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LevyO =c!Job Fairness in Queue Scheduling:""$ JKWhy Fairness in Queues?  _Why Fairness in Queues? (2)2$$Recent studies, Rafaeli et. al. [2003] (experimental psychology): Experiments on humans in queue scenarios Fairness in queue is very important to people Perhaps even more than delay itself! 6B}B~,The Size vs. Seniority Dilemma2WMr. Short vs. Mrs. Long Is it more fair to serve Short ahead of Long? By how much?XX`Outline $ $tQueue Model Job-Based systems, Flow-Based systems + applications Prior work  Requirements The performance issue: Delay vs. Service The granularity level: How fine& Dealing with stochastics The physical entities: seniority, service requirement, resources The Fairness Measures - Overview + properties: Seniority based fairness Service time based fairness Resource allocation based fairness Mixture based Application perspective References2ZfZ#Z               ~Queue Model (single server)  %&History: Queueing Theory and Fairness''$bQueueing theory: Decades of research Delay of individual Practical Applications: many & diverse Fairness in queues: Many importance statements: Importance of fairness: Larson (1988), Palm (1953), Mann (1969), Whitt (1984), Rothkopf & Rech (1987) Analysis: was Little, now growing(job fairness): Morris & Wang (85) Gordon (87) Avi-Itzhak & Levy (96) Bender, Chakrabarti . Muthukrishnan (98), Wierman & Harchol-Balter (03), Harchol-Balter et. al. (03) Avi-Itzhak, Levy & Raz (05), Raz, Avi-Itzhak & Levy (04, 05a,b), Raz, Levy& Avi-Itzhak (04), Brosh, Levy & Avi-Itzhak (05) Sandmann (05) (more is coming) .%Z=ZZZfZ1Z8Zf"      8^X   *History: Queueing Theory and Fairness (2)++$ We know only little about queue (job) fairness! More complex than measuring individual delay!bcZ/-Gm&Designing a Metrics - Keep in mind:''$GTo be used by: Researchers Designers / operators Customers (appeal to),99k+The performance issues: Delay vs. Service ,,$~Delay: Job delay (waiting time, sojourn time) Traditional queueing-theory measure The major factor when service is guaranteed PZKZ-ZK+}l$Granularity of Fairness Evaluation %%$8At what granularity level, should fairness be evaluated .88nThe Physical Factors (queues)  orSize and Seniority preference principles ( requirements )::$Seniority SizerSize and Seniority preference principles ( requirements )::$4Seniority principle Weak: All jobs same service times if ai< aj then more fair to complete service of Ji before Jj Strong: Ji and Jj same service times0b%' t;& CHow Scheduling policies meet the principles (are fair by principle)DD$ pThe Size vs. Seniority Dilemma2WMr. Short vs. Mrs. Long Is it more fair to serve Short ahead of Long? By how much?XXReview of Measures (job based)*$(Seniority basedr(Approach 1: Order (seniority) Fairness *)&$(,Gordon (87)  Ph.D MIT Deals with skips and slips: Performance measure of overtaking to quantify the level of  social justice B skips A (A experiences a slip): A arrives before B, B leaves before A Considers several Markovian models Analyses distribution of #slips, #skips Measure: No explicit suggestion Lets try: E[#skips ] - E [ # slips] Problem: E[#skips ] - E [ # slips]=0 So perhaps: E[#skips ] 3ZLZHZZZ"L1Approach 1: Order (seniority) Fairness: results *2/$(,Systems analyzed : 2 M/M/1 in parallel 2 M/M/1 s with one SJQ  smart customer Multi server system: M/M/m Infinite server system: M/G/Inf Analysis: distribution of SKIP and SLIP Results: AVG(#skips) = AVG (#slips) Most systems: Dist(#skips) != Dist (#slips) Smart customer: increases # skips, decreases # slips M/U/Inf with symmetric service time dist: Dist(#skips) = Dist (#slips) [only system found] tZwZ2ZZw2,W:Approach 1: Order (seniority) Fairness: How do I use it? *;8$(Compute: Dist(#skips), Dist (#slips) Analysis or simulation How to use for fairness measure  open issue. j&0 0tHMeasure 2:  service-time Fairness *%"(($Bender, Chakrabarti . Muthukrishnan (1998), Harchol-Balter et. al. (2003) Wierman & Harchol-Balter (2003): Propose a Fairness Criterion Emphasis on service requirement Slowdown: for job of size x compute E[T(x)/x] If the slowdown is lower then 1/(1-) for all x - FAIR Classification of a large variety of policies: Always fair: fair for all dist. + loads Always unfair: unfair for all dist. + loads kZZUZZI )Jc/       ( w0Measure 3: Resource Allocation Fairness (RAQFM)*1'$ (Raz, Levy, Avi-Itzhak (04) Aim at the dilemma between size and seniority Focus on: fair share of resources Ideal: At t, each customer deserves 1/N(t) of system resources (N(t)= # customers(t)) Compare warranted service with granted service lZPZO  , /AAnalysis of Resource Allocation Queueing Fairness Measure (RAQFM)BB$NRAQFM yields to analysis via standard queueing theory techniques We compute for M/M/1 E[D|k]  Discrimination given number seen on arrival Var[D] - system unfairness XWPW4 X  -    0 FCFS Analysis .Time can be slotted by arrivals and departures, slot size is independent State description: a customers ahead of C, b customers behind C. If we assume C is in state (a,b) in slot i customer arrives  probability , state (a,b+1) customer departs - probability , state (a-1,b) b\cJ/1 FCFS Analysis D(a,b) is the discrimination of a walk starting in (a,b), with moment d(a,b) is the momentary discrimination at (a,b) t the slot size $$M?@ FCFS Analysis  A FCFS Analysis  B FCFS Analysis  D FCFS Analysis  2 FCFS Analysis Solving the recursive equation: Choose a maximum value of b, say N Run through the matrix iteratively, column by column O(N2) time, O(N) spaced o 83zIndividual discrimination for FCFS k  number seen on arrival>#(=  %Resource allocation Fairness: Results*&%((2Adhering to principles: STRONG Seniority service principles  YES WEAK Service-time service principle  YES STRONG Service-time service principle  NOTJ*VU,x*Resource allocation Fairness: Results (2) *+)((rPS most fair Reacts to both s.time and seniority FCFS > LCFS (seniority dominant) FCFS < PLCFS (s. time dominant)L1B $  )Resource allocation Fairness: Results (3)**)((:Multiple server more fair than single server with same combined rate Single Queue more fair than Multi-Queue Jockeying increases fairness Jockeying from head more fair than jockeying from tail Prioritizing short jobs is more fair in most cases, but not if the jobs are almost as large as the rest of the population;;"z+Resource Allocation Fairness: Applicability,,( -Resource Allocation Fairness: How Do I use it..( y What fits? Go by the application*! $$ h#How People Perceive Queue Fairness $$#$ Concluding remarks $$ E7Closing Words: Why Study Fairness in Queues (5 reasons)$87$ { THANK YOU    V Homework   'Job-Based vs. Flow-Based +Applications (&$'  !CDealing with Stochastics: Actual measures vs. Expected values (2) 4D$'$ ,"Actual measure: Harder to compute &#"2Dealing with Stochastics: The Black Box question 43$ $ %Customer does not see other customers&&9Measure 4: Mixture Fairness measure: ,:Measure 4 - Mixture : results  (Adhering to principles: STRONG Seniority service principles  YES STRONG Service-time service principle  YES Difficulties: Asymmetry in sensitivity to size + seniority E.g.: X arrives with 100 sec s.time, and waits an hour. Y arrives 1 hour later with 99 sec s.time. It is as fair to serve in both orders. Same if 10 hours. TV;V;;&Measure 4 - Mixture : How do I use it  '%(Analysis of skips  see Gordon (87)  Markovian  can do. Analysis of Large  not provided yet (perhaps in the making). {{</Job-Based vs. Flow-Based +Applications (repeat)00$/  =A word on flow-based measures Deal with flows (of packets) Interested mainly in throughput Literature: Fair bandwidth allocation (network) MinMax fairness (Jaffe (81)) Proportional Fairness (Kelly (97)) Fair Scheduling Weighted Fair Queueing (WFQ) Demers, Keshav and Shenker (1990), Greenberg and Madras (1992), Parekh (1992), Parekh and Gallager (1993), (1994), Golestani (1994), Rexford, Greenberg and Bonomi (1996), Bennet and Zhang (1996), others. KZ$ZAZZZZ    , $A  on%  >+Measure 5: PS proximity WFQ/RFB literature ,*sScheduling fairness measures Worst Case deviation from PS (extreme values) Relative Fairness Bound (Golestani (94))PtZ $ d ?+Measure 5: PS proximity WFQ/RFB literature ,*RAbsolute Fairness Bound (AFB) (Greenberg and Madras (1992) and Keshav (1997)) P-   $>  J'Measure 1: Order (seniority) Fairness *(%$(iAvi-Itzhak & Levy (96, 04) Axioms (for G/D/1): what happens to unfairness measure when interchanging customers: P1: Monotonicity in seniority difference of interchanged neighbors P2: Reversibility of neighbor interchange P3: Independence on position and time P4: Fairness change is not affected by customers not interchanged P4G: interchange of non-neighbors Vq   &"> $`KOrder Fairness: resultsOThm : Let (W, W*) be the steady state waiting time under (policy, FIFO), then: 2PZHMLOrder Fairness: results (2) M*Order Fairness: Properties & Applicability++(* N9Measure 1: Order (seniority) Fairness: How do I use it? *:7$( Compute (  PD Service-time Fairness: Results *#!((Classification (not measure) of a large variety of policies Any preemptive size based policy is always unfair (all loads & all service dists). All non-size based non-preemptive policies are always unfair for service time dist defined on neighborhood of zero (short jobs discriminated). Age based policies are always unfair FCFS is always UNFAIR LCFS (preemptive) +PS are always FAIR<<RbQL Service-time Fairness: Results (2) *'%((Adhering to principles: Seniority service principles  NOT Service-time service principle  Open question(QQ R,S. time Fairness: Properties & Applicability--( S"S. time Fairness: How do I use it ##( #  /K  !O"T#U$ ` ` ̙33` 333MMM` ff3333f` f` f` 3>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> (    0H "P  T Click to edit Master title style! !$  0 "  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  0Ԕ "Pp  >*   0H "P`    @*   0 "P  @* H  0޽h ? ̙33 Default Design 0 zrP  (     0` ;9   P*    0d u 9  R*  d  c $ ?>s    0a  :v  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  6k /;h   P*    6|q /u h  R*  H  06gq ? ̙3380___PPT10.Op 0 0P(    0h ;9   D* B   0` u 9 q F* B   6| /;h   D* B   6 /u h  F* B H  06gq ? ̙3380___PPT10.O0z>  0 ~(     0`     0(   `@ Q May 2005, ( G  H@?#" 0 u;Hanoch Levy School of Computer Science Tel Aviv University<(2<EH  0޽h ? ̙33'   ` m (     0<$D 0   l  P  Q ,$D 0 O C *APE04195_P ,$D 0t  j P  ,$D 0`  S 0Aj0243209  J ` C S 0A BD07630_ 9 ` D S 0A BD07630_ P ` E S 0A BD07630_ ` F S 0A BD07630_ Z K C *A BD07630_ `Z L C *Aj0243209@0 jZ N C *Aj0243209 p  <A)?#" `0,$D 0 _ BGźH]?"p p,$D 0 h Not Fair!!! 0(GC  b 6 ?"  ,$D 0 b&To provide FAIRNESS in waiting/service '(2'G l Pp  i0` ,$D 0N p  h p 2N p  g  p  S S 0A PE04195_Fp ,$D 0` U S 0A j02432090 ' ` V S 0A  BD07630_ `  ` W S 0A  BD07630_g0 M ` X S 0A  BD07630_4 ; ` Y S 0A  BD07630_' ` P} ` Z S 0A  BD07630_0 k ` [ S 0A j0243209;` S@ ` \ S 0A j0243209u p 8 ` H4G7wH6~? 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BCDE(F2   @`M Y  / BCDE<FF         $@`  H 0 BBCEDE`Fj"$*+5/>3EBAA<</5 ,&  24@`q !  1 BCDEF"  @`  8 2 BC,DEXFb?? # ) ,*&"  .0@`   3 BCDE(F2??   @`   4 B(CUDEF--"$'*.27:>@DFHK MPTUUT SOKHD#>%7'1(+(&('&&%$" \`@` 7 H  0޽h ? ̙33V  (     0 <$D 0     0 @P$D 0bZ___PPT9<4 Rafaeli et. al. (2005): Queue experiments on humans FCFS is FAIR (seniority) Violation of FCFS == unfair Regardless if close to the person asked or away of it. Size-issue  not addressed yet. Multi-server: Multi-Queue (MQ) less fair than single queue. One queue in MQ is shorter less fair. If people PAY for the short Q (first-class) Fair. k! Y! ! ! kEWEEEI E B  E  E X @`  HA ? ?"W8 $D  0H  0޽h ? ̙33  h0(  h h  0 *<$D 0   z h 0* @P$D 0___PPT9nf JFairness in Queues is important Measures must Fit applications Agree with one s intuition / be consistent Researcher, designer, customer Yield to analysis Research of subject in it s early stages Much more to study: Scheduling policies Weights Multiple queues /servers Complex structures Relations between measures Other measures& Z!! !0Z>!0Z 0-Z0 Z=0 Zs0 Z EEE>E E  E  G E=ErGE @` h HA I? ?"W8 I$D  0H h 0޽h ? ̙33N  (     0|-0<$D 0     0$   $D 0___PPT9|t xThe Fundamental: ( Q = fairness ) Isn t fairness why we have queues (for human services) in the first place? The Scientific evidence: (Rafaeli et. al. [2003]) Fairness in queues important to people / perhaps > delay The Inductive reasoning: WFQ: 10 s of papers  fairness on O(1) microsecond jobs!! The Challenge: We know very little on Queue fairness The problem is harder than Q delay!(! K0 Z2!0Z:0 Z0 Z;0 Z0 ZJ0 ZEEGCGEGEEG: G E9GEGE%EG$E,w @` z  P    ,$D  0P  C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl1\PE04195_.wmfP ,$D 0   j    ,$D 0  C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmf  J   C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf 9    C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf P    C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf    C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf    C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf `   C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmf@0 j  C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmf p  6A)?#"  ,$D  0  0b  Ppt$D  0@8___PPT9 BThe Practical: Relax your nerves& H"!0Z EGE @`H  0޽h ? ̙33.  n(     0q  <$D 0   6  0Tz   p$D 0<4___PPT9 ^"! E  @` z  P   P  ,$D  0P  C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl1\PE04195_.wmfP ,$D 0   j    ,$D 0  C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmf  J   C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf 9    C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf P    C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf    C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf    C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmf `   C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmf@0 j  C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl61\j0243209.wmf p  6A)?#"  A ,$D  0H  0޽h ? ̙33y  `XL(  L~ L s *ԁP    L s *A&     L <\ ?"p j V Repeat FCFS analysis for LCFS 2 L 6@A#    \  G  H L 0޽h ? f  ___PPT10 .-0+lD ' ^= @B D ' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*M%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*M}%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*}%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+8+0+0 +&  $$:(  ~  s *P    F       <  ?"p(  AServer  2Gz  <f?"z  <̙?"z  <?"z  <?"z   <?"-B   BDjJ?"h T  00   # zB  B <DԔ?" 0zB  B <DԔ?" 0 00 zB  <Do?"000 2  H o?"    < ?">% ;Q 2G  <H ?"@, QJobs 0 2GG  c $A g??\x gdS z `   ` ,$D 0  <0 ?"( AServer  2Gz  <?"5z  <?"5z  <?"z  <?"Cz  <?"` } B  BDjJ?" 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YT  00  # RzB B <DԔ?" 0zB B <DԔ?" 0 00 zB  <Do?"000 2  H o?"P   <$ ?">5% ;Q 2G ! < ?" | QJobs 0 2GG " c $A ?? J x d # <L ?"P ,$D 0 P JOB BASED Customer = Job Applications: Networking: Application level equipment: Web server, file server Supermarket, Bank, public office + alike Call center Computer system * 2  2 GGGG $ <| ?" 0 ` ,$D 0 )u FLOW BASED Customer = Flow Applications: Networking:network level equipment: Routers, gateways, load-balancers , 2&  2$  2G G G&G$GH  0޽h ? f___PPT10.N#{+z,Dh' = @B D#' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*}%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*}D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*}Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*~%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*~D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*~Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*+ 4  `e(     0 *``<$D 0      <*  0<$D 0    0;  ,$D 0  0Z0 Z0Z0 Z0 Z0ZEGEE G G H  0޽h ? ̙33//___PPT10/.+TKdD/' 2= @B D.' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$'%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$'D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$'D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$'T%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$'TD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$'TD' =%(DB' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$T]%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$T]D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$T]D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$]w%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$]wD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$]wD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$w%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$wD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$wD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$E%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$ED' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$EDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*>$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*>$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*>$D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*?$'%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*?$'D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*?$'+p+0+$0 ++0+?$0 +9    p Z (     0@C <$D 0      < D  `<$D 0  F        c $A ??e@~ C  $D 0dT  0\U  ,$D 0 RFB: f0Z0 Z0ZEGGL  0@ #    c $A. ?? 0  $D 0d   08k  0@,$D 0 Can we apply it to jobs (problematic): Not  continuously active Try on L, S: assume FCFS (L arrives before): RFB=L Try on L, S: assume LCFS (L arrives after): RFB=L General M/G/1 (FCFS, LCFS): infinity!'0Z0 Z'EEEGGGGGGGG&GGH  0޽h ? ̙33//___PPT10/.+TKdD/' 2= @B D.' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$'%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$'D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$'D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$'T%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$'TD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$'TD' =%(DB' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$T]%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$T]D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$T]D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$]w%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$]wD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$]wD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$w%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$wD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$wD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$E%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$ED' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$EDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*>$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*>$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*>$D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*?$'%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*?$'D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*?$'+p+0+$0 ++0+?$0 +4  xp(     0\rP<$D 0      <y 0<$D 0  T  0t 0@,$D 0 Maximum (time) discrepancy between schedule and PS Applying to jobs: Try PS completion discrepancy of job LCFS = FCFS = infinity! Most non-PS based (non-WFQ): infinity! (SJF, LJF, SRPT..) Good for very precise PS imitationsE0Z&0ZR0 Z$0ZEEEE ERG$EH  0޽h ? ̙33//___PPT10/.+TKdD/' 2= @B D.' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$'%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$'D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$'D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$'T%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$'TD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$'TD' =%(DB' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$T]%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$T]D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$T]D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$]w%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$]wD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$]wD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$w%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$wD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$wD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$E%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$ED' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$EDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*>$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*>$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*>$D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*?$'%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*?$'D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*?$'+p+0+$0 ++0+?$0 +F"  !!^!(     0`<$D 0     c $0<$D 0  z      P,$D 0P  BCDEdFn)r:bLP]@m/}|xk&]6OF?U0b p48@` ><^T `  # BV]N G*    p  @BgCDEtF~ !|+k5Y>HI6S%]bcc egfedXL)@<5P)cv<@@`,P0   B$C/DETF^"&)) )+, /!#!! $  ,0@`ju   B2ClDEF11> AD#G.L:NFSRV]Zh]u`cfijllcZQI >3%'2"  th] R#E':*.."36 :>dh@`v'   B#CCDEDFNCC >:5( " # #-7C$(@`r   BCDE4F>MMa#1@U-lBP\fpw #/:GTbo}xfTC0| tmf]TLC9/u!j_UMF@>61]-0* $ 1Ma@`,P   BCDEF%% ,AWm (0:DNZdo{}vwcnPg>a.Z)R#KD;3 +# LP@`bP  BHCDEdFn'9J Ziu%2=FzHmF`BR>E974*.&  48@`l0  B5CmDETF^7@ JT^f"k*m5k4]1P.D*7%+  &7,0@`o  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> &%#     & @`  BCDEF%%s^F.,& p[F 1,@T WZ']3`@cLfZiflsnqsvz}LP@`p  @BOCDEtF~  ) 08AIIJLNNNN O F <3*  <@@`Pj0  B(CDETF^, ?Rct"(%!s`M: &,0@`UcP  BDCCDEdFn@B"B(B.B3B:B?BDC@3< 5*%   "2@48@`xP  BCCBDEdFn9;<$>*?0@7@=BCB>0:4)$  ,948@`0  B2CFDETF^B)F1E2?05+)&"!  (:B,0@`p  @BRCFDEtF~=?"@*B2B:CCDJDRFO<M0K#IF A8,&!  /=<@@`P  B:CFDEdFn:F976)3. ) "   -;>@A#C*C/D5D:F48@`0  B;C%DETF^  # (",#1#5%;%95 /' ,0@`  B=C/DEDFN #(*),3-=/=82 *  $(@`0  B-C,DETF^ (&()#,(,,+-(,+(#  (,0@`P  BMC7DEdFn '(+&-..61>3F6M7K+I E? 91(   '48@` P  B7C>DEdFn .136"7':,<2=7>613#0,'"   # .48@`  BCZ DEDFN).Qx Hn{{tmjlor w~$1=IItFeCUAFC6G(Sf~ -Mm{v3qTpip}omspie^#ZNXzX[cn~@c/LTY\\~ZuWmTeQ^IW@P9H3>/5,+, -049= CIPVamvzyv!q&o-4;ESd,z=DA@@@@@?<)  ~zuqlhd`^elry+7DP]jx 2&EMVtft{ |# : M P S V Y Z Z Y W L ? 1 # !  ! !   y_F-3MfoIu#hYJ8=CHLPTY^}RfGO:7/ #  &w/Z7=> GOU[biouz~,9AGGCDFIJIA34 7<@ C(C0A8<;,<9 6<BHLKIFB<71,xqjd]}_Ze6lurvqY@'&7J\m} )9 J\n!&()%  &3@N\jz ztmid%c+f3p6}789>FT\ckry|}n^M|7u!l d`\XT]_]Zccm^IS&E4#}sjaYQJC;p6c.U)H!5# +8FSam~yqcrAga`aeviJnqrpj_`MD3- {pe ZPF< 2').$(@`G*Q   BCDEF-Ry{pg \INpJ}E?81)!   $23CEPW]khp{pe[POMKHyCs<o5l,nrz uM(.>N^n}<e0-,+))+,-9FVfouvxvszrpoke^Xn{hU)[#yfUE6*(#xmcW I:*   &-dh@`.n0 ! BCcDEFL55G&DV@;4-"%V  !/>*K:VJ^[cmca^YUR y/L "&()+++}+o)b)T(G&lp@`XTp " @B8CDEtF~-/1-a(   !'*+16a8.421/-<@@`!z4 # BC+DE4F>  % +%   @`G $ BC.DE4F>   (.(   @`FK % B&C0DEDFNL!& ),-.#0&#$  $(@` & BCDEF--CMU ^gnt$z+~19@GPYblsxpdZUS|SvToTiTeQ]GT>J4A*8!/( "  *3;C\`@`,P ' B>C,DEdFnL # $')* ,&,,,3*8'=#>=94-'! 48@`BV ( BCKDE4F> K?3()>K @` ) B"C>DE4F> >6+"#3 > @`0 * B/C4DETF^'(* -0344 3$'),/& ',0@`& + BCDEF11 ;!U-m;K^vrcUF;-%#/<IUbmy~wpha[UI?o5],L$9& dh@`'  , BCDE$F.?6X'|,.03<@HcPuYblw+9FS`n{xeP=*~sfYL>0....:ENYblu~oS8 |pdYMC|9l.Z%J9 98865320-*~(q%b"UG:52. * & "( Ox6@`iC p - @BCDEFL==2/+:$DP\g s }!v&p*l0i4i9g>iBjFmIrLwSSU^immkieca}awctfrjopvtw{ycP{=r-i^UMGC @=: 7)2/|@`LyP . BeCzDEdFn? -<$I.V8bCoMzQ_V@]"eedccWK ? 2% 48@`Nj / BCDE4F>LMM ", 6HYhp#y*1001|1y6u;u>xC{FJNSW]aed}ax[rWlThRbT\ZUc\kcsl|ry}o]L<8/%&089998-# qdWJ = 1# @`!y]P 0 BCDEF?99'- *$!!""(@/[5x<@EJPX`ity}ylbZRLtH`EJC2@$>:2+%  tx@`K p 1 @BmC=DEtF~L ")/5(9/=6=><F:N7V5^0f,m'lf_ YNC 6+ <@@`ep 2 @BCBDEtF~L7)Z;N`o~B=72-{oblSGB#1+$   <@@`%4 3 BiCODEF?11QL2IMDl?8.  &3 @FJO'O,I-C-=.6&6!2) ! &-3:@ES]dhgiLg2aYWU SQdh@`BMz 4 6A'?#" ` z 5 6A$?#"   <^T `  6# `Of V]N G* 7   p 8 @BgCDEtF~ !|+k5Y>HI6S%]bcc egfedXL)@<5P)cv<@@`,P0 9 B$C/DETF^"&)) )+, /!#!! $  ,0@`ju : B2ClDEF11> AD#G.L:NFSRV]Zh]u`cfijllcZQI >3%'2"  th] R#E':*.."36 :>dh@`v' ; B#CCDEDFNCC >:5( " # #-7C$(@`r < BCDE4F>MMa#1@U-lBP\fpw #/:GTbo}xfTC0| tmf]TLC9/u!j_UMF@>61]-0* $ 1Ma@`,P = BCDEF%% ,AWm (0:DNZdo{}vwcnPg>a.Z)R#KD;3 +# LP@`bP > BHCDEdFn'9J Ziu%2=FzHmF`BR>E974*.&  48@`l0 ? 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(:B,0@`p w @BRCFDEtF~=?"@*B2B:CCDJDRFO<M0K#IF A8,&!  /=<@@`P x B:CFDEdFn:F976)3. ) "   -;>@A#C*C/D5D:F48@`0 y B;C%DETF^  # (",#1#5%;%95 /' ,0@` z B=C/DEDFN #(*),3-=/=82 *  $(@`0 { B-C,DETF^ (&()#,(,,+-(,+(#  (,0@`P | BMC7DEdFn '(+&-..61>3F6M7K+I E? 91(   '48@` P } B7C>DEdFn .136"7':,<2=7>613#0,'"   # .48@` ~ BCZ DEDFN).Qx Hn{{tmjlor w~$1=IItFeCUAFC6G(Sf~ -Mm{v3qTpip}omspie^#ZNXzX[cn~@c/LTY\\~ZuWmTeQ^IW@P9H3>/5,+, -049= CIPVamvzyv!q&o-4;ESd,z=DA@@@@@?<)  ~zuqlhd`^elry+7DP]jx 2&EMVtft{ |# : M P S V Y Z Z Y W L ? 1 # !  ! !   y_F-3MfoIu#hYJ8=CHLPTY^}RfGO:7/ #  &w/Z7=> GOU[biouz~,9AGGCDFIJIA34 7<@ C(C0A8<;,<9 6<BHLKIFB<71,xqjd]}_Ze6lurvqY@'&7J\m} )9 J\n!&()%  &3@N\jz ztmid%c+f3p6}789>FT\ckry|}n^M|7u!l d`\XT]_]Zccm^IS&E4#}sjaYQJC;p6c.U)H!5# +8FSam~yqcrAga`aeviJnqrpj_`MD3- {pe ZPF< 2').$(@`G*Q  BCDEF-Ry{pg \INpJ}E?81)!   $23CEPW]khp{pe[POMKHyCs<o5l,nrz uM(.>N^n}<e0-,+))+,-9FVfouvxvszrpoke^Xn{hU)[#yfUE6*(#xmcW I:*   &-dh@`.n0  BCcDEFL55G&DV@;4-"%V  !/>*K:VJ^[cmca^YUR y/L "&()+++}+o)b)T(G&lp@`XTp  @B8CDEtF~-/1-a(   !'*+16a8.421/-<@@`!z4  BC+DE4F>  % +%   @`G  BC.DE4F>   (.(   @`FK  B&C0DEDFNL!& ),-.#0&#$  $(@`  BCDEF--CMU ^gnt$z+~19@GPYblsxpdZUS|SvToTiTeQ]GT>J4A*8!/( "  *3;C\`@`,P  B>C,DEdFnL # $')* ,&,,,3*8'=#>=94-'! 48@`BV  BCKDE4F> K?3()>K @`  B"C>DE4F> >6+"#3 > @`0  B/C4DETF^'(* -0344 3$'),/& ',0@`&  BCDEF11 ;!U-m;K^vrcUF;-%#/<IUbmy~wpha[UI?o5],L$9& dh@`'   BCDE$F.?6X'|,.03<@HcPuYblw+9FS`n{xeP=*~sfYL>0....:ENYblu~oS8 |pdYMC|9l.Z%J9 98865320-*~(q%b"UG:52. * & "( Ox6@`iC p  @BCDEFL==2/+:$DP\g s }!v&p*l0i4i9g>iBjFmIrLwSSU^immkieca}awctfrjopvtw{ycP{=r-i^UMGC @=: 7)2/|@`LyP  BeCzDEdFn? -<$I.V8bCoMzQ_V@]"eedccWK ? 2% 48@`Nj  BCDE4F>LMM ", 6HYhp#y*1001|1y6u;u>xC{FJNSW]aed}ax[rWlThRbT\ZUc\kcsl|ry}o]L<8/%&089998-# qdWJ = 1# @`!y]P  BCDEF?99'- *$!!""(@/[5x<@EJPX`ity}ylbZRLtH`EJC2@$>:2+%  tx@`K p  @BmC=DEtF~L ")/5(9/=6=><F:N7V5^0f,m'lf_ YNC 6+ <@@`ep  @BCBDEtF~L7)Z;N`o~B=72-{oblSGB#1+$   <@@`%4  BiCODEF?11QL2IMDl?8.  &3 @FJO'O,I-C-=.6&6!2) ! &-3:@ES]dhgiLg2aYWU SQdh@`BMz  6A'?#" ` r  ZGФHXI޽V?"_z U  ?5,$D 0  << U Seniority (Arrival Time)<0  gc `  C 0A rdlmwnuw[1] z H  0޽h ?  ̙33   n f   (     0HP0<$D 0     c $` P<$D 0    c $A ??F  $D 0dA  c $A ??@@/ $D 0d  0( @,$D 0 ai - Arrival time of customer i Di - Waiting displacement of customer i C > 0, arbitrary constant Expected fairness per customer b   GOGGO#GGGGGG G $`z       ,$D 0  c $A ??P <   $D 0d)   0   ,$D 0 Claim: Under FCFS: H0Z    0  0 ,$D 0 FCFS most fair (LCFS least)80Zz }   P?,$D 0   <}  Seniority (Arrival Time)<0  gc `   C 0A rdlmwnuw[1] z H  0޽h ? ̙333   s(       0P0<$D 0      0P @,$D 0 eAdhering to principles: Strong seniority service principle: YES Service-time service principle: NOT ^ L  G LG G z }   P?,$D 0   <L}  Seniority (Arrival Time)<0  gc `   C 0A rdlmwnuw[1] z H   0޽h ? ̙33$ " F>$(  $ $  00<$D 0    $ <$ ?"0@ ,$D 0  Good for: S. times identical S. times don t matter Issue is: Job completion Applications: Scarce-ticket lines Some call-centers % 2+  +1 ( - GE*EG)EE&EG z  p` $ p` 0 ,$D 0T   $#   $ C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl4\BD10456_.wmf  $ C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmfPb $ C A C:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl3\BD07630_.wmfnP  $ C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl0\TR00722_.wmf~Y=,$D 0P  $ C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl0\TR00722_.wmfw1^,$D 0P  $ C AC:\Documents and Settings\anat\Application Data\Microsoft\Media Catalog\Downloaded Clips\cl0\TR00722_.wmfj#,$D 0  $ H  ?"5 `k   $ N G2OH4^ >?" p  \My seat is gone....(G $ <% ?"p B,$D 0 n FCFS is most fair (LCFS least) Intuition & concepts: Peoples strong belief in order fairness!% 2! 2+ -2EEE)Gz } $ ?o,$D 0 $ <$#}  Seniority (Arrival Time)<0  gc ` $ C 0A rdlmwnuw[1] z H $ 0޽h ? 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Levy   .&&  . 2 1.--- !HH--- @BComic Sans MS CwCw w0- .92 }k!Job Fairness in Queue Scheduling:   *! .--a( -- @BComic Sans MS jCwCw w0- .2 sMay 2005.--l)-- @BComic Sans MS CwCw w0- .2 { Hanoch Levy . .02 %School of Computer Science      . .$2 ^JTel Aviv University    .--"System !8)Bw-&TNPP &՜.+,0$     On-screen Shown-sƶ7/?  HTimes New RomanComic Sans MSArial WingdingsArial Unicode MSDefault DesignMathType 5.0 EquationMicrosoft Equation 3.0Microsoft Clip Gallery"Job Fairness in Queue Scheduling:Why Fairness in Queues?Why Fairness in Queues? (2)The Size vs. Seniority Dilemma Outline Queue Model (single server)'History: Queueing Theory and Fairness+History: Queueing Theory and Fairness (2)'Designing a Metrics - Keep in mind:,The performance issues: Delay vs. Service %Granularity of Fairness Evaluation The Physical Factors (queues):Size and Seniority preference principles (requirements):Size and Seniority preference principles (requirements)DHow Scheduling policies meet the principles (are fair by principle)The Size vs. Seniority DilemmaReview of Measures (job based))Approach 1: Order (seniority) Fairness 2Approach 1: Order (seniority) Fairness: results ;Approach 1: Order (seniority) Fairness: How do I use it? %Measure 2: service-time Fairness  1Measure 3: Resource Allocation Fairness (RAQFM)BAnalysis of Resource Allocation Queueing Fairness Measure (RAQFM)FCFS AnalysisFCFS AnalysisFCFS AnalysisFCFS AnalysisFCFS AnalysisFCFS AnalysisFCFS Analysis>Individual discrimination for FCFS k number seen on arrival&Resource allocation Fairness: Results+Resource allocation Fairness: Results (2) *Resource allocation Fairness: Results (3),Resource Allocation Fairness: Applicability.Resource Allocation Fairness: How Do I use it!What fits? Go by the application$How People Perceive Queue Fairness Concluding remarks 8Closing Words: Why Study Fairness in Queues (5 reasons) THANK YOU Homework (Job-Based vs. Flow-Based +Applications DDealing with Stochastics: Actual measures vs. Expected values (2) 3Dealing with Stochastics: The Black Box question Measure 4: Mixture Measure 4 - Mixture : results 'Measure 4 - Mixture : How do I use it 0Job-Based vs. Flow-Based +Applications (repeat)A word on flow-based measures ,Measure 5: PS proximity WFQ/RFB literature ,Measure 5: PS proximity WFQ/RFB literature (Measure 1: Order (seniority) Fairness Order Fairness: resultsOrder Fairness: results (2)+Order Fairness: Properties & Applicability:Measure 1: Order (seniority) Fairness: How do I use it? #Service-time Fairness: Results 'Service-time Fairness: Results (2) -S. time Fairness: Properties & Applicability#S. time Fairness: How do I use it PowerPoint Presentation  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles?_4anatanat  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                           ! 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