A Strategy-proof Pricing Scheme for Multiple Resource Type - PowerPoint PPT Presentation

A Strategy-proof Pricing Scheme for Multiple Resource Type Allocations Marian Mihailescu and Yong Meng Teo Department of Computer Science National University of Singapore

Overview • Introduction and Related Work • Our Approach • Proposed Mechanism • Example • Simulation Results • Conclusions and Future Work 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 2

Introduction • Large scale resource sharing  Grid  Peer-to-peer  Cloud Computing • Fundamental problem: resource allocation • Difficulty: rational users  Maximize their own interest in sharing  Affect the performance of the system 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 3

Mechanism Design • Provides a framework to design protocols that give rational agents incentives to interact in particular ways, such that social welfare is “maximized” at equilibrium Problem Solution • Mechanism • Mechanism design problem M = ( f , p 1 ,..., p n )  Social choice function f  Outcome specification determines the outcome  Set of user valuations for a f ( t 1 … t n ) = max o ∑ u i specific outcome v i ( t i , o )  User payment i p i 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 4

Desired Properties Economic Computational • • Computational Efficiency Multiple Resource Types A buyer request contains more than one Optimal allocation requires   NP-complete algorithm resource type • Strategy-proof Users gain higher welfare from participating  and have no incentives to declare false information • Budget Balance Sum of all user payments is 0, and allocations  do not result in deficit or surplus • Economic Efficiency Resources are allocated to the user that values  them the most; total welfare is maximized 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 5

Desired Properties Economic Computational • • Computational Efficiency Multiple Resource Types A buyer request contains more than one Optimal allocation requires   NP-complete algorithm resource type • Strategy-proof Users gain higher welfare from participating  and have no incentives to declare false Myerson-Satterthwite information Impossibility Theorem : • Budget Balance no mechanism achieves Sum of all user payments is 0, and allocations  strategy-proof, budget balance do not result in deficit or surplus and economic efficiency • Economic Efficiency at the same time Resources are allocated to the user that values  them the most; total welfare is maximized 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 6

Related Work Tycoon (2004) [8] Popcorn (1998) [14] Mirage (2005) [3] REXEC (2000) [4] Nimrod/G (2002) [2] Spawn (1992) [18] Bellagio (2004) [1] Proportional Combinatorial Property Bargaining Auctions Share Auctions Economic Multiple Resource Types ✔ ✔ ✕ ✔ Strategy-proof ✕ ✕ ✔ ✔ Budget Balance ✔ ✔ ✔ ✕ Pareto Efficiency ✕ ✕ ✕ ✔ Computational Algorithm Complexity low low low high 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 7

Our Approach Trade-off Strategy-proof Pareto Efficiency Trade-off Budget Balance Multiple Resource Types Computational Efficiency 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 8

Market-based Resource Allocation Problem • Buyers submit requests for multiple resource types • Buyer private information Maximum price the buyer is willing to pay such that, for each  resource type, resources are allocated to satisfy its request • Sellers publish each resource type separately • Seller private information for each resource type Underlying costs for the respective resource type, such as power  consumption, bandwidth costs, etc. • For a particular request, the goal is to allocate resources such that the underlying costs are minimized 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 9

Winner Determination • Centralized market-maker  Manage requests and resources  Determine winners and compute payments • Reverse Auction based Winner Determination  Select one request (buyer winner)  For each resource type in the request Select resources with minimum cost (seller winner) o 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 10

Payment Functions • Seller payment function  0 s does not contribute resources to allocate the request p s =  − c M | s = ∞ + c M | s = 0 s contributes with resources to allocate the request  c M | s = ∞ minimum cost to allocate the request without the resources of seller s VCG payment function: strategy-proof, Pareto-efficient, NOT budget-balanced c M | s =0 minimum cost to allocate the request when the resource cost of seller s is 0 • Buyer payment function ∑ p b = − p s s ∈ S 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 11

Payment Functions • Seller payment function  0 s does not contribute resources to allocate the request p s =  − c M | s = ∞ + c M | s = 0 s contributes with resources to allocate the request  c M | s = ∞ minimum cost to allocate the request without the resources of seller s c M | s =0 minimum cost to allocate the request when the resource cost of seller s is 0 • Buyer payment function ∑ p b = − p s s ∈ S 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 12

Achieved Properties • Multiple Resource Type • Seller Payment Function:  Strategy-proof  Economic Efficiency • Buyer Payment Function:  Strategy-proof (FCFS buyer requests)  Budget Balance • Computational Efficiency 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 13

Example B1 CPU+DISK $5 S1 CPU $1 B2 S2 CPU+DISK $6 CPU $2 S2 S3 DISK $2 DISK $1 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 14

Proposed Mechanism Winner Determination Market Maker Sellers Resources Buyers CPU [S1] = $1 CPU DISK CPU [S2] = $2 B1 ($5) S1 ($1) S2 ($2) DISK [S2] = $2 DISK [S3] = $1 B2 ($6) S2 ($2) S3 ($1) Requests CPU + DISK [B1] = $5 CPU + DISK [B2] = $6 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 15

Proposed Mechanism Winner Determination Market Maker Resources Payment Computation CPU [S1] = $1 CPU [S2] = $2 DISK [S2] = $2 Agent Payment DISK [S3] = $1 c M | s = ∞ c M | s =0 Requests S1 2 + 1 = 3 0 + 1 = 1 -3 + 1 = -2 CPU + DISK [B1] = $5 S3 1 + 2 = 3 1 + 0 = 1 -3 + 1 = -2 CPU + DISK [B2] = $6 B1 - - 2 + 2 = 4 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 16

Optimal Allocation Winner Determination Market Maker Resources Total Welfare Exchange CPU [S1] = $1 w/o S1 6 – 2 – 1 = 3 B2 buys from S2, S3 CPU [S2] = $2 DISK [S2] = $2 w/o S2 6 – 1 – 1 = 4 B2 buys from S1, S3 DISK [S3] = $1 w/o S3 6 – 1 – 2 = 3 B2 buys from S1, S2 Requests CPU + DISK [B1] = $5 w/o B1 6 – 1 – 1 = 4 B2 buys from S1, S3 CPU + DISK [B2] = $6 w/o B2 5 – 1 – 1 = 3 B1 buys from S1, S3 maximum 6 – 1 – 1 = 4 B2 buys from S1, S3 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 17

Optimal Allocation Winner Determination Market Maker Resources Payment Computation CPU [S1] = $1 CPU [S2] = $2 DISK [S2] = $2 Agent Payment DISK [S3] = $1 Requests S1 -1 – (4 – 3) = -2 CPU + DISK [B1] = $5 S3 -1 – (4 – 3) = -2 CPU + DISK [B2] = $6 B2 6 – (4 – 3) = 5 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 18

Implementation Impact of Untruthful Users • Discrete event auctions simulator 8.5 8 Number of Successful Requests (log) • jCase – open-source combinatorial auctions simulator 7.5 7 • FreePastry-based implementation 6.5 on PlanetLab truthful 10% untruthful, 10% price change 6 10% untruthful, 20% price change 30% untruthful, 10% price change 30% untruthful, 20% price change 5.5 1000 2000 3000 4000 5000 6000 7000 8000 Number of Requests 38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria 19

Comparison with Traditional One-sided Auctions Successful Buyer Requests (%) Price Diversity Traditional Increase Proposed 10 (%) Auctions (%) 9 Under-Demand Number of Successful Requests (log) 8 10 66.4 78.9 26.5 7 20 66.4 79 27.1 6 40 66.3 79 26.6 5 Balanced Market 4 10 54.7 69.2 18.9 3 20 54.6 69.3 19.0 2 40 54.5 69.0 19.2 24 48 72 96 120 144 168 Simulation Time (hours) Over-Demand traditional auctions, 1 rt proposed mechanism, 1 rt traditional auctions, 4 rt proposed mechanism, 4 rt 10 33.5 39.1 16.7 traditional auctions, 8 rt proposed mechanism, 8 rt traditional auctions, 16 rt proposed mechanism, 16 rt 20 33.8 39.1 15.6 40 33.6 39.1 16.3 20