Energy Minimization with Deadline Feasibility Rachel Ferst Alan
Energy Minimization with Deadline Feasibility Rachel Ferst Alan Papir
Motivation l Since the early 1970 s, the power densities in microprocessors has doubled every three years. l l l Power consumption of computing devices rising exponentially. Cooling costs rising exponentially. Energy consumption is a problem for battery operated devices. l Battery capacity increasing at a rate slower than power consumption is growing.
Problem l Two energy minimization problems l l l Energy minimization with deadline feasibility Minimizing flow time and energy processes without deadlines Two papers of interest: l l YDS. A Scheduling Model for Reduced CPU Energy. [YDS, 1995] Pruhs, et al. Getting the Best Response for Your Erg. [Pruhs, 2008]
Problem l Variable speed processor l l Allows an operating system to reduce energy consumption by scheduling jobs at different speeds while meeting deadline requirements. Scope l l Implemented YDS algorithm under different sets of data and compared with naïve models Discuss Pruhs, et al. approach
YDS Algorithm l Off-line algorithm that computes the minimumenergy schedule for any set of jobs. l l l Power function must be convex We used P(s) = s 3 An instance of the scheduling problem is the set J of jobs to be executed during a fixed time interval [t 0, t 1] defined by: l l l Arrival time, aj Deadline, bj Required number of CPU cycles Rj
YDS Algorithm l Notation: l A schedule is a pair S=(s(t), job(t)) l s(t) is the speed at time t l job(t) defines the job or idleness being executed at time t Let the interval of a job j be [aj, bj]. l l 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).
YDS Algorithm Definitions l l 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’] l g(I) is a lower bound on the average speed needed in interval I l l 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*.
YDS Algorithm l Algorithm 1. Schedule the jobs in JI* by EDD policy. Run all jobs in JI* at speed g(I*) 2. 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*.
Naïve Algorithms l Created two algorithms that guarantee a deadline feasible solution with little regard for energy consumption: l 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]. li Naïve 2: Find the minimum speed necessary to complete every job before its deadline. Run every job at that speed.
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Results
Results
Results
A World Without Deadlines l Deadline feasibility may not be realistic… li li l Most processes do not have natural deadlines. Windows and Unix do not have deadline based schedulers So, how do we measure quality of service? l Average flow time
A World Without Deadlines l Bi-criteria optimization problem l l Minimize average flow time Minimize energy consumed Objectives are contradictory Methodology: l l Bound one objective and optimize the other More natural to bound energy
A World Without Deadlines
Works Cited
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- Slides: 19
