Fairness in Speed Scaling Design

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

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

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

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

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

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 T(x): Response Time of a job with size x Policy P is fair if: [Wierman et al. 2003] Normalized response time or slowdown

7. E[T(x)] / x x Fairness of Schedulers • PS: Always Fair • FCFS: Always Unfair • SRPT: Sometimes Fair • ... • Fair and Optimal? SRPT High enough load E[T(x)] / x PS FCFS x PS Light load SRPT

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 • 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 SRPT PS E[T(x)] / x FSP x

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

10. The tradeoff • Combined Goal: Linear combination of the goals: • Other objectives considered: • Minimize energy for jobs with deadlines • Minimize response time subject to energy budget • response-time x energy How much reduction in response time justifies using one extra joule β: cost of energy energy response-time

11. Dynamic speed scaling P(s) = sα n: jobs in the system Which job to serve? What speed? Job scheduling SRPT • Speed Scaling Policy + ? [Bansal et al. 2009]: 3-competitive for arbitrary power function

12. Fairness and speed scaling [Andrew et al. 2010]: Jobs that run when the queue is big, run faster Biased towards big jobs Biased towards small jobs FCFS SRPT PS FSP Treats all the same ?

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

14. SIMULATION study • Discrete event simulator written in C++ • Scheduling policies: FCFS, PS, SRPT, FSP • Speed Scaling: • Workload: • Poisson Arrival: rate λ • Exponentially distributed job sizes: rate μ

15. Results: constant speedLoad: 0.5

16. Results: constant speedLoad: 0.8

17. Results: Dynamic speed scalingLoad: 0.5

18. Results: Dynamic speed scalingLoad: 0.8

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

20. Questions? Thank you!