A Pricing Model for Cloud
Computing Services
By: Huang Jianhui Ma Dan
Gartner: Cloud Computing Market
Revenue
Usage pricing with Consolidation Burst pricing Reserved : Upfront fee + Usage pricing Spot: Usage pricing On demand: Usage pricing 3 2006 2011 Spot: Usage pricing On demand: Usage pricing Burst pricing 2009 2012 Average Price Reserved : Upfront fee + Usage pricing Usage pricing with Consolidation
Cloud Pricing – Historical Evolvement
Grid and Utility Computing : Free 1990s Overall trend :
1. Average price decreased
Spot Services Price
Amazon EC2 Spot Instance reserve price
An Example of Amazon Spot
Sercive Price
Basic Research Setting
Vendor
Client
Reserved Services
(fixed price and guaranteed services)
Spot Services
(dynamic price but interruptible services)
Related Work
• Sridhar, B., Bhattacharya, S., and Krishnan, V. 2009. Pricing Information Goods: A Strategic Analysis of the Selling and On-demand Pricing
Mechanisms. Working paper.
• Fishburn, P.C. , Odlyzko, A.M., and Siders, R.C. 1997. Fixed fee versus unit pricing for information goods: competition, equilibria, and price wars. First Monday. 2, 7 (July 1997).
• Sundararajan, A. 2004. Nonlinear Pricing of Information Goods. Manage. Sci. 50, 12 (Dec. 2004), 1660-1673.
• Varian, H. R. 1995. Pricing Information Goods. In Proceedings of
Scholarship in the New Information Environment Symposium, Harvard Law School, Boston, MA.
• Etzion, H., Pinker, E., and Seidmann, A. 2006. Analyzing the simultaneous use of auctions and posted prices for online selling. Manuf. Serv. Op. 8, 1 (Winter 2006), 68–91.
Research Questions
Multiple pricing methods has been studied
(Vakrat and Seidmann 1999,
Etzion et al. 2006).
Vendor
Client
Reserved Services
(fixed price and guaranteed services)
Spot Services
(dynamic price but interruptible services)
Interplay
(1) How should a vendor optimize its prices for reserved services, when spot services may or may not be offered? (2) How does the spot services market interact with the
reserved services market?
(3) How will the offering of spot services affect the vendor’s profit, clients’ surplus and social welfare?
• One cloud services vendor offers two types of services: reserved and spot services
• Fixed price for reserved service – Reserved contract (T, N)
• Dynamic price for spot service – Spot price
• Two price levels: low price and high price (pL, pH) • Each price is associated with a probability (θL, θH) • Clients with job arrivals (λ1, λ2, λ3…)
• Job value for clients is uniformly distributed in [vL, vH] • Clients’ sensitivity to service interruption: γ
Model Settings
Buy reserved contract (T, N) or not
1 2 3 4 5 6 …… k-1 k Time
: time points for ps(t) change
λi λi λi
k
Stage Timeline
pS(4) pS (5)> pS(4) Job j pS(5) ≤ pS(4) Completed Interrupted pS(5) Pay 0, U = -γv ← ↓ Pay p4, U = vAnalysis Process
11 Vendor maximizes profit Impact of θL; γ; vL; vH; pL; pH Market segmentation Reserved service only Dual services marketSpot service only θL
(T, N) and θL (T, N)
Market Expansion and Cannibalization
Reserved Service 0 λ0 𝜆 Reserved service λ0 = 𝜆 213
Market Expansion and Cannibalization
Spot Service
0 𝜆
Market Expansion and Cannibalization
Reserved Service
Spot Service
Clients shift from reserved service to spot service: 𝑝𝑆𝜆 2 2𝑣 1 + 𝛾 𝜃𝐿𝜃𝐻 + 𝑝𝑆 (𝑝𝑆 = 𝑝𝐿 ⋅ 𝜃𝐿2 + 𝑝𝐻 ⋅ 𝜃𝐻, 𝑣 = 𝑣𝐿 + 𝑣𝐻 2 ) 0 λ0 𝜆 Reserved service λ0 > 𝜆 2 Spot service λ0 increased by: 2 2𝑣 1+𝛾 𝜃𝑝𝑆𝜆 𝐿𝜃𝐻+𝑝𝑆 (𝑝𝑆 = 𝑝𝐿 ⋅ 𝜃𝐿2 + 𝑝𝐻 ⋅ 𝜃𝐻, 𝑣 = 𝑣𝐿 + 𝑣𝐻 2 )
Profit Changes
Dual market Reserved-only market Spot-only market > > 𝑣𝑣𝐻 𝐿 > 3 + 4 1 + 𝛾 𝑝 𝑆 𝑣 > 1 2 (𝑝 𝑆 = 𝑝𝐿 ⋅ 𝜃𝐿2 + 𝑝𝐻 ⋅ 𝜃𝐻, 𝑣 = 𝑣𝐿 + 𝑣𝐻 2 ) 15Dual market Spot-only
market 1. 2. 3. Reserved-only market >
Impact of Important Factors
• When clients are highly sensitive to service failure, the vendor should increase the likelihood of spot service interruption.
– More clients use reserved – Higher reserved price
• Condition for vendor to achieve higher profit using dual
pricing strategy : Expected payment for spot service is close to clients’ expected job value and difference between high and low spot price levels are small.
Findings
17 Dual services market is social welfare maximizing.
Consumer surplus maybe higher in spot services only
market than in dual services market.
When clients are more sensitive to services interruptions
• In spot services only market, vendor should decrease
probability of services interruption.
• In dual services market, vendor should increase
Conclusion
• Offering spot services in addition to reserved services reduces vendor’s profit from reserved services and market share of reserved services.
• Profit from spot service will compensate profit loss under certain conditions. In such case, the coexistence of both services is optimal for the provider.
• Dual services market achieve highest social welfare.
Consumer surplus however may be lower in the optimal setting.
19
Thank you.
21
Task finish rate (stdev) when interrupted
Task finish rate (standardized stdev) when
interrupted
23 Variable Name Definition
T Fixed price for reserved services contract
N Resource capacity of reserved services contract
v Value of a single job
vL Lower bound of job value
vH Upper bound of job value
θL Probability of low spot price
θH Probability of high spot price, θH = 1 - θL
pL Low spot price
pH High spot price
γ Clients’ sensitivity coefficient to services interruption
λi Job arrival rate of client i
