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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)