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1.On-Line Algorithms 2.Energy efficient utilization of resources in cloud. Raziel Hess-Green. On-Line Algorithms. A small intro Raziel Hess-Green. Elevator or S tairs problem. More known as: “ski-rental problem” Stairs: takes time S Elevator: takes time L
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1. On-Line Algorithms
2. Energy efficient utilization of resources in cloud
Raziel Hess-Green
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On-Line AlgorithmsA 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?
Elevator or Stairs problem
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Competitive ratio – Alg/OPT◦ worst case over all possible events◦ Alg = cost of algorithm◦ OPT = optimal cost in hindsight.
Evaluate on-line algorithms
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Wait until elevator comes◦ What if it’s broken?
Take stairs immediately◦ Bad competitive ratio - S/L
Back to elevators and stairs
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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.
Case 2: ◦ Elevator comes after: you paid 2S-L, OPT paid S.
Ratio = 2 - L/S.
2-competitive
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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.
That’s the best possible
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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.
On-line bin packing:◦ Each item must be placed in a bin before the size
of the next item is given.
Stay tuned for more..
Bin Packing
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Energy efficient utilization of resources in cloud
computing systemsYoung Choon Lee, Albert Y. Zomaya
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2000 – 2005◦ Doubled!◦ 2005 cost 7.2 bn US$
2005-2010◦ Predicted by the EPA at 2007 to double again◦ Actually added around 56% (J. Koomey)
Mainly due to 2008 recession 2011
◦ 2% of USA electricity
Elictricity in Data Centers
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Electricity Bill With Great Power Comes Huge:
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Cloud Computing allows for fuller utilization of hardware
Energy consumption is turning into a major issue Costly CO2 emission
Must hold enough resources to handle peak demand
Energy grows linearly with utilization
Utility Computing
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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
Turn Off Power?
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Must have the server totally unutilized to enable sleep mode
Dynamic Voltage and Frequency Scaling (DVFS)◦ Intel SpeedStep◦AMD PowerNow!
Started in laptops and mobile devices Now used in servers Much more research on this:
◦ PowerNap (ASPLOS ’09)
Power Saving Mode
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Cloud Application Energy
Model
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Resources◦ set R of r resources/processors
fully interconnected Homogeneous
◦ Communication◦ Same DC
Live Migration
Cloud Model
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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
Application Model
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linear relationshipwith processing time and utilization:
◦ - utilization of task on
Energy during Power Save mode:
Energy Model
jt
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Assigning a set N of n tasksto a set R of r cloud resources
Maximize resource utilization◦ In order to minimize energy consumption◦ By enabling resources to sleep
Without violating constraints◦ time◦ Usage◦ Hard constraints
Task consolidation problem
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Two algorithms presented, differ only in cost function
ECTC ◦ Explicitly computes energy consumption
MaxUtil◦ Average utilization -
during processing time of the task to schedule◦ Increase consolidation density
The Algorithms
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The Algorithm:
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τ0 – ((τ1 +.τ2)
◦ - utilization rate of the task ◦ - total processing time of the task◦ τ1- time task will run alone◦ τ2- time task will run in parallel
ECTC
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Maximize average consolidation density◦ Over all processing time of task j
MaxUtil0
1,
0
i
i j
Uf
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Example ECTC
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Example MaxUtil
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Random ECTC MaxUtil
1,500 experiments◦ 50 different number of tasks
100-5,000 with intervals of 100◦ 10 mean inter-arrival times (10 -100)
Poisson process
Experimental evaluation
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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
Usage patterns
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Task processing time◦ Exponential distribution
◦ Assume: 300-200 watt active mode consumption
_m◦ Adding migration
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Relative energy savings◦ MaxUtil◦ ECTC
Different resource usage patterns◦ Low◦ High◦ Random
Results
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MaxUtil and ECTC vs Random
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Low resource usage
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High resource usage
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Random resource usage
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Important problem Strict modeling
◦ All demands known exactly (time, usage)◦ Communication is “free”
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”
Ending Remarks
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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
SBP David Breitgand, Amir Epstein (IBM, Haifa)