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 one-round optimization problems A online –Design a truthful auction for one-round allocation problems A round –Design an approximation algorithm for one-round optimization 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 VM VM VM 3 $10 OR 4 VM VM VM 3 $8

Model User Budget –Connects different rounds Social welfare = total valuation –Maximize The amount of resources in one bundle Total amount of resources Valuation Allocation Budget

Online Problem What difficulties could the budget bring? –One item each round –Greedy vs Optimal User A B n =$20 Round 1 $6 Round 2 $7 Round 3 $10 User B B n =$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 B n =$20 Round 1 $6 Round 2 $7 Round 3 $10 User B B n =$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 B n =$20 Round 1 $6 Round 2 $7 Round 3 $10 User B B n =$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 A online : adjusted valuation, multiplying the original valuation with

The Online Framework A online Run A round based on the adjusted valuation. Suppose A round gives us a good solution for the one-round problem

The Online Framework A online 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 A round simply choose the user with largest adjusted valuation User A B n =$20 Round 1 $6 Round 2 $7 Round 3 $10 User B B n =$20 Round 1 $3 Round 2 $6 Round 3 $2

Example User A B n =$20 x n =0 Round 1 $6 Adjusted: $6*(1-0)=$6 Update: x n =0.24 User B B n =$20 x n =0 Round 1 $3 Adjusted: $3*(1-0)=$3

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

Example User A B n =$20 x n =0.24 Round 1 $6 Round 2 $7 Round 3 $10 Adjusted: $10*(1-0.24)=$7.6 Update: x n =0.76 User B B n =$20 x n =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: Decomposed Pr = 0.3 Integer solution Pr = 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 A round 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 A online 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 original decomposition method

Simulation With different numbers of rounds Alloc: online allocation algorithm AucBS: online auction with binary search improvement Auc: online auction with original 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