pricing cloud bandwidth reservations under demand uncertainty

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Pricing Cloud Bandwidth Pricing Cloud Bandwidth Reservations under Demand Reservations under Demand

UncertaintyUncertainty

Di NiuDi Niu, , Chen Feng, Baochun LiChen Feng, Baochun Li

Department of Electrical and Computer EngineeringDepartment of Electrical and Computer EngineeringUniversity of TorontoUniversity of Toronto

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RoadmapRoadmap

Part 1Part 1 A cloud bandwidth reservation A cloud bandwidth reservation modelmodel

Part 2Part 2 Price such reservations Price such reservations

Large-scale distributed optimizationLarge-scale distributed optimization

Part 3Part 3 Trace-driven simulations Trace-driven simulations


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Cloud TenantsCloud Tenants

WWWWWWWWWWWW

Problem:Problem: No bandwidth guarantee No bandwidth guaranteeNot good for Video-on-Demand, transaction Not good for Video-on-Demand, transaction processing web applications, etc.processing web applications, etc.

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DaysDays00 11 22

DemandDemand

10 Gbps Dedicated 10 Gbps Dedicated NetworkNetwork

Amazon Cluster Compute Amazon Cluster Compute B

an

dw

idth

Ban

dw

idth

Over-provisionOver-provision

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H. Ballani, et al.H. Ballani, et al.

Towards Predictable Datacenter NetworksTowards Predictable Datacenter Networks ACM ACM SIGCOMM ‘11SIGCOMM ‘11C. Guo, et al.C. Guo, et al.SecondNet: a Data Center Network SecondNet: a Data Center Network Virtualization Architecture with Bandwidth Virtualization Architecture with Bandwidth GuaranteesGuaranteesACM ACM CoNEXT ‘10CoNEXT ‘10

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

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ReservatioReservationn

DaysDays00 11 22

Ban

dw

idth

Ban

dw

idth

DemandDemand

reduces cost due to better reduces cost due to better utilizationutilization

Dynamic Bandwidth Dynamic Bandwidth ReservationReservation

DifficultyDifficulty: tenants don’t really know their : tenants don’t really know their demand!demand!

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A New Bandwidth Reservation A New Bandwidth Reservation ServiceServiceA tenant specifies a A tenant specifies a percentage of its percentage of its

bandwidth demandbandwidth demand to be served with to be served with guaranteed performance;guaranteed performance;The remaining demand will be served with The remaining demand will be served with best effortbest effort

Bandwidth Reservation Bandwidth Reservation

TenantTenant Cloud Cloud ProviderProvider

DemandDemandPredictionPrediction

Workload history Workload history of the tenantof the tenantGuaranteedGuaranteed

PortionPortion

(e.g., 95%)(e.g., 95%)QoSQoSLevelLevel

repeated periodicallyrepeated periodically

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Tenant Demand ModelTenant Demand Model

Each tenant Each tenant ii has a has a randomrandom demand demand DDi i

Assume Assume DDii is is GaussianGaussian, with, with

meanmean μμii = = EE[[DDii]]

variance variance σσii22

= = varvar[[DDii]]

covariance matrix covariance matrix Σ = [Σ = [σσijij]]

Service Level Agreement: Outage w.p. Service Level Agreement: Outage w.p.

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RoadmapRoadmap





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Objective 1: Pricing the Objective 1: Pricing the reservationsreservations

A reservation fee on top of the A reservation fee on top of the usage feeusage fee

Objective 2: Resource AllocationObjective 2: Resource Allocation

Price affects demand, which affects Price affects demand, which affects price in turnprice in turn

Social Welfare MaximizationSocial Welfare Maximization

ObjectivesObjectives

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Tenant Tenant ii can specify a guaranteed portion can specify a guaranteed portion wwiiTenant Tenant ii’s ’s expectedexpected utility utility (revenue)(revenue)

Concave, twice differentiable, increasing Concave, twice differentiable, increasing

Utility depends not only on demand, but alsoUtility depends not only on demand, but also

on the guaranteed portion!on the guaranteed portion!

Tenant Utility Tenant Utility (e.g., Netflix)(e.g., Netflix)

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Bandwidth Bandwidth ReservationReservationGiven submitted guaranteed portionsGiven submitted guaranteed portions

the cloud will guarantee the the cloud will guarantee the demandsdemands

Non-multiplexingNon-multiplexing::

MultiplexingMultiplexing::

Service costService coste.g.e.g.

It needs to reserve a total bandwidth It needs to reserve a total bandwidth capacitycapacity

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Cloud Objective: Cloud Objective: Social Welfare Social Welfare MaximizationMaximization

Social Social WelfareWelfare

Impossible: the cloud does not know Impossible: the cloud does not know UUii

Surplus of Surplus of tenanttenant ii

Profit of the Profit of the Cloud Cloud ProviderProvider

PricePrice

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Surplus Surplus (Profit)(Profit)

Pricing functionPricing function

Under Under PPii((⋅⋅)), tenant , tenant ii will choose will choose

Price guaranteed Price guaranteed portion, portion,

not absolute not absolute bandwidth!bandwidth!

Example: Linear pricingExample: Linear pricing

Pricing FunctionPricing Function

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Pricing as a Distributed Pricing as a Distributed SolutionSolution

Challenge: Challenge: Cost not decomposable for Cost not decomposable for multiplexingmultiplexing

SurplusSurplus

wherewhereSocial WelfareSocial Welfare

Determine pricing policy toDetermine pricing policy to

A Simple Case: Non-A Simple Case: Non-MultiplexingMultiplexing

Determine pricing policy toDetermine pricing policy to

wherewhere

MeanMean StdStd

SinceSince , for , for GaussianGaussian

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The General Case:The General Case:Lagrange Dual DecompositionLagrange Dual Decomposition

M. Chiang, S. Low, A. Calderbank, J. Doyle.M. Chiang, S. Low, A. Calderbank, J. Doyle.Layering as optimization decomposition: A Layering as optimization decomposition: A mathematical theory of network architectures.mathematical theory of network architectures. Proc. of IEEE 2007Proc. of IEEE 2007

Lagrange dual Lagrange dual

Dual problemDual problem

Original problemOriginal problem

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Lagrange multiplier Lagrange multiplier kki i as price: as price: PPi i ((wwii)) :=:= k ki i wwi i

Lagrange dual Lagrange dual

Dual problemDual problem

Subgradient Algorithm:Subgradient Algorithm:

a subgradient of a subgradient of

For dual minimization, update price:For dual minimization, update price:

decomposedecompose

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Weakness of the Subgradient Weakness of the Subgradient MethodMethod

Social Welfare Social Welfare (SW)(SW)

SurplusSurplus

Tenant Tenant ii

Cloud ProviderCloud Provider

. . .. . .. . .. . .Tenant Tenant 11 Tenant Tenant NN

Step size is a issue! Convergence is slow.Step size is a issue! Convergence is slow.

2222

PricePrice 1111Guaranteed Guaranteed PortionPortion3333

4444UpdateUpdate to to

increaseincrease

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Our Algorithm: Equation Our Algorithm: Equation UpdatesUpdates

1111 3333

Tenant Tenant ii

Cloud ProviderCloud Provider

. . .. . .. . .. . .

4444

2222 SetSet

SolveSolve

KKT Conditions ofKKT Conditions of

Linear pricingLinear pricing PPi i ((wwii)) == k ki i wwi i suffices!suffices!

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Theorem 1 (Convergence)Theorem 1 (Convergence)Equation updates converge if for Equation updates converge if for all all ii

for allfor all betweenbetween andand

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Convergence: A Single Tenant (1-D)Convergence: A Single Tenant (1-D)Subgradient Subgradient

methodmethodEquation Equation UpdatesUpdates

Not convergingNot converging

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The Case of MultiplexingThe Case of Multiplexing

Covariance matrix:Covariance matrix:symmetric, positive symmetric, positive semi-definitesemi-definite

is a cone centered at is a cone centered at 00

Satisfies Theorem 1, algorithm converges.Satisfies Theorem 1, algorithm converges.

and is smalland is smallis not zerois not zeroifif

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RoadmapRoadmap





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Data Mining: VoD Demand Data Mining: VoD Demand TracesTraces

200+ GB traces (binary) from 200+ GB traces (binary) from UUSee Inc.UUSee Inc.

reports from online users every 10 reports from online users every 10 minutesminutes

Aggregate into Aggregate into video channelsvideo channels

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Bandw

idth

(M

bps)

Bandw

idth

(M

bps)

Predict Expected Demand via Predict Expected Demand via Seasonal ARIMASeasonal ARIMA

Time periods (1 period = 10 minutes)Time periods (1 period = 10 minutes)

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Mbps

Mbps

Predict Demand Variation via GARCHPredict Demand Variation via GARCH

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Prediction ResultsPrediction Results

Each tenant Each tenant ii has a has a randomrandom demand demand DDi i in each “10 minutes”in each “10 minutes”

DDii is is GaussianGaussian, with, with

meanmean μμii = = EE[[DDii]]

variance variance σσii22

= = varvar[[DDii]]

covariance matrix covariance matrix Σ = [Σ = [σσijij]]

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Dimension Reduction via Dimension Reduction via PCAPCA

A channel’s demand = A channel’s demand = weighted sumweighted sum of of factorsfactors

Find factors using Principal Find factors using Principal Component Analysis (PCA)Component Analysis (PCA)

Predict factors firstPredict factors first, then each , then each channelchannel

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Bandw

idth

(M

bps)

Bandw

idth

(M

bps)

3 Biggest Channels of 452 Channels3 Biggest Channels of 452 Channels

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Mbps

Mbps

The First 3 Principal ComponentsThe First 3 Principal Components

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Number of principal componentsNumber of principal components

98%98%8 components8 components

Complexity Reduction:Complexity Reduction:

452 channels452 channels 8 components8 components

Data Variance ExplainedData Variance Explained

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Pricing: Parameter Pricing: Parameter SettingsSettings

Utility of tenant Utility of tenant ii (conservative estimate)(conservative estimate)

Linear revenueLinear revenueReputation loss for Reputation loss for

demand not demand not guaranteedguaranteed

Usage of tenant Usage of tenant ii::

w.h.p.w.h.p.

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CDFCDF

Convergence Iteration of the Convergence Iteration of the LastLast Tenant Tenant

Mean = 6 roundsMean = 6 rounds

Mean = 158 roundsMean = 158 rounds

100100 tenants (channels), tenants (channels), 8181 time periods ( time periods (81 81 xx 10 10 Minutes)Minutes)

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Related WorkRelated WorkPrimal/Dual Decomposition [Chiang Primal/Dual Decomposition [Chiang et al.et al. 07] 07]

Contraction Mapping Contraction Mapping xx := := TT((xx))

D. P. Bertsekas, J. Tsitsiklis, "Parallel and D. P. Bertsekas, J. Tsitsiklis, "Parallel and distributed computation: numerical methods"distributed computation: numerical methods"

Game Theory [Kelly 97]Game Theory [Kelly 97]

Each user submits a price (bid), expects a Each user submits a price (bid), expects a payoff payoff

Equilibrium Equilibrium maymay or or may notmay not be social optimal be social optimal

Time Series PredictionTime Series Prediction

HMM [Silva 12], PCA [Gürsun 11], ARIMA [Niu HMM [Silva 12], PCA [Gürsun 11], ARIMA [Niu 11]11]

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ConclusionsConclusions

A cloud bandwidth reservation model A cloud bandwidth reservation model based on based on guaranteed portionsguaranteed portions

Pricing for social welfare maximizationPricing for social welfare maximization

Future work: Future work:

new decomposition and iterative new decomposition and iterative methods for very large-scale methods for very large-scale distributed optimization distributed optimization

more general convergence conditionsmore general convergence conditions

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Thank youThank you

Di NiuDi NiuDepartment of Electrical and Computer Department of Electrical and Computer

EngineeringEngineeringUniversity of TorontoUniversity of Toronto

http://iqua.ece.toronto.edu/~dniu

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RM

SE (

Mbps)

in L

og

RM

SE (

Mbps)

in L

og

Sca

leSca

le

Channel IndexChannel Index

Root mean squared errors (RMSEs) over 1.25 days

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Optimal Pricing Optimal Pricing when each tenant requires when each tenant requires wwii ≡ ≡ 11

Correlation to the Correlation to the market, in [-1, 1]market, in [-1, 1]

ExpectedExpectedDemandDemand

DemandDemandStandard DeviationStandard Deviation

With With multiplexing,multiplexing,

Without Without multiplexing,multiplexing,

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Histogram of Price Discounts due to MultiplexingHistogram of Price Discounts due to Multiplexing

Discounts of All Tenants in All Test PeriodsDiscounts of All Tenants in All Test Periods

Counts

Counts

mean discount 44%mean discount 44%total cost saving 35%total cost saving 35%

Risk Risk neutralizersneutralizers

MajorityMajority

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Aggre

gate

bandw

idth

(M

bps)

Aggre

gate

bandw

idth

(M

bps)

Video Channel: F190EVideo Channel: F190E

Time periods (one period = 10 minutes)Time periods (one period = 10 minutes)

pricing cloud bandwidth reservations under demand uncertainty

Documents

bandwidth demand

absolute bandwidth

bandwidth guaranteenot

bandwidth guaranteesacm

random demand di

guaranteed portionsthe

demand uncertaintydi

tenant utility