1. Maryam Elahi bmelahi@ucalgary.ca Fairness in Speed Scaling Design Joint work with: Carey Williamson and Philipp Woelfel

2. SCHEDULING Sharing resources Maximize efficiency Minimize cost Datacenters Locks Databases Routers Internet And more… Requests (Jobs) Queue Arrival Rate (λ) Shared Resource (server) CPUs Fixed Service Rates 2

3. THE DECISION Scheduler: Which job to serve? Preemptive Non-preemptive Goal(s): 1: Minimize response time Simple Model ? M/M/1 3

4. SCHEDULERS FCFS: First-Come-First-Served PS: Processor Sharing SRPT: Shortest-Remaining- Processing-Time... System Load 0 0.25 0.5 0.75 Mean Response Time PS SRPT FCFS SRPT is proved optimal, but in practice often PS is used. 4

5. OTHER GOALS? Goal(s): 1: Minimize response time Other QoS: 2: Fairness 3: Robustness … Optimizes response time Is it fair to large jobs? What is fair ? SRPT 5

6. JUSTIFICATION Aristotle's notion of fairness Treat like cases alike Treated different cases differently, in proportion to their differences Response times should be proportional to job sizes E[T(x)]/x should be constant Normalized response time or slowdown T(x): Response Time of a job with size x 6 Policy P is fair if: [Wierman et al. 2003]

7. x E[T(x)] / x FAIRNESS OF SCHEDULERS PS: Always Fair FCFS: Always Unfair SRPT: Sometimes Fair... Fair and Optimal? FCFS SRPT PS x E[T(x)] / x SRPT PS Light load 7 High enough load

8. FAIR AND OPTIMAL? FSP: Fair Sojourn Protocol [Friedman, et al. 2003] Implement SRPT on the PS remaining times Slowdown : never worse than PS Mean response time : close to that of SRPT E[T(x)] / x SRPT PS FSP x Compute the completion time under virtual PS Order the jobs based on their virtual completion times Execute the job with the earliest PS completion time 8

9. THE DECISION S Scheduler: Which job to serve? What speed to use? Dynamic speed scaling Gated-static (shut-down) Goal(s): 1: Minimize response time ( T ) 2: Minimize energy usage ( E ) ? Adjustable Service Rates Speed Power P(s) = s α 9

10. THE TRADEOFF response-timeenergy How much reduction in response time justifies using one extra joule β: cost of energy 10

11. DYNAMIC SPEED SCALING Which job to serve? What speed? Job scheduling SRPT ? P(s) = s α n: jobs in the system + [Bansal et al. 2009]: 3-competitive for arbitrary power function 11

12. FAIRNESS AND SPEED SCALING FCFS SRPTPSFSP Biased towards big jobs Biased towards small jobs Treats all the same ? [Andrew et al. 2010]: Jobs that run when the queue is big, run faster 12

13. FAIRNESS AND SPEED SCALING Is Slowdown of PS still the right criterion for fairness? 13 [Andrew et al. 2010]: - For PS with speed scaling, stays constant. - Dynamic Speed Scaling magnifies unfairness under SRPT and non-preemptive policies like FCFS.

14. SIMULATION STUDY 14

15. RESULTS: CONSTANT SPEED LOAD: 0.5 15

16. RESULTS: CONSTANT SPEED LOAD: 0.8 16

17. RESULTS: DYNAMIC SPEED SCALING LOAD: 0.5 17

18. RESULTS: DYNAMIC SPEED SCALING LOAD: 0.8 18

19. CONCLUSIONS FSP with speed scaling shows better fairness behavior in comparison to speed scaled SRPT The definition of fairness for scheduling with speed scaling requires further investigations 19

20. QUESTIONS? THANK YOU!