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Pricing Cloud Bandwidth Reservations under Demand Uncertainty

This paper presents a comprehensive model for cloud bandwidth reservations that addresses the challenges of demand uncertainty. It details a framework for pricing these reservations and includes large-scale distributed optimization and trace-driven simulations. With a focus on guaranteed performance for varying tenant demands, the study explores the interplay between resource allocation and social welfare maximization. Future sections will delve into practical applications and simulations to validate the proposed reservation strategies.

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Pricing Cloud Bandwidth Reservations under Demand Uncertainty

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  1. Pricing Cloud Bandwidth Reservations under Demand Uncertainty Di Niu, Chen Feng, Baochun Li Department of Electrical and Computer Engineering University of Toronto

  2. Roadmap • Part 1A cloud bandwidth reservation model • Part 2 Price such reservations • Large-scale distributed optimization • Part 3 Trace-driven simulations • Part 1A cloud bandwidth reservation model

  3. WWW Cloud Tenants Problem: No bandwidth guarantee Not good for Video-on-Demand, transaction processing web applications, etc.

  4. Amazon Cluster Compute 10 Gbps Dedicated Network Bandwidth Demand 0 1 2 Days Over-provision

  5. Good News: Bandwidth reservations are becoming feasible between a VM and the Internet H. Ballani, et al. Towards Predictable Datacenter Networks ACM SIGCOMM ‘11 C. Guo, et al. SecondNet: a Data Center Network Virtualization Architecture with Bandwidth Guarantees ACM CoNEXT ‘10

  6. Dynamic Bandwidth Reservation reduces cost due to better utilization Reservation Bandwidth Demand 0 1 2 Days Difficulty: tenants don’t really know their demand!

  7. QoS Level (e.g., 95%) Workload history of the tenant Cloud Provider Tenant Guaranteed Portion Demand Prediction A New Bandwidth Reservation Service A tenant specifies a percentage of its bandwidth demand to be served with guaranteed performance; The remaining demand will be served with best effort repeated periodically Bandwidth Reservation

  8. Tenant Demand Model • Each tenant i has a random demand Di • Assume Di is Gaussian, with • meanμi = E[Di] • variance σi2 = var[Di] • covariance matrix Σ = [σij] • Service Level Agreement: Outage w.p.

  9. Roadmap • Part 1A cloud bandwidth reservation model • Part 2 Price such reservations • Large-scale distributed optimization • Part 3 Trace-driven simulations

  10. Objectives • Objective 1: Pricing the reservations • A reservation fee on top of the usage fee • Objective 2: Resource Allocation • Price affects demand, which affects price in turn • Social Welfare Maximization

  11. Tenant i’s expected utility (revenue) Tenant Utility (e.g., Netflix) Tenant i can specify a guaranteed portion wi Concave, twice differentiable, increasing Utility depends not only on demand, but also on the guaranteed portion!

  12. Non-multiplexing: Multiplexing: e.g. Service cost Bandwidth Reservation • Given submitted guaranteed portions the cloud will guarantee the demands • It needs to reserve a total bandwidth capacity

  13. Surplus of tenanti Profit of the Cloud Provider Price Cloud Objective: Social Welfare Maximization Social Welfare Impossible: the cloud does not know Ui

  14. Pricing function Under Pi(⋅), tenant i will choose Example: Linear pricing Surplus (Profit) Pricing Function Price guaranteed portion, not absolute bandwidth!

  15. where Determine pricing policy to Social Welfare Surplus Pricing as a Distributed Solution Challenge: Cost not decomposable for multiplexing

  16. Since , for Gaussian Mean Std A Simple Case: Non-Multiplexing • Determine pricing policy to where

  17. Lagrange dual Dual problem Original problem The General Case:Lagrange Dual Decomposition M. Chiang, S. Low, A. Calderbank, J. Doyle.Layering as optimization decomposition: A mathematical theory of network architectures.Proc. of IEEE 2007

  18. Subgradient Algorithm: For dual minimization, update price: Lagrange dual a subgradient of Dual problem decompose Lagrange multiplier ki as price: Pi (wi):= ki wi

  19. 2 4 Social Welfare (SW) Cloud Provider 1 3 Guaranteed Portion Price Surplus Update to increase . . . . . . Tenant i Tenant 1 Tenant N Weakness of the Subgradient Method Step size is a issue! Convergence is slow.

  20. Solve KKT Conditions of Cloud Provider 2 Set 1 3 . . . . . . Tenant i Our Algorithm: Equation Updates 4 Linear pricingPi (wi)= ki wi suffices!

  21. Theorem 1 (Convergence)Equation updates converge if for all i for all between and

  22. Convergence: A Single Tenant (1-D) Subgradient method Equation Updates Not converging

  23. Covariance matrix: is a cone centered at 0 if is not zero and is small symmetric, positive semi-definite The Case of Multiplexing Satisfies Theorem 1, algorithm converges.

  24. Roadmap • Part 1A cloud bandwidth reservation model • Part 2 Price such reservations • Large-scale distributed optimization • Part 3 Trace-driven simulations

  25. Data Mining: VoD Demand Traces • 200+ GB traces (binary) from UUSee Inc. • reports from online users every 10 minutes • Aggregate into video channels

  26. Predict Expected Demand via Seasonal ARIMA Bandwidth (Mbps) Time periods (1 period = 10 minutes)

  27. Predict Demand Variation via GARCH Mbps Time periods (1 period = 10 minutes)

  28. Prediction Results • Each tenant i has a random demand Di in each “10 minutes” • Di is Gaussian, with • meanμi = E[Di] • variance σi2 = var[Di] • covariance matrix Σ = [σij]

  29. Dimension Reduction via PCA • A channel’s demand = weighted sum of factors • Find factors using Principal Component Analysis (PCA) • Predict factors first, then each channel

  30. 3 Biggest Channels of 452 Channels Bandwidth (Mbps) Time periods (1 period = 10 minutes)

  31. The First 3 Principal Components Mbps Time periods (1 period = 10 minutes)

  32. Complexity Reduction: 98% 8 components 452 channels 8 components Data Variance Explained Number of principal components

  33. Utility of tenant i(conservative estimate) Usage of tenant i: w.h.p. Reputation loss for demand not guaranteed Linear revenue Pricing: Parameter Settings

  34. CDF Mean = 6 rounds Mean = 158 rounds Convergence Iteration of the Last Tenant 100 tenants (channels), 81 time periods (81 x 10 Minutes)

  35. Related Work • Primal/Dual Decomposition [Chiang et al. 07] • Contraction Mapping x := T(x) • D. P. Bertsekas, J. Tsitsiklis, "Parallel and distributed computation: numerical methods" • Game Theory [Kelly 97] • Each user submits a price (bid), expects a payoff • Equilibrium may or may not be social optimal • Time Series Prediction • HMM [Silva 12], PCA [Gürsun 11], ARIMA [Niu 11]

  36. Conclusions • A cloud bandwidth reservation model based on guaranteed portions • Pricing for social welfare maximization • Future work: • new decomposition and iterative methods for very large-scale distributed optimization • more general convergence conditions

  37. Thank you Di Niu Department of Electrical and Computer Engineering University of Toronto http://iqua.ece.toronto.edu/~dniu

  38. Root mean squared errors (RMSEs) over 1.25 days RMSE (Mbps) in Log Scale Channel Index

  39. Without multiplexing, Correlation to the market, in [-1, 1] Expected Demand Demand Standard Deviation With multiplexing, Optimal Pricing when each tenant requires wi ≡ 1

  40. Risk neutralizers Majority Histogram of Price Discounts due to Multiplexing mean discount 44% total cost saving 35% Counts Discounts of All Tenants in All Test Periods

  41. Video Channel: F190E Aggregate bandwidth (Mbps) Time periods (one period = 10 minutes)

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