Minimizing Expected Energy Consumption in Real-Time Systems through Dynamic Voltage

Scaling

Ruibin Xu, Daniel Mosse’, and Rami Melhem

Problems Theme

• Context: Frame-based hard real time systems• Given one or more tasks with– Same period– deadline = period– Order of execution of tasks

• Probability distribution of execution cycles of each task

• One processor with DVS support• Goal: Schedule tasks (time allocation, speed) to

minimize expected energy consumption

Problems & System Models

Problems

Intra-Task DVS Inter-Task DVS Hybrid

System Model

Ideal Realistic

Problems

• Intra-Task DVS– Only one task– Compute speed of each cycle or group of consecutive

cycles.• Inter-Task DVS

– Multiple Tasks and their order of execution– Compute fraction of remaining time to allot to each task– At run time, speed changes only at the boundary of a task

• Hybrid– Combine Intra and Inter-task DVS

System Models

• Ideal Model– Unrestricted continuous speed– No time or energy overhead for changing speed– Well defined power-frequency relation.

p(f) = c0+c1f α

• Realistic Model– Predefined set of discrete speeds– Changing speed costs time and energy overhead– No assumption on power-frequency relation

Intra-Task DVS + Ideal System

• Minimize , where

• Subject to

• Optimal solution is • Algorithms: PACE, GRACE.

Intra-Task DVS + Realistic System

• First approach: patch solution obtained under ideal system

• GRACE: round speed up to closest discrete frequency• PACE: round speed up or down to closest discrete

frequency• Problems?

– Can miss deadline– Ignore speed change overhead

• PACE: scan all phases and adjust speed, subtract maximum time penalty from allotted time

Intra-Task DVS + Realistic System

• Second Approach: Design DVS considering the realistic system model (PPACE).

• Change speed time penalty • Change speed energy penalty• Given r transition points, partition the range of

execution cycles [1, W] into r+1 phases: [b0, b1-1], [b1, b2-1],…, [br, br+1-1], where b0=1,

br+1=W+1• Not necessarily the optimal partitioning!

Intra-Task DVS + Realistic System

1

0

b0=1 b1 b2 b3 br

cdf(x)

Xf0 f1 f2 fr…

………

*Graph borrowed from presentation by Ruibin Xu

Intra-Task DVS + Realistic System

• Minimize • Subject to

• Where

Intra-Task DVS + Realistic System

• An energy-time label l is a 2-tuple (e,t), where e and t denote energy and time, respectively

*Graph borrowed from presentation by Ruibin Xu

Intra-Task DVS + Realistic System

v0 v1 v2 v3

|LABEL(0)|=1 |LABEL(1)|=M |LABEL(2)|=M2

|LABEL(3)|=M3

Exponential growth!

*Animation borrowed from presentation by Ruibin Xu

Intra-Task DVS + Realistic System

• Use Approximation– Approximations that preserve optimality but do

not guarantee polynomial running time– Approximation based on factor є so that solution

is within (1+є) of optimal, and we get a polynomial running time.

Intra-Task DVS + Realistic System

v0 v1 v2 v3

|LABEL(0)|=1 |LABEL(1)|=M |LABEL(2)|=M2

|LABEL(3)|=M3

|LABEL(1)|<<M,

Hopefully!|LABEL(2)|<<M2

Hopefully!

*Animation borrowed from presentation by Ruibin Xu

Intra-Task DVS + Realistic System

Intra-Task DVS + Realistic System

Intra-Task DVS + Realistic System

Inter-Task DVS + Ideal System

Algorithm: OITDVS

slack

β1D (1-β1)D

D

β1

*Animation borrowed from presentation by Ruibin Xu

Inter-Task DVS + Ideal System

β4=100%

β3=xx%

vs.

T1 T2 T3 T4

β2=xx%

vs.

vs.

β1=xx%

*Animation borrowed from presentation by Ruibin Xu

Inter-Task DVS + Realistic System

• Use the ideal system to compute allotted fractions of system time to each task

• Patch the solution to work on the realistic system:– Before computing the speed of a task, subtract from

remaining time the maximum possible time penalty for all remaining speed changes.

– Make sure a task runs at one of the discrete speed steps

• Algorithms PITDVS, PITDVS2

Hybrid (Intra + Inter-Task DVS) + Ideal System

• Combine intra and inter-task DVS.• Compute fractions per cycle per task, instead

of just per task.• Algorithm: GOPDVS

Hybrid (Intra + Inter-Task DVS) + Realistic System

• Two approaches• First (PGOPDVS):– Compute time allocation fraction per phase (instead

of cycle) per task.– From the above fractions, compute fraction per task.– At run time, use task fractions to allot time to each

task.– Compute task speed by applying patches as in inter-

task DVS

Hybrid (Intra + Inter-Task DVS) + Realistic System

• Second (PIT-PPACE):– Compute time allocation fraction per task (inter-

task DVS).– At run time, use intra-task DVS to compute speed

schedule of each task according to allotted time.– Because the above step is time consuming, we can

compute a set of solutions of intra-task DVS for each task and apply the best one at run time.

Hybrid (Intra + Inter-Task DVS) + Realistic System

Hybrid (Intra + Inter-Task DVS) + Realistic System

Questions?

Energy-Aware Scheduling for Streaming Applications on Chip Multiprocessors

Ruibin Xu, Rami Melhem, Daniel Mosse’

Problem

• Streaming applications operate on streams of data and are compute intensive. Examples: video streaming, automatic target recognition

• A stream of data can be abstracted as a sequence of requests.

• Thus a streaming application can be modeled as a periodic task in real-time systems.

• QoS: Throughput (T), and Deadline (D)

Problem

• Streaming applications are highly parallelizable and thus we can use CMPs to run them.

• CMPs support:– Turning off cores to reduce leakage– DVS to reduce dynamic energy consumption

• Goal: Schedule tasks so as to minimize energy consumption and meet QoS requirements.

Models

• Application is modeled as a DAG where nodes represent tasks, and edges represent precedence relations and communication requirements.

• Communication cost of transferring B bits– Delay is– Energy is

• Each processor has M discrete frequency steps

Decompose the Problem

Effect of Static Power

• Power function of a processor core

• Consider Y-oriented load only• Assume job consists of c cycles, and we use y

cores, then each is assigned cycles, and runs with speed

• Energy consumption is • To minimize energy consumption• Similar result for X-oriented load

Scheduling for Y-Oriented Load• Solution has recursive nature• Let denote optimal scheduling of

tasks i through n, with end-to-end delay = t• Computes singleValue of

i,i+1,..,j

d t-d

q

WCEC

Running time

Energy

Scheduling for Y-Oriented Load• We need to consider all M frequencies and all possible n-i+1

mappings of consecutive tasks i through n to first stage.

Scheduling for X-Oriented Load

• Use List scheduling to map tasks to cores in the same stage.

• Perform speed computation for tasks of the stage.• Use hill-climbing to improve solution.

Scheduleing2D

Simulation Results

• Comparing Schedling2D against baseline.• Baseline Algorithm– Period = deadline– Try all possible number of cores to find minimum

energy consumption.– Use ETF heuristic to perform task mapping.– Uses convex programming approach to obtain

execution speed of each task given task mapping.

Simulation Results

• Percentage of static power in total power:– 70nm: 22%– 50nm: 44%– 35nm: 67%

• As static power increases, energy savings obtained by Scheduling2D decreases

Simulation Results

Simulation Results

• As period increases, energy savings decrease• For a given period, increasing deadline will

initially result in increased energy savings

Thanks!