Online Power Saving Strategies

Sandy Irani

Joint work with Rajesh Gupta, Sandeep Shukla, Dinesh Ramanathan

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..

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.

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.

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.

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

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

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.

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.

T

T

T

dttpTdttpt )(]1)(minarg0

Multi-state Case

• Let there be k+1 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 i+1 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).

Lower Envelope Idea

Energy

Time

State 4

State1 State2 State3

t1 t2 t3

ii TimeEnergy )(For each state i, plot:

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 i+1.

• 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.

Probabilistic Lower Envelope Algorithm

• Use same order of states as determined by lower envelope function.

• Our approach:– Determine threshold for transitioning from state i to

state i+1 by solving the optimization problem where i and i+1 are the only states in the system.

T

iii

T

iiT

i

dttpTtT

dttptT

)(])(

)(][minarg

1

0

11

Probabilistic Lower Envelope Algorithm

• Can show that:

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

kTTT 21

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.

Experimental Study: IBM Mobile Hard Drive

0s02.4Active/Busy

40ms0.560.9Idle

1.5s1.5750.2Stand-by

5s4.750Sleep

Transition Time to Active

Start-up Energy (Joules)

Power Consumption

State

Trace data with arrival times of disk accesses Trace data with arrival times of disk accesses from Auspex file server archive.from Auspex file server archive.

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]

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 c=5).– Let T1 ,…, Tk be discontinuities of Lower Envelope (i.e.

thresholds for the Lower Envelope Algorithm).– Partition range [Ti, Ti+1 ] into c equal size bins.

Histogram Sample

Bin Low-end High-end Range Count

1 0 11.2 11.2 35

2 11.2 22.4 11.2 2

3 22.4 33.6 11.2 4

4 33.6 44.8 11.2 7

5 44.8 56 11.2 4

6 56 478.8 422.8 5

7 478.8 901.6 422.8 3

8 901.6 1324.4 422.8 2

9 1324.4 1747.2 422.8 0

10 1747.2 2170 422.8 4

Histogram Example, cont.Bin Low High Range Count

11 2170 4911 2741 7

12 4911 7652 2741 9

13 7652 10393 2741 2

14 10393 13134 2741 5

15 13134 15875 2741 4

16 15875 19050 3175 2

17 19050 22225 3175 3

18 22225 25400 3175 1

19 25400 28575 3175 0

20 28575 1

Experimental Results

0

0.5

1

1.5

2

2.5

0 500 1000 1500 2000 2500

Latency

Co

mp

etit

ive

Ra

tio w

rt

En

erg

y U

sag

e

Optimal

LEA

PLEA

LAST:P

LAST:NP

TREE:P

EXP:P

EXP:NP

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.

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:

j

j

b

a

jRdtjtjobts )),(()(

1

0

))(()(cost

t

dttsPSt

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.

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:

1

0

))(),(()(cost

t

dtthtsPkSt

Capabilities: vibration, acoustic,accelerometer, magnetometer,temperature sensing

Processor Seismic Sensor Radio Power (mW)Active On Rx 751.6Active On Idle 727.5Active On Sleep 416.3Active On Removed 383.3Active Removed Removed 360.0Active On Tx (36.3 mW) 1080.5

Tx (27.5 mW) 1033.3Tx (19.1 mW) 986.0Tx (13.8 mW) 942.6Tx (10.0 mW) 910.9Tx (3.47 mW) 815.5Tx (2.51 mW) 807.5Tx (1.78 mW) 799.5Tx (1.32 mW) 791.5Tx (0.955 mW) 787.5Tx (0.437 mW) 775.5Tx (0.302 mW) 773.9Tx (0.229 mW) 772.7Tx (0.158 mW) 771.5Tx (0.117 mW) 771.1

Summary

Processor = 360 mW

doing repeatedtransmit/receive

Sensor = 23 mW

Processor : Tx = 1 : 2

Processor : Rx = 1 : 1

Total Tx : Rx = 4 : 3at maximum range

CommunicationSubsystem

RadioModem

GPS

MicroController

Rest of the Node

CPU Sensor

Rockwell WINS Node

SmartBadge

• Battery-powered embedded system.– Sharp’s display, wireless local area network (WLAN) card,

StrongARM-1100 processor, Micron’s 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]

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 <t<bj

= 0 otherwise.

•

• job(t): Earliest Deadline First.

– Competitive ratio of Average Rate c, where power function p is a degree-d polynomial:

ddd dcd 12

)()( tstsj

j

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

)())()(( yxPyPxPd

}6,3),1(max{ dcd

Optimal Offline Algorithm for DVS-NS[Yao, 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’].

)',()',(

zzl

Rzzg j

]',[][ , zzba jj

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’].

Optimal Offline Algorithm for DVS-NS Example

Speed

Time1

2

3

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.

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?

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 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.

Offline Algorithm for DVS-S Example

Speed

Time

Scrit

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 < 1/ becomes an on interval.– Idle intervals of length > 1/ becomes a sleep interval.

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.

OPT

LTR

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 .

dtPtsPSt )]0())(([)(cos

Power=P(0)

P(Scrit)

ACTLTR

IDLELTR

RUNLTR

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

– RUNLTR is at most ACTOPT + RUNOPT .

OPT

LTR

– IDLELTR is at most ONOPT + 3 SLEEPOPT .

Speed

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

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.

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.

Procrastinator Example

Scrit

Procrastinator Example

Scrit

Procrastinator Example

Scrit

Procrastinator Example

Scrit

• 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.

• 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

)())()(( yxPyPxPd

}6,3),1(max{ dcd

• 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

)())()(( yxPyPxPd

}6,3),1(max{ dcd

2x3x

d c

2

4

4/8

27/108 108/540

8/24

c.r.

P(s)

• 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

)()()( 21 yxPyPdxPd

}6,3,max{ 21 cdcd

3x

c

27/108 66/193

c.r.

P(s)

3x 27/108 108/540

Open Problems

• Optimize constants in algorithm.– Don’t wait until last minute to return to active

state.

• Experimental Study: coming this summer.

• Offline problem NP-complete?

• Improve online algorithms for DVS-NS.

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.