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Mor Harchol-Balter Carnegie Mellon University Computer Science

Heavy Tails: Performance Models & Scheduling Disciplines. Part IV: Scheduling in Practice: The SYNC Project. Mor Harchol-Balter Carnegie Mellon University Computer Science. FCFS. jobs. jobs. PS. SRPT. jobs. Q: Which minimizes mean response time?. “size” = service requirement.

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Mor Harchol-Balter Carnegie Mellon University Computer Science

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  1. Heavy Tails: Performance Models & Scheduling Disciplines Part IV: Scheduling in Practice: The SYNC Project Mor Harchol-Balter Carnegie Mellon University Computer Science

  2. FCFS jobs jobs PS SRPT jobs Q: Which minimizes mean response time? “size” = service requirement load r < 1

  3. Q: Which best represents scheduling in web servers ? FCFS jobs “size” = service requirement load r < 1 jobs PS SRPT jobs

  4. Request for file Requested file IDEA: Use SRPT instead of PS in Web servers client 1 “Get File 1” 1 APACHE WEB SERVER 2 client 2 3 Internet “Get File 2” 1000 client 3 Linux 0.S. “Get File 3”

  5. Objections to SRPT: Ö • Need to know “size” of request • Unfairness to requests for big files

  6. THEORY THEORY IMPLEMENT Outline of Talk I:Investigating Unfairness in SRPT (M/G/1, c.f.m.f.v.)[Sigmetrics 01] II:Unfairness in All Scheduling Policies (M/G/1, c.f.m.f.v.)[Performance 02], [Sigmetrics 03] III:Implementation of SRPT in Web servers [Transactions on Computer Systems 03], [ITC03] Papers are joint with Adam Wierman & Bianca Schroeder

  7. THEORY THEORY IMPLEMENT Outline of Talk I:Investigating Unfairness in SRPT (M/G/1, c.f.m.f.v.)[Sigmetrics 01] II:Unfairness in All Scheduling Policies (M/G/1, c.f.m.f.v.)[Performance 02], [Sigmetrics 03] III:Implementation of SRPT in Web servers [Transactions on Computer Systems 03], [ITC03] www.cs.cmu.edu/~harchol/

  8. SRPT has a long history ... 1966 Schrage & Miller derive M/G/1/SRPT response time: 1968 Schrage proves optimality 1979 Pechinkin & Solovyev & Yashkov generalize 1990 Schassberger derives distribution on queue length BUT WHAT DOES IT ALL MEAN?

  9. SRPT has a long history (cont.) 1990 - 97 7-year long study at Univ. of Aachen under Schreiber SRPT WINS BIG ON MEAN! 1998, 1999 Slowdown for SRPT under adversary: Rajmohan, Gehrke, Muthukrishnan, Rajaraman, Shaheen, Bender, Chakrabarti, etc. SRPT STARVES BIG JOBS! Various o.s. books: Silberschatz, Stallings, Tannenbaum: Warn about starvation of big jobs ... Kleinrock’s Conservation Law: “Preferential treatment given to one class of customers is afforded at the expense of other customers.”

  10. Real-world job sizes are Heavy Tailed log-log plot Heavy-tailed Property: “Largest 1% of jobs comprise half the load.” Job size (x seconds) [Sigmetrics 96]

  11. ? PS ? SRPT Unfairness Question Let r=0.9. Let G: Bounded Pareto(a = 1.1, max=1010) Question: Which queue does biggest job prefer? M/G/1 M/G/1

  12. PS SRPT I SRPT Results on Unfairness Let r=0.9. Let G: Bounded Pareto(a = 1.1, max=1010)

  13. Results on Unfairness Let G: Bounded Pareto(a = 1.1, max=1010) PS SRPT

  14. Unfairness – General Distribution All-can-win-theorem: For all distributions, if r< ½, E[T(x)]SRPT< E[T(x)]PSfor all x.

  15. x ò 2 + x F ( x ) 2 t f ( t ) dt l l x dt ò 0 - r ( - r ( 2 2 ( 1 x )) 1 t ) 0 All-can-win-theorem: Forall distributions, if r< ½, E[T(x)]SRPTE[T(x)]PSfor all x. £ Proof: + E[Wait(x)]SRPT E[Res(x)]SRPT E[T(x)]PS

  16. x ò 2 + x F ( x ) 2 t f ( t ) dt l l x dt ò 0 - r ( - r ( 2 2 ( 1 x )) 1 t ) 0 All-can-win-theorem: For all distributions, if r< ½, E[T(x)]SRPTE[T(x)]PSfor all x. £ Proof cont. - Need sufficient condition s.t.

  17. x ò 2 + x F ( x ) 2 t f ( t ) dt l l 0 - r ( 2 2 ( 1 x )) All-can-win-theorem: For all distributions, if r< ½, E[T(x)]SRPTE[T(x)]PSfor all x. £ Proof cont. Need sufficient condition s.t.

  18. x ò 2 + x F ( x ) 2 t f ( t ) dt l l 0 - r ( 2 2 ( 1 x )) All-can-win-theorem: For all distributions, if r< ½, E[T(x)]SRPTE[T(x)]PSfor all x. £ Proof cont. Need sufficient condition s.t. Observe:

  19. x x ò ò 2 2 + + x x F F ( ( x x ) ) 2 2 t t f f ( ( t t ) ) dt dt l l l l 0 0 All-can-win-theorem: For all distributions, if r< ½, E[T(x)]SRPTE[T(x)]PSfor all x. £ Proof cont. - r ( 2 2 ( 1 x )) - r 1 Suffices that: 2(1 - r(x))2 > 1 - r. Suffices that r(x) < 1/2

  20. 1) All-can-win-theorem: For all distributions, if r< ½, E[T(x)]SRPTE[T(x)]PSfor all x. 2) Under Bounded Pareto distribution (a = 1.1), r < 0.96, E[T(x)]SRPT < E[T(x)]PSfor all x. *HT Property* £ E[Wait(x)] E[Res(x)]: small small Intuition

  21. THEORY THEORY IMPLEMENT Outline of Talk I:Investigating Unfairness in SRPT (M/G/1, c.f.m.f.v.)[Sigmetrics 01] II:Unfairness in All Scheduling Policies (M/G/1, c.f.m.f.v.)[Performance 02], [Sigmetrics 03] III:Implementation of SRPT in Web servers [Transactions on Computer Systems 03], [ITC03] www.cs.cmu.edu/~harchol/

  22. What is fair? Response time for job of size x Slowdown for job of size x Slowdown is independent of size PS does not bias towards any particular job size. Definition: A policy P isfairifE[S(x)]P≤ E[S(x)]PSfor all x. Otherwise, P isunfair.

  23. Always Unfair Always Fair Sometimes Unfair Fair for all loads and distributions Fair for some loads, and unfair for other loads* Unfair for all loads and distributions Classification of Scheduling Policies * and distributions

  24. Always Fair Always Unfair Sometimes Unfair Fair for all loads and distributions Fair for some loads, and unfair for other loads* Unfair for all loads and distributions • Where does SRPT lie? __________ • What about other policies that prioritize based on remaining size? ____ • What about preemptive policies that prioritize based on age? _____ • What about preemptive policies that prioritize based on size? _____ Testing your intuition: * and distributions

  25. Classification of Scheduling Policies SJF LJF FCFS PS FB Non-preemptive FSP Age- Based Policies Always Unfair Sometimes Unfair Always FAIR Preemptive Size-based Policies Preemptive Remaining-size based Policies PLCFS PSJF SRPT LRPT Lots of open problems…

  26. Always Unfair Theorem: Any preemptive, size based policy, P, is Always Unfair. Always Unfair Case1: A finite size, y, receives lowest priority Case 2: No finite size receives lowest priority (2a) Priorities decrease monotonically -- PSJF (2b) Priorities decrease non-monotonically. Unfair for all loads and distributions

  27. Always Unfair Theorem: Any preemptive, size based policy, P, is Always Unfair. Always Unfair Case1: A finite size, y, receives lowest priority Unfair for all loads and distributions y V = Work in System

  28. Always Unfair Theorem: Any preemptive, size based policy, P, is Always Unfair. Always Unfair Case2a: Priorities decrease monotonically (PSJF) Infinite sized job has lowest priority ... Unfair for all loads and distributions … but that job is treated fairly?

  29. Always Unfair Theorem: Any preemptive, size based policy, P, is Always Unfair. Always Unfair Case2a: Priorities decrease monotonically (PSJF) E[S(x)] PS PSJF Unfair for all loads and distributions x 0 Finding a hump shows PSJF is Always Unfair

  30. Always Unfair Theorem: Any preemptive, size based policy, P, is Always Unfair. Always Unfair Case2b: Priorities decrease non-monotonically E[S(x)] PS PSJF Unfair for all loads and distributions x 0 Find y beyond which PSJF treats all jobs unfairly. Find x > y, where x has lower priority than y. => x is treated unfairly.

  31. The mysterious hump PS PSJF E[S(x)] x 0 x • This hump appears in many common policies, • PSJF • FB • SRPT • SJF 0

  32. THEORY THEORY IMPLEMENT Outline of Talk I:Investigating Unfairness in SRPT (M/G/1, c.f.m.f.v.)[Sigmetrics 01] II:Unfairness in All Scheduling Policies (M/G/1, c.f.m.f.v.)[Performance 02], [Sigmetrics 03] III:Implementation of SRPT in Web servers [Transactions on Computer Systems 03], [ITC03] www.cs.cmu.edu/~harchol/

  33. From theory to practice: What does SRPT mean within aWeb server? • Many devices: Where to do the scheduling? • Many jobs at once.

  34. Server’s Performance Bottleneck Site buys limited fraction of ISP’s bandwidth client 1 “Get File 1” WEB SERVER client 2 (Apache) Rest of Internet “Get File 2” ISP Linux 0.S. client 3 “Get File 3” 5 We schedule bandwidth at server’s uplink.

  35. Web Server Network/O.S. insides of traditional Web server Socket 1 Client1 Network Card Socket 2 Client2 BOTTLENECK Client3 Socket 3 Sockets take turns draining --- FAIR = PS.

  36. Web Server Network/O.S. insides of our improved Web server Socket 1 Client1 S Network Card 1st Socket 2 Client2 2nd M BOTTLENECK 3rd Client3 Socket 3 L priority queues. Socket corresponding to file with smallest remaining data gets to feed first.

  37. Experimental Setup 1 2 WAN EMU 3 1 200 APACHE WEB SERVER Linux 2 1 3 2 WAN EMU 3 switch 200 Linux Linux 0.S. 1 2 WAN EMU 3 200 Linux Implementation SRPT-based scheduling: 1) Modifications to Linux O.S.: 6 priority Levels 2) Modifications to Apache Web server 3) Priority algorithm design.

  38. Flash Experimental Setup Apache 10Mbps uplink 1 2 WAN EMU 3 100Mbps uplink APACHE WEB SERVER 1 200 Linux 2 Surge 1 3 2 Trace-based WAN EMU 3 switch 200 Linux Open system Linux 0.S. 1 Partly-open 2 WAN EMU 3 200 WAN EMU Linux Geographically- dispersed clients Trace-based workload: Number requests made: 1,000,000 Size of file requested: 41B -- 2 MB Distribution of file sizes requested has HT property. Load < 1 Transient overload + Other effects: initial RTO; user abort/reload; persistent connections, etc.

  39. Results: Mean Response Time . . . Mean Response Time (sec) . FAIR . SRPT . Load

  40. Mean Response Time vs. Size Percentile Load =0.8 FAIR Mean Response time (ms) SRPT Percentile of Request Size

  41. Transient Overload -- Mean response time FAIR SRPT

  42. Transient overload Response time as function of job size FAIR SRPT small jobs win big! big jobs aren’t hurt!

  43. Database Internet High-Priority Client Low-Priority Client Locks CPU(s) Disks New project: Scheduling dynamic web requests “$$$buy$$$” Web Server (eg: Apache/Linux) Internet “buy” “buy” Need to schedule the database ...

  44. Conclusion Misconceptions about unfairness Discrimination against high-performance scheduling policies Classifying policies with respect to unfairness is counter-intuitive. Good news: Many high-performing policies are also fair in practice!

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