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Can we quantify them?\rOutline Define packet forwarding paradigms: Vanilla IP, OSPF, MPLS, general bifurcation Compare their relative strength: upper and lower bounds on performance ratio A centralized heuristic for vanilla IP forwarding control is centralized anyway achieves good performancet$,!,28$,!,28 Packet forwarding in practiceVanilla IP forward all packets destined to some addr. to a selected shortest path OSPF like above, but allow equal splitting when multiple shortest paths exist MPLS pre-select routes for flows. GI G.    0Forwarding Modelling Network as a graph: G(V,E), |V|=n, |E|=m. Nv  the set of neighbors of node v. ce >0  the capacity of link e E D={di,j}  the demand matrix Routing assignment: R: V4 [0..1], u,v(i,j) is the relative amount of (i,j)-flow that is routed from a node u to a neighbor v. 1. For all u,i,jV: v Nu u,v(i,j)=1 2. For all u,i,j,vV, v Nu: u,v(i,j)=0r*ZpZ&ZZ "    ""        t/'%0source invarianceA routing assignment R is source invariant if it does not depend on the source: u,v(i1,j) = u,v(i2,j) u,v(j) Q#;      Routing Paradigms4Unrestricted Splitable Routing (US-R) Restricted Splitable Routing (RS-R) Split over at most L outgoing links Special case: Unsplittable flow problem (RS-R1) Standard IP Forwarding (IP-R) Source invariant RS-R1 OSPF Routing (OSPF-R) Source invariant routing assignments splitting flow evenly among next hops.JTLJ=  4      >  B  How packets are splitted?VOption 1 (basic): packet sprinkler each packet chooses next hop with prob. u,v(j) may cause reordering hurts performance. Option 2 (flow-cached): hashing each flow is hashed to next hop with prob. u,v(j) may not result in splitting at desired ratios can we afford double hashing/buckets at core?#Y  (   +] Performance MeasuresDecide on an allocation matrix say use max-min fairness Min Congestion congestion factor (CF) = link flow / link capacity hard constraint: congestion 1, soft constraints minimize the penalty Max Flow (MF)|3   Hardness Result)IP-R is NP even for a single destination!(*   Hardness Resultnode i has demand ai node x is connected to dest with capacity B node y is connected to dest with capacity S ai -B t   P( Comparison between paradigmsLower Bound on ratio: Example that shows the ratio is at least as high as W(f(n)) Upper Bound on ratio: Show that a ratio of, at least, O(g(n)) can always be achieved. If f(n)=g(n) the bound is tight Q(g(n)). <@+  4    IP-R vs RS-R1 and OSPF-R* $ $ $<Lower bound (N) IP-R: single path CF=N RS-R1: separate routes CF=1 OSPF-R: divide equally CF=1 Upper bound O(N) IP-R can use the highest flow of RS-R1/OSPF-R. % IP-R vs RS-R1 and OSPF-R* $ $ $dLower bound (N) IP-R: single path CF=N, MF=1 RS-R1: separate routes CF=1, MF=N OSPF-R: divide equally CF=1 , MF=N Upper bound O(N) IP-R can use the highest flow of RS-R1/OSPF-R   .   %!OSPF-R vs. RS-R1 Max Flow (basic)6"( ( $(pN flows, each carry a unit demand OSPF-R use single path thruput is 1 use two paths thruput is 2 use more - still limited by 2 (due to the first split) RS-R1 can do N Lower bound (N) )o!)66  ,9^'OSPF-R vs. RS-R1 Max Flow (flow-cached)6(( ( $(XN flows, each carry a unit demand OSPF-R to max. throughput must split the flows max thruput is log N given log* N stages: max thruput is 2 RS-R1 can do N Lower bound (N) )c!)a  ,U#'/OSPF-R vs. RS-R1 Congestion Factor (both cases)60( ( $(N flows, each carry a unit demand OSPF-R use single path CF=N use two paths CF=N/2 on the down link RS-R1 can do CF=1 Lower bound (N) );$)&   What do we have thus far?IP-R vs. RS-R1 and OSPF-R q(N) in both criteria. OSPF-R vs. RS-R1 O(N) in all criteria and cases. But, we sometime used fairly complex topologies! What if topologies are simple? or very simple?b    A Simple Topology!OSPF-R vs. RS-R1 Max Flow (basic)6"( ( $(OSPF-R cl non-decreasing use all links from l* and above. throughput is given by: (L- l* +1) cl* = C/ ln Lf >V!OSPF-R vs. RS-R1 Max Flow (basic)6"( ( $(OSPF-R cl non-decreasing use all links from l* and above. throughput is given by: (L- l* +1) cl* = C/ ln Lf >V!OSPF-R vs. RS-R1 Max Flow (basic)6"( ( $(OSPF-R cl non-decreasing use all links from l* and above. throughput is given by: (L- l* +1) cl* = C/ ln L RS-R1 can achieve C Lower bound (log L) We can also show that for any capacity allocation OSPF-R can achieve, at least, C/ ln L, hence q(log L) f   4 PV+#Hn-ln n01A centralized heuristic for vanilla IP forwardingAim: improve performance of centrally controlled IP networks. Why centralized? networks are centrally controlled anyway: IPNC. Static weight setting sucks! `O0801A centralized heuristic for vanilla IP forwarding|Aim: improve performance of centrally controlled IP networks. Why centralized? networks are centrally controlled anyway: IPNC. Static weight setting sucks! dynamic link weights adjustment\O0@80"! Link WeightsThe family of exponential weights: Proved to perform well by [AAP93] for related problems. [Fortz, Thorup,2000] used a piece-wise linear approximation of it. a control the routing sensitivity to load.$*^h" AlgorithmInput: network topology & demand matrix Output: forwarding tables 1. sort flows 2. initialize link weights 3. for every flow in sort order 4. route flow along SP with IP constraint 5. adjust weights( #Simulation SettingVTwo types of random networks: Flat & Inet demand di,j {1,2,3& }. D = i,j di,j Demand matrices Destinations  uniformly chosen Sources  uniformly or Zipf-like chosen (param.=.5) Link capacities  all 1 Infinite bandwidth requirements Three heuristics: rand, sort, dest =/D, =0,1,20,100,D aZTZwZ1T\% I]$ %(! Total FlowzWhen b=D (Max Sensitivity) the flow increase by 30-50% All other cases, the total flow is almost the same. Even b=1 improved performance significantly with almost no penalty in added flow.&Histogram - Inet, Zipf, '  Inet, Zipf$)"Summary~At least, in theory OSPF cannot compete with MPLS abilities. In practice vanilla IP may be enough if you have central control. ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> f(    6ޘ P  T Click to edit Master title style! !  08   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     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B 8@ ZD?? p B 8@ ZD??  B 8 ZD?? @ B 8 ZD??  B 8 ZD?? @ B 8 ZD??  B 8@ ZD??   8 Z jJ??   Sn(2 H 8 0޽h ? ̙33y___PPT10Y+D=' = @B +  *"D( 4D Dr D S P   x D c $p    D ZS jJ??0  S1(2  D Z jJ??  S2(2  D Z jJ??0  S3(2  D ZЕ jJ??p Sn(2 @ D T ??`PH@___PPT9"@ d& & 2    D Z jJ??d  Sx(2   D Z jJ??  Xdest(2 B  D ZD?? PdB  D ZD??@PdB  D@ ZD??Pd D Z jJ?? ` P  .(2 D Z jJ??   .(2 D Z jJ?? `P  .(2@ D T ??  PH@___PPT9"@ d& & 2  B D ZD??PdB D@ ZD??  B D@ ZD?? p B D@ ZD??  B D ZD?? @ B D ZD??  B D ZD?? @ B D ZD??  B D@ ZD??   D Z  jJ??   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DUH ( 9lR Hl H C 辻   ^2 H 6jJ ` ^2 H 6jJ p ^2  H 6jJ  ^2  H 6jJ0 0 ^2  H 6jJ  ^2 H 6jJ@^2 H 6jJ@`^2 H 6jJ@ ^2  H 6jJ@`  !H xBTCDEFT@ 4J XB "H 0D `0 XB #H 0D 0 XB $H@ 0D @`  %H xBCDEF@ vXB &H 0D `XB 'H@ 0D XB (H@ 0DR2 )H s *p PR2 +H s *pR2 0H s *pX 8 F `]P  >H`F ]P f2 H 6jJ `f2 H 6jJp f2  H 6jJ`p`B  H 0D  `B HB 0D `B H 0Dp  H xB{CvDEF{v@6`B H 0D` H  ~BlCtDEFlt@Z:`B H 0D @ Z2 *H s *P Z2 ,H s * 0 Z2 -H s *  PP Z2 .H s *h P Z2 /H s *0 ` Z2 1H s * P  2H <λ`}Z 3N-1 3H <@һF I C  11 4H <ջpj  11 5H <ػ  11 6H <ܻ = 3N-2 7H <`߻] 3N-3 8H <P0 J 11 :H S ~0e0eP     ;H <PJ 1NXB +B#style.visibility= `B<* dD' =1:Bvisible*o3>+B#style.visibility<* d%(D' =-o6Bdissolve*<3<* dD' =%(D' =%(DW' =4@BB BB%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<* dD' =1:Bvisible*o3>+B#style.visibility<* d%(D' =-o6Bdissolve*<3<* dD' =%(D' =%(Dw' =4@BB BB%(E<' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<* d%(D' =1:Bvisible*o3>+B#style.visibility<* d%(D' =-o6Bdissolve*<3<* dD' =%(Dw' =4@BB BB%(E<' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<* d%(D' =1:Bvisible*o3>+B#style.visibility<* d%(D' =-o6Bdissolve*<3<* d+5  \T`( Xy0+ `r ` S P   ` S ~`0e0eP    ` ` c $A ??P x H ` 0޽h ? ̙33y___PPT10Y+D=' = @B +N  P N(  r  S djP P  P     \0e0eA     (@  5% 8c8c     ?A)BCD|E||Large checker board P H  0޽h ? ̙3380___PPT10.pGa  h(  hl h C P   l h C ``  H h 0޽h ? ̙33y___PPT10Y+D=' = @B +: aY@*-l(  l^2 l 6jJ `2 l <DjJ p ;22 l <jJ   ;1^2 l 6jJ`02 l <@ jJ  =n  l  ~BTCDEFT@ 4zXB l 0D``XB  l 0D`XB  l@ 0D@^2  l 6jJ`0 ^2  l 6jJp0 ^2  l 6jJ 0 ^2 l 6jJ 0p ^2 l 6jJ0  l  ~BTCDEFT@0 4 XB l 0D0 ` XB l 0D0  XB l@ 0D0 @ ^2 l 6jJ ` 2 l BjJ p  ;22 l BljJ   ;12 l BjJ   =n  l  ~BTCDEFT@p 4: XB l 0Dp ` XB l 0Dp  XB l 0Dp @P R2 l s * P R2  l s *h R2 !l s * R2 "l s *P PR2 #l s *PhR2 $l s *PR2 %l s *P P R2 &l s *P h R2 'l s *P   (l  ~BTCDEFT@ 4XB )l 0D`XB *l 0DXB +l 0D@ ,l  #A( ?Large checker board 7sources -l  4'A( ?Large checker board@ ` < destinations  H l 0޽h ? ̙33y___PPT10Y+D=' = @B +m  t$(  tr t S p,P   r t S 0-`  H t 0޽h ? ̙33y___PPT10Y+D=' = @B +  x( @ O xl x C x2P   l x C 3  ` x c $A ??0 H x 0޽h ? ̙33y___PPT10Y+D=' = @B +m  |$( -(A& |l | C T:P   x | c $(;   H | 0޽h ? ̙33y___PPT10Y+D=' = @B +a  ( ,@ l  C CP   l  C D  H  0޽h ? ̙33y___PPT10Y+D=' = @B +;  bZ ( @ l  C RP   F  C Aiz@P`H  0޽h ? ̙33y___PPT10Y+D=' = @B +;  bZ(   l  C TP   F  C Aiu50H  0޽h ? ̙33y___PPT10Y+D=' = @B +a  0(  l  C 8PP  P l  C P P H  0޽h ? ̙33y___PPT10Y+D=' = @B +E  ld(  P  C (A iszhist@l  C  ^P   H  0޽h ? ̙33y___PPT10Y+D=' = @B +I  ph( F l  C aP   T  C ,A iz100histH  0޽h ? ̙33y___PPT10Y+D=' = @B +a  `(  l  C eP   l  C f  H  0޽h ? ̙33y___PPT10Y+D=' = @B +BxMOSApvᅃr1`,@z`WCxzz^$ Zgv<c^?H};3;33ѭg+΃j->&!5]jv t ={5^v߁1W~JGOf 55|)U۾֙r2jH y`D0vL͆P?[$?q;=i= '[ WuܜO[ jO΍L] #. {#|!?S4s b:32.<^s/'Pu%c198pYfx(QTa8k>δt[B|Kb}Ю+a ض@ U7$dDi6ECURc7SrAX b+~xY|j#yy8D&TM6dZj>kLc$;lӟCDg4]w?#9!zEk{n-m۲<.#8W2k}S+qÔ͑]@/e?dIt٦7N">;mzHA-N(ALMeIwٚMMN`~E: Uw'"zU݌R2Nɐ~l$.> &0Y^08faXIr'} HŖ2[ ʥ.)9$` /4r-W2Osp-o{BxMOSApvᅃr1`,@z`WCxzz^$ Zgv<c^?H};3;33ѭg+΃j->&!5]jv t ={5^v߁1W~JGOf 55|)U۾֙r2jH y`D0vL͆P?[$?q;=i= '[ WuܜO[ jO΍L] #. {#|!?S4s b:32.<^s/'Pu%c198pYfx(QTa8k>δt[B|Kb}Ю+a ض@ U7$dDi6ECURc7SrAX b+~xY|j#yy8D&TM6dZj>kLc$;lӟCDg4]w?#9!zEk{n-m۲<.#8W2k}S+qÔ͑]@/e?dIt٦7N">;mzHA-N(ALMeIwٚMMN`~E: Uw'"zU݌R2Nɐ~l$.> &0Y^08faXIr'} HŖ2[ ʥ.)9$` /4r-W2Osp-o{BxMOSApvᅃr1`,@z`WCxzz^$ Zgv<c^?H};3;33ѭg+΃j->&!5]jv t ={5^v߁1W~JGOf 55|)U۾֙r2jH y`D0vL͆P?[$?q;=i= '[ WuܜO[ jO΍L] #. {#|!?S4s b:32.<^s/'Pu%c198pYfx(QTa8k>δt[B|Kb}Ю+a ض@ U7$dDi6ECURc7SrAX b+~xY|j#yy8D&TM6dZj>kLc$;lӟCDg4]w?#9!zEk{n-m۲<.#8W2k}S+qÔ͑]@/e?dIt٦7N">;mzHA-N(ALMeIwٚMMN`~E: Uw'"zU݌R2Nɐ~l$.> &0Y^08faXIr'} HŖ2[ ʥ.)9$` /4r-W2Osp-o{xVOQmR4~@Ch88jb!Xv.ɳ x4z/&Lf.e`KTҤy3ٝwo?<[]Z̔kzSR8a126M(}(#By5Mwjm\0h=fua5␢1ϝ2_"BS_@S>R޼ O=:H3qKj!>JN1>mj]1~`TFܭ`]9qrvIs)]u\^K⫸#pqsTģ$j*ٸ]UlU]4B֤EkK;\BBVc)ZǺЫ;O&6Ǩ67&ɌsgHn|*"9ei)!>E/atmߣǣ}b=[^r~=g_ awvPO(\ɟ(}#$g*9;!f(!_Wij!3S}8tgg+IH7S)9VֈmYNZ)L`2kCQ5 FbS}!WZ'8Bx,)- u*qxfmj .txHe26q*dHMF?@{rW3`cbeg"jl|<G|cz*$} C)JMIbAdgjmln\supw+HF"? ,+Oh+'0 hp  No Slide Title S Sshavitt63vMicrosoft PowerPointP@¬@PI"@о7Gg  6  -- @ !--'@Times New Roman-. 3362 ]The strength of routing Schemes%"/."System-՜.+,0    'On-screen Show -sv#A )Times New RomanSymbolScript MT BoldTahomaDefault DesignMicrosoft Equation 3.0 The strength of routing Schemes Main issues Outline Packet forwarding in practiceForwarding Modellingsource invarianceRouting ParadigmsHow packets are splitted?Performance MeasuresHardness ResultHardness ResultComparison between paradigmsIP-R vs RS-R1 and OSPF-RIP-R vs RS-R1 and OSPF-R"OSPF-R vs. RS-R1 Max Flow (basic)(OSPF-R vs. RS-R1 Max Flow (flow-cached)0OSPF-R vs. RS-R1 Congestion Factor (both cases)What do we have thus far?A Simple Topology"OSPF-R vs. RS-R1 Max Flow (basic)"OSPF-R vs. RS-R1 Max Flow (basic)"OSPF-R vs. RS-R1 Max Flow (basic)Hn-ln n2A centralized heuristic for vanilla IP forwarding Slide 252A centralized heuristic for vanilla IP forwarding Link Weights AlgorithmSimulation Setting Slide 30 Slide 31 Total FlowHistogram - Inet, Zipf Inet, ZipfSummary  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles#_P shavittshavitt  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwyz{|}~      !"#$%&'()*+,-./0123456789:;<>?@ABCDFGHIJKLNOPQRSTYRoot EntrydO)PicturesCurrent UserMSummaryInformation(=PowerPoint Document(xDocumentSummaryInformation8E