Optimal Integration of InterTask and IntraTask Dynamic Voltage Scaling Techniques for Hard RealTime

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Optimal Integration ofInter-Task and Intra-Task
Dynamic Voltage Scaling Techniques for Hard
Real-Time Applications

• Jaewon Seo, Samsung Electronics
• Taewhan Kim, Seoul National University
• Nikil D. Dutt, University of California, Irvine

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OUTLINE

• INTRODUCTION AND RELATED WORK
• DEFINITIONS AND PROBLEM FORMULATION
• THE COMBINED DVS TECHNIQUE
• EXPERIMENTAL RESULTS
• CONCLUSIONS

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INTRODUCTION

• Minimizing energy consumption
• Important concern in system design
• Energy consumption in CMOS circuits
• Energy ? VDD2
• Lowering VDD - most effective technique for
  reducing energy
• Dynamic Voltage Scaling (DVS)
• Dynamic adjustment of supply voltage
• Energy saving vs. Increased execution time
• VDD ? clock freq. ( operating speed)

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INTRODUCTION (contd)

• Inter-task DVS vs. Intra-task DVS

Inter-task DVS Task 1 1 Specified by
WCET Reclaimed by other tasks
Intra-task DVS Basic block 1 1 CFG No slack
Scaling unit of tasks of Vs/task Task
model Slack handling
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• Control Flow Graph (CFG) for a Task

statements // b0 if (cond) then
statements // b1 else statements // b2
b0 n0200
p1 0.1
p2 0.9
b1 n1 800
b2 n2 100
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Task set with dependency and/or deadlines
t1 10
t3 40
t2 5
t4 75
t5 20
deadline300
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Related Work

• D. Shin, J. Kim, L. Lee, Intra-task voltage
  scheduling for low-energy , IEEE Design Test
  of Computers, 2001
• J. Seo, T. Kim, K. Chung, Profile-based optimal
  intra-task voltage scheduling for hard real-time
  , DAC 2004
• F. Yao, A. Demer, S. Shenker, A scheduling model
  for reduced CPU energy, FOCS 1995
• Y. Zhang, X. Hu, D. Chen, Task scheduling and
  voltage selection for energy minimization, DAC
  2002
• W. Kwon, T. Kim, Optimal voltage allocation
  techniques for dynamically variable voltage
  processors, DAC 2003
• M. Schmitz, B. Al-Hashimi, P. Eles,
  Energy-efficient mapping distributed embedded
  system, DATE 2002
• G. Varatkar, R. Rarculescu, Communication-aware
  task scheduling and voltage selection for total
  , ICCAD 2003
• A. Andrei, et al., Overhead-conscious voltage
  selection for dynamic and leakage energy
  reduction , DATE 2004

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ENERGY MODEL

• Energy consumption
• Clock frequency ( speed)
• Average energy consumption

Supply voltage
Total of inst. cycles executed

• Energy (speed)2 x distance

Velocity saturation index
Threshold voltage
Energy consumption for p
Probability that execution follows p
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PROBLEM FORMULATION

• Application model
• N communicating tasks Tt1, t2, , tN
  represented by a DAG
• Arc (ti, tj) ti must be executed before tj
• Local deadline
• Sink (global deadline)
• Task parameters
• si starting time
• ei ending time (ei si),
• ti execution time (ti ei - si)
• di deadline

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PROBLEM FORMULATION (contd)

• Combined Inter- and Intra-task DVS problem
• Given an instance of tasks
• Find
• Inter-task schedule
• Intra-task voltage scaling
• With
• Feasible schedule for every possible exec. path
  of tasks
• Minimum total average energy consumption

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OPTIMAL INTRA-TASK DVS

• Control Flow Graph (CFG)

bi basic block ni of execution cycles pi
probability that execution follows the edge
statements // b0 if (cond) then
statements // b1 else statements // b2
b0 n0200
p1 0.1
p2 0.9
b1 n1 800
b2 n2 100
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OPTIMAL INTRA-TASK DVS (CONTD)

• For unknown initial speed x

x MHz
b0 n0200
p1 0.1
p2 0.9
b1 n1 800
b2 n2 100
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OPTIMAL INTRA-TASK DVS (CONTD)

• Find x that minimizes ( find the inflection
  point)
• We have

Energy consumptions for b0, b1 and b2
Length of ROEP
x speed of b0 ni length of bi pi prob. of
bi T deadline
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OPTIMAL INTRA-TASK DVS (CONTD)

• In general,
• di Length of ROEP for bi
• Optimal speed for bi
• Resultant minimum energy

If bi has no successor in CFG
, otherwise
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PROPOSED TECHNIQUE (IntraDVS)

• Before executing the task
• Compute length of ROEP (say di) for each basic
  block bi
• Insert change_f_V(di/remaining_time()) at the
  beginning of bi

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Speed 2.93 ? 3.24 ? 3.14 ? 3.14 ? 2.26 ? 2.26
B0 B2 B3 B5
B6 B8
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COMBINED DVS TECHNIQUE

• Two-step method
• Determine si and ei for each task ti
• Considering future use of intra-task scaling
• Execute ti within si , ei while varying
  processor speed
• Using optimal intra-task DVS scheme

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CASE 1 TASKS WITH A GLOBAL DEADLINE ONLY

• Each task has no deadline other than sink
• Can be solved easily by properly distributing the
  permitted execution time ( dsink)
• Lemma 1
• Minimum energy consumption is achieved when each
  task is assigned the execution time proportional
  to its energy-optimal execution path length
• ti dsink

?i
?1 ?N
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CASE 1 (CONTD)

• Without loss of generality assume sequence (t1,
  t2, , tN) does not violate precedence
  relations
• Starting and ending time are determined
• si and ei si ti

0 for i 0 ei-1, for i 1
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CASE2 TASKS WITH ARBITRARY DEADLINES

• Divide the problem into a collection of
  subproblems of Case 1
• E.g.,
• Let (t1, t2, , tN)
• Obtained by EDF (Earliest Deadline First)
  scheduling
• Only two tasks ti, tj (iltj) have deadlines
• Partition into three groups
• (t1, , ti, , tj, , tN)
• gt (t1, , ti) (ti1, , tj) (tj1,
  , tN)
• Then, apply the method of Case 1

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t1 5
t3 65
t2 15
t5 5
t4 15
t6 20
deadline40
deadline120
t7 35
sink
deadline200
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AN IMPROVED INTER-TASK DVS TECHNIQUE

• Previous method is not optimal
• Yao et als algorithm
• Well-known optimal inter-task scheduling
  algorithm with academic task model
• No dependency between tasks
• Each task always takes its WCEP
• Task parameters
• (ai, di, ri) arrival time, deadline, req. of
  cycles
• Resultant energy consumption

Assigned execution time for minimum energy
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AN IMPROVED INTER-TASK DVS TECHNIQUE (CONTD)

• Transforming original problem
• Supertask
• t1 t1, , ti
• t2 ti1, , tj
• t3 tj1, , tN
• Arrival time
• a1 0
• a2 0
• a3 0
• Deadline
• d1 di
• d2 dj
• d3 dN

• Req. of cycles
• r1 ?1 ?i
• r2 ?i1 ?j
• r3 ?j1 ?N

(?i d0 value of task ti)
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AN IMPROVED INTER-TASK DVS TECHNIQUE (CONTD)

• After applying the optimal intraDVS, resultant
  energy consumption becomes

Minimum energy consumption (by Theorem 2 in
section 4.3.2)
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t1 5
t3 65
t2 15
t5 5
t4 15
t6 20
deadline40
deadline120
t7 35
sink
deadline200
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EXPERIMENTAL RESULTS

• Task sets are generated by TGFF v3.0 2
• Used the example input files (tgffopt)
• Each task is generated randomly
• 1 branches 100
• Branch probability is drawn from random normal
  dist. (s1.0, µ0.5)
• Length of the longest basic block
• Length of the shortest basic block
• Slack factor 0.2
• Compared to ILP based approach (Zhang 11)

100
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CONCLUSIONS

• To deal with the combined inter- and intra-task
  DVS problem
• We devised the method setting energy-optimal
  execution time to each task
• Divided the task set into several task groups
  s.t. each task group can be scheduled optimally
  within the group boundary
• Determined the group boundaries using existing
  inter-task DVS technique
• Then applied our optimal intra-task DVS technique
• Experimental results show 10.6 reduction of
  energy consumption over the previous approach