a strategy-proof pricing scheme for multiple resource type...
TRANSCRIPT
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A Strategy-proof Pricing Scheme for Multiple Resource Type
Allocations
Marian Mihailescu and Yong Meng Teo Department of Computer Science National University of Singapore
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Overview
• Introduction and Related Work
• Our Approach
• Proposed Mechanism
• Example
• Simulation Results
• Conclusions and Future Work
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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
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Mechanism Design
Problem
• Mechanism design problem
Outcome specification
Set of user valuations for a specific outcome
Solution
• Mechanism
Social choice function f determines the outcome
User payment
4
• Provides a framework to design protocols that give rational agents incentives to interact in particular ways, such that social welfare is “maximized” at equilibrium
€
M = ( f , p1,..., pn )
€
f (t1…tn ) =maxo uii∑
€
pi
€
vi(ti,o)
38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria
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• Computational Efficiency Optimal allocation requires
NP-complete algorithm
Desired Properties
Economic
• Multiple Resource Types A buyer request contains more than one
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
Computational
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• Computational Efficiency Optimal allocation requires
NP-complete algorithm
Myerson-Satterthwite
Impossibility Theorem:
no mechanism achieves strategy-proof, budget balance
and economic efficiency
at the same time
Desired Properties
Economic
• Multiple Resource Types A buyer request contains more than one
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
Computational
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Related Work
Property Proportional
Share Bargaining Auctions
Combinatorial Auctions
Economic
Multiple Resource Types ✔ ✔ ✕ ✔
Strategy-proof ✕ ✕ ✔ ✔
Budget Balance ✔ ✔ ✔ ✕
Pareto Efficiency ✕ ✕ ✕ ✔
Computational
Algorithm Complexity low low low high
Tycoon (2004) [8] REXEC (2000) [4] Nimrod/G (2002) [2]
Popcorn (1998) [14] Spawn (1992) [18]
Mirage (2005) [3] Bellagio (2004) [1]
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Our Approach
8
Pareto Efficiency
Computational Efficiency
Budget Balance
Strategy-proof
Multiple Resource Types
Trade-off
Trade-off
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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
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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 o Select resources with minimum cost (seller winner)
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Payment Functions
• Seller payment function
• Buyer payment function €
ps =0 s does not contribute resources to allocate the request
−cM |s=∞ + cM |s=0 s contributes with resources to allocate the request
€
pb = − pss∈S∑
11
€
cM |s=∞ minimum cost to allocate the request without the resources of seller scM |s=0 minimum cost to allocate the request when the resource cost of seller s is 0VCG payment function: strategy-proof, Pareto-efficient, NOT budget-balanced
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Payment Functions
• Seller payment function
• Buyer payment function €
ps =0 s does not contribute resources to allocate the request
−cM |s=∞ + cM |s=0 s contributes with resources to allocate the request
€
pb = − pss∈S∑
12
€
cM |s=∞ minimum cost to allocate the request without the resources of seller scM |s=0 minimum cost to allocate the request when the resource cost of seller s is 0
38th International Conference on Parallel Processing, 22-25 September 2009, Vienna, Austria
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Achieved Properties
• Multiple Resource Type
• Seller Payment Function: Strategy-proof Economic Efficiency
• Buyer Payment Function: Strategy-proof (FCFS buyer requests) Budget Balance
• Computational Efficiency
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Example
14
S1 CPU $1
S2 DISK $2 S3
DISK $1
S2 CPU $2
B1 CPU+DISK $5
B2 CPU+DISK $6
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Proposed Mechanism
15
Market Maker
Resources
Requests
CPU [S1] = $1 CPU [S2] = $2
DISK [S2] = $2 DISK [S3] = $1
CPU + DISK [B1] = $5 CPU + DISK [B2] = $6
Winner Determination
Buyers Sellers
CPU DISK
B1 ($5) S1 ($1) S2 ($2)
B2 ($6) S2 ($2) S3 ($1)
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Payment Computation
Proposed Mechanism
16
Market Maker
Resources
Requests
CPU [S1] = $1 CPU [S2] = $2
DISK [S2] = $2 DISK [S3] = $1
CPU + DISK [B1] = $5 CPU + DISK [B2] = $6
Winner Determination
Agent Payment
S1 2 + 1 = 3 0 + 1 = 1 -3 + 1 = -2
S3 1 + 2 = 3 1 + 0 = 1 -3 + 1 = -2
B1 - - 2 + 2 = 4
cM |s=! cM |s=0
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Optimal Allocation
17
Market Maker
Resources
Requests
CPU [S1] = $1 CPU [S2] = $2
DISK [S2] = $2 DISK [S3] = $1
CPU + DISK [B1] = $5 CPU + DISK [B2] = $6
Winner Determination
Total Welfare Exchange
w/o S1 6 – 2 – 1 = 3 B2 buys from S2, S3
w/o S2 6 – 1 – 1 = 4 B2 buys from S1, S3
w/o S3 6 – 1 – 2 = 3 B2 buys from S1, S2
w/o B1 6 – 1 – 1 = 4 B2 buys from S1, S3
w/o B2 5 – 1 – 1 = 3 B1 buys from S1, S3
maximum 6 – 1 – 1 = 4 B2 buys from S1, S3
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Payment Computation
Optimal Allocation
18
Market Maker
Resources
Requests
CPU [S1] = $1 CPU [S2] = $2
DISK [S2] = $2 DISK [S3] = $1
CPU + DISK [B1] = $5 CPU + DISK [B2] = $6
Winner Determination
Agent Payment
S1 -1 – (4 – 3) = -2
S3 -1 – (4 – 3) = -2
B2 6 – (4 – 3) = 5
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Implementation
• Discrete event auctions simulator
• jCase – open-source combinatorial auctions simulator
• FreePastry-based implementation on PlanetLab
Impact of Untruthful Users
5.5
6
6.5
7
7.5
8
8.5
1000 2000 3000 4000 5000 6000 7000 8000
Nu
mb
er o
f S
ucc
essf
ul
Req
ues
ts (
log
)
Number of Requests
truthful10% untruthful, 10% price change10% untruthful, 20% price change30% untruthful, 10% price change30% untruthful, 20% price change
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Comparison with Traditional One-sided Auctions
2
3
4
5
6
7
8
9
10
24 48 72 96 120 144 168
Num
ber
of
Succ
essf
ul
Req
ues
ts (
log)
Simulation Time (hours)
traditional auctions, 1 rttraditional auctions, 4 rttraditional auctions, 8 rt
traditional auctions, 16 rt
proposed mechanism, 1 rtproposed mechanism, 4 rtproposed mechanism, 8 rtproposed mechanism, 16 rt
20
Price Diversity
(%)
Successful Buyer Requests (%)
Traditional Auctions
Proposed Increase
(%)
Under-Demand
10 66.4 78.9 26.5
20 66.4 79 27.1
40 66.3 79 26.6
Balanced Market
10 54.7 69.2 18.9
20 54.6 69.3 19.0
40 54.5 69.0 19.2
Over-Demand
10 33.5 39.1 16.7
20 33.8 39.1 15.6
40 33.6 39.1 16.3
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Comparison with Combinatorial Auctions
Pricing Mechanism
Number of Users
Properties Performance
IC BB EE Runtime Succ. Buyer Requests (%)
Alloc. Seller Items (%)
Combinatorial Auctions (VCG)
20 40 80
✔ ✔ ✔
-1,402 -1,544 -1,557
2,470 6,321
14,384
9.6 min 2.5 hrs
67.4 hrs
44.5 52.5 54.2
44.8 57.2 64.0
Combinatorial Auctions
(Threshold)
20 40 80
✕ ✕ ✕
5 9 6
2,491 6,223
14,567
9.8 min 2.5 hrs
49.5 hrs
44.4 49.6 58.8
48.3 59.8 65.1
Proposed
20 40 80 100 200 500
✔ ✔ ✔
✔ ✔ ✔
0 0 0 0 0 0
1,871 5,483
11,561 14,369 28,564 65,948
1 sec 3 sec 5 sec 7 sec
20 sec 1.9 min
36.3 48.5 52.8 54.1 53.5 52.6
32.5 55.3 68.0 71.6 76.5 80.2
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• Scalability Centralized market-maker that processes requests sequentially
Vertical – increase the number of resource types
Horizontal – increase the number of users
• Monopolistic Sellers [Pham, H.N. et.al., An Approach to Vickrey-based Resource Allocation in the Presence of Monopolistic Sellers, In Proc. 7th Australasian Symposium on Grid Computing and e-Research (AusGrid 2009), pp. 77-83, Wellington, New Zealand]
Limitations
22
S1 CPU $1
S3 DISK $1
B1 CPU+DISK $5
S2 CPU $2
S2 DISK $2
B2 CPU+DISK $6
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Conclusions
• Resource pricing and allocation scheme that: Allocates multiple resource types
Provide incentives for rational buyers and sellers
Achieves budget balance
Computational efficiency
• Future Work Distributed pricing scheme – improve horizontal and
vertical scalability
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Thank you !
Y. M. Teo and M. Mihailescu, A Strategy-proof Pricing Scheme for Multiple Resource Type Allocations, in Proceedings of 38th International Conference on Parallel Processing, pp. 172-179, IEEE Computer Society Press, Vienna, Austria, September 22-25, 2009