Online Power Saving Strategies

1
Online Power Saving Strategies

• Sandy Irani
• Joint work with Rajesh Gupta, Sandeep Shukla,
  Dinesh Ramanathan

2
Motivation

• System Level/ Application controlled power
  management is gaining importance.
• Power is becoming first class design parameter
  for software and applications
• Greater power savings is possible if knowledge of
  the applications demands are taken into account..

3
Power Savings Mechanisms

• Dynamic Power Management
• When a device is idle, it can transition to
  low-power sleep states. .
• Dynamic Voltage Scaling
• A device can be run at different speeds with
  different power usage rates.
• Execution of jobs can be slowed down to save
  power as long as all jobs are completed by their
  deadline.

4
This Talk

• Extend work on dynamic power management to handle
  devices with multiple sleep states.
• Design and analyze algorithms for systems that
  allow both dynamic power management and dynamic
  voltage scaling.

5
Dynamic Power Management

• Current Trend
• Design Devices with sleep states
• Provide driver hooks to change the power states
  under operating system control
• For power-hungry peripheral devices it is
  common
• Disk-Drives
• Network Interface cards (Wireless card)
• Display devices
• DRAM
• O/S designers design Dynamic Power Management
  Strategies to take advantage of that.

6
Dynamic Power Management

• When a device becomes idle, it can transition to
  lower power usage state.
• A fixed amount of 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
  the sleep state?
• Too soon pay start-up cost too frequently.
• Too late spend too much time in the high-power
  state

7
2-state vs. Multi-state

• 2-state case
• One idle state
• One power saving state
• Multi-State
• Idle state, and multiple power saving States.
• Each power saving state has different power
  characteristics, and transition penalty.
• Example IBM Disk Drive
• Idle, standby, sleep

8
Previous Work

• Deterministic algorithm (ski rental)
• Transition to sleep state when the cost of being
  in active state is at least the cost of waking
  up.
• Normalize cost of transitioning from sleep to
  active state to 1.
• Power consumption rate of active state is ?.
• This algorithm is 2-competitive.
• 2 is the best possible competitive ratio for any
  deterministic algorithm.

9
Previous Work, cont.

• Idle period length generated by known
  distribution with density function p(t).
• Choose threshold T to minimize cost
• Theorem Karlin, Manasse, McGeough and Owicki
• For any distribution p(t), the expected cost of
  the above algorithm is within e/(e-1) of the
  optimal cost. Furthermore, there is a
  distribution for which no algorithm can be better
  than e/(e-1) times optimal.

10
Multi-state Case

• Let there be k1 states
• Let State k be the shut-down state and 0 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 ?i1 ? ?i
• ?k 0 and ?0 0 (without loss of generality).
• Power down energy cost can be incorporated in the
  power up cost for analysis (if additive).

11
Lower Envelope Idea
State1
State2
State3
State 4
Energy
t1
t2
t3
Time
For each state i, plot
12
Deterministic Lower Envelope Algorithm

• 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.

13
Probabilistic Lower Envelope Algorithm

• Use same order of states as determined by lower
  envelope function.
• Our approach
• Determine threshold for transitioning from state
  i-1 to state i by solving the optimization
  problem where i-1 and i are the only states in
  the system.

14
Probabilistic Lower Envelope Algorithm

• Can show that
• THEOREM The Probabilistic Lower Envelope
  Algorithm is e/(e-1)-competitive.

15
Power-Latency Tradeoff

• Tasks arrive through time and take time to run
• If the device is busy when a task arrives, it
  waits in a queue
• Idle period begins when device finishes current
  job and the queue is empty
• If device transitions to sleep state in an idle
  period, some latency is incurred as device
  transitions to active state.
• This in turn effects (shortens) the length of
  future idle periods.
• Power-Latency tradeoff extremes
• Minimize latency always stay in the active
  state.
• Minimize energy usage delay completing any tasks
  until they have all arrived.

16
Experimental Study IBM Mobile Hard Drive
Trace data with arrival times of disk accesses
from Auspex file server archive.
17
Histogram for the Probabilistic Lower Envelope
Algorithm

• Create histogram
• Partition possible idle period range (0,?) into
  intervals
• Let ri denote the left end of the ith interval
• Keep a counter for the number of idle periods
  among last w idle periods that fall in the range
  ri-1 , ri)
• Update thresholds every r idle periods
• Use Probabilistic Lower Envelope Algorithm to
  calculate thresholds using histogram as estimate
  of probability distribution generating upcoming
  idle period.
• Takes time O( bins states )
• Similar to Keshav, Lund, Phillips, Reingold,
  Saran

18
Histogram for the Probabilistic Lower Envelope
Algorithm

• How many partitions do we need for the histogram?
• More partitions, more accurate estimation
• More partition, more expensive computation
• Where should we partition?
• Our method
• Pick a constant c. (we chose c5).
• Let T1 ,, Tk be discontinuities of Lower
  Envelope (i.e. thresholds for the Lower Envelope
  Algorithm).
• Partition range Ti, Ti1 into c equal size
  bins.

19
Histogram Sample
20
Histogram Example, cont.
21
Experimental Results
22
Dynamic Voltage Scaling

• Device which can run at any speed s.
• Power consumed if running in state s is given by
  convex function P(s).
• Jobs arrive through time. Job j has
• Arrival time aj
• Deadline bj
• Work required Rj
• Schedule S (s, job)
• s(t) is the speed of the device at time t.
• job(t) is which job is executed at time t.

23
Dynamic Voltage Scaling(Dynamic Voltage Scaling
- No Sleep DVS-NS)

• Schedule S is feasible for set of jobs J if for
  every j in J
• Cost of Schedule S is

24
DVS with Sleep State (DVS-S)

• Schedule S ( s, job, h )
• h(t) sleep or on
• If h(t) sleep, then s(t) 0.
• Power is a function of speed and state
• P(s, state) P(s) if state on.
• P(s, state) 0 if state sleep.
• P(0) ? is power required to keep device active
  with no tasks running.

25
DVS with Sleep State (DVS-S)

• Requirements for a feasible schedule are the
  same.
• Let k be the number of times the device
  transitions from sleep state to the on state
• Cost of a schedule S is

26
SmartBadge

• Battery-powered embedded system.
• Sharps display, wireless local area network
  (WLAN) card, StrongARM-1100 processor, Microns
  SDRAM memory, FLASH memory, sensors, modem/audio
  analog front-end on printed circuit board.
• Goal allow computer or human user to provide
  location and environmental information to a
  location server through a heterogeneous network.
• Operates as part of a client-server system
  initiates and terminates communication sessions.
• Simunic, 2001, PhD Thesis, Stanford University

27
Previous Work on DVS-NS

• Yao, Demers and Shenkel
• Polynomial time offline algorithm to find the
  optimal schedule for a set of jobs.
• Algorithms Average Rate
• sj (t) Rj /(bj aj) for t aj lttltbj
• 0 otherwise.
• job(t) Earliest Deadline First.
• Competitive ratio of Average Rate c, where power
  function p is a degree-d polynomial

28
Our Results on DVS-S

• Offline algorithm whose cost is within a factor
  of 3 of optimal
• Online algorithm
• Let A be an online algorithm for DVS-NS that
  achieves a competitive ratio of c.
• Let d be the smallest constant such that for all
  x,y greater than 0,
• Theorem the Competitive ratio of the online
  algorithm is at most

29
Optimal Offline Algorithm for DVS-NSYao,
Demers, and Shenker

• The algorithm schedules jobs as it goes and
  blacks-out intervals of time for which the device
  has already been scheduled.
• A job j is contained in an interval z,z if
• For interval z,z, define l(z,z) to be the
  length of the interval minus the blackout times.
• Define the intensity of interval z,z to be
• where the sum is taken over all unscheduled jobs
  j that are contained in z,z.

30
Optimal Offline Algorithm for DVS-NS

• Repeat until all jobs are scheduled
• Find the interval z,z with the maximum
  intensity.
• Set s(t) g(z,z) for all t in z,z.
• Blackout the interval z,z.
• Remove all jobs that are contained in z,z.

31
Optimal Offline Algorithm for DVS-NS Example
Speed
1
Time
2
3
32
Critical Speed

• If the cost to transition from sleep state to the
  on state were 0, the optimal speed for all jobs
  would be the s that minimizes (Rj/s)
  P(s)
• This is the s that satisfies P(s) s P(s).
• Call this Scrit, the critical speed for ?.
• If we compress the execution of a task by x,
• we expend additional energy because we execute
  the job faster
• we save ? x.
• Scrit is the point at which it is no longer
  beneficial to compress the execution of a task.

33
Offline Algorithm for DVS-S

• Run the optimal offline algorithm for DVS-NS
  until the maximum intensity interval has
  intensity less than ?s.
• Now we must decide how to schedule the remaining
  tasks.
• There is a feasible schedule in which all jobs
  are run at a speed Scrit or less.
• First decide on intervals of time in which device
  will sleep. Then run optimal DVS-NS algorithm
  with these intervals blacked out to determine
  device speed.
• How to decide on the sleep intervals?

34
Idea

• Run the device at speed 0 or Scrit.
• Interval in which s(t) 0 is an idle interval
• Interval in which s(t) Scrit is an active
  interval.
• The active time is the same over all schedules.
• The cost of an idle interval of length i is the
  minimum of ?i and 1.
• Try and minimize the cost of all idle intervals.
• Want fewer, longer intervals.
• Ignoring the fact that compressing some jobs to a
  speed of ?s is more costly for some jobs than
  others.

35
Offline Algorithm for DVS-S Example
Scrit
Speed
Time
36
Left-To-Right Algorithm

• Decide on Active/Idle Intervals
• Sweep from left to right.
• While active, run as many jobs as possible until
  there are no pending jobs in the system. Then
  device must become idle.
• While idle, remain idle until it is necessary to
  start running jobs again in order to run all jobs
  by their deadline at a speed of Scrit
• Decide on Sleep/On Intervals
• Active interval becomes an on interval.
• Idle interval of length lt 1/? becomes an on
  interval.
• Idle intervals of length gt 1/? becomes a sleep
  interval.

37
Results

• Theorem the cost of Left-To-Right on any set of
  jobs is within a factor of three of optimal.
• Lemma no idle interval for the optimal algorithm
  can contain two idle intervals of Left-To-Right.

38
OPT
LTR
39
Proof for LTR

• Divide LTR cost into three components
• ACTLTR P(0) times the length of all the active
  components
• RUNLTR The cost to run the jobs beyond the
  energy spent keeping the device on
• where the interval is taken over all active
  intervals.
• IDLELTR The cost of each idle period.
• Either 1 or the length times ?.

40
P(Scrit)
?P(0)
Power
ACTLTR
IDLELTR
RUNLTR
41

• ACTLTR is at most ACTOPT .
• Optimal will not run any job faster than Scrit.
• RUNLTR is at most ACTOPT RUNOPT .

OPT
LTR
Speed

• IDLELTR is at most ONOPT 3 SLEEPOPT .

42
IDLELTR is at most ONOPT 3 SLEEPOPT

• Consider an interval I in which LTR is idle.
• If OPT is ON during all of I, then the cost of I
  is covered by the cost incurred by OPT in keeping
  device on during I.
• Consider all intervals I such that OPT is asleep
  during a portion of I. The number of such
  intervals is at most 3 times the number of times
  OPT is in sleep state

OPT on/sleep
LTR active/idle
43
Online Algorithm for DVS-S

• Decide on Active/Idle Intervals
• Sweep from left to right.
• While active, run as many jobs as possible until
  there are no pending jobs in the system. Then
  device must become idle.
• While idle, remain idle until it is necessary to
  start running jobs again in order to run all jobs
  (that we know about) by their deadline at a speed
  of Scrit
• Algorithm name PROCRASTINATOR
• Decide on Sleep/On Intervals
• If idle, stay on until cost of staying equals
  cost of waking up.

44
Online Algorithm for DVS-S

• Decide on device speed.
• Let A be an online algorithm for DVS-NS.
• Whenever feasible, run device at speed Scrit
• If a job arrives which makes it impossible to
  complete all jobs at a speed of Scrit by their
  deadline, schedule new job according to A. Add
  the speed of this job to the speed already
  allocated to other jobs.

45
Procrastinator Example
Scrit
46
Procrastinator Example
Scrit
47
Procrastinator Example
Scrit
48
Procrastinator Example
Scrit
49

• The time Procrastinator is active is less than
  the time LTR is active. (Procrastinator runs
  tasks at least as fast as LTR).
• Can bound cost to keep device on and cost to
  wake-up for Procrastinator by cost of LTR.
• Extra cost comes from doubling up jobs scheduled
  at speed Scrit and jobs scheduled by algorithm A.

50

• Let A be an online algorithm for DVS-NS that
  achieves a competitive ratio of c.
• Let d be the smallest constant such that for all
  x,y greater than 0,
• Theorem the Competitive ratio of Procrastinator
  is at most

51

• Let A be an online algorithm for DVS-NS that
  achieves a competitive ratio of c.
• Let d be the smallest constant such that for all
  x,y greater than 0,
• Theorem the Competitive ratio of Procrastinator
  is at most

c
c.r.
d
8/24
2
4/8
P(s)
4
27/108
108/540
52

• Let A be an online algorithm for DVS-NS that
  achieves a competitive ratio of c.
• Let d1 and d2 be such for all x,y greater than 0,
• Theorem the Competitive ratio of Procrastinator
  is at most

c
c.r.
27/108
108/540
P(s)
27/108
66/193
53
Open Problems

• Optimize constants in algorithm.
• Dont wait until last minute to return to active
  state.
• Experimental Study coming this summer.
• Offline problem NP-complete?
• Improve online algorithms for DVS-NS.

54
Papers

• Competitive Analysis of Dynamic Power Management
  Strategies for Systems with Multiple Power Saving
  States.With Sandeep Shukla and Rajesh Gupta.
  Proceedings of Design Automation and Test in
  Europe (DATE), 2002.
• Online Strategies for Dynamic Power Management in
  Systems with Multiple Power Saving States. With
  Sandeep Shukla and Rajesh Gupta. Submitted to ACM
  Transactions on Embedded Computing Systems,
  Special Issue on Power-Aware Embedded Computing.
• Dynamic Voltage Scaling for Systems with Sleep
  States. Manuscript.