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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
Part 1Part 1 A cloud bandwidth reservation A cloud bandwidth reservation modelmodel
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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
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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
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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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
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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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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Time periods (1 period = 10 minutes)Time periods (1 period = 10 minutes)
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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Time periods (1 period = 10 minutes)Time periods (1 period = 10 minutes)
Bandw
idth
(M
bps)
Bandw
idth
(M
bps)
3 Biggest Channels of 452 Channels3 Biggest Channels of 452 Channels
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Time periods (1 period = 10 minutes)Time periods (1 period = 10 minutes)
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
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Video Channel: F190EVideo Channel: F190E
Time periods (one period = 10 minutes)Time periods (one period = 10 minutes)