A Resource Allocation Mechanism of Data Center for Public Cloud Service

Copyright © 2012, [email protected]

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A Resource Allocation Mechanism of Data Center for Public Cloud Service

指導教授：王國禎學生：連懷恩國立交通大學資訊工程系行動計算與寬頻網路實驗室


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Outline

• Background and scenario review• Basics of linear programming• A simple linear programming approach• Conclusion


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Background and Scenario Review

• Dealing with Number of active servers, number of VMs for each application, VM placement problem, and optimization over a series of time slots.

• Applying an existing load-prediction method to get the forecast of resource demand of each application over a series of time slots.


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Background and Scenario Review• To reduce the problem complexity, we split it into a two-

phase problem.

• In phase 1, we only consider the number of active servers and VMs for each app in each time slot. That is, set the VM migration cost to 0 thus ignoring the VM placement problem.

• We have showed a branch-and-bound approach for the phase 1 problem last time. This time we try a different way using a linear programming approach to solve the phase 1 problem.


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Basics of Linear Programming• A standard form of a minimization problem:

minimize cxsubject to Ax ≤ b, x ≥ 0

where A is a m × n matrix over reals, with m ≤ n, x is an n-dimensional column vector over reals, c is an n-dimensional row vector over reals, and b is an m-dimensional column vector over reals.

• n variables in x form a convex polytope in a n-dimension space.

• Three possible conditions; try to find optimal solution on vertices.


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Basics of Linear Programming

• By the state-of-the-art interior method, we can solve the real number linear programming problem in .

• But an integer programming problem is NP-hard.

• A typical approach would be: Integer programming relax => Linear programming => Real number solution rounding => Integer solution

)( 5.3nO


A Simple Linear Programming Approach – The Power Consumption Model


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A Simple Linear Programming Approach - Denotations

• PVM = Energy cost of a VM in a time slot• Pserver = Basic energy cost of a idle server in a time slot• δVM = Switching cost to switch on/off a VM• δServer = Switching cost to switch on/off a server• Each server can host at most capacity VMs• Total N apps, infinite number of free servers• Forecast of resource demand is up to T time slots


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Basics of Linear Programming

Minimize

Subject to

Server

T

jjjVM

TjNi

jijiji

T

jjServer

TjNi

jijiVM yyxxyPxP

1

11

1,

1,1,1,

1

,

1,1,

jibx jiji ,,0,,

capacityyxj ji

N

iji

,

1,,


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Basics of Linear Programming – Solving the Linear Programming Problem

Add free variables to transform the absolute form intolinear form, and inequality into equality, ex. Transform into , in which

Totally, we need 5T(N+1) - 3N - 3 variables.Note that we have a running time .

VM

TjNi

jijiji xx

1,

1,1,1, VM

TjNi

jijix

1,

1,1,'

0',0''0,0'

''

,,,,1,

,,,,1,

,,1,

,,1,

jijijijiji

jijijijiji

jijiji

jijiji

rrxxxrrxxx

xxxxxx

)( 5.3nO


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A Simple Linear Programming Approach – Rounding to Integer Solution

If we round up to the closest integer Since Optreal ≤ Optinteger ≤ Rounding, and α Optreal ≥ Rounding → α Optinteger ≥ Rounding → α =

Not a constant performance ratio. It depends on the input size.

If we can estimate the frequency of break-event time event, the performance ratio will be lower.

realrealServerVM OptOptTcapacity

NPNTP /))1((


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A Simple Linear Programming Approach – Rounding to Integer Solution

• We can further improve the performance ratio if we use threshold 0.5 to round # of VMs.

• In every VM break-even time event, the increment of switching cost ≤ δVM, the amortized increment of energy cost is 0.


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Conclusion

• Try to improve the performance ratio.

• As a baseline approach comparing with our heuristic approach.

• How to combine the linear programming approach with the phase 2 algorithm?


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Reference

[1] A Taxonomy and Survey of Energy-Efficient Data Centers and Cloud Computing Systems - Advances in Computers, Vol 82, Anton Beloglazov, Rajkumar Buyya, Young Choon Lee, and Albert Zomaya

A Resource Allocation Mechanism of Data Center for Public Cloud Service

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