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

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

4 Days012 Demand 10 Gbps Dedicated Network Amazon Cluster Compute Bandwidth Over-provision

5 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 Good News: Bandwidth reservations are becoming feasible between a VM and the Internet

6 Reservation Days012 Bandwidth Demand reduces cost due to better utilization Dynamic Bandwidth Reservation Difficulty: tenants don’t really know their demand!

7 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 Bandwidth Reservation Tenant CloudProvider DemandPrediction Workload history of the tenant GuaranteedPortion (e.g., 95%) QoSLevel repeated periodically

8 Tenant Demand Model Each tenant i has a random demand D i Assume D i is Gaussian, with mean μ i = E [ D i ] variance σ i 2 = var [ D i ] covariance matrix Σ = [σ ij ] Service Level Agreement: Outage w.p.

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

10 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 Objectives

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

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

13 Cloud Objective: Social Welfare Maximization Social Welfare Impossible: the cloud does not know U i Surplus of tenant i Profit of the Cloud Provider Price

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

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

A Simple Case: Non- Multiplexing Determine pricing policy to where Mean StdSince, for Gaussian

17 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 Lagrange dual Dual problem Original problem

18 Lagrange multiplier k i as price: P i (w i ) := k i w i Lagrange dual Dual problem Subgradient Algorithm: a subgradient of For dual minimization, update price: decompose

19 Weakness of the Subgradient Method Social Welfare (SW) Surplus Tenant i Cloud Provider... Tenant 1 Tenant N Step size is a issue! Convergence is slow. 22 Price 11 Guaranteed Portion Update to increase

20 Our Algorithm: Equation Updates Tenant i Cloud Provider Set Solve KKT Conditions of Linear pricing P i (w i ) = k i w i suffices!

21 Theorem 1 (Convergence) Equation updates converge if for all i for all betweenand

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

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

24 Roadmap Part 1 A 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 Bandwidth (Mbps) Predict Expected Demand via Seasonal ARIMA Time periods (1 period = 10 minutes)

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

28 Prediction Results Each tenant i has a random demand D i in each “10 minutes” D i is Gaussian, with mean μ i = E [ D i ] variance σ i 2 = var [ D i ] covariance matrix Σ = [σ ij ]

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

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

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

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

34 CDF Convergence Iteration of the Last Tenant Mean = 6 rounds Mean = 158 rounds 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

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

40 Optimal Pricing when each tenant requires w i ≡ 1 Correlation to the market, in [-1, 1] ExpectedDemand Demand Standard Deviation With multiplexing, Without multiplexing,

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

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