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1 Analysis of Topographical Leverage- driven Capacity Trading in Internet Storage Infrastructures Anna Ye Du (SUNY, Buffalo), Xianjun Geng (UW, Seattle), Ram Gopal (UC, Storrs), Ram Ramesh (SUNY, Buffalo), Andrew B. Whinston (UT, Austin)

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2 Summary of the Presentation The concept of Capacity Provision Networks (CPN) Properties of CPN Capacity discounting Concavity of discounting Empirical study on CPN properties CPN operation Capacity allocation Surplus sharing

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3 Problem Context Transit Connection Internet Service Provider (SP) A A’s Local market Storage server to store the contents Storage capacity Content Providers Demand Volatilities

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4 Bilateral Trading Internet SP A Capacity for own use SP B Capacity for own use Shortfall of capacity Excess of capacity Peering Line Shortfall of capacity Shortfall solved Excess of capacity Capacity utilized Content Providers

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5 Bilateral Trading with Intermediation SP A Capacity for own use SP B Capacity for own use Shortfall of capacity Capacity from B Excess of capacity Capacity for A to use SP C Capacity for own use Capacity for A to use Capacity for C to use Capacity from C

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6 Trading in a CPN SP A Capacity for own use SP B Capacity for own use Shortfall of capacity Excess of capacity SP C Capacity for own use SP D Capacity for own use Shortfall of capacity SP E Capacity for own use Excess of capacity

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7 Properties of CPN Capacity discounting Concavity of discounting

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8 Content Providers Average delay t 2 : Average delay t 1 : Quality of Service Internet SP j SP i Storage server to store the contents t0t0 tctc Peering Line trtr

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9 To make average delay time unchanged: Capacity Discounting Internet SP j Content Providers SP i Storage server to store the contents t0t0 tctc Peering Line trtr Define discount factor:

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10 Generally, (t) is monotonically decreasing and concave. SP 1 SP 2 SP 3 t 1,2 t 2,3 t 1,3 Suppose t 1,3 t 1,2 + t 2,3, then given the same t 0, the discounting effect is convex 1,3 < 1,2 · 2,3 If the concavity property holds, intermediated trading (1 2 3) is better than direct trading (1 3). Concavity of Discounting

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11 Topographical Arbitrage Trading without intermediation: 1,3 ·s* Trading with intermediation: 1,2 · 2,3 ·s*, where 1,3 < 1,2 · 2,3 SP 1 SP 3 s* s*: allocation made available by SP 1

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12 Experiment An Internet-based field experiment Four simulated SP nodes Seattle Austin Buffalo Connecticut

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13 Empirical Design Parameters Volatility Temporal Stability Size Stability Concavity Research Design A Longitudinal study of 5 months on a 24 x 7 basis 17,622 observations 12 discount factors Empirical Model

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14 Findings The discount factors More stable than network delays Independent of hour of a day, or days in a work week Concavity property exists

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15 A Market Maker (MM) Mechanism for Cooperative Capacity Trading Allocation Plan Centralized approach global optimization Linear programming (LP) Sharing Plan Global surplus individual participants Cooperative games Shapley values (fair and equitable allocation) [Mas- Colell et al, 1995] MM hub SP Local demand Information ’s among the SPs Allocation plan Sharing plan Subscribe

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16 MM LP Model for Allocation To minimize the total penalty Total capacity provided by i should be equal to its available capacity Supply nodes should never face a shortfall Demand nodes should never buy more than what is required Nonnegativity constraint

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17 Surplus Sharing using Shapley Values Consider any subset K N. Let denote the optimal sharing plan under the MM model on the subset K only. Define subset surplus Shapley value for SP i is i ’ s expected value of marginal contribution to a permutation of N (there are N! permutations.) Shapley value-based surplus sharing induces truth telling Direct computation of Shapley value is of exponential order -O(2 N )

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18 Heuristic Algorithm – Sequential Permutation Sampling Select initial sample size m Generate m random permutations of the N SPs Compute the marginal contributions of each SP in each permutation Compute the sample means and var. of the marginal contribution of each SP Regard each SP ’ s marginal contributions in the N! permutations as a population Increase sample size from m to m+1 The changes of sample means and var. > a small positive number Use the sample means of marginal contributions to estimate Shapley values Yes No

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19 Positive Network Effect The average surplus per SP exhibited a strong upward trend.

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20 Computational Efficiency of the Heuristic Algorithm The sample sizes required, even for large networks, are fairly small

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21 Quality of Heuristic Allocation Vast majority of the estimated Shapley values are within 20% of the true Shapley values.

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22 Stability of the Solutions The estimated Shapley values are relatively stable to the sample that is drawn.

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23 Convergence of the Estimator The cumulative estimated Shapley values converge to the cumulative true Shapley values over time.

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24 Extension of CPN to Distributed Computational Economics (DCE) Topographical leveraging in different service domains Decentralized mechanism design Marketplace architecture Next Steps

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