Pricing Cloud Bandwidth Reservations under Demand Uncertainty Di

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

Roadmap Part 11 A A cloud bandwidth reservation model Part 2 Price such reservations Large-scale distributed optimization Part 3 Trace-driven simulations 2

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

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

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. Second. Net: a Data Center Network Virtualization Architecture with Bandwidth Guarantees ACM Co. NEXT ‘ 10 5

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

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 Workload history (e. g. , 95%) Qo. S of the tenant Level Guaranteed Portion Cloud Demand Tenant Provider Prediction repeated periodically Bandwidth Reservation 7

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

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

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 10

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

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

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

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

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

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

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 Original problem Lagrange dual Dual problem 17

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

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

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

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

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

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

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

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

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

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

Prediction Results Each tenant i has a random demand Di in each “ 10 minutes” Di is Gaussian, with mean μi = E[Di] variance 2 σi = var[Di] covariance matrix Σ = [σij] 28

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 29

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

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

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

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

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

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] 35

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 36

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

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RMSE (Mbps) in Log Scale Root mean squared errors (RMSEs) over 1. 25 days Channel Index 39

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

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

Aggregate bandwidth (Mbps) Video Channel: F 190 E Time periods (one period = 10 minutes) 42