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Pricing Cloud Bandwidth Reservations under Demand Uncertainty

This paper presents a cloud bandwidth reservation model and pricing strategy for reservations under demand uncertainty. The study includes large-scale distributed optimization and trace-driven simulations.

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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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