1 Pricing Cloud Bandwidth Pricing Cloud Bandwidth Reservations under Demand Reservations under Demand Uncertainty Uncertainty Di Niu Di Niu , , Chen Feng, Baochun Li Chen Feng, Baochun Li Department of Electrical and Computer Engineering Department of Electrical and Computer Engineering University of Toronto University of Toronto
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Pricing Cloud Bandwidth Reservations under Demand Uncertainty
Pricing Cloud Bandwidth Reservations under Demand Uncertainty. Di Niu , Chen Feng, Baochun Li Department of Electrical and Computer Engineering University of Toronto. Roadmap. Part 1 A cloud bandwidth reservation model Part 2 Price such reservations Large-scale distributed optimization - PowerPoint PPT Presentation
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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
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.
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
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
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)
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
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
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