Providing Real-Time Guarantees

Transcription

1 ntegrate Servces: ntegraton of varety of servces wth fferent requrements (real-tme an non-real-tme) Traffc (worloa) characterzaton Scheulng mechansms Amsson control / Access control (polcng) Determnstc vs. stochastc analyss Traffc characterzaton Performance guarantees Provng Real-Tme Guarantees sener applcaton recever applcaton networ servce traffc specfcaton pacet szes pacet nter-arrval tmes general traffc escrptors performance requrements elay tter banwth pacet loss As long as the traffc generate by the sener oes not excee the specfe bouns, the networ servce wll guarantee the requre performance.

2 Real-Tme Guarantees: Mechansms sener applcaton recever applcaton networ servce Enforcement: polcng traffc shapng rgorous (an robust) elay computaton etermnstc pacet scheulng n swtches an routers real-tme-connecton establshment connecton-orente servce Traffc Descrpton: Traffc Bounng Functons rate [b/sec] a(t) A(t) t Arrval as stochastc process A = {A(t), t 0} A an a are poor traffc escrptors: tme epenent Determnstc traffc arrval escrptors (tme-nepenent) Maxmum Traffc Functon b() max t>0 {A(t+) A(t)} Maxmum Rate Functon b()/ max t>0 {A(t+) A(t)}/ 2

3 Maxmum Traffc Functons b()/ Pea Rate Max. Data Rate [Mb/sec] observe max. rate functon b()/ b ( ) / = max ( A( t + ) A( t )) / t 0 Average Rate ,000 0,000 00,000 Tme nterval [msec] Traffc Bounng Functons b()/ 40 Pea Rate Pea-Rate Max. Data Rate [Mb/sec] observe max. rate functon b()/ Average Rate 0 00,000 0,000 00,000 Tme nterval [msec] Leay Bucet Par 3

4 Maxmum Rate vs. Maxmum Traffc Functons Maxmum Rate Representaton b()/ b() Maxmum Traffc Representaton b()/ b() 2 2 Determnstc:. Peroc moel: (e, p) Traffc Moels 2. Deferre Server, Sporac Server moel: (e S, p S ) 3. (σ, ρ) moel [Cruz] 4. Leay bucet moel [Turner,...]: (β, ρ) 5. (x mn, x ave,, s max ) moel [Ferrar & Verma] 6. D-BND moel (Determnstc Bounng nterval Length Depenent) [Knghtly & Zhang] 7. Γ-functons [Zhao] Probablstc:. S-BND moel (Stochastc Bounng nterval) [Knghtly] 2. Marov-Moulate Posson Processes 4

5 Traffc Bounng Functon b(.) Let b(.) be a monotoncally ncreasng functon. b(.) s a etermnstc traffc constrant functon of a connecton f urng any nterval of length, the number of bts arrvng urng the nterval s no greater than b(). Let A[t,t2] be the number of pacets arrvng urng nterval [t,t2]. Then, b(.) s a traffc constrant functon f Each moel efnes nherently a traffc constrant functon. The accuracy of moels can be compare by comparng ther constrant functons. Cruz (σ, ρ) Moel f the traffc s fe to a server that wors at rate ρ whle there s wor to be one, the sze of the baclog wll never be larger than σ. OW: The number of obs/cells release urng any nterval oes not excee ρ+σ. Graphcal representaton: worst case number b(.) of obs/cells release σ ρ 5

6 The Leay Bucet Moel ata ρ β mplementaton: Mantan counter for each traffc stream. ncrement counter at rate ρ, to maxmum of β. Each tme a pacet s offere, the counter s chece to be > 0. f so, ecrement counter an forwar pacet; otherwse rop pacet. worst case number of obs/cells release β ρ Concatenatng Leay Bucets What about lmtng the maxmum cell rate? β β 2 = ρ ρ 2 ata worst case number of obs/cells release ρ 2 β ρ β 2 x 6

7 (x mn, x ave, ave, s max ) moel [Ferrar & Verma] x mn : mnmum pacet nterarrval tme x ave : average pacet nterarrval tme ave : averagng nterval length s max : maxmum pacet length t mo ave ave b( xmn, xave, ave, smax)( ) mn, = + s x x mn ave ave max worst case number of obs/cells release /x ave /x mn ave D-BND [Knghtly & Zhang] Other moels o not accurately escrbe burstness. Rate-nterval representaton: bounng rate [Mbps].6 avertsements lecture long-term average rate nterval length [sec] Moel traffc by multple rate-nterval pars: (R, ), where rate R s the worst-case rate over every nterval of length. 7

8 D-BND (2) Constrant functon for D-BND moel wth P rate-nterval pars: R R b t = ( ) ( t ) + R, t b(0) = 0 b( t) = b( t t / ) for t > P P Comparson: x mn,... (σ, ρ) maxmum bts D-BND nterval length Polcng for the D-BND Moel Lemma: f b(t) s pece-wse lnear concave, then R s strctly ecreasng wth ncreasng. Lemma: f a pece-wse lnear constrant functon b(t) wth P lnear segments s concave, then the source may be fully polce wth a cascae of P leay bucets. concave hull ln rate 8

9 Delay Computaton: Overvew Delay computaton for FFO server wth etermnstcally constrant nput traffc: = max b ( ) R / R FFO 0 > R b ()+b 2 () b 2 () b () En-to-En Analyss F X () F Y () X Y Traffc regulaton: reshape traffc to ahere to traffc functon. Alternatve: re-characterze by accountng for burstness ae by queueng elays where Y s elay on Server Y. Determnstc Case: F Y () = F X (+ Y ) 9

10 Swtch Scheulng Wor-conservng (greey) vs. non-wor-conservng (non-greey) mechansms. Rate-allocatng scplnes: Allow pacets to be serve at hgher rates than the guarantee rate. Rate-controlle scplnes: Ensures each connecton the guarantee rate, but oes not allow pacets to be serve above guarantee rate. Prorty-base scheulng: far queung vrtual cloc earlest ue ate (EDD) rate-controlle statc prorty (RCSP) Weghte Roun-Robn scheulng: WRR Bt-by-Bt Weghte Roun-Robn bt-by-bt roun robn each connecton s gven a weght each queue serve n FFO orer w 0

11 Far Queueng [Demers, Keshav, Shener] Emulate Bt-by-Bt Roun Robn by prortzng pacets. Prortze pacets on bass of ther fnsh tme f : a : arrval tme of -th pacet e : length of pacet f : fnsh tme BW: allocate fracton of ln banwth f Example: = max( f, a ) + e / BW Complcatons: 4.5 What f connectons ynamcally change? Vrtual Cloc Algorthm [L.Zhang] Emulate tme-vson multplex (TDM) mechansm However: TDM: when some connectons le, the slots assgne are le VC: le slots are elete from TDM frames auxlary vrtual cloc (auxvc ): fnsh tme of -th pacet. vrtual tc (Vtc ) :tme to complete transmsson of reay -th pacet. Vtc = e /BW Replace f by Vtc : VC becomes entcal to WFQ algorthm! Wll analyze elay analyss later.

12 Rate-Controlle Statc Prorty (RCSP) [Zhang&Ferrar] prorty queues RCSP (2) rate controller prorty queues 2

13 Traffc Regulaton n RCSP rate controller prorty queues Hol pacets n regulator to guarantee mnmum nter-pacet arrval tme. r, = max(a,, r,- +p ) mplementaton: buffer an tmers n traffc regulator. Buffer requrements: B = ( ) + p p e s t Necessary to Regulate? [Lebeherr, Wrege, Ferrar, Transactons on Networng, 995] Generalzaton of scheulablty for arbtrary traffc constrant functons b(): Theorem: A set N of connectons that s gven by {b, } s scheulable accorng to a statc-prorty algorthm f an only f for all prortes p, an for all >= 0 there s a t wth t <= p - s p mn such that: p mn mn, t p s p : + t b ( ) s + p b (( + t ) ) + max sr r > p C p q = C q max { } 3

14 Earlest Due Date (EDD) [Ferrar] base on EDF elay-edd vs. tter-edd wors for peroc message moels (sngle pacet n pero): (p,, D) partton en-to-en ealne D nto local ealnes D, urng connecton establshment proceure. 2-Phase establshment proceure: Phase : tentatve establshment Sener OK? Recever Phase 2: relaxaton Sener Fne! Recever Delay EDD Upon arrval of Pacet of Connecton : Determne effectve arrval tme: a e, = max(ae,- + p, a, ) Stamp pacet wth local ealne:, = a e, + D, Process pacets n EDF orer. Delay EDD s greey. Can be mappe nto specal case of Sporac Server. Acceptance test (Δ = total ensty): Δ + /p < - /p mn Offere local ealne: LD = mn(p, /(-Δ-/p mn )) Problem wth EDD: tter max en-to-en elay over swtches: mn en-to-en elay over swtches: D, 4

15 Jtter EDD Problem wth Delay-EDD: oes not control tter. Ths has effect on buffer requrements. Jtter-EDD mantans Ahea Tme ah,, whch s the fference between local relatve ealne D,- an actual elay at Swtch -. Ahea tme s store n pacet heaer (alternatvely, we use global tme synchronzaton) Upon recevng the -th pacet of Connecton wth ah, at tme a, : Calculate reay tme as Swtch : a e,=max(a e,- + p, a, ) r, = max(a e,, a, + ah, ) Stamp pacet wth ealne, =r, +D, an process accorng to EDF startng from reay tme r,. Result: Regenerate traffc at each swtch. Rate Control Rate Control vs. Jtter Control Jtter Control 5

16 6 Smple EDF wth Arbtrary Arrval Functons [Lebeherr, Wrege, Ferrar: Transactons on Networng, 995] Theorem: A set Π of connectons that s gven by {b ; } επ an whenever < s EDF scheulable f an only f for all : where nformal proof : A ealne volaton occurs at tme f the maxmum traffc arrvals wth ealne before or at tme,.e. excees. { } Π > + s b max,max ) ( { } { }, for s Π > > max 0 max max, Π < b ) ( For some traffc moels, close-form expressons for the scheulablty test exst. For (σ, ρ) traffc: A close form for the elay can be gven as follows: EDF Test for Specal Cases: Example (σ,ρ) { } + Π < < + + Π Π = + > = s for ) ( : for max ) ( max ρ σ ρ σ { } = = > + + = max max ) ( s ρ ρ σ σ

17 Weghte Roun Robn (WRR) w Each connecton s assgne a weght w,.e., t s allocate w slots urng each roun. Slot: tme to transmt maxmum-sze pacet. Traffc moel: peroc (p, e, D ) varable bt rate moels possble Realzatons: greey WRR Stop-an-Go (SG) Herarchcal Roun Robn (HRR) Throughput an Delay Guarantees Each connecton s guarantee w slots n each rouns. Roun length RL : upper boun on sum of weghts (esgn parameter) w RL Constrants: Delays:. 2. RL p mn e w p RL e at frst swtch: RL w ownstream: once pacet passes frst swtch, t s mmeately elgble on swtches ownstream -> has to wat at most RL => en-to-en elay through N swtches: W ( e w + N ) RL p + ( N RL ) 7

18 Problems wth Greey WRR Greey WRR oes not control tter: Frst Swtch mn en-to-en elay: e +(N-) max en-to-en elay: p +(N-)RL tter: p -e +(N-)(RL-) Buffer neee at -th swtch for Connecton : ( + ( )( RL ) / p ) e Nee traffc shapng at each swtch. Non-Greey WRR Actual length of rouns n greey WRR vares wth amount of traffc at swtch. Non-greey WRR schemes fx roun length nto fxe-length frames. Stop-an-Go [Golestan] Herarchcal Roun Robn [Kalmane, K., K.] 8

19 Stop & Go [Golestan, 990] Frame-base: ve tme n frames of length RL. Pacet arrvng urng frame at nput ln s elgble for transmsson urng next frame on output ln. nput frames output frames nput frames Stop-an-Go s not wor-conservng. Traffc moel [(r, RL) smooth traffc]: urng each frame of length RL, the total number of bts transmtte by source oes not excee rrl bts. Proposton: f the connecton satsfes (r,rl) smoothness at the nput of the frst server, an each server ensures that pacets wll always go out on the next epartng frame, the connecton wll satsfy (r,rl) smoothness at each server throughout the networ. Stop & Go: mplementaton mplementaton of scheuler s not efne by Stop-an-Go framewors. mplementaton : FFO scheuler wth ouble-queue structure mplementaton 2: 9

20 Mult-Frame Stop-an-Go [For example, Zhang&Knghtly: Comparson of RCSP an SG, ACM Multmea, 4(6) 996] Problem wth Stop-an-Go (or any other frame-base approach): elaybanwth couplng Delay of pacet s boune by a multple of frame tme. Ths s a problem, for example for low-banwth, low-elay connectons. (Why?) Soluton: Use mult-level framng. Example: RL 2 RL Herarchcal framng wth n levels wth frame szes RL,..., RL n, where RL m+ =K m RL m for m =,..., n-. Stop-an-Go rule for pacets of level-p connecton: Pacets that arrve urng a RL p frame wll not become elgble untl the start of the next RL p frame. Pacets wth smaller frame sze have hgher prorty (non-preemptvely) over pacets wth larger frame sze. Herarchcal Roun Robn [Kalmane, Kanaa, Keshav, 990] En-to-en elay an tter of S&G epens on RL only. How about havng multple S&G servers, wth fferent RL s, an multplex them on the same outgong ln? Server X w RL x sw x Server S Server X s seen as peroc stream of requests by Server S, wth e x = sw x, p x = RL x, D x = RL x scheule usng rate-monotonc scheuler Confguraton tme test: chec whether tas set {(sw x,rl x,rl x )} s scheulable. Amsson Control Test: Banwth test: chec sum of requre w s <= sw x Delay test: En-to-en elay: p + N RL x Jtter test: 2 RL x, wth buffer requrement 2 w 20