ΗΥ537: Έλεγχος Πόρων και Επίδοση σε Ευρυζωνικά Δίκτυα,

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1 ΗΥ537: Έλεγχος Πόρων και Επίδοση σε Ευρυζωνικά Δίκτυα Βασίλειος Σύρης Τμήμα Επιστήμης Υπολογιστών Πανεπιστήμιο Κρήτης Εαρινό εξάμηνο 2008 Contents Effectve Bandwdths and Chargng of VBR servces Tme- and Volume-based Chargng of VBR servces Smple Chargng Scheme Propertes and Incentves Examples Smplfcatons CBR Chargng Guaranteed Servces- 2

2 Outlne of the VBR-Chargng Approach Total charge for a call s a( )T+b( )V+c( ) where T = duraton of call (e.g. seconds) V = volume of call (e.g. Mbts or Mcells) a( ), b( ), c( ) capture QoS, UNI choces (peak rate, etc), user s choce of tarff User-network contract: QoS requested User traffc parameters User choce of tarff User ATM traffc Call-Acceptance Control Calculaton of actual charge Accountng nformaton Guaranteed Servces- 3 Effectve Bandwdths Remnder k traffc classes class contrbutes n sources n n k... B: buffer C: capacty Whch do not volate QoS constrant (e.g. CLP < e - γ ( n,, nk ) )? K Acceptance Regon: lnear constrants of the form n α + K+ n α C k k * where [ ] sx t α j st (,) logee j [, ] = 0 st Guaranteed Servces- 4 2

3 Effectve Bandwdth Formula Effectve bandwdth of a source of type j [ ] sx t α j st = 0 (,) logee j [, ] st X j [0,t]: load produced by source of type j n wndow t The effectve bandwdth α j (s,t) quantfes resource usage for a partcular operatng pont (s,t) Effectve bandwdth for connecton k of type j can be computed usng emprcal estmate T / t k sx [( ) t, t ] jk αˆ = jk ( s, t) log e st T k = Tk: duraton of connecton k t: nterval length Guaranteed Servces- 5 Economc theory remnder Socal welfare maxmsaton: max U ( n) n st.. n A A n α + K+ n α C n * k k * Prces defned by shadow costs of effectve bandwdth constrants p eb = p j eb j Prcng n proporton to effectve bandwdths: captures QoS requrements ncentve compatble content ndependent well understood theory IS IT OBVIOUS? Guaranteed Servces- 6 3

4 The slow ON/OFF Source Model At an nterval of duraton t << Ton, : Toff ether OFF: X=0 (wth probablty -p) or ON: X=ht (wth probablty p) on h off m h mean rate m = p*h effectve bandwdth t α on/ off sth ( e ) m ( s, t) = log + st h ON/OFF has the largest possble effectve bandwdth (over all traffc models) for gven m and h and operatng pont Guaranteed Servces- 7 Chargng VBR Servces - Idea Apply CAC wth effectve bandwdths and Charge (per unt tme) each VBR call proportonally to effectve bandwdth Pro: Theoretcally justfable and far Con: Requres accurate a pror knowledge of complex traffc statstcs If emprcal estmate from samplng prevous calls s used, users have the wrong ncentve to reach ths value user wll tend to overload the network => smlar to overeatng n allyou-can-eat restaurants Guaranteed Servces- 8 4

5 Chargng VBR Servces - Idea 2 Use traffc contracts specfyng: peak rate α worst sustanable cell rate, max burst sze Apply CAC wth the worst-case effectve bandwdths for contracts and Charge each VBR call proportonally to worst-case effectve bandwdth ( SCR, MBS, h) curve for fxed h, MBS SCR Pro: No complcated traffc statstcs Cons: Unfar to users wth mean rate < SCR, or peak rate < h Provdes the wrong ncentve to ncrease traffc Guaranteed Servces- 9 Dscusson Prevous approaches only based on statc a pror varables, determned by traffc contract Provded wrong ncentves to exhaust the resource usage permssble by contract Chargng should also employ dynamc a posteror varables, measured durng call Guaranteed Servces- 0 5

6 Chargng VBR Servces - Idea 3 Measure the effectve bandwdth durng each VBR call, and charge proportonally to t Pro: Provdes the rght ncentves Con: Incompatble wth statc CAC If eb estmated emprcally, dffcult for users to understand charges users may possbly not pay for all the resources reserved by CAC e.g. a user wth no traffc, would face 0 charge Guaranteed Servces- What s Needed? Charge accordng to both: statc varables reflectng traffc contract and resources reserved by CAC dynamc varables reflectng actual usage Fnal charge should be close to actual effectve bandwdth Allow the user to select a tarff: selecton should reveal some mportant addtonal nformaton to the network Guaranteed Servces- 2 6

7 Defnng the problem A reasonable model H = set of traffc contracts M = traffc parameters measured (mean, etc.) for each h H the avalable tarffs are functons of measurements M, ndexed by User chooses at call set up the traffc contract h the best tarff from F h by solvng arg mn Efh ( M) F = { f ( M)} h h Network computes statc at end of call dynamc h M fh ( M) Guaranteed Servces- 3 Defnng the problem (cont.) What s a reasonable choce of chargng functons f h charge corresponds to effectve bandwdth choce of tarff reveals useful nformaton requred measurements are smple (eg. T,V) h M fh ( M) Not obvous!! Use only statc parameters: f = worst case eb (peak rate) bad ncentves, all you can eat problem Use only measurements: f = actual eb of traffc sent no account of resource reservaton at call set up Combne statc wth dynamc parameters f = worst case eb gven h, M Guaranteed Servces- 4 7

8 An nterestng structural property for tarffs Boxes arrve to be packed a pror nfo: W charge = concave functon max a posteror nfo: W of weght Can tarffs make users reveal W? Charge W max slope b(m) tangent tarff-lne f( mw ; ) = am ( ) + bm ( ) W g( W) penalty due to naccurate tarff selecton a(m) m m W max W accurate selecton charge = g( W) Guaranteed Servces- 5 Applcaton: Smple Chargng Scheme for VBR Chargng of VBR calls a pror nformaton: peak rate h (polced) a posteror nformaton: mean rate M (measured) Use as chargng functon an effectve bandwdth eb(m) M for example, ht α on / off ( M) = [ + ( concave n M st h e )] charge = worst case eb gven h, M Construct tarffs as tangents to ponts m of the eb curve f( m; M) = am ( ) + bm ( ) M actual mean rate, measured as M = V/T = Volume / Tme user predcton of mean rate - defnes tarff Implct declaraton of M by users Guaranteed Servces- 6 8

9 Smple Chargng Scheme for VBR α on / off ( s, t) slope b(m) penalty due to naccurate declaraton tangent tarff-lne f( mm ; ) = am ( ) + bm ( ) M charge = T * f( m; M) = a( m) T + b( m) V effectve bandwdth α ON / OFF a(m) accurate declaraton charge = T α * ON / OFF Each traffc contract h defnes a famly of tarff lnes m declared M Guaranteed Servces- 7 Propertes of Smple Chargng Scheme Total charge = T [ am ( ) + bm ( ) M] = am ( ) T+ bm ( ) V Accounts both for resource reservaton => tme-component actual usage => volume-component Smple Accountng Requres only smple measurements: T and V Flexblty added to traffc contracts Ratonal users pay n proporton to ther effectve use Tarff coeffcents depend on traffc contract parameters Guaranteed Servces- 8 9

10 Incentves to the User Provdes the user wth the rght ncentves. In partcular: Incentve to accurately declare the mean rate M, f known a pror For random mean rate M : Expected charge s mnmsed for m=e[m] user has the ncentve to estmate ths (from emprcal nformaton), and declare t to the network Incentve to shape traffc, thus reducng peak rate h and the charge Guaranteed Servces- 9 Incentve Compatblty User s optmal declaraton of m s nformatve to the network provder Can be used by network provder n more effcent allocaton of resources, thus mprovng operaton of the network User s ncentve to shape traffc reduces burstness, thus also leadng to more effcent operaton of the network Guaranteed Servces- 20 0

11 Computaton of a(m) and b(m) Both a(m) and b(m) can be expressed n closed form If t=, then Approprate values of s,t can be derved numercally Guaranteed Servces- 2 Examples of Tarffs h = 3 Mbps st = sec/mbt M a(m) b(m) 0.20 Mbps Mbps Mbps Mbps Mbps h =.5 Mbps st = sec/mbt M a(m) b(m) 0.20 Mbps Mbps Mbps a(m) => $/sec b(m) => $/Mbt h = 3 Mbps st = 2 sec/mbt M a(m) b(m) 0.20 Mbps Mbps Mbps Mbps Mbps Guaranteed Servces- 22

12 How a(m) and b(m) Vary Guaranteed Servces- 23 How a(m) and b(m) Vary Guaranteed Servces- 24 2

13 How a(m) and b(m) Vary For fxed h, s, t, as m ncreases: a(m) ncreases b(m) decreases charge for tme ncreases, whle charge for volume decreases, because the ablty for multplexng dmnshes α on b(m 2 ) slope b(m ) / off ( s, t) a(m ) a(m 2 ) m m 2 M Guaranteed Servces- 25 How a(m) and b(m) Vary (contnued) For fxed m, s, t, as h ncreases : both a(m) and b(m) ncrease the source s more bursty, thus reservng and usng more resources α on / off ( s, t) m h h 2 M Guaranteed Servces- 26 3

14 How a(m) and b(m) Vary (contnued) For fxed m, h (.e. source parameters), when st decreases : a(m) decreases b(m) ncreases and α on / off ( s, t) then decreases to for small st tme-charge decreases, and volume-charge ncreases, because the ablty for multplexng ncreases 45 o decreasng st m st = 0 M Guaranteed Servces- 27 Improvng accuracy of Smple Chargng Scheme The smple chargng scheme bounds the effectve bandwdth accordng to the ON/OFF bound does not capture general traffc contracts for VBR Other bounds can also be used functons of mean rate and the LBs of the traffc contract Same approach: charge per unt tme derved accordng to the tangent selected by the user slope b(m) a(m) α bound (,) st f( m; M ) = a( m) + b( m) M m declared M Guaranteed Servces- 28 4

15 Takng nto account leaky bucket constrants ON/OFF bound corresponds α to a sngle leaky bucket, on / constranng only the peak rate sth ( e ) m ( s, t) = log + st h For traffc contracts nvolvng multple leaky buckets, we tm sh() t can use the tghter bound α lb (,) st = log + ( e ) st Ht () where H(): t = mn{ ρ kt + β k} k K ρt + β off H() t Domnant LB t Guaranteed Servces- 29 Splttng of traffc peak rate = h mean rate = m effectve bandwdth = a total VC peak rate = h/2, mean rate = m/2 effectve bandwdth = a splt VC 2 Splttng can be benefcal to the user => possbly less total charge, because 2a splt < a total correlated traffc streams are erroneously charged as ndependent ones Guaranteed Servces- 30 5

16 Dscouragng splttng - fxed charge Traffc splttng s undesrable to provder, because: may lead to reduced revenue set of avalable VPI/VCI may be exhausted ncreased sgnallng overhead for settng more VCs Splttng should be dscouraged => add a fxed charge per VC Total Charge = am ( ) T + bm ( ) V + cm ( ) However, traffc splttng could be benefcal to provder, f substreams can only be accommodated through dfferent routes Guaranteed Servces- 3 Examples of a, b,c Tarffs h = 3 Mbps st = sec/mbt M a(m) b(m) c(m) 0.20 Mbps Mbps Mbps Mbps Mbps Fxed charge c(m) s expressed n $ was taken (n the examples) as a(m)*5sec+ Guaranteed Servces- 32 6

17 Dscouragng splttng of traffc (cont.) Use homothetc tarffs α( h, M) α( h, M) = kα( h / k, M / k) M h Pros: convexty makes users reveal ther mean rates, no ncentve to splt Cons: charge not proportonal to eb (but close!) Guaranteed Servces- 33 Smpler Chargng: Dspensng wth Duraton The tme-component of charge can be elmnated total charge = bv + c tarff wll be smpler dependence of usage-charge on QoS wll be clearer Reasonng: c can be set to account for typcal tme-charge, or we can assume a typcal value for m and nfer T V / m, hence a ( m) T+ b( m) V + c( m) a( m) ( V/ m) + b( m) V + c( m) = b'( m) V + c( m) However, users wll have no ncentve to close connectons set of avalable VPI/VCI may be exhausted provder can lmt the maxmum number of VPI/VCIs permssble per user Guaranteed Servces- 34 7

18 Chargng CBR Servces Smple chargng scheme can also be appled to CBR servces users should declare m = h Total Charge = a ( h) T + b( h) V + c( h) Volume-charge does not vansh, because b( h) 0 CBR servces should be charged only on the bass of tme, f ther peak rate s really reserved, and CBR s not multplexed statstcally smpler scheme already adopted n practce Guaranteed Servces- 35 Chargng PVCs So far have only dealt wth Swtched VCs for VBR servces (SVCs) Smple chargng scheme can also be appled to Permanent VCs (PVCs) for VBR servces However, PVCs can also be charged only on the bass of tme, f they are not multplexed statstcally, due to ther long duraton smpler scheme already adopted n practce Guaranteed Servces- 36 8

19 Takng nto account leaky bucket constrants ON/OFF bound corresponds α to a sngle leaky bucket, on / constranng only the peak rate sth ( e ) m ( s, t) = log + st h For traffc contracts nvolvng multple leaky buckets, we tm sh() t can use the tghter bound α lb (,) st = log + ( e ) st Ht () where H(): t = mn{ ρ kt + β k} k K ρt + β off H() t Domnant LB t Guaranteed Servces- 37 Effectve bandwdth of a traffc contract Smple bound of a traffc contract s effectve bandwdth: sh (t) ( e ) tscr α( SCR, PCR, MBS) = log + st H ( t) where { ρ t + β ρ + } H ( t) = mn t β 0 0, ( ( 0 ρ0, β ) = ( PCR,0) ρ, β ) = ( SCR,( MBS )( SCR / PCR) + ) Guaranteed Servces- 38 9

20 Effect of traffc mx and lnk capacty C=34 Mb/s C=55 Mb/s PCR=3 Mbt/s, MBS=200 Buffer=4 msec, MPEG- & voce traffc Guaranteed Servces- 39 Effect of PCR, SCR, MBS PCR= Mb/s PCR=3 Mb/s C=55 Mbt/s, Buffer=4 msec, 20% voce connectons Guaranteed Servces

21 Brtsh Telecom s (BT) tarffs Based on prce multplers Guaranteed Servces- 4 BT vs. EB tarffs BT EB PCR=5 Mbt/s C=55 Mbt/s, Buffer=4 msec, mx wth 20% voce traffc Guaranteed Servces- 42 2

22 BT vs. EB tarffs (2) MBS=200 PCR= Mbt/s C=55 Mbt/s, Buffer=4 msec PCR=5 Mbt/s Guaranteed Servces- 43 BT vs. EB tarffs (3) PCR/SCR=5, MBS=200 C=55 Mbt/s, Buffer=4 msec, mx wth 20% voce traffc Guaranteed Servces

23 The PCR/SCR<.8 condton EB EB PCR/2 PCR PCR/2 PCR Left graph s wthout the condton: f PCR/SCR<.8 then prce as MBS=200 Guaranteed Servces- 45 Χρέωση ΑΤΜ VBR VCs βάσει χρόνου Τέλος: a(x) T x παράμετροι σύνδεσης, T = διάρκεια της υπηρεσίας a(x): ι.ε.ζ. της μέγιστης κίνησης σύμφωνη με το συμβόλαιο x Για μεγάλο βαθμό στατιστικής πολυπλεξίας, η χρήση πόρων εξαρτάται από το PCR, SCR μόνο μέσω του λόγου τους PCR/SCR Υπολογισμός τελών σύνδεσης VBR βάσει των τελών σύνδεσης CBR με την χρήση πολλαπλασιαστών a VBR ( PCR,SCR,MBS) M( PCR/ SCR) M2( MBS,PCR/ SCR) a Μ : πολλαπλασιαστής του λόγου εκρηκτικότητας PCR/SCR Μ 2 : πολλαπλασιαστής του μεγέθους έκρηξης MBS CBR ( SCR) Guaranteed Servces

24 Prce Multplers for chargng Guaranteed Servces- 47 Prce Multplers Guaranteed Servces

25 Prce Multplers for chargng Guaranteed Servces- 49 Prce Multpler M2 Guaranteed Servces

26 Παραδείγματα χρέωσης ΑΤΜ VBR VCs βάσει χρόνου Burst Rato (PCR/SCR) Multpler MBS Multpler (PCR/SCR.8) Multpler (PCR/SCR<.8) Μεγάλη στατιστική πολυπλεξία (π.χ. PCR,SCR μέχρι % της χωρητικότητας) Burst Rato (PCR/SCR) Multpler MBS Multpler (PCR/SCR.8) Multpler (PCR/SCR<.8) Μικρή στατιστική πολυπλεξία (π.χ. PCR,SCR μέχρι 0 % της χωρητικότητας) Μικρότερη στατιστική πολυπλεξία οι πολλαπλασιαστές είναι πιο κοντά στην μονάδα Guaranteed Servces- 5 Brtsh Telecom s (BT) tarffs Based on prce multplers Guaranteed Servces

27 Comparson of EB and BT prce multplers Guaranteed Servces- 53 Comparson of EB and BT prce multplers (2) Guaranteed Servces

28 Chargng and CAC Consstency of CAC and chargng functon: Natural to charge wth the eb used n CAC Suppose CAC accordng to PCR. How to charge? Not a compettve CAC Better provde ncentves to reduce volume a b at + bv + c, a >> b Suppose perfect dynamc CAC s used call arrval and departures occur every T control mechansm (by blockng calls) acheves QoS at all tmes effectve bandwdth of a call = average of actual effectve bandwdth n each perod T = almost the mean rate!! PCR Guaranteed Servces- 55 More general chargng schemes 2-tax band scheme h A tme V 2 V V: volume of data durng ntervals wth less than A bytes V2: volume of data durng ntervals wth more than A Charge s f ( V = a + a V + a V, V2 ) where a < a 2 Guaranteed Servces

29 More general chargng schemes Smple scheme can not dstngush users havng the same mean mean Need for more detaled traffc measurements Consder the general lnear tarff f ( X ) = a0 + ag( X ) + K+ algl ( X ) X = X, K, X T, g ( X ) = measurement functon ( = X j ) T j=, T Other possble functons: ( = { X j > 0.9h} T j=, T Evaluate mplementaton cost vs accuracy gan Guaranteed Servces- 57 More general chargng schemes (cont.) Approach used n Smple Chargng Scheme can be extended Defne the effectve bandwdth to be the functon sx[, t] α( hm, ) = sup 0 logee X st t st.. Eg( X) = M, Xt Ξ( h) concave n M Construct lnear tarffs = tangent hyperplanes to α( M ) Example: the 2-tax band scheme K M 2 Guaranteed Servces- 58 M tme 29

30 Tme-of-day prcng Assume two perods, off-peak and on-peak, t= and 2 User utlty Socal welfare maxmzaton problem u ( x, x2 ) max N { x, x } 2 = 2 u ( x, x ), subject to N = x t C, t t =,2 User problem max[ u ( x, x2 ) px p2x2 ] x, x2 p, p2 set usng a tatonnement Guaranteed Servces- 59 Smple Tme-Volume scheme for ABR rate MCR tme at + bv + c can be used for ABR User buys an amount m of MCR at posted prce p MCR Network charges for a perod of usage T: p MCR m T for the data sent wthn MCR pubr V where V s the volume sent on top of MCR c (for sgnallng congeston, dscourage splttng) No ncentve for splttng connectons f excess capacty allocated proportonally to the amounts of MCR (note that c>0) Guaranteed Servces

31 Incentve compatblty and user-network nteracton Operatng pont of a lnk and tarffs are nter-related n a crcular fashon: tarffs Users Network traffc contracts Incentve compatblty: tarffs nduce users to select contracts that mnmze ther charges, and lead to socal welfare maxmum of the system Guaranteed Servces- 6 Equlbrum under determnstc multplexng We assume dentcal users & sngle leaky bucket Users-network nteract n lock-step fashon For determnstc multplexng (zero CLP): In both cases, operatng pont moves towards Q Q: maxmum number of users and Cβ Q =Bρ Q β t=0 Q=(ρ Q,β Q ) t = ρ Guaranteed Servces- 62 3