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F  ApplicationsrNetwork Games Subscribers = players Messages = events in the region of the game world to which the player belongs Common events must be seen in the same order for consistency Messaging Chat rooms, buddy lists Example of messages in a chat room Alice:  Who wants to go to Sydney? Bob:  I do Connor:  Who wants to go to Melbourne? Diane:  I am going Bob goes to Sydney, Diane goes to Melbourne Diane goes to Sydney, Bob goes to Melbourne6ZZ ZZ#PZZ #      +,NNaive solution LNaive solution M Our solution PGroupsGROUP: all subscribers with the same subscription Order among messages is enforced across groups RULE 1: A sequencer (ingress-only sequencer) is associated with each group and establishes order among all messages addressed to the group except for& gZZZNbDouble Overlapped GroupsDOUBLE OVERLAPPED GROUPS: groups that have at least two subscribers in common Receivers may make inconsistent decisions about message order when they belong to double overlaps RULE 2: A sequencer is associated with each double overlap X<5m%Sequencing schemeqSEQUENCING NETWORK A sequencer is created for each double overlap between groups and for each group that has no double overlaps MESSAGE TRANSMISSION Messages traverse the sequencing network and receive sequence numbers from all sequencers associated with the destination group MESSAGE RECEPTION Subscribers order messages unambiguously according to the sequence numbersmKmKT Sequencing Network: Construction YSequencing Network: Operation  VSequencing Network: Conditions WLoop-free sequencing network w'Loop-free sequencing network g Results QUESTIONS What is the delay penalty incurred by the sequencing network? How many sequence numbers does each message receive? EXPERIMENT SETUP Packet-level simulator over a 10,000 node topology End-hosts arranged into similar sized clusters distributed uniformly at random through the topology Each host belongs to zero or more groups The size of groups is generated from a Zipf distribution Sequencers are assigned to physical nodes using a heuristic that minimizes the distance between sequencers on the same path  PuPPP swdLatency StretchqLatency Stretch ratio between the time taken for a message to traverse the sequencing network and time taken using the direct unicast path expresses the delay penalty of an individual node when unambiguous delivery is required worst case results since shortest unicast paths are rarely followed in publish/subscribe systems How is the increase in delay distributed? xZ4ZZ+ZZ6+e Distribution of latency increases&Sequencers on a PatheHow many sequence numbers a message must collect Vector timestamp approaches Sender belongs to the destination group Append to a message information about the last message received from all the other members of the group, for each group O(n x g) information [n nodes, g groups] Our approach Appends to a message information for each sequencer traversed O(g)M CM  >[fSequencers on a PathhConclusions and Future WorkUCONCLUSIONS Method for ordering messages in a publish/subscribe system Practical and scalable Key insight: only messages to groups with two or more common members must be ordered FUTURE WORK Scheme for optimizing the sequencing network and the placement of sequencers on physical nodes Dynamic behavior Different models for group membershipX    y(  j" Backup slides n$Sequencer stateState maintained by a sequencer Sequence number Group-local sequence number Forwarding table Reverse-path table Output retransmission buffer Buffer for messages from previous sequencers,  k#Placing sequencersaCo-locating sequencers on the same physical node 1. Place on the same physical node any sequencers whose corresponding overlaps have a subset relationship between them 2. Co-locate sequencers whose overlaps do not have a subset relationship but share at least a node Mapping co-located sequencers (sequencing node) to physical machines 1. If no sequencing node associated with a group has been mapped, map one at random 2. If there are sequencing nodes already mapped to a physical node, pick the closest unassigned sequencing node on the path associated to the group and map it to neighboring physical nodes8b1Ei!StressStress of a sequencing node  ratio between the number of groups for which it has to forward messages and the total number of groups"j/XZ[\a c l opqrtuvxP  ` 33PP` 13` 3333` Q_{` 333fpKNāvI` j@v۩ῑ΂H>?" dd@(t?dd@  @` n?" dd@   @@``PR    @ ` ` p>> aYp \(  \$  \ 0$ "`   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     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All destinations can make an immediate decision of whether to deliver or buffer arriving messages@H@2e He8X2 T T1?"6@ NNN?N` @G ,$D" 0 < Properties H T 0޽h ? 3333@@___PPT10@.e+D->' = @B D=' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(Df' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* T%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =%(Df' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T-%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(Df' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(DH' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T-9%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*T%(DL' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(Df' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =%(Dx' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D`' =%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<* T%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<* T%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(+h+0+T ++0+T ++0+T ++0+ T ++0+ T ++0+T ++0+T ++0+T ++0+T ++0+T ++0+T +} ; FxFP 0Vh@E(  h h S t0e0e    BCfDE4F @  Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| X<n {Y%7fH `I @    s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abp  h C N0e0e    BCDEF @  Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||t8@  s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab0  h S 0e0e    BCDEXF( @  Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||&41ppi8QPa9Py y@       s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab p x h c $t \   x h c $ \`  t 2 h ZLԔ?"6@ NNN?N   4Q02  h ZԔ?"6@ NNN?N Pp  4Q1G  h Z 1?"6@ NNN?N )G0 = {A, B, C} G1 = {B, C} G2 = {A, B, D}:*   h Z 1?"6@ NNN?N4 .  ;to G0  h Z@ 1?"6@ NNN?N0 *  ;to G2  h Z$ 1?"6@ NNN?N0 *  ;to G1z  p *h  p,$@ 05" h # l(o?"6@`NNN?NP @ S m0| | . 2 h  `/1?"6@ NNN?N 0 p @ B h TD1?"0@NNN?N P @ h NH. 1?"6@`NNN?N ,$ 0 When a message arrives, the receiver checks the sequence numbers assigned by the relevant sequencers and decides whether to deliver or buffer the message:Q6l `  Vh ,$D 09 h Z8 Ԕ?"6@ NNN?N`  i7 Q0 Q1 m0 m1 m2 88 h Z$: 1?"6@ NNN?N C  11 h ZHA 1?"6@ NNN?N`#  12  h Z< 1?"6@ NNN?N`# 11 !h ZHG 1?"6@ NNN?NC 12z  `  >h  ` ,$@ 0w" 6h # lKo?"6@`NNN?N `   m1| | p 2 7h  `T1?"6@ NNN?N  @ B 8h TD1?"0@NNN?N z 0`  Hh 0` ,$@ 0w" Eh # lXo?"6@`NNN?N0p  m2| | p 2 Fh  `b1?"6@ NNN?N` `  @ B Gh TD1?"0@NNN?Np0 z   Qh   ,$D 0x" Nh # ldo?"6@`NNN?N   m2| | 1 p 2 Oh  `$n1?"6@ NNN?NP   @ B Ph TD1?"0@NNN?N @ z   4h   ,$D 0N" 1h # l(ro?"6@`NNN?N0  l m0| 1 | 2 F 2 2h  `y1?"6@ NNN?N   @ B 3h TD1?"0@NNN?N 0 {" Sh # lD}o?"6@`NNN?N ,$D 0 m m#| Q0 | Q1 B z   /h  ,$D 0M" ,h # l܄o?"6@`NNN?N  k m0| 1 | F 2 -h  `،1?"6@ NNN?N `  @ B .h TD1?"0@NNN?N ` z P  Ch P ,$@ 0w" @h # lo?"6@`NNN?Np   m1| 2 | p 2 Ah  `1?"6@ NNN?NP `  @ B Bh TD1?"0@NNN?N `p H h 0޽h ? 333366___PPT106.e+WD6' = @B D5' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<**h%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*>h%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Hh%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Sh%(D' =%(Dv' =%(D' =4@BBBB%()?)?Dr' =.:7 BBBBBoM 1.38889E-6 2.25769E-6 C -0.00869 0.00717 -0.01719 0.01457 -0.02396 0.02244 C -0.03073 0.0303 -0.03473 0.03747 -0.04098 0.04672 C -0.04723 0.05598 -0.05434 0.06731 -0.06146 0.07865 *3>*B ppt_xB ppt_y=0BB aaaA<**hD' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<**h%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*/h%(D' =%(D ' =%(D' =4@BBBB%()?)?Dh' =.07 BBBBBeM 5.83333E-6 7.72843E-6 C -0.00642 0.01319 -0.01284 0.02661 -0.02048 0.04026 C -0.02812 0.0539 -0.0394 0.07079 -0.04565 0.08189 C -0.0519 0.093 -0.05485 0.10017 -0.0578 0.10757 *3>*B ppt_xB ppt_y=0BB aaaA<*/hD' =4@BBBB%()?)?D(' =.7 BBBBB!M -6.38889E-6 4.33264E-6 C 0.00659 0.00532 0.01319 0.01064 0.01926 0.01596 C 0.02534 0.02128 0.0309 0.02591 0.03628 0.03215 C 0.04166 0.0384 0.04669 0.04464 0.0519 0.05297 C 0.05711 0.0613 0.06319 0.07425 0.06753 0.08189 C 0.07187 0.08952 0.07518 0.09438 0.07847 0.09947 *3>*B ppt_xB ppt_y=!0BBaaaaaA<*>hD' =4@BBBB%()?)?D' =.7 BBBBBM 5.55556E-6 6.7777E-6 C 0.00782 0.01319 0.01563 0.02638 0.02657 0.04003 C 0.03751 0.05367 0.05122 0.06778 0.06511 0.0819 *3>*B ppt_xB ppt_y=0BB aaA<*HhD|' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*>h%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*Hh%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Ch%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Qh%(D@ ' =%(Dz ' =%(D' =4@BBBB%()?)?D' =.7 BBBBBM -4.16667E-6 7.40227E-7 C 0.00851 0.00902 0.01719 0.01827 0.02656 0.02729 C 0.03594 0.03632 0.04636 0.04534 0.05677 0.05459 *3>*B ppt_xB ppt_y=0BB aaA<*QhD' =4@BBBB%()?)?D' =.7 BBBBBM 3.33333E-6 -3.91395E-6 C 0.00729 0.00995 0.01475 0.02013 0.04323 0.06593 C 0.0717 0.11173 0.14965 0.23988 0.171 0.27458 *3>*B ppt_xB ppt_y=B0BB aaapBB=B&w ><*ChD' =4@BBBB%()?)?D' =.7 BBBBBM -0.05782 0.10757 C -0.06441 0.11867 -0.07084 0.13 -0.07587 0.13972 C -0.08091 0.14944 -0.08282 0.15383 -0.08802 0.1654 C -0.09323 0.17696 -0.10087 0.19477 -0.1073 0.20865 C -0.11372 0.22253 -0.12014 0.23572 -0.12657 0.2489 *3>*B ppt_xB ppt_y=F0BB aaaaApBB B~=<*/hDf' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*/h%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4h%(D' =%(Dp' =%(D' =4@BBBB%()?)?Dl' =.47 BBBBBiM 4.16667E-6 -9.50729E-7 C -0.00833 0.01018 -0.01667 0.02036 -0.02413 0.02891 C -0.0316 0.03747 -0.03924 0.04511 -0.04462 0.05135 C -0.05 0.0576 -0.05347 0.06176 -0.05677 0.06593 *3>*B ppt_xB ppt_y=0BB aaaA<*4hD4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Vh%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(+p+0+h ++0+Sh ++ ; **  \B*(  \" \  `||>?"6@`NNN?N P`@ xC1: A single path must connect sequencers associated to each group C2: The undirected sequencing graph must be loop freePy ^ r \ S  \   r \ S   \`   V&8 `?  \` `  \ S d0e0e    B2CDE(F @  Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| 2<x`L9 @   s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab   \ S t0e0e    BCfDE4F @  Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| X<n {Y%7fH `I @    s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`?  \ C N0e0e    BCDEF @  Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||t8@  s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`  \ S 0e0e    BCDEXF( @  Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||&41ppi8QPa9Py y@       s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abg 2 \ ZԔ?"6@ NNN?N @  4Q02  \ ZPԔ?"6@ NNN?N  4Q12  \ ZԔ?"6@ NNN?NP pp  4Q2 \ T1?"6@ NNN?N %  < Conditions H \ 0޽h ? 3333___PPT10i. ,+D=' = @B +ܤ ; SS0 >W` =S(  ` ` S t0e0e    BCfDE4F @  Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| X<n {Y%7fH `I @    s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abp`  ` S T0e0e    B C9DEF @  Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||a -M39^& "@  s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab wn  ` S 0e0e    BCDEXF( @  Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||&41ppi8QPa9Py y@       s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab x ` c $ \   x ` c $| \`   2 ` ZԔ?"6@ NNN?N`   4Q02  ` ZlԔ?"6@ NNN?NP Ppp  4Q1Z  ` Z| 1?"6@ NNN?N ,G0 = {A, B, D} G1 = {A, B, C} G2 = {B, C, D}J-  ` Z 1?"6@ NNN?N   ;to G0  ` Zx 1?"6@ NNN?N   ;to G2  ` Z( 1?"6@ NNN?N   ;to G12 ` ZԔ?"6@ NNN?N @@  4Q2l  PA *`0,$D 0 ` Z| Ԕ?"6@ NNN?N PA O Q0 Q1 Q2 m0 m1 m2 ` Z 1?"6@ NNN?N@ 11 ` Z 1?"6@ NNN?N@ 12  ` Z 1?"6@ NNN?N 11 !` Z 1?"6@ NNN?N 12 "` Z4 1?"6@ NNN?N  11 #` Z 1?"6@ NNN?N  12> $` Z8 1?"6@ NNN?N F ,$ 0 B B: m0 < m1 9 %` Z % o?"6@ NNN?N g ,$D! 0 = AMBIGUOUS l    +` ,$@ 0R" '` # l o?"6@`NNN?N   pm0| | | F2 (`  `1?"6@ NNN?N p  @ B )` TD1?"0@NNN?N p z  p ;`  p,$@ 0:" 7` # lPo?"6@`NNN?N  Xm1| | | . 2 8`  `1?"6@ NNN?N p @ B 9` TD1?"0@NNN?N0 @z P  P @`  ,$@ 0R" =` # lo?"6@`NNN?NP   pm1| 2 | | F2 >`  `8&1?"6@ NNN?NP  P @ B ?` TD1?"0@NNN?N  z  `   E` `  ,$D 0S" B` # lo?"6@`NNN?N `   qm1| 2 | | 1 F2 C`  `T01?"6@ NNN?N  @ B D` TD1?"0@NNN?N  z @`   J` ` @ ,$@ 0:" G` # l4o?"6@`NNN?N@`   Xm2| | | . 2 H`  `\;1?"6@ NNN?N   @ B I` TD1?"0@NNN?N  z    O`    ,$D 0R" L` # lP>o?"6@`NNN?N P  pm2| | 1 | F2 M`  `D1?"6@ NNN?N @  @ B N` TD1?"0@NNN?NP @ z  `   T` `  ,$D 0S" Q` # l+B#style.visibility<*+`%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*;`%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*J`%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*U`%(D8' =%(Dr' =%(D' =4@BBBB%()?)?Dn' =.67 BBBBBkM -5.55556E-7 2.63706E-6 C -0.00729 0.00786 -0.01441 0.01573 -0.0217 0.02428 C -0.029 0.03284 -0.03802 0.04256 -0.04341 0.05158 C -0.04879 0.0606 -0.05157 0.06962 -0.05434 0.07888 *3>*B ppt_xB ppt_y=0BB aaaA<*+`Df' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*+`%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0`%(D' =%(D ' =%(D9' =4@BBBB%()?)?D' =.U7 BBBBBcM 0.00399 0.00115 C -0.00069 0.01156 -0.00538 0.02197 -0.01059 0.03146 C -0.0158 0.04094 -0.02048 0.04649 -0.02743 0.05875 C -0.03437 0.07101 -0.04844 0.09761 -0.05278 0.10548 *3>*B ppt_xB ppt_y=D0BB aaaApBB>鼐Bo/U=<*0`D' =4@BBBB%()?)?D,' =.7 BBBBB%M 2.77778E-7 -2.08883E-6 C 0.00712 0.00555 0.01441 0.01133 0.02049 0.01619 C 0.02657 0.02105 0.03143 0.02313 0.03629 0.02891 C 0.04115 0.0347 0.04462 0.04395 0.04948 0.05135 C 0.05434 0.05875 0.06025 0.06662 0.06511 0.07379 C 0.06997 0.08096 0.07414 0.0879 0.07848 0.09484 *3>*B ppt_xB ppt_y=!0BBaaaaaA<*;`D3' =4@BBBB%()?)?D' =.O7 BBBBB]M -0.00209 1.11022E-16 C 0.00225 0.00046 0.01302 0.00162 0.02448 0.00231 C 0.03593 0.00301 0.05468 0.00394 0.06666 0.00394 C 0.07864 0.00394 0.09062 0.00255 0.09687 0.00231 *3>*B ppt_xB ppt_y=D0BB aaaapBBJ=Bֹ:<*J`D|' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*;`%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*J`%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@`%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*O`%(D ' =%(D@' =%(D9' =4@BBBB%()?)?D' =.U7 BBBBBcM -0.00312 -0.0088 C 0.00139 -0.00856 0.01684 -0.00741 0.02535 -0.00717 C 0.03386 -0.00694 0.03681 -0.00694 0.04827 -0.00717 C 0.05973 -0.00741 0.08455 -0.00833 0.0941 -0.0088 *3>*B ppt_xB ppt_y=D0BB aaaapBBrG=Bֹr:<*O`D' =4@BBBB%()?)?D' =.7 BBBBBM -0.05278 0.10548 C -0.05868 0.11566 -0.06441 0.12607 -0.06962 0.13602 C -0.07482 0.14596 -0.07986 0.15499 -0.0842 0.16493 C -0.08854 0.17488 -0.08958 0.18159 -0.09618 0.19547 C -0.10278 0.20935 -0.11337 0.22878 -0.12396 0.24844 *3>*B ppt_xB ppt_y=F0BB aaaaApBBB"c=<*0`Df' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*0`%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*:`%(DS' =%(D' =%(D5' =4@BBBB%()?)?D' =.Q7 BBBBB_M -3.33333E-6 -2.21374E-6 C 0.00261 0.00463 0.00139 0.00393 0.01563 0.0273 C 0.02986 0.05066 0.06545 0.10664 0.08559 0.13972 C 0.10573 0.1728 0.12622 0.20842 0.13698 0.22647 *3>*B ppt_xB ppt_y=D0BB aaaapBB=BN=<*@`Df' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*@`%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*E`%(D ' =%(D ' =%(D' =4@BBBB%()?)?D' =.7 BBBBBM 0.00521 0.00486 C 0.00139 0.01018 -0.01007 0.02544 -0.0177 0.03539 C -0.02534 0.04534 -0.03593 0.05829 -0.04062 0.0643 *3>*B ppt_xB ppt_y=B0BB aaapBBB<<*:`D' =4@BBBB%()?)?D#' =.7 BBBBBM 3.33333E-6 -3.62248E-6 C 0.00434 0.00879 0.00468 0.01134 0.01441 0.0273 C 0.02413 0.04326 0.04913 0.08143 0.05816 0.09554 *3>*B ppt_xB ppt_y=B0BB aaapBB؂<B.C=<*E`D' =4@BBBB%()?)?DS' =.7 BBBBB%M 0.09532 -0.0088 C 0.10174 -0.00903 0.12309 -0.01042 0.13386 -0.01042 C 0.14462 -0.01042 0.15313 -0.00903 0.16042 -0.0088 C 0.16771 -0.00856 0.17309 -0.0088 0.17795 -0.0088 C 0.18282 -0.0088 0.17709 -0.0088 0.18924 -0.0088 C 0.20139 -0.0088 0.23785 -0.0088 0.2507 -0.0088 *3>*B ppt_xB ppt_y=H0BBaaaaaapBB=Ba 6<*O`Df' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*O`%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T`%(D' =%(D' =%(DJ' =4@BBBB%()?)?D' =.f7 BBBBBM -5.55556E-7 1.85185E-6 C 0.02396 -0.00046 0.04809 -0.00093 0.05764 -0.00116 *3>*B ppt_xB ppt_y=0BBaA<*T`D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<**`%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$`%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*V`%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*W`%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%`%(++0+$` 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Z1?"6@ NNN?N @  @ B / ND1?"0@NNN?NP @ z  `   0 `  ,$D 0M" 1  f8o?"6@`NNN?N `   qm2| | 1 | 1 F2 2 Z1?"6@ NNN?N  @ B 3 ND1?"0@NNN?N z  0  4   0 ,$D 0d" 5  f o?"6@`NNN?N@p 0  m0| 1 | 2 | ^2 6 Z1?"6@ NNN?N   @ B 7 ND1?"0@NNN?N p z P `  8 `P  ,$D 0d" 9  fo?"6@`NNN?Np `  m0| 1 | | ^2 : ZD!1?"6@ NNN?NP   @ B ; ND1?"0@NNN?N p z" <  f#o?"6@`NNN?N0 ,$D 0 r m#| Q0 | Q1 | Q2 Bz  `   $  @ ,$D 0M" %  f*o?"6@`NNN?N `   qm1| 2 | | 2 F2 & Z11?"6@ NNN?N  @ B ' ND1?"0@NNN?N  z P  P   p ,$@ 0L" !  f$6o?"6@`NNN?NP   pm1| 2 | | F2 " Z|=1?"6@ NNN?NP  P @ B # ND1?"0@NNN?N  H  0޽h ? 3333}RuR___PPT10UR.e+q!DQ' = @B D+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D8' =%(Dr' =%(D' =4@BBBB%()?)?Dn' =.67 BBBBBkM -5.55556E-7 2.63706E-6 C -0.00729 0.00786 -0.01441 0.01573 -0.0217 0.02428 C -0.029 0.03284 -0.03802 0.04256 -0.04341 0.05158 C -0.04879 0.0606 -0.05157 0.06962 -0.05434 0.07888 *3>*B ppt_xB ppt_y=0BB aaaA<*Df' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =%(D ' =%(D9' =4@BBBB%()?)?D' =.U7 BBBBBcM 0.00399 0.00115 C -0.00069 0.01156 -0.00538 0.02197 -0.01059 0.03146 C -0.0158 0.04094 -0.02048 0.04649 -0.02743 0.05875 C -0.03437 0.07101 -0.04844 0.09761 -0.05278 0.10548 *3>*B ppt_xB ppt_y=D0BB aaaApBB>鼐Bo/U=<*8D' =4@BBBB%()?)?D&' =.7 BBBBBM 7.5E-6 -6.66667E-6 C 0.00817 0.00393 0.01633 0.00786 0.02223 0.01296 C 0.02813 0.01805 0.03074 0.02384 0.0356 0.03078 C 0.04046 0.03773 0.04705 0.04699 0.05174 0.05462 C 0.05643 0.06226 0.06112 0.06967 0.06337 0.07615 C 0.06563 0.08263 0.06528 0.08773 0.06511 0.09282 *3>*B ppt_xB ppt_y=!0BBaaaaaA<*D3' =4@BBBB%()?)?D' =.O7 BBBBB]M -0.00209 1.11022E-16 C 0.00225 0.00046 0.01302 0.00162 0.02448 0.00231 C 0.03593 0.00301 0.05468 0.00394 0.06666 0.00394 C 0.07864 0.00394 0.09062 0.00255 0.09687 0.00231 *3>*B ppt_xB ppt_y=D0BB aaaapBBJ=Bֹ:<*(D|' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*(%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D ' =%(D@' =%(D9' =4@BBBB%()?)?D' =.U7 BBBBBcM -0.00312 -0.0088 C 0.00139 -0.00856 0.01684 -0.00741 0.02535 -0.00717 C 0.03386 -0.00694 0.03681 -0.00694 0.04827 -0.00717 C 0.05973 -0.00741 0.08455 -0.00833 0.0941 -0.0088 *3>*B ppt_xB ppt_y=D0BB aaaapBBrG=Bֹr:<*,D' =4@BBBB%()?)?D' =.7 BBBBBM -0.05278 0.10548 C -0.05868 0.11566 -0.06441 0.12607 -0.06962 0.13602 C -0.07482 0.14596 -0.07986 0.15499 -0.0842 0.16493 C -0.08854 0.17488 -0.08958 0.18159 -0.09618 0.19547 C -0.10278 0.20935 -0.11337 0.22878 -0.12396 0.24844 *3>*B ppt_xB ppt_y=F0BB aaaaApBBB"c=<*8Df' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(DP' =%(D ' =%(D' =4@BBBB%()?)?D' =.7 BBBBBM 0.00521 0.00486 C 0.00139 0.01018 -0.01007 0.02544 -0.0177 0.03539 C -0.02534 0.04534 -0.03593 0.05829 -0.04062 0.0643 *3>*B ppt_xB ppt_y=B0BB aaapBBB<<*4DZ' =4@BBBB%()?)?D' =.v7 BBBBBM -4.16667E-6 -5.92593E-6 C -0.0026 0.01157 -0.0052 0.02314 -0.00885 0.03333 C -0.0125 0.04351 -0.01111 0.04143 -0.02222 0.06064 C -0.03333 0.07985 -0.06336 0.12708 -0.07586 0.14884 C -0.08836 0.17059 -0.0927 0.18032 -0.09722 0.19166 C -0.10173 0.203 -0.10312 0.20925 -0.10347 0.21666 C -0.10382 0.22407 -0.10138 0.23032 -0.09895 0.2368 *3>*B ppt_xB ppt_y=#0BBaaaaaaA<* D' =4@BBBB%()?)?DS' =.7 BBBBB%M 0.09532 -0.0088 C 0.10174 -0.00903 0.12309 -0.01042 0.13386 -0.01042 C 0.14462 -0.01042 0.15313 -0.00903 0.16042 -0.0088 C 0.16771 -0.00856 0.17309 -0.0088 0.17795 -0.0088 C 0.18282 -0.0088 0.17709 -0.0088 0.18924 -0.0088 C 0.20139 -0.0088 0.23785 -0.0088 0.2507 -0.0088 *3>*B ppt_xB ppt_y=H0BBaaaaaapBB=Ba 6<*,Df' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D= ' =%(Dw' =%(DJ' =4@BBBB%()?)?D' =.f7 BBBBBM -5.55556E-7 1.85185E-6 C 0.02396 -0.00046 0.04809 -0.00093 0.05764 -0.00116 *3>*B ppt_xB ppt_y=0BBaA<*0D' =4@BBBB%()?)?D!' =.7 BBBBBM -0.09896 0.23681 C -0.09688 0.24167 -0.09479 0.24653 -0.09011 0.25 C -0.08542 0.25347 -0.07899 0.25671 -0.07031 0.25833 C -0.06163 0.25995 -0.05052 0.25949 -0.0382 0.25949 C -0.02587 0.25949 -0.01389 0.25926 0.00364 0.25833 C 0.02118 0.25741 0.04896 0.25463 0.06719 0.25347 C 0.08542 0.25232 0.10087 0.2507 0.11354 0.25116 C 0.12621 0.25162 0.13455 0.2537 0.14305 0.25579 *3>*B ppt_xB ppt_y=L0BBaaaaaaaApBB}=B/=<<* Df' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<* %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(DC' =%(D' =%(D' =4@BBBB%()?)?D' =.7 BBBBBM 3.33333E-6 4.44444E-6 C 0.00729 0.00185 0.01458 0.00393 0.01961 0.00717 C 0.02465 0.01041 0.02708 0.01435 0.03021 0.01898 C 0.03333 0.02361 0.03507 0.02731 0.03836 0.03449 C 0.04166 0.04166 0.04583 0.05162 0.05 0.0618 *3>*B ppt_xB ppt_y=F0BB aaaaApBB<B5<<*$D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(++0+ ++0+ ++0+< +} ;  $(  r  S pV \   r  S DW \`   H  0޽h ? 3333___PPT10i. ௌR+D=' = @B +2 ;  /(   /  A  \latency-stretch_ 0<$D 0 r % S g \    & S h \@<$@ 0  ?" ) Zio?"6@ NNN?N ,$D 0 Csub-linear growthH  0޽h ? 3333  ___PPT10 . B+CDS ' = @B D ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*/%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*&Fd%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*&dq%(+8+0+) + ; qi0 (     A6 \latency-stretch-vs-latency0@ <$D 0 r  S  \   "   TTo?"6@`NNN?NP ,$D 0 cThe highest ratios correspond to pairs in which sender and destination are very close to each otherdd2  TP o?"6@ NNN?N  ,$@ 0B @ TD1?"0@NNN?N ,$@ 0   A& \latency-stretch-640@  H  0޽h ? 3333/ ' ___PPT10 . +ZD' = @B D^' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DY' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(+8+0+  +} ; `$(  r  S w \  w r  S w \`  w H  0޽h ? 3333___PPT10i.R s+D=' = @B + ;  woP (     |A \seq_atoms_cdf0p r  S ԓ \   "  NDo?"6@`NNN?N0  ,$D 0 cThe number of sequencers on a path is less than half of the total number of nodes that participate "dbH  0޽h ? 3333___PPT10. +-|DO' = @B D ' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(+8+0+ +} ;  $(  r  S D \   r  S  \`   H  0޽h ? 3333___PPT10i. J+D=' = @B +< (    N 1?"6@ NNN?N@@ < 2   Nt 1?"6@ NNN?N @@ @ Thank You! (2 (r  S  ` @@   H  0޽h ? 33___PPT10i. R+D=' = @B +}<  $(  r  S | `@@   r  S P ` @@   H  0޽h ? 3333___PPT10i. `Ό+D=' = @B +} ; $(  r  S  \   r  S  \`   H  0޽h ? 3333___PPT10i. p@*+D=' = @B +} ;  $(  r  S tt \   r  S  \`   H  0޽h ? 3333___PPT10i. i+D=' = @B +M ; d\  (  r  S  \C   x  c $` \`     A" \seqstress-vs-grph H  0޽h ? 3333___PPT10i. `%k#+D=' = @B +; 0 @ dK(  dX d C     d S dL 0   M9How do you detect loops How does a receiver detect order?H d 0޽h ? 3380___PPT10.0| 0 ` l(  lX l C     l S R 0   FHow does a receiver order messages? Seq numb in msg Start m0 before m1,$ H l 0޽h ? 3380___PPT10.p  0 @8p p(  pX p C    8 p S P 0`  H@___PPT9" Why do we need ordering in pub/sub Assume: A set of users interested in disseminating some type of information (publishers) A set of users interested in receiving the information (subscribers) Each subscriber receives a message from each publisher Take subscribers A and B, they receive messages m1 and m2 from publishers P1 and P2 It is possible that, due to the different paths messages take from publishers to subscribers, A sees m1 first and B sees m2 first Bottom line, diff font, larger, brighter Some node& b#-- -# H p 0޽h ? 3380___PPT10.@Y 0  t(  tX t C     t S  0  w Instead of a single sequencer we use a network of sequencers (we distribute the task of ordering across them) Messages have specific paths through this network and they get one sequence number form each sequencer they traverse Receivers will be able to order messages on arrival based on these sequence numbers This is better! Why? Scalable  sequencers do not see more messages than the most active receiver Practical  messages are not required to traverse paths much longer than necessary - the additional info appended to a message is proportional in the worst case to the number of groups We focus on the ordering scheme and the construction of the sequencing network, we do not focus on how messages reach the sequencing network or how they travel from it to destinations jLiLi H t 0޽h ? 3380___PPT10. @ X 0  h(  X  C      S  0   j:How do we build the sequencing network? First, let s make some key observations All subscribers that have the same subscription will receive the same set of messages and can be considered to be part of the same group Thus we only need to enforce order among messages across groups (a receiver must receive the same order as all other receivers in the same group) and not across the whole system (unless all subscribers have one common subscription there are no messages going to all nodes) Immediate observation: we can associate one sequencer with each group --- this sequencer will help establishing order among messages addressed to the group This would be fine but& H  0޽h ? 3380___PPT10.9 S8 0 *" (  ^  S      c $ 0   There are double overlapped groups (groups that have at least two subscribers in common) Key observation: receivers may make inconsistent decisions about message order only when they belong to double overlapped groups Thus we will associate a sequencer with each double overlap between groups Messages to both G0 and G1 will traverse the sequencers associated with any double overlapsH  0޽h ? 3380___PPT10.9 S8 0   (  X  C      S $dw 0   "Change ox axisH  0޽h ? 3380___PPT10.  _   0    (  X  C       S ( 0   Why is ordering important? Where does it count? There are some applications built on the pub/sub model that could benefit from an ordering protocol Stock tickers Consider several brokerage firms that subscribe to see certain stock market trades It is important for consistency that all firms that are subscribed to see the same trades see them in the same order Network Games There have been attempts to implement multiplayer online game applications using the pub/sub model In these implementations the subscribers are the players and they subscribe to see events in the region of the game world they belong to Needless to say that ambiguous ordering of these events has a significant impact on the consistency of the game Messaging Internet messaging applications typical follow the pub/sub paradigm For example, a user may publish whether he is online or offline, while other user may subscribe to be notified when a friends comes online by adding him to the buddy list Ordering is not  critical for correctness in messaging, but enforcing that all the messages appear in the same order to the users should make such a system easier to use\    \    H  0޽h ? 3380___PPT10. => 0 0N(  X  C      S  0   PBefore going over our solution to the ordering problem, let us see a nave approach to the problem. If messages need to be ordered, let s make the pass through a specialized node (called sequencer) where they will receive a sequence number Receivers will order messages on arrival based on these sequence numbers Problems? As the number of messages increases, a single node will have a hard time supporting all of them and& may be overloaded and fail (limits feasible system size and introduces cfp) How do we fix this? Experience taught us that if something does not scale, to build a tree, and that is what we will do<CxCxzH  0޽h ? 3380___PPT10. &  0 @6(  X  C      S $ 0   8We have used simulation to validate the performance of our protocol We focus on the properties of the protocol when the group membership is static or does not change very often Questions first Overhead penalty = how many seq no. H  0޽h ? 3380___PPT10.Q @f9) 0 P9(  X  C      S  0T  <4___PPT9 To compute the latency stretch, we have each host send a message to each group, first using the sequencer network and then directly, using the shortest path No green on white Font size on graph -H  0޽h ? 3380___PPT10.Q Pu; 0 pK(  X  C      S ' 0   M9Align groups or highlight overlaps Properties bigger fontH  0޽h ? 3380___PPT10. 0m& 0 /(  X  C      S  0   1Immediate delivery not as in H  0޽h ? 33