Dynamic Power Management for Systems with Multiple Power Saving States

1
Dynamic Power Management for Systems with
Multiple Power Saving States

• Sandy Irani, Sandeep Shukla, Rajesh Gupta

2
Canonical Power Management

• Observations
• Tuning power-performance control knobs often has
  time and/or energy cost
• Decision procedures needed, e.g., transition to a
  lower power state.
• Question
• How effective is a specific power-aware resource
  management policy in terms of energy saved and
  timing constraints observed?

Latency Energy
3
Effectiveness of Power Mgmt.

• Model
• Functionality composed of individual tasks
• Each task dissipates power to service requests
  that arrive over time
• Inter-arrival time of requests is unknown
• Requests are of different sizes and must be
  served in the order received
• Task can choose to move to power minimizing
  states
• DPM is an on-line problem
• Input sequence is received at runtime
• Characteristics of the input sequence is not
  known
• Any algorithm to solve the problem can not make
  static decisions about the input
• Competitive analysis provides a framework for
  understanding online strategies.

4
The DPM Problem Addressed

• When device becomes idle, can transition to lower
  power usage state.
• Additional time and energy are required to
  transition back to active state when a new
  request for service arrives.
• What is the best time threshold to transition to
  sleep state?
• Too soon pay start-up costs too frequently
• Too late spend too much time in high-power state

5
Competitive Analysis

• Strategy S is a c-competitive
• if for all input sequence, s, CS(s) lt c. Copt(s)
• Competitive ratio (CR) of S is infimum over all
  c, such that S is c-competitive
• Assume an adversary that generates inputs to S
  knowing only the strategy S
• If S has a ratio r against this adversary, then
  in the worst case it would dissipate as much
  power as against an optimal offline strategy.
• Adversary can be generated automatically through
  constraint generation and property checking.
• DPM bounds are useful in strategy
  characterization.

6
DPM Bounds

• DPM strategies can be non-adaptive or adaptive
• Known DPM bounds with one idle state, one power
  saving state
• Non-adaptive strategies
• 2 1/k where k is discretized break-even
  time
• It is also shown that this bound is tight, i.e.,
  no deterministic strategy has a better CR
• Adaptive strategies (shutdown after variable
  time)
• e/(e-1) 1.6
• No adaptive algorithm has a better CR
• CR akin to complexity lower bounds
• Represent the worst possible scenario
• Two limitations
• Worst case is really too pessimistic to be useful
• Most interesting devices have multiple states
• Multiple power saving states
• Multiple active states
• Each state has different power characteristic and
  transition penalty.

7
Multi-State DPM CR Bounds

• Let there be k1 states
• Let State 0 be the shut-down state and k be the
  active state
• Let ?I be the power dissipation rate at state I
• Let ?I be the total energy dissipated to move
  back to State k
• States are ordered such that ?I ? ?I1
• Let ?0 0
• Assume
• Power down energy cost can be incorporated in the
  power up cost for analysis
• Idle time duration is unknown.

8
Lower Envelope Algorithm
State1
State2
State3
State 4
Energy
Time
t1
t2
t3
9
Deterministic Algorithm (LEA)

• The Lower Envelope Defines an ordering of the
  states.
• Throw out states that do not appear on lower
  envelope
• Given this ordering, only need to determine
  thresholds
• When to transition from state I to state I1.
• Lower Envelope Algorithm Transitions from one
  state to the next at the discontinuities of the
  lower envelope curve.
• Theorem Lower Envelope Algorithm is
  2-competitive.
• This ratio can be improved by considering input
  distribution
• Which can be learned on-line.

10
Stochastic Modeling in DPM

• Using recent history in access patterns,
  determine the distribution which governs idle
  period length
• An important issue but not covered here.
• Formulate an optimization problem which gives the
  exact timings when the power states should be
  changed.
• This approach works for any distribution over
  idle period lengths and adapts dynamically to
  patterns in the input sequence.

11
Probability-based LEA

• Use same order of states as determined by lower
  envelope function.
• Two state case can be solved by expressing
  expected cost as a function of the threshold and
  minimizing total energy consumption.
• Our approach
• Determine threshold for transitioning from state
  I to state I1 by solving the optimization
  problem where I and I1 are the only states in
  the system.
• THEOREM PLEA is e/(e-1)-competitive.

12
Experimental Framework

• Use trace data to obtain realistic probability
  distributions governing idle period length.
• Simulate algorithms for idle periods generated by
  these distributions.
• Algorithms tested
• Optimal Offline
• Lower Envelope Algorithm (LEA)
• Probabilistic Lower Envelope Algorithm (PLEA)

13
IBM Mobile Hard Drive
Trace data with arrival times of disk accesses
from Auspex file server archive.
14
Experimental Evaluation
15
Summary

• This paper builds up our earlier work to make the
  adversary-based approach to characterization of
  the DPM algorithms
• Extension of results on DPM bounds from 2-state
  case to multi-state case
• Improve DPM bounds by using additional
  information regarding the input.
• Analytical results match bounds for 2-state case.
• Experimental results show that probability-based
  algorithm improves upon deterministic by
  25bringing the strategy to within 23 of optimal.