Energy Minimization with Deadline Feasibility

1. Energy Minimization with Deadline Feasibility Rachel Ferst Alan Papir

2. Motivation • Since the early 1970s, the power densities in microprocessors has doubled every three years. • Power consumption of computing devices rising exponentially. • Cooling costs rising exponentially. • Energy consumption is a problem for battery operated devices. • Battery capacity increasing at a rate slower than power consumption is growing.

3. Problem • Two energy minimization problems • Energy minimization with deadline feasibility • Minimizing flow time and energy processes without deadlines • Two papers of interest: • YDS. A Scheduling Model for Reduced CPU Energy. [YDS, 1995] • Pruhs, et al. Getting the Best Response for Your Erg. [Pruhs, 2008]

4. Problem • Variable speed processor • Allows an operating system to reduce energy consumption by scheduling jobs at different speeds while meeting deadline requirements. • Scope • Implemented YDS algorithm under different sets of data and compared with naïve models • Discuss Pruhs, et al. approach

5. YDS Algorithm • Off-line algorithm that computes the minimum-energy schedule for any set of jobs. • Power function must be convex • We used P(s) = s3 • An instance of the scheduling problem is the set J of jobs to be executed during a fixed time interval [t0,t1] defined by: • Arrival time, aj • Deadline, bj • Required number of CPU cycles Rj

6. YDS Algorithm • Notation: • A schedule is a pair S=(s(t),job(t)) • s(t) is the speed at time t • job(t) defines the job or idleness being executed at time t • Let the interval of a job j be [aj,bj]. • A schedule is feasible if S gives each job j the required number of CPU cycles between its arrival time and deadline (with preemption possible).

7. YDS AlgorithmDefinitions • Energy: • Let the intensity, g(I), of an interval, I=[z,z’] be • Where the sum is taken over all jobs with aj,bj contained in the interval [z,z’] • g(I) is a lower bound on the average speed needed in interval I • Call I*=[z,z’] a critical interval for J if I* maximizes g(I), and the set of jobs within that interval the critical group, JI*.

8. YDS Algorithm • Algorithm • Schedule the jobs in JI* by EDD policy. Run all jobs in JI*at speed g(I*) • Modify the problem to reflect the deletion of JI*and I*. • Remove jobs JI*from J. • Update arrival times and deadlines to ensure no job outside of JI*is scheduled in the interval I*.

9. Naïve Algorithms • Created two algorithms that guarantee a deadline feasible solution with little regard for energy consumption: • Naïve 1: Run each job, j, at a speed such that the completion time of job j is min[release time of j+1, deadline of j]. Naïve 2: Find the minimum speed necessary to complete every job before its deadline. Run every job at that speed. • i

10. Data

11. Results

12. Results

13. Results

14. Results

15. A World Without Deadlines • Deadline feasibility may not be realistic… • So, how do we measure quality of service? • Average flow time • Most processes do not have natural deadlines. • Windows and Unix do not have deadline based schedulers • i • i

16. A World Without Deadlines • Bi-criteria optimization problem • Minimize average flow time • Minimize energy consumed • Objectives are contradictory • Methodology: • Bound one objective and optimize the other • More natural to bound energy

17. A World Without Deadlines

18. Works Cited

19. Questions?