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Practical Applications: Efficient control / operation of: Bank, computer system, web server, telecom Fairness in queues: Many statements:  this is fair ,  that system is unfair . Very little analysis (job fairness): Larson (1988), Palm (1953), Mann (1969), Whitt (1984): Discuss justice related / overtaking Morris & Wang (85). Avi-Itzhak & Levy (96) Wierman & Harchol-Balter (Sigmetrics 2003): We don t know how to quantify queue fairness! =ZZ;Z+ZZbZZ1Z,79!+  (        .t  8 %How Important is fairness in queues? $&$$Recent studies, Rafaeli et. al. [2003] (experimental psychology): Experiments on humans in multi-queue and single queue Fairness in queue is very important to people Perhaps even more than delay itself! PBZZZB 8 So  What is the problem?  ( /Motivation / Questions 'Should Long be served ahead of Short? (Z(j#:Motivation / Questions (2): Do You like your supermarket? ;; #How fair is a scheduling policy? T"Z" ZZ"8B.Motivation / Questions (3): and your airport? $/-$ >HApplications (computer world) HIRelated Work(1)Avi-Itzhak & Levy (96): Axiomatic approach Departure point+emphasis: Seniority (Order of service) If service times are identical variance of waiting time measures fairness Extend to service times When is it good? ZZF 4,  $]Recent Related WorkWierman & Harchol-Balter (Sigmetrics 2003): Propose a Fairness Criterion Class-based approach: For job of size x compute E[T(x)/x] If this is bounded by 1/(1-rho) for all x FAIR. Results: Analyze the classification for a large variety of policies. FIFO (FCFS)  is  Always UNFAIR LIFO (preemptive)  is FAIR. When is it good?4Z3ZEZ@ZZ?  (E=Z |IJConflicting (disturbing) Views NM.Basic Requirements of a Queue Fairness measure//zAim for standard: Have a consistent view/intuition Deal with individual, scenario, and system Account for both seniority and service requirement: Seniority: Service times are identical: Fairness is a function of seniority FIFO most fair / LIFO most unfair Senior ahead of junior is more fair Service requirement: Arrival times are identical Fairness is a function of service requirement Short ahead of long is more fair Yields to analysis $" Z)" Z% ZG" Z2" Z. Z!" Z" Z     %G  .!  &6RAQFM: A Resource Allocation Queueing Fairness Measure77(^Aims at meeting these requirements In particular: Long vs. Short Seniority vs. service times b3+#+cQ#Approach: individual discrimination$$#(dTo whom should a job be compared? (moving target!) Compare to the  public . Focus on server resources (aim at equal division) Weigh the warranted service with the granted serviceVZ oRBasic Properties of RAQFMVResource allocation is proper = zero-sum discrimination (work conserving, non idling) VWZ TN1Property 1: Processor Sharing: Ultimate Fairness22$kSingle server queue Processor sharing service policy (Kleinrock (64), (67), Coffman, Muntz & Trotter (70)) 6lZ56,6 YO0Property 2: SENIORITY (identical service times)61 $ $$Single server queue Service times are all identical Arrival times are arbitrary Theorem 2: Serving by order of seniority (FIFO) is most fair Serving in reverse order of seniority (LIFO) is most unfair Pushing a junior ahead of senior reduces fairnessB]] xS3Property 3: Service Time (identical arrival times)64 $ $$QSingle server queue Arrival times are all identical Service times are arbitrary pQ   {T1Property 4: More advanced The Long vs. Short case62$$$=Single server queue Long and short arrive at different times <=)W-Property 5: Bounds How bad (good) can it be? ..$LBound on individual discrimination Use for scale of reference / sanity check$M+"Y#Property 6: Locality of Comparison $$$Measure can be evaluated by comparing all customers (across busy periods) Unique to RAQFM within a large function family. Important for fairness: One should compare only relevant customers (within busy periods). Z6]\6Property 7: Discrimination Monotonic in Service time 77$THM: For an arbitrary system, if service decision is independent of service time, then: Discrimination monotonically increases with service time (deterministic) Larger customers get preferential service Discrimination monotonically increases with service time distribution justification to the prioritization of short jobs! YZIZ*Z{ZZYI,4  VRAQFM is Analyzable $ 1@VIndividual discrimination under FIFO: M/M/1 ( conditioned on # customers found ahead) 4W, ) :Discrimination as a function of # customers found at queue;;~U.System Unfairness: Compare operation policies // .System Unfairness as a function of system load//X+How other measures relate: Bridging the gap,, Wierman & Harchol-Balter (2003) FIFO (FCFS)  is UNFAIR LIFO (preemptive)  is FAIR t!Z6ZZ!6?+/RAQFM: account for all factors - bridge the gap00( [Comparison of Methods ^Summary Z Closing Words /PlK U Z py| ` ` ̙33` 333MMM` ff3333f` f` f` 3>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> f(    68 P  T Click to edit Master title style! !  0   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  0į Pp  >*   0h P`    @*   0  P  @* H  0޽h ? ̙33 Default Design 0 zr@  (     0s P    P*    0 x     R*  d  c $ ?    0t  @  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  6~ `P   P*    6 `   R*  H  0޽h ? ̙33 X(    0  P   8 F* b   0l4    8 H* b   6DX `P   F* b   68 `   H* b H  0޽h ? ̙33  ia  (     0,P     0,o  `@ P March, 2004( (   Hs?#"  ;Hanoch Levy School of Computer Science, Tel Aviv University<(2<6^   Hw?#"  @+ VJointly with Benjamin Avi-Itzhak, RUTGERS University David Raz, Tel-Aviv University W(2W>H  0޽h ? ̙33   phPj (     0P<$D 0    l  P  Q ,$D 0P O C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl1\PE04195_.wmfP ,$D 0 t  j P  ,$D 0$  S AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmf  J " C S A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf 9 " D S A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf P " E S A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf " F S A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf  K C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf ` L C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmf@0 j N C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmf p  <A)?#" `0,$D 0 _ B\KGźH]?"p p,$D 0 d Not Fair!!! ,( b 68P ?"  ,$D 0 ^&To provide FAIRNESS in waiting/service'(2' 3 l Pp  i0` ,$D 0 N p  h p  N p  g  p V S S A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl1\PE04195_.wmfFp ,$D 0$ U S A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmf0 ' " V S A  C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf `  " W S A  C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmfg0 M " X S A  C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf4 ; " Y S A  C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf' ` P} " Z S A  C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf0 k $ [ S A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmf;` S@ $ \ S A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmfu p 4 ` HxVG7wH6~? 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What is the  PIE ? A  moving target & ,/ 2-4 z= 6t+?" @,$D 0 8The difficulty (A): Whom to compare a customer against? 89(23#33! |= <L0 ?"@,$D 0 s+ The problem in a nutshell: Short vs. Long,, 2*H < 0޽h ? ̙33Rs  sr>1r(  0 0  0A 0<$D 0    0 c $A0 <$D 0  2 0 s *@ P` ,$D  0 0 0D  ,$D 0 \ Is it fair?  0Z " 0 0L @@ p ,$D 0 >How fair (how much fair) is it to serve Short Ahead of Long? ?0Z?1 0 0([  @,$D  0 -Quantify/ Measure Fairness in Waiting lines! >-0Z0Z2+mF  T  0  p z  0 6A'?#" Xp  0 @BgCDEtF~ !|+k5Y>HI6S%]bcc egfedXL)@<5P)cv<@@`';V_P  0 BCDEdFn)r:bLP]@m/}|xk&]6OF?U0b p48@`JNyq0  0 B$C/DETF^"&)) )+, /!#!! $  ,0@`y  0 B2ClDEF11> AD#G.L:NFSRV]Zh]u`cfijllcZQI >3%'2"  th] R#E':*.."36 :>dh@`a 0 B#CCDEDFNCC >:5( " # #-7C$(@`A 0 BCDE4F>MMa#1@U-lBP\fpw #/:GTbo}xfTC0| tmf]TLC9/u!j_UMF@>61]-0* $ 1Ma@`G# 0 BCDEF%% ,AWm (0:DNZdo{}vwcnPg>a.Z)R#KD;3 +# LP@`aqP 0 BHCDEdFn'9J Ziu%2=FzHmF`BR>E974*.&  48@`V{0 0 B5CmDETF^7@ JT^f"k*m5k4]1P.D*7%+  &7,0@`S~hZT ` Q  0# 9`  0 BGCDEFݿqq `m| !%)))*+17>DHKKHDB@?EJOTZ_dijjjjoysdWzOoIkIhIfFeBe=g<j:k:q:w<|?BFJPV_is|vpjd_WO,F2I:F?@C7>3</>,A'D#GGC6 (  "v'f,V2H4@96=/B'GMSZ `@` Q4  0 BC&DE4F> &%#     & @`  * 0 BCDEFݿ55'2 8:>=$=+;2:88>8C8G8GB@J8P2W,a'k#u&~-z5w;qAkGeM^QUW]Yj[w^e{lrqgu[xP|B7+}vj\OA 5' 'lp@` I L  0 zBCDEF%%s^F.,& p[F 1,@T WZ']3`@cLfZiflsnqsvz}LP@` LN j 0 :BOCDEtF~  ) 08AIIJLNNNN O F <3*  <@@`z D N * 0 B(CDETF^, ?Rct"(%!s`M: &,0@` c J 0 BDCCDEdFn@B"B(B.B3B:B?BDC@3< 5*%   "2@48@` 5 J 0 BCCBDEdFn9;<$>*?0@7@=BCB>0:4)$  ,948@`/ r * 0 B2CFDETF^B)F1E2?05+)&"!  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BCDE$F.?6X'|,.03<@HcPuYblw+9FS`n{xeP=*~sfYL>0....:ENYblu~oS8 |pdYMC|9l.Z%J9 98865320-*~(q%b"UG:52. * & "( Ox6@` 7 j / :BCDEFL==2/+:$DP\g s }!v&p*l0i4i9g>iBjFmIrLwSSU^immkieca}awctfrjopvtw{ycP{=r-i^UMGC @=: 7)2/|@`P J J 0 BeCzDEdFn? -<$I.V8bCoMzQ_V@]"eedccWK ? 2% 48@`b O  1 BCDE4F>LMM ", 6HYhp#y*1001|1y6u;u>xC{FJNSW]aed}ax[rWlThRbT\ZUc\kcsl|ry}o]L<8/%&089998-# qdWJ = 1# @`  J 2 BCDEF?99'- *$!!""(@/[5x<@EJPX`ity}ylbZRLtH`EJC2@$>:2+%  tx@`m t j 3 :BmC=DEtF~L ")/5(9/=6=><F:N7V5^0f,m'lf_ YNC 6+ <@@` ' j 4 :BCBDEtF~L7)Z;N`o~B=72-{oblSGB#1+$   <@@`] B   5 BiCODEF?11QL2IMDl?8.  &3 @FJO'O,I-C-=.6&6!2) ! &-3:@ES]dhgiLg2aYWU SQdh@` O y z 6 6A'?#"  UO z 7 6A)?#" l _ z 8 6A$?#" &`   9 B,?#"  $   =S ( 2b : B?#" 4O o  LL .( 2b`H  0޽h ? ̙33  LD (@(     00<$D 0     c $,P@<$ 0  z  @q  ( @ q ,$D 0B   Hx ?" @`  T Equal Share philosophy ( axiom ): at t: D+(    s *A; - ??pq x - d8z 3 s    $s ,$D 0  s *A" ?? ! x d  s *A! ?? s x d  H ?"3    \ Warranted service of *(z  !  $  ! ,$D 0  H ?"   Z Granted service of *(N @ !  # @ !   s *A" ??@ O x d  s *A# ?? ! x dFl P  %P ,$D 0  c $A% ??` x d  H$ ?"P  2 Individual discrimination of (net service) 6( 2 " c $A" ??p  x dH & C A?C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl0\BS00917_.wmf  ,$D 0H  0޽h ? ̙33     0  (     00<$D 0     c $0<$ 0    c $A< ??@@ $D 0d,l pgq  g,$D 0  c $A& ??pD q x d  c $A> ?? g x dZl  0p   ` ,$D 0  0H  p  @System measure of discrimination: aggregate statistics of (A  !  c $A ??@ 0@ x dA  6X  ,$D 0 mEliminate: Expected discrimination Reasonable: distance from mean, Var(D), E[|D-E[D]|]. Measure of Unfairness8n  CB(Oz        ,$D 0  60  @  uIndividual discrimination:(   s *A ?? x dAH  0޽h ? ̙33Q   @ (     0)`<$D 0     c $*<$ 0  #l P   P ,$D 0  c $A ?? 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B/C4DETF^'(* -0344 3$'),/& ',0@`Wf  / BCDEF11 ;!U-m;K^vrcUF;-%#/<IUbmy~wpha[UI?o5],L$9& dh@`-g4 0 BCDE$F.?6X'|,.03<@HcPuYblw+9FS`n{xeP=*~sfYL>0....:ENYblu~oS8 |pdYMC|9l.Z%J9 98865320-*~(q%b"UG:52. * & "( Ox6@`ZLp 1 @BCDEFL==2/+:$DP\g s }!v&p*l0i4i9g>iBjFmIrLwSSU^immkieca}awctfrjopvtw{ycP{=r-i^UMGC @=: 7)2/|@`_}P 2 BeCzDEdFn? -<$I.V8bCoMzQ_V@]"eedccWK ? 2% 48@`4aUs 3 BCDE4F>LMM ", 6HYhp#y*1001|1y6u;u>xC{FJNSW]aed}ax[rWlThRbT\ZUc\kcsl|ry}o]L<8/%&089998-# qdWJ = 1# @`a}p 5 @BmC=DEtF~L ")/5(9/=6=><F:N7V5^0f,m'lf_ YNC 6+ <@@`p 6 @BCBDEtF~L7)Z;N`o~B=72-{oblSGB#1+$   <@@`2e 7 BiCODEF?11QL2IMDl?8.  &3 @FJO'O,I-C-=.6&6!2) ! &-3:@ES]dhgiLg2aYWU SQdh@`_   <A'?#"  E bN  V s  Vp @ @BgCDEtF~ !|+k5Y>HI6S%]bcc egfedXL)@<5P)cv<@@`;P A BCDEdFn)r:bLP]@m/}|xk&]6OF?U0b p48@`1V B B#CCDEDFNCC >:5( " # #-7C$(@`* C BCZ DEDFN).Qx Hn{{tmjlor w~$1=IItFeCUAFC6G(Sf~ -Mm{v3qTpip}omspie^#ZNXzX[cn~@c/LTY\\~ZuWmTeQ^IW@P9H3>/5,+, -049= CIPVamvzyv!q&o-4;ESd,z=DA@@@@@?<)  ~zuqlhd`^elry+7DP]jx 2&EMVtft{ |# : M P S V Y Z Z Y W L ? 1 # !  ! !   y_F-3MfoIu#hYJ8=CHLPTY^}RfGO:7/ #  &w/Z7=> GOU[biouz~,9AGGCDFIJIA34 7<@ C(C0A8<;,<9 6<BHLKIFB<71,xqjd]}_Ze6lurvqY@'&7J\m} )9 J\n!&()%  &3@N\jz ztmid%c+f3p6}789>FT\ckry|}n^M|7u!l d`\XT]_]Zccm^IS&E4#}sjaYQJC;p6c.U)H!5# +8FSam~yqcrAga`aeviJnqrpj_`MD3- {pe ZPF< 2').$(@` P D BCDEF?99'- *$!!""(@/[5x<@EJPX`ity}ylbZRLtH`EJC2@$>:2+%  tx@` E H8?#" C LL .( 2b`JT  dE  F#  E0 G B$C/DETF^"&)) )+, /!#!! $  ,0@`F H B2ClDEF11> AD#G.L:NFSRV]Zh]u`cfijllcZQI >3%'2"  th] R#E':*.."36 :>dh@`Y I BCDE4F>MMa#1@U-lBP\fpw #/:GTbo}xfTC0| tmf]TLC9/u!j_UMF@>61]-0* $ 1Ma@`;d J BCDEF%% ,AWm (0:DNZdo{}vwcnPg>a.Z)R#KD;3 +# LP@`n$P K BHCDEdFn'9J Ziu%2=FzHmF`BR>E974*.&  48@`u0 L B5CmDETF^7@ JT^f"k*m5k4]1P.D*7%+  &7,0@`v M BGCDEFݿqq `m| !%)))*+17>DHKKHDB@?EJOTZ_dijjjjoysdWzOoIkIhIfFeBe=g<j:k:q:w<|?BFJPV_is|vpjd_WO,F2I:F?@C7>3</>,A'D#GGC6 (  "v'f,V2H4@96=/B'GMSZ `@`( N BC&DE4F> &%#     & @`0 O BCDEFݿ55'2 8:>=$=+;2:88>8C8G8GB@J8P2W,a'k#u&~-z5w;qAkGeM^QUW]Yj[w^e{lrqgu[xP|B7+}vj\OA 5' 'lp@` P BCDEF%%s^F.,& p[F 1,@T WZ']3`@cLfZiflsnqsvz}LP@`&p Q @BOCDEtF~  ) 08AIIJLNNNN O F <3*  <@@`0 R B(CDETF^, ?Rct"(%!s`M: &,0@`P S BDCCDEdFn@B"B(B.B3B:B?BDC@3< 5*%   "2@48@`P T BCCBDEdFn9;<$>*?0@7@=BCB>0:4)$  ,948@`0 U B2CFDETF^B)F1E2?05+)&"!  (:B,0@`p V @BRCFDEtF~=?"@*B2B:CCDJDRFO<M0K#IF A8,&!  /=<@@`P W B:CFDEdFn:F976)3. ) "   -;>@A#C*C/D5D:F48@`0 X B;C%DETF^  # (",#1#5%;%95 /' ,0@` Y B=C/DEDFN #(*),3-=/=82 *  $(@`0 Z B-C,DETF^ (&()#,(,,+-(,+(#  (,0@`P [ BMC7DEdFn '(+&-..61>3F6M7K+I E? 91(   '48@` P \ B7C>DEdFn .136"7':,<2=7>613#0,'"   # .48@`  ] BCDEF-Ry{pg \INpJ}E?81)!   $23CEPW]khp{pe[POMKHyCs<o5l,nrz uM(.>N^n}<e0-,+))+,-9FVfouvxvszrpoke^Xn{hU)[#yfUE6*(#xmcW I:*   &-dh@` 0 ^ BCcDEFL55G&DV@;4-"%V  !/>*K:VJ^[cmca^YUR y/L "&()+++}+o)b)T(G&lp@`6p _ @B8CDEtF~-/1-a(   !'*+16a8.421/-<@@`at ` BC+DE4F>  % +%   @`T a BC.DE4F>   (.(   @` b B&C0DEDFNL!& ),-.#0&#$  $(@`/; c BCDEF--CMU ^gnt$z+~19@GPYblsxpdZUS|SvToTiTeQ]GT>J4A*8!/( "  *3;C\`@`@lP d B>C,DEdFnL # $')* ,&,,,3*8'=#>=94-'! 48@` e BCKDE4F> K?3()>K @`Fu f B"C>DE4F> >6+"#3 > @`OZ 0 g B/C4DETF^'(* -0344 3$'),/& ',0@`Wf  h BCDEF11 ;!U-m;K^vrcUF;-%#/<IUbmy~wpha[UI?o5],L$9& dh@`-g4 i BCDE$F.?6X'|,.03<@HcPuYblw+9FS`n{xeP=*~sfYL>0....:ENYblu~oS8 |pdYMC|9l.Z%J9 98865320-*~(q%b"UG:52. * & "( Ox6@`ZLp j @BCDEFL==2/+:$DP\g s }!v&p*l0i4i9g>iBjFmIrLwSSU^immkieca}awctfrjopvtw{ycP{=r-i^UMGC @=: 7)2/|@`_}P k BeCzDEdFn? -<$I.V8bCoMzQ_V@]"eedccWK ? 2% 48@`4aUs l BCDE4F>LMM ", 6HYhp#y*1001|1y6u;u>xC{FJNSW]aed}ax[rWlThRbT\ZUc\kcsl|ry}o]L<8/%&089998-# qdWJ = 1# @`a}p m @BmC=DEtF~L ")/5(9/=6=><F:N7V5^0f,m'lf_ YNC 6+ <@@`p n @BCBDEtF~L7)Z;N`o~B=72-{oblSGB#1+$   <@@`2e o BiCODEF?11QL2IMDl?8.  &3 @FJO'O,I-C-=.6&6!2) ! &-3:@ES]dhgiLg2aYWU SQdh@`_ z p 6A'?#"  E H  0޽h ? ̙33,v  uu`@C \u(     0h`<$D 0     c $H@<$D 0  Ml pU  pU ,$D 0  0p pP ,$D 0 Y Theorem 3:       c $AC ??pU x dA|  < ?" p7,$D 0 p Serving shortest job first (SJF) is most fair Serving Longest job first (LJF) is most unfair Pushing a large job ahead of small job reduces fairness   (2*)  Eol   C ,$D 0z2 B <?"R Gnt   A ,$D 0z2 @ <?"@ P   <A'?#" Af p   @BgCDEtF~ !|+k5Y>HI6S%]bcc egfedXL)@<5P)cv<@@`P   BCDEdFn)r:bLP]@m/}|xk&]6OF?U0b p48@`0   B$C/DETF^"&)) )+, /!#!! $  ,0@`F  B2ClDEF11> AD#G.L:NFSRV]Zh]u`cfijllcZQI >3%'2"  th] R#E':*.."36 :>dh@`Y  B#CCDEDFNCC >:5( " # #-7C$(@`  BCDE4F>MMa#1@U-lBP\fpw #/:GTbo}xfTC0| tmf]TLC9/u!j_UMF@>61]-0* $ 1Ma@`;d  BCDEF%% ,AWm (0:DNZdo{}vwcnPg>a.Z)R#KD;3 +# LP@`n$P  BHCDEdFn'9J Ziu%2=FzHmF`BR>E974*.&  48@`u0  B5CmDETF^7@ JT^f"k*m5k4]1P.D*7%+  &7,0@`v  BGCDEFݿqq `m| !%)))*+17>DHKKHDB@?EJOTZ_dijjjjoysdWzOoIkIhIfFeBe=g<j:k:q:w<|?BFJPV_is|vpjd_WO,F2I:F?@C7>3</>,A'D#GGC6 (  "v'f,V2H4@96=/B'GMSZ `@`(  BC&DE4F> &%#     & @`0  BCDEFݿ55'2 8:>=$=+;2:88>8C8G8GB@J8P2W,a'k#u&~-z5w;qAkGeM^QUW]Yj[w^e{lrqgu[xP|B7+}vj\OA 5' 'lp@`  BCDEF%%s^F.,& p[F 1,@T WZ']3`@cLfZiflsnqsvz}LP@`&p  @BOCDEtF~  ) 08AIIJLNNNN O F <3*  <@@`0  B(CDETF^, ?Rct"(%!s`M: &,0@`P  BDCCDEdFn@B"B(B.B3B:B?BDC@3< 5*%   "2@48@`P  BCCBDEdFn9;<$>*?0@7@=BCB>0:4)$  ,948@`0  B2CFDETF^B)F1E2?05+)&"!  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(:B,0@`m j U  :BRCFDEtF~=?"@*B2B:CCDJDRFO<M0K#IF A8,&!  /=<@@` J V  B:CFDEdFn:F976)3. ) "   -;>@A#C*C/D5D:F48@`  * W  B;C%DETF^  # (",#1#5%;%95 /' ,0@` G   X  B=C/DEDFN #(*),3-=/=82 *  $(@`D * Y  B-C,DETF^ (&()#,(,,+-(,+(#  (,0@` J Z  BMC7DEdFn '(+&-..61>3F6M7K+I E? 91(   '48@` J [  B7C>DEdFn .136"7':,<2=7>613#0,'"   # .48@` /   \  BCZ DEDFN).Qx Hn{{tmjlor w~$1=IItFeCUAFC6G(Sf~ -Mm{v3qTpip}omspie^#ZNXzX[cn~@c/LTY\\~ZuWmTeQ^IW@P9H3>/5,+, -049= CIPVamvzyv!q&o-4;ESd,z=DA@@@@@?<)  ~zuqlhd`^elry+7DP]jx 2&EMVtft{ |# : M P S V Y Z Z Y W L ? 1 # !  ! !   y_F-3MfoIu#hYJ8=CHLPTY^}RfGO:7/ #  &w/Z7=> GOU[biouz~,9AGGCDFIJIA34 7<@ C(C0A8<;,<9 6<BHLKIFB<71,xqjd]}_Ze6lurvqY@'&7J\m} )9 J\n!&()%  &3@N\jz ztmid%c+f3p6}789>FT\ckry|}n^M|7u!l d`\XT]_]Zccm^IS&E4#}sjaYQJC;p6c.U)H!5# +8FSam~yqcrAga`aeviJnqrpj_`MD3- {pe ZPF< 2').$(@``    ]  BCDEF-Ry{pg \INpJ}E?81)!   $23CEPW]khp{pe[POMKHyCs<o5l,nrz uM(.>N^n}<e0-,+))+,-9FVfouvxvszrpoke^Xn{hU)[#yfUE6*(#xmcW I:*   &-dh@`  8* ^  BCcDEFL55G&DV@;4-"%V  !/>*K:VJ^[cmca^YUR y/L "&()+++}+o)b)T(G&lp@`g 9 jj _  :B8CDEtF~-/1-a(   !'*+16a8.421/-<@@` &  `  BC+DE4F>  % +%   @` `  a  BC.DE4F>   (.(   @`[ k   b  B&C0DEDFNL!& ),-.#0&#$  $(@`R x  c  BCDEF--CMU ^gnt$z+~19@GPYblsxpdZUS|SvToTiTeQ]GT>J4A*8!/( "  *3;C\`@`  @J d  B>C,DEdFnL # $')* ,&,,,3*8'=#>=94-'! 48@`O   e  BCKDE4F> K?3()>K @`   f  BCDE$F.  +wfY?*+sGFC A CGN T Zg.sBzVk{m[C*gF#+T{>Wn#.:GTbp-=N]kyvz vkaVG6#{vplhfP]=+, X   6f )4ANAXM^Zdiiwnv]--D{]Sx+|++.1~8}=>@@AADHMT[f&p:}L^p;Ncv}sV;! saSsDd7U*E5$jWC/)#|~}vcSGmD\;M0?#0! +@`   g  B"C>DE4F> >6+"#3 > @`  -* h  B/C4DETF^'(* -0344 3$'),/& ',0@`  9  i  BCDEF11 ;!U-m;K^vrcUF;-%#/<IUbmy~wpha[UI?o5],L$9& dh@`M d  j  BCDE$F.?6X'|,.03<@HcPuYblw+9FS`n{xeP=*~sfYL>0....:ENYblu~oS8 |pdYMC|9l.Z%J9 98865320-*~(q%b"UG:52. * & "( Ox6@` 7 j k  :BCDEFL==2/+:$DP\g s }!v&p*l0i4i9g>iBjFmIrLwSSU^immkieca}awctfrjopvtw{ycP{=r-i^UMGC @=: 7)2/|@`P J J l  BeCzDEdFn? -<$I.V8bCoMzQ_V@]"eedccWK ? 2% 48@`b O  m  BCDE4F>LMM ", 6HYhp#y*1001|1y6u;u>xC{FJNSW]aed}ax[rWlThRbT\ZUc\kcsl|ry}o]L<8/%&089998-# qdWJ = 1# @`  J n  BCDEF?99'- *$!!""(@/[5x<@EJPX`ity}ylbZRLtH`EJC2@$>:2+%  tx@`m t j o  :BmC=DEtF~L ")/5(9/=6=><F:N7V5^0f,m'lf_ YNC 6+ <@@` ' j p  :BCBDEtF~L7)Z;N`o~B=72-{oblSGB#1+$   <@@`] B   q  BiCODEF?11QL2IMDl?8.  &3 @FJO'O,I-C-=.6&6!2) ! &-3:@ES]dhgiLg2aYWU SQdh@` O y  r  <A'?#"  %  s  <A)?#" <O /  t  <A$?#"    u  Hhw?#"    =S ( 2b v  H`*?#"     LL .( 2b`2 w  <?"0 ,$D 02 x  <?"0 ,$D 0^ {  0x  `,$D 0 RFairness of two orders depends on relative seniority and relative service times. FR  Q   H   0޽h ? ̙33   g _ ` @ (       0 <$D 0      c $6  <$D 0  hz 0  ]  0 ,$D 0 F  6 9 0 ,$D 0 X How good:      G  s *A .?? x .d L  6D  ,$D 0 X(service time) fz    \    ,$D 0 @  60  ` ,$D 0 VHow bad:     B  s *A, ,??  x ,d O  6,U @  ,$D 0 X(waiting time)  V  0ē   ,$D 0 mBound on system discrimination:    Vl   [  ,$D 0 X  6`  ,$D 0 VHow bad:     Y  s *A: *??P nx *d `  s *A8 - ??P ^ - $D 0dH   0޽h ? ̙33T   ,(  , ,  0l`<$D 0    , c $L 0 <$D 0  H , 0޽h ? ̙33T  <(  < <  0hk`<$D 0    < c $4l 0 <$D 0  H < 0޽h ? ̙33  6.D(     00`<$D 0    D <( ?"PR,$D 0 (@ RAQFM yields to analysis via standard queueing theory techniques Can compute E[D| x] (class discrimination) Var[D] (system unfairness) Conducted analysis for M/M/1 type: Variety of service orders (FIFO, LIFO, ROS, more& ). Conducted analysis for Multi-queue / multi-class systems. O 2> 2 26pH  0޽h ? ̙33    }  (     0`p<$D 0     c $p<$D 0  l 0\ 0\,$D 0x   3 A ?0\,$D 0  <01 ?" @w  C Utilization (2 !l p p,$D 0  BȜGzH?"p  C Time to cry (   BG,H{?"0  JTraffic jam at 4AM(  BG@H'Z?"0@,$D 0 D Indifferent  ( /l `@ @,$D 0  BGyH?"`  E Time to smile(  B\G+H?"` `@ VEmpty super-market Friday noon(H  0޽h ?_P   ̙33  D< |(     0`<$D 0     c $x<$D 0    S A9 Q??8 Q$D 0   HGH ?" ,$D 0 WEmpty system: everyone is alone (    BGHk?"0,$D 0 ]%LIFO: Severe seniority discrimination&(&  H$G8H??"p ,$D 0 Z"FIFO: no seniority discrimination #(#  BTG&Hs?"` ,$D 0 NPS: Absolute Fairness!(H  0޽h ?O@   ̙33N  !( ~(  ( (  0`<$D 0   Fl    (  ,$D 0 ( H ?"  X  @` ( H ?"   X3  @` ( H ?"   ZLIFO (preemptive)  @` ( Hx ?"   X  @` ( H  ?"   X3  @`  ( HX  ?"    LFIFO @`  ( B<?"    vQueueing theory (WHB 2003)* @`  ( B"?"   XOrdinary person  @`  ( H$ ?"     View Policy< @`B  ( Bo ?"  zB ( <1 ?"   zB ( <1 ?"   B ( Bo ?"  B ( Bo ?"  zB ( <1 ?"  zB ( <1 ?"  zB ( <1 ?"   B ( Bo ?"   ( <|0 ?"pP p 0,$D 0 hUnfair L< (2 ( <45 ?"` `C,$D 0 d Fair J<(2333 ( < : ?"` `s ,$D 0 hUnfair L< (2 ( <? ?" p s ,$D 0 d Fair J<(2333 (  xA0e0e `pp0<$D 0   ( <D?"0 ,$D 0 ` Seniority 8 2 (2(2   ( <tJ?"0  ,$D 0 d Service times 8 2(2(2H ( 0޽h ? ̙33       N (       0!`<$D 0      S A9 ??  8 $D 0   B 1?"  ,$D 0 `Seniority + service time differences play role (MOST CASES!) RAQFM agrees with ordinary persontF 2#(2D~   <b 33?" B,$D 0  Service time differences very radical (A few cases) RAQFM agrees with Wierman & Harchol Balter; 2,(233333333333333333333,M   < ?"  ,$D 0 B 2    c $A+ ??0   $D 0d334z  p*    p*,$D 0<   B` ?" p*,$D 0 (FIFO: 0.9 LIFO: 0.15 <) 23333fN  P     P 2   B33?" P 2   B3333?" P P H   0޽h ? ̙33  8'(  8 8  0(iPp<$D 0   7 8 <$ ?"P,$D 0 + [AL96]: (SENIORITY) Easy to compute Order fairness: When the issue is ORDER [WHB03]: (SERVICE TIMES) Easy to compute When jobs do not see each other / do not care of each other. RAQFM: (SENIORITY & SERVICE TIMES) Somewhat harder to compute When issue is waiting time. Also for ORDER fairness. , 28 2 2N 2$ 2R 2 8 NR   @`H 8 0޽h ? ̙33  | H(  H H  0``Pp<$D 0   $ H <(a ?"Pp$D 0~___PPT9`X  Fairness is fundamental for queueing systems No agreed upon measure exists RAQFM is a queueing fairness measure that: Has a consistent view Deals with individuals, scenario, and system Accounts for both seniority and service requirement Admits logically to special cases: Service times are identical: Senior ahead of junior is more fair Arrival times are identical Short ahead of long is more fair Yields to analysis We analyzed a large variety of queueing systems Much more work is neededx 20Z0Z$0 Z0Z!0 Z0ZI0Zx    #$  !  I @`H H 0޽h ? ̙33   04 2(  4 4  0\Pp<$D 0    4 < ?"  ,$D 0 2Thank you If you have applications at which fairness is relevant  we will be glad to hear. 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Levy, CS, TAU    .&&  . 2 1.--- !x0@H--- @Times New RomanCwCw w0- 33.(2 How Fair is your Queue*+*.--a( -- 33@Times New RomanCwCw w0- 33.2 t March, 2004   .--Cx-- 33@Times New RomanCwCw w0- 33.2 rHanoch. 33. 2 Levy. 33.N2 5/School of Computer Science, Tel Aviv University          .--^A`-- 33 33.2  Jointly with    . 33.2  Benjamin    . 33. 2 5Aviy . 33. 2 e- . 33.2 oItzhak . 33.%2 , RUTGERS University   . 33.2 David  . 33. 2 \Razy. 33.2 , Tel . 33. 2 - . 33.2 Aviv University     .--"System !)Bw-&TNPP &՜.+,0    xOn-screen Shown-s2    $Times New Roman WingdingsDefault DesignMicrosoft Equation 3.0 Bitmap ImageHow Fair is your Queue Why QUEUES?%Queueing Theory, queues and fairness&How Important is fairness in queues? So What is the problem? Motivation / Questions ;Motivation / Questions (2): Do You like your supermarket? /Motivation / Questions (3): and your airport? Applications (computer world)Related Work(1)Recent Related WorkConflicting (disturbing) Views/Basic Requirements of a Queue Fairness measure7RAQFM: A Resource Allocation Queueing Fairness Measure$Approach: individual discriminationBasic Properties of RAQFM2Property 1: Processor Sharing: Ultimate Fairness1Property 2: SENIORITY (identical service times)4Property 3: Service Time (identical arrival times)2Property 4: More advanced The Long vs. Short case.Property 5: Bounds How bad (good) can it be? $Property 6: Locality of Comparison 7Property 7: Discrimination Monotonic in Service time RAQFM is Analyzable WIndividual discrimination under FIFO: M/M/1 ( conditioned on # customers found ahead) /System Unfairness: Compare operation policies ,How other measures relate: Bridging the gap0RAQFM: account for all factors - bridge the gapComparison of MethodsSummaryClosing Words  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles_ anatanat  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntrydO)Pictures!Current UserSummaryInformation(PowerPoint Document(^ DocumentSummaryInformation8