Raziel Hess-Green
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A small intro
Raziel Hess-Green
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More known as:
“ski-rental problem”
Stairs: takes time S
Elevator: takes time L<S
The ultimate question:
How long to wait?
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Competitive ratio – Alg/OPT
◦ worst case over all possible events
◦ Alg = cost of algorithm
◦ OPT = optimal cost in hindsight.
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Wait until elevator comes
◦ What if it’s broken?
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Take stairs immediately
◦ Bad competitive ratio - S/L
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Wait until you should have taken the stairs,
then take the stairs
Case 1:
◦ Elevator comes before time S-L: optimal.
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Case 2:
◦ Elevator comes after: you paid 2S-L, OPT paid S.
Ratio = 2 - L/S.
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Elevator arrives right after you give up:
◦ If you wait longer,
numerator goes up but the denominator stays the
same, so your ratio is worse.
◦ If you wait less, then the numerator and the
denominator go down by the same amount, worse.
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BP:
◦ Given N items with sizes s1, s2,…, sN, where 0  si  1.
The bin packing is to pack these items in the fewest
bins, given that each bin has unit capacity.
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On-line bin packing:
◦ Each item must be placed in a bin before the size of
the next item is given.
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Stay tuned for more..
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Young Choon Lee, Albert Y. Zomaya
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2000 – 2005
◦ Doubled!
◦ 2005 cost 7.2 bn US$
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2005-2010
◦ Predicted by the EPA at 2007 to double again
◦ Actually added around 56% (J. Koomey)
 Mainly due to 2008 recession
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2011
◦ 2% of USA electricity
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Electricity Bill
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Cloud Computing allows for fuller utilization of
hardware
Energy consumption is turning into a major issue
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Costly
CO2 emission
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Must hold enough resources to handle peak
demand
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Energy grows linearly with utilization
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20% utilization
Idle servers can use 60% of full utilization
Turning off is problematic
◦ Long turn on time
◦ May increase failure rate
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Must have the server totally unutilized to
enable sleep mode
Dynamic Voltage and Frequency Scaling (DVFS)
◦ Intel SpeedStep
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◦ AMD PowerNow!
Started in laptops and mobile devices
Now used in servers
Much more research on this:
◦ PowerNap (ASPLOS ’09)
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Cloud
Application
Energy
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Resources
◦ set R of r resources/processors
fully interconnected
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Homogeneous
◦ Communication
◦ Same DC
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Live Migration
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IaaS, SaaS or PaaS
regarded as tasks
Assumed: known time and CPU demand
◦ IaaS has predefined time/CPU requirements
◦ For SaaS and PaaS- obtain estimates from history
and/or from consumer
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linear relationship
with processing time and utilization:
𝑈𝑖 = 𝑛𝑗=1 𝑢𝑖,𝑗
◦ 𝑢𝑖,𝑗 - utilization of task t j on 𝑟𝑖
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𝐸𝑖 = 𝑈𝑖 𝑃𝑚𝑎𝑥 − 𝑃𝑚𝑖𝑛 + 𝑃𝑚𝑖𝑛
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Energy during Power Save mode: 10% 𝑃𝑚𝑖𝑛
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Assigning a set N of n tasks
to a set R of r cloud resources
Maximize resource utilization
◦ In order to minimize energy consumption
◦ By enabling resources to sleep
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Without violating constraints
◦ time
◦ Usage
◦ Hard constraints
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Two algorithms presented,
differ only in cost function
ECTC
◦ Explicitly computes energy consumption
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MaxUtil
◦ Average utilization during processing time of the task to schedule
◦ Increase consolidation density
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𝑓𝑖,𝑗 =
(𝑝∆ . 𝑢𝑗 + 𝑝𝑚𝑖𝑛 )τ0 – ((𝑝∆ . 𝑢𝑗 + 𝑝𝑚𝑖𝑛 )τ1 +𝑝∆ . 𝑢𝑗 .τ2)
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𝑊ℎ𝑒𝑟𝑒
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𝑝∆ = 𝑝𝑚𝑎𝑥 − 𝑝𝑚𝑖𝑛
𝑢𝑗- utilization rate of the task 𝑡𝑗
τ0 - total processing time of the task
τ1- time task will run alone
τ2- time task will run in parallel
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fi , j 
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U
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i
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Maximize average consolidation density
◦ Over all processing time of task j
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Random
ECTC
MaxUtil
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1,500 experiments
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◦ 50 different number of tasks
 100-5,000 with intervals of 100
◦ 10 mean inter-arrival times (10 -100)
 Poisson process
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Three usage patterns
◦ Random
 Uniformly distributed between 0.1 and 1
◦ Low
 Gaussian, mean utilization rates of 0.3
◦ High
 Gaussian, mean utilization rates of 0.7
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Task processing time
◦ Exponential distribution
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𝑃𝑚𝑎𝑥 = 30, 𝑃𝑚𝑖𝑛 = 20
◦ Assume: 300-200 watt active mode consumption
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_m
◦ Adding migration
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Relative energy savings
◦ MaxUtil
◦ ECTC
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Different resource usage patterns
◦ Low
◦ High
◦ Random
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Important problem
Strict modeling
◦ All demands known exactly (time, usage)
◦ Communication is “free”
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And yet: No sophisticated algorithms
No “make sense” for results
No comparing to previous work
◦ “existing task consolidation algorithms are not
directly comparable to our heuristics”
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Stochastic Bin Packing (SBP) problem
◦ each virtual machine's bandwidth demand is treated
as a random variable.
◦ both offline and online versions are treated
◦ assumption: VMs' bandwidth consumption obeys
normal distribution
◦ show a 2-approximation algorithm for the offline
version
◦ (2+Ɛ)-competitive algorithm for online version
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