal multlexng has rovded success to the Internet roect. Router load, Pacet loss rate, etc. Performance means: bts er second destnaton τ Traffc Fnte buffer source Prorty acets Bacground traffc Internetworng characterstcs Performance means: Throughut, Delay ( τ) Quantty of the connected users, Communcaton channels load level Performance means: number of users, alcatons and etc. 3
II. Networ Performance : Influence Factors Networ structure Networ envronment factors that reduce traffc erformance: Informaton system Alcaton secfc control congeston rocessng and queung delays Logcal structure TCP connectons Payload ACK Dynamc system n stochastc envronment Inut λ networ connectons outut IP acets Stochastc system and envronment N acets Physcal sgnal Physcal bnary sgnals Electromagnetc nose level level 0 acet loss buffer overflow Vrtual channel erformance factors :. Number of delvered acets er sec. Source-destnaton acets delvery delay 4
II. Vrtual Channel Performance: Throughut and Pacet Delay Asects Source Destnaton Pacets n vrtual channel Increase throughut - ncrease number of acets n vrtual transort channel N Pacets n heavy loaded channel Lttle s law N = λ T. By ncreasng average number of acets (N) and eeng arrval rate (λ), bandwdth and erformance of acet swtchers - we ncrease average tme acet sends n vrtual channel ( T), where t s erformance measure tme, t/ T>> Challenge : Tradeoff between Throughut (N/ t) and acet delay factor ( T). 5
III. The Sace Exerment "Contour Aboard ISS λ λ µ ρ = 0, ρ =, 6
III. Smle Model of Telematcs Devce n Comuter Networ Source Source Vdeo stream Comuter Networ Destnaton Destnaton λ λ acet fnte buffer µ Control acets α Pacet loss α For ρ =λ /µ=0. and ρ =λ /µ=. : P loss <0,0, P loss <0, : 0,695<α<0,787 - reemtve rorty 0,884<α<0,886 non-reemtve rorty 7
III. Formal Model of Telematcs Devce Extended Kendal s classfcaton: M M // / / f M M Exonental dstrbuted arrval tme of two customers tye Exonental servce tme dstrbuton α One server Fnte buffer sze f ab a rorty tye ( - reemtve rorty) b ush-out mechansm ( - randomzed) 8
III. Proosed Model Use Condtons P loss λ λ >,5 µ ~lnear λ λ < µ ~lnear 0 M / M // / f M M / M?// / f / M // f α=0 analytcal soluton 0<α< µ < λ λ <,5 µ α / α= analytcal soluton 9
III. System M /M///f State Grah Number of non-rorty acets n buffer Number of rorty acets n buffer. The number of rortes determnes the matrx dmenson (rorty tyes number). The buffer sze s the matrx sze 3. The randomzed ush-out mechansm determnes the robablty of a relacement mechansm α Numercal soluton comlexty ~ rorty tyes number Trangular matrx x wth ()/ entres Prevent from gettng analytcal soluton 0
III. Analytcal Calculatons ), (, ) ( ] ) [( ) (,, 0 = = = ρ α ξ ξ ρ α ζ ρ ρ ), 0, ; 0, ( 0, )] ( ) ( ) ( ) ( [,,,,,,0,,0,0,,,, = = = αλ δ λ λ µδ µ δ δ µ δ λ δ δ αλ δ λ System of ()/ lnear equatons System of lnear equatons Usng the method of generatng functons and some arorstc data about our system we can receve the dstrbuton of the generatng functon and calculate the characterstcs of the ntal system.
IV. Comarson of the P loss Grahs Wth Nonreemtve Prorty Queung ρ = 0, ρ =, Grahs are close to lnear curves α stronger nfluences the grahs, than rorty tye ρ =, ρ = 0, Grahs aren t lnear curves The rorty tye doesn t nfluence the grahs P loss vary from 0,03 to,83*0- P loss ncreased for % from 0, to 0,
IV. Results : Relatve Throughut of the Traffc ӕ ab = ӕ a / ӕ b = ( P (a) loss ) / ( P(b) loss ) Low loaded networ (ρ =0,5) Heavy loaded networ (ρ =,5) Monotonous curves In low loaded networ curves are close to lnear ρ =0, ρ =0,5 3 ρ =,0 4 ρ =,3 5 ρ =,5 6 ρ =,7 7 ρ =,9 8 ρ =,5 Curves wth extremums There s otmum value of a when non-rorty traffc has the lowest loss rate 3
IV. Results : The Tme That Pacets Send n Queung ( ) s n queue θ = = ρ, =, ( =,). ( ) τ τ ( Ploss ) λ Prorty acets Non-rorty acets The relatve tme that acets send n queung does not exceed some value For low loaded networs t s close to zero ρ =0, ρ =0,5 3 ρ =,0 4 ρ =,3 5 ρ =,5 6 ρ =,7 7 ρ =,9 8 ρ =,5 The relatve tme that acets send n queung fast grows wth loadng growth In heavy loaded networs t can be used to bloc undesrable or suscous traffc 4
IV. Future Develoment. Telematcs devce 3D sace 4. Practcal ntroducton. Influence of the sze of the buffer on the system s characterstcs and traffc locng 3. Herarchcal rorty 5
V. Concluson Offered comutng algorthm allows networ engneers and desgners to estmate ossble varants of networ traffc load. In overload networs, then λ λ >µ, the deendence of loss rorty from varable s not lnear and even not monotonous functon. One of the real ractcal alcaton for our model s sace exerment Contour. Proosed ossble ways to mrove model are: Varable buffer sze ; More comlex, herarchcal rorty. 6
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