An Online Auction Framework for Dynamic Resource Provisioning in - - PowerPoint PPT Presentation

An Online Auction Framework for Dynamic Resource Provisioning in Cloud Computing

Weijie Shi*, Linquan Zhang+, Chuan Wu*, Zongpeng Li+, Francis C.M. Lau*

*The University of Hong Kong

+University of Calgary

Fixed Pricing

• Amazon EC2

Why Online Auction?

• Effectively reflect market dynamics

–Need no estimation –Discover the “right price” –Bring more profit than fixed pricing

Related Work

• Amazon Spot Instance

–Not truthful

• When clouds meets Ebay (Infocom 2012)

–Only one round

• COCA (Infocom 2013)

–“A Framework for Truthful Online Auctions in Cloud Computing with Heterogeneous User Demands”

–Only one type of VM

Properties

• Online

–Users’ demands arrive over time. Provider responds instantly, with no prior information

• Combinatorial

–Multiple types of Vms –Dynamic resource provisioning

Our Contributions

• Three main modules

–Translating online optimization into a series of

• ne-round optimization problems Aonline

–Design a truthful auction for one-round allocation problems Around –Design an approximation algorithm for one-round

• ptimization problems
• Social welfare competitive ratio:

–In typical scenarios

Model

Datacenters Cloud provider Users Valuation Quantity

Model

Datacenters Cloud provider Users Allocation Decision

Model

• At time slot t, user n, k-th bundle

–Specify # type m VM at each datacenter q –Valuation for this bundle –Win at most one bundle in one round: = 0 or 1

2 VM1 + 3 VM2 + 5 VM3 $10 OR 4 VM1 + 1 VM2 + 3 VM3 $8

Model

• User Budget

–Connects different rounds

• Social welfare = total valuation

–Maximize

The amount

• f resources

in one bundle Total amount

• f resources

Valuation Allocation Budget

Online Problem

• What difficulties could the budget bring?

–One item each round –Greedy vs Optimal

User A Bn=$20 Round 1 $6 Round 2 $7 Round 3 $10 User B Bn=$20 Round 1 $3 Round 2 $6 Round 3 $2

Online Problem

• What difficulties could the budget bring?

User A Round 1 $6 Remaining Budget: $14 User B Round 1 $3 Remaining Budget: $20

Online Problem

• What difficulties could the budget bring?

User A Round 1 $6 Round 2 $7 Remaining Budget: $7 User B Round 1 $3 Round 2 $6 Remaining Budget: $20

Online Problem

• What difficulties could the budget bring?

User A Round 1 $6 Round 2 $7 Round 3 $10 Remaining Budget: $7 User B Round 1 $3 Round 2 $6 Round 3 $2 Remaining Budget: $18

Online Problem

• What difficulties could the budget bring?

Greedy algorithm: social welfare $15

User A Bn=$20 Round 1 $6 Round 2 $7 Round 3 $10 User B Bn=$20 Round 1 $3 Round 2 $6 Round 3 $2

Online Problem

• What difficulties could the budget bring?

Greedy algorithm: social welfare $15 Optimal solution: social welfare $22

User A Bn=$20 Round 1 $6 Round 2 $7 Round 3 $10 User B Bn=$20 Round 1 $3 Round 2 $6 Round 3 $2

Lesson Learned

• Do not exhaust users’ budgets early

– Lose all the opportunities on this user – But, how to seize the best opportunity? – Classic online optimization dilemma

Budget Coefficient

• Higher priority for user with higher

(remaining) budget

–Original valuation × Budget coefficient

1

The Online Framework Aonline

: adjusted valuation, multiplying the original valuation with

The Online Framework Aonline

Run Around based on the adjusted valuation. Suppose Around gives us a good solution for the one-round problem

The Online Framework Aonline

Update the value of budget coefficient after each round, based on the ratio of consumed budget and the total budget.

Example

• We simulate the online framework on the

previous example

–Only one item, so Around simply choose the user with largest adjusted valuation

User A Bn=$20 Round 1 $6 Round 2 $7 Round 3 $10 User B Bn=$20 Round 1 $3 Round 2 $6 Round 3 $2

Example

User A Bn=$20 xn=0 Round 1 $6 Adjusted: $6*(1-0)=$6 Update: xn=0.24 User B Bn=$20 xn=0 Round 1 $3 Adjusted: $3*(1-0)=$3

Example

User A Bn=$20 xn=0.24 Round 1 $6 Round 2 $7 Adjusted: $7*(1-0.24)=$5.32 User B Bn=$20 xn=0 Round 1 $3 Round 2 $6 Adjusted: $6*(1-0)=$6 Update: xn=0.24

Example

User A Bn=$20 xn=0.24 Round 1 $6 Round 2 $7 Round 3 $10 Adjusted: $10*(1-0.24)=$7.6 Update: xn=0.76 User B Bn=$20 xn=0.24 Round 1 $3 Round 2 $6 Round 3 $2 Adjusted: $2*(1-0.24)=$1.52

Greedy algorithm: social welfare $15 Optimal solution: social welfare $22 Online algorithm: social welfare $22

One-round Auction Design

• Truthfulness

–No user can gain unfair utility by manipulating the results

• Payment is the key in satisfying truthfulness

–Provide monetary incentives to encourage truthful bidding –Can be very difficult to design

• VCG Auction

–A useful mechanism in achieving truthfulness

VCG Auction

• Calculate the exact optimal allocation (cannot

be approximate solution)

–NP-hard in our one-round allocation problem

• Decide the payment rule by opportunity cost

–Guarantee truthfulness

One-round Allocation

: Adjusted valuation : Resources required in a bundle : Total resources : Decision variable, bundle allocated or not

(NP-Hard)

Fractional VCG

• Relax on
• Calculate optimal fractional allocation: LP
• Use the same payment rule
• But, fractional allocation is infeasible

–Cannot provide 0.3 instance of VM –Decompose the fraction solution into a combination of integer solutions –The allocation in expectation remains the same

Randomized Decomposition

User A User B User C Fractional solution: 0.3 0.8 0.5 Decomposed 1 1 0 Pr = 0.3 Integer solution 0 1 1 Pr = 0.5 0 0 0 Pr = 0.2 Scale-down ratio

Randomized Decomposition

• Scale-down the optimal fraction solution by

some ratio

–Divide the solution by a ratio (integrality gap of the LP/IP)

• Solve the dual of the decomposition problem

Randomized Decomposition

• Difficulty: too many constraints

–Cannot be input directly –Simulated by an equivalent oracle

• Search for the solution: ellipsoid method

–An approximation algorithm for the one-round problem is employed as an oracle –Find a cutting plane and narrow down the ellipsoid at each iteration –Finish in polynomial iterations

One-round Allocation

Dual variable of the resource

• constraint. Acts as the unit

price of each type of resources Divide the valuation of a bundle by the cost of a

• bundle. (Profit compared

with cost) Update the unit price of recourses. Higher price with larger amount of consumed resources.

Theoretical Analysis

• Around is a truthful auction with ≈λ-competitive

ratio

–λ is the competitive ratio of the one-round approximation algorithm, as well as the scale- down ratio

• Aonline is a truthful auction with ≈λ-competitive

ratio

–A binary search process can improve the performance in average cases

Simulation

• Simulation setup

–Google cluster trace –6 types of VMs, 3 types of resources –3 datacenters –3 bundles each user –300 ~ 3000 users –300 ~ 3000 rounds

Simulation

• With different numbers of users

Alloc: online allocation algorithm AucBS: online auction with binary search improvement Auc: online auction with

• riginal decomposition

method

Simulation

• With different numbers of rounds

Alloc: online allocation algorithm AucBS: online auction with binary search improvement Auc: online auction with

• riginal decomposition

method

Simulation

• With different numbers of datacenters (using

AucBS)

Conclusion

• Combine three algorithms

–An online framework which monitors each user’s budget –A randomized auction based on the fractional VCG algorithm and the ellipsoid algorithm –An approximation algorithm for the one-round problem, employed as the oracle in the ellipsoid algorithm

• Future work: auctions on bandwidth