Energy-Aware Modeling and Scheduling of Real-Time Tasks for Dynamic Voltage Scaling

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Energy-Aware Modeling and Scheduling of Real-Time
Tasks for Dynamic Voltage Scaling

• Xiliang Zhong and Cheng-Zhong Xu
• Dept. of Electrical Computer Engg.
• Wayne State University
• Detroit, Michigan
• http//www.cic.eng.wayne.edu

2
Outline

• Introduction and Related Work
• A Filtering Model for DVS
• Time-invariant Scaling
• Time-variant Scaling
• Statistical Deadline Guarantee
• Evaluation
• Conclusion

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Motivation

• Mobile/Embedded devices power critical
• Energy-Performance tradeoff
• Processor speed designed for peak performance
• Slowdown the processor when not fully utilized
  (DVS)
• Challenges
• Maximize energy saving while providing deadline
  guarantee
• Real-time tasks could be periodic/aperiodic w/
  highly variable execution time
• Aperiodic tasks have irregular release times,
  which calls for online decision making

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Related Work

• Intensive studies for periodical tasks
• Algorithms for aperiodic tasks
• Offline (Yao et al95, Quan Hu01)
• Online all timing information known only after
  job releases
• Soft real-time improve responsiveness (Aydin
  Yang04)
• Occasionally uncontrollable deadline misses
  (Sinha Chakrabarty01)
• Hard real-time w/complex admission control (Hong
  et al 98)
• Maximize energy saving w/ frequency scaling(Qadi
  et al 03, DVSST)
• On-line slack management for a general input (Lee
  Shin 04,OLDVS)
• Objectives of this paper
• Hard/statistical deadline guarantee for general
  input w/o assumptions of task periodicity
• Unified, online solutions for both WCET based
  scheduling and slack management

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Task Model

• Independent tasks, preemptive w/ dynamic
  priorities
• Job releases (requests) to system are
  characterized by a compound process in a discrete
  time domain
• wi (t) is the size (WCET) of ith jobs arrived
  during time t-1,t)
• n(t) stands for number of jobs arrived, each
  w/deadline td

Input arrivals
w1(1) w1(2) w2(3)

time
2
1
0
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System Model

• Processor Model
• Support a continuous range of speed levels
• Energy Model
• t scheduling time slot, f(t) speed at time t,
  t1)
• l(t) load, cycle allocated to all jobs during
  t, t1)
• P(l(t)) power as a function of load
• E(S) energy consumed according to a schedule S

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A Filtering Model of Speed Scaling

• Allocation function denotes the cycles
  allocated to one job wi(t) during t, t1)
• Decomposition of allocation function
• g(), the impact of job sizes (WCETs) on
  scheduling
• h(), scaling function
• s(), the load feedback to scheduling

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A Filtering Model (cont.)

• Load Function l(t) is a sum of allocation to all
  jobs

• Each job should be finished in td time
  g(wi(t))wi(t)

• Non-adaptive to load s(l(t)) 1

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A Filtering Model (cont.)

• The load function becomes a convolution of
  compounded input request process and scaling
  function,
• Scaling function h(t) Portion of resource
  allocated at each scheduling epoch from the
  arrival time ts to finish time tstd
• Design of scaling algorithm in a fitlerng system

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Time-Invariant Scheduling

• Treat h(t) as a time-invariant scaling function

• The optimal policy is to find an allocation

where

• The optimality is determined by the covariance
  matrix ? of the input process w(t) in the order
  of deadline td
• The optimization has a unique, closed form
  solution

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Example Solutions with Different Input

• Two multimedia traffic patterns (Krunz00)
• Shifted Exponential Scene-length Distribution
  (ACFExp)
• Subgeometric scene-length distribution
  (ACFSubgeo)
• Fractional Gaussian Noise (FGN) process with
  Hurst para. H0.89
• Simpsons MPEG Video Trace of 20,000 frames

Auto-Correlations of Traffic
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Example Solution (td10)

• Higher degree of input autocorrelation has a more
  convexed scaling function
• The uniform distributed allocation is a
  generalization of several existing algorithms for
• Periodic tasks
• Sporadic tasks
• Aperiodic tasks

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Time-Variant Scaling

• Energy consumption can be reduced if the scaling
  function h(t) is adaptive in response to change
  of input load

• Make td runnable queues. Jobs with deadline j are
  put to queue j

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Time-Variant Scaling

• Minimize energy consumption is to

subject to
where qj(t) is the backlog of queue j at time t.

• The optimization has a unique solution

Resource cap of queue j at time t
Committed resource for jobs in queue j at time t
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Illustration

• Determine cap of queue 5 at time 0 S5(0)

load

• First determine current committed resource

• Distribute the job as late as possible

• The job is distributed to early slots as its size
  increases

0 1 2 3 4 5 time
slot
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Example Solution for a Sporadic Task
Input J(WCET) J1(1) released at 0, 5, J2(2) at
1, 7, J3 (1) at 3, 9. Deadline of all jobs 4.
Ji,j jth instance of task i
1. Schduling using EDF w/o scaling
2. Schduling using the Time Variant Scaling
Using a square energy function 35 more energy
saving compared to EDF. 8 to DVSST
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Statistical Deadline Guarantee

• Worst case scenario schedulability test
• Conservative
• pi minimum interarrival

• Statistical guarantee
• Overload probability vprob(l(t) gt fmax)

cumulative probability
1
v
F(x)
fmax
worst case f
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Statistical Deadline Guarantee (cont.)

• Load tail distribution
• A general bound w/ load mean and variance
• Tight bounds based on load distribution
• Exact output distribution if input distribution
  known
• Estimate output distribution using a histogram

fmax
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Evaluation

• Objectives
• Effectiveness in energy savings
• Effectiveness of the deadline miss bound
• Scheduling based on WCET
• No-DVS run jobs with the maximum speed.
• Offline Offline optimal algorithm of Yao95 et
  a.
• DVSST On-line algorithm for sporadic tasks
  QadiRTSS03 et al.
• TimeInvar Time-invariant voltage scaling.
• TimeVar Time-variant voltage scaling.
• On-line slack management
• DVSSTCC (Cycle-conserving EDF) Worst case
  schedule using DVSST with the reclaiming
  algorithm of Pillai and Shin (SOSP01).
• TimeVarOLDVS The time-variant voltage scaling
  and the reclaiming algorithm of Lee and
  ShinRTSS2004.
• TimeVarTimeVar A unified solution.

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Energy Savings

• Energy consumption with the Robotic Highway
  Safety Marker application A scenario in which
  robot keeps moving

DVSST
Offline
TimeVariant

• TimeVar is energy-efficient, close to Offline
  (5) 7-11 better than DVSST

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Energy Savings w/ Workload Variation

• tasks30
• Interarrival exp(50 ms)
• WCET n(100, 10)K
• Workload variation characterized by actual
  execution time over worst case (BCET/WCET)

TimeVariant adapts with workload variation
effectively
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Computation Speed Configuration
Required speed (MHz)

• Target deadline guarantee 99

Mean Interarrival time (ms)

• Computation requirement based on a general bound
  is better than worst case with mean interarrivals
  gt 60 ms
• Tight bounds reduce the computation speed in half
  as interarrivals gt 40 ms

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Statistical Deadline Guarantee

• No deadline misses under bound derived based on a
  general input 100MHz
• Statistics of TimeVar/TimeInvar under a tight
  bound 40MHz
• Overload handling reject new jobs or serve
  unfinished jobs in a best-effort mode
• Target deadline guarantee 99

Scheduling TimeInvariant TimeInvariant TimeVariant TimeVariant
Scheduling Reject Besteffort Reject Besteffort
Load mean (106) 21.6 21.7 21.6 21.74
Load var 166.7 168.9 141.3 142.8
Time mean 10.1 10.09 10.4 10.07
Time variance 8.7 8.4 8.4 8.8
Overload/Deadline misses 0.63 0.63 0.61 0.61
Deadline miss rate is effectively bounded
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Conclusion

• Voltage/Speed scaling for a general task model
• A Filtering Model for DVS
• Two online policies to minimize energy usage
• Time-invariant A generalization of several
  existing approaches
• Time-variant Optimal in the sense it is online
  w/o future task timing information. Also
  effective for on-line slack management
• Statistical deadline guarantee based on
  computation speed configuration.
• Future work
• System-wide energy savings, e.g., wireless
  communication and its interaction with CPU

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Energy-Aware Modeling and Scheduling of Real-Time
Tasks for Dynamic Voltage Scaling
Thank you!