Cloud Computing: . . . Financial Aspect of . . . Resulting Questions Why This Is Important . . . Optimizing Cloud Use Case of Complete . . . under Resulting Formula for . . . Optimization: General . . . Interval Uncertainty Case of Interval . . . When Is It Beneficial . . . Vladik Kreinovich and Esthela Gallardo Home Page Title Page Department of Computer Science University of Texas at El Paso ◭◭ ◮◮ El Paso, TX 79968, USA ◭ ◮ vladik@utep.edu, egallardo5@miners.utep.edu Page 1 of 14 Go Back Full Screen Close Quit
Cloud Computing: . . . Financial Aspect of . . . 1. Cloud Computing: Official Definition by Resulting Questions the US National Institute of Standards and Why This Is Important . . . Technology (NIST) Case of Complete . . . Cloud computing is a model for Resulting Formula for . . . Optimization: General . . . • enabling ubiquitous, convenient, on-demand network Case of Interval . . . access When Is It Beneficial . . . • to a shared pool of configurable computing resources, Home Page such as: Title Page – networks, ◭◭ ◮◮ – servers, ◭ ◮ – storage, Page 2 of 14 – applications, and Go Back – services Full Screen • that can be rapidly provisioned and released with min- imal management effort or service provider interaction. Close Quit
Cloud Computing: . . . Financial Aspect of . . . 2. Financial Aspect of Cloud Computing Resulting Questions • One of the important aspects of cloud computing is Why This Is Important . . . that: Case of Complete . . . Resulting Formula for . . . – instead of performing all the computations on his/her Optimization: General . . . own computer, Case of Interval . . . – a user can sometimes rent computing time from a When Is It Beneficial . . . computer-time-rental company. Home Page • Renting is usually more expensive than buying and Title Page maintaining one’s own computer. ◭◭ ◮◮ • So, if the user needs the same amount of computations day after day, cloud computing is not a good option. ◭ ◮ • However, if a peak need for computing occurs rarely: Page 3 of 14 – then it is often cheaper to rent the corresponding Go Back computation time Full Screen – than to buy a lot of computing power and idle it Close most of the time. Quit
Cloud Computing: . . . Financial Aspect of . . . 3. Resulting Questions Resulting Questions • Once the user knows its computational requirements, Why This Is Important . . . the first question is: should we use the cloud at all? Case of Complete . . . Resulting Formula for . . . • If yes: Optimization: General . . . – how much computing power should we buy for in- Case of Interval . . . house computations and When Is It Beneficial . . . – how much computation time should we rent from Home Page the cloud company? Title Page – how much will it cost? ◭◭ ◮◮ • Finally, if a cloud company offers a multi-year deal with ◭ ◮ fixed rates: Page 4 of 14 – should we take it or Go Back – should we buy computation time on a year-by-year Full Screen basis? Close Quit
Cloud Computing: . . . Financial Aspect of . . . 4. Why This Is Important and What We Propose Resulting Questions • One of the main purposes of cloud computing is to save Why This Is Important . . . user’s money. Case of Complete . . . Resulting Formula for . . . • However, most cloud users are computer folks with lit- Optimization: General . . . tle knowledge of economics. Case of Interval . . . • As a result, often, they make wrong financial decisions When Is It Beneficial . . . about the cloud use. Home Page • It is therefore important to come up with proper rec- Title Page ommendations for using cloud computing. ◭◭ ◮◮ • In this talk, we describe the desired financial recom- ◭ ◮ mendations: Page 5 of 14 – first under the idealized assumption that we have Go Back a complete information, and – then, in a more realistic situation of interval uncer- Full Screen tainty. Close Quit
Cloud Computing: . . . Financial Aspect of . . . 5. Case of Complete Information Resulting Questions • Let c 0 be the overall cost of buying and maintaining Why This Is Important . . . one unit (e.g., Teraflops). Case of Complete . . . Resulting Formula for . . . • Then, if we buy computers with computational ability Optimization: General . . . x 0 , we pay c 0 · x 0 for these computers. Case of Interval . . . • Let c 1 be a per-unit cost of computing in the cloud. When Is It Beneficial . . . • Then, if we need to perform x computations in the Home Page cloud, we have to pay the amount c 1 · x . Title Page • Complete knowledge means that for each possible daily ◭◭ ◮◮ computation need x : ◭ ◮ – we know the probability p ( x ) that we need x com- Page 6 of 14 putations; – this probability p ( x ) can be estimated by analyzing Go Back the previous needs; Full Screen – for example, if we needed x computations in 10% Close of the days, this means that p ( x ) = 0 . 1. Quit
Cloud Computing: . . . Financial Aspect of . . . 6. Resulting Formula for the Cost Resulting Questions • We want to select the amount x 0 of computing power Why This Is Important . . . to buy. Case of Complete . . . Resulting Formula for . . . • Then, everything in excess of x 0 will be sent to the Optimization: General . . . cloud. Case of Interval . . . • We want to select this amount so that the expected When Is It Beneficial . . . overall cost of computations is the smallest possible. Home Page • Th in-house cost is c 0 · x 0 . Title Page • For each value x > x 0 , the cost is c 1 · ( x − x 0 ), the ◭◭ ◮◮ probability is p ( x ) ≈ ρ ( x ) · ∆ x . ◭ ◮ • Thus, the overall cost is Page 7 of 14 � ∞ Go Back C ( x 0 ) = c 0 · x 0 + c 1 · ( x − x 0 ) · ρ ( x ) dx. x 0 Full Screen Close Quit
Cloud Computing: . . . Financial Aspect of . . . 7. Optimization: General Case Resulting Questions • We want to minimize the overall cost Why This Is Important . . . � ∞ Case of Complete . . . C ( x 0 ) = c 0 · x 0 + c 1 · ( x − x 0 ) · ρ ( x ) dx. Resulting Formula for . . . x 0 Optimization: General . . . • Differentiating this expression w.r.t. x 0 and equating Case of Interval . . . derivative to 0, we get F ( x 0 ) = 1 − c 0 . When Is It Beneficial . . . c 1 Home Page • So, the optimal amount x 0 of computational power to buy is a quantile corresponding to p = 1 − c 0 Title Page . c 1 ◭◭ ◮◮ • When c 1 = c 0 , there is no sense to buy anything at all: ◭ ◮ we can perform all the computations in the cloud. Page 8 of 14 • As the cloud costs c 1 increases, the threshold x 0 in- creases. Go Back Full Screen • So, when c 1 is very high, it does not make sense to use the cloud at all. Close Quit
Cloud Computing: . . . Financial Aspect of . . . 8. Optimization: Example Resulting Questions • The user’s need is usually described by the power law Why This Is Important . . . � x � − α Case of Complete . . . distribution: F ( x ) = 1 − for all x ≥ t . t Resulting Formula for . . . � 1 /α � c 1 Optimization: General . . . • In this case, x 0 = t · , and the resulting cost is c 0 Case of Interval . . . 1 When Is It Beneficial . . . C ( x 0 ) = c 0 · x 0 · . 1 − 1 Home Page α Title Page • The difference between the overall cost and the in- ◭◭ ◮◮ house cost c 0 · x 0 is the expected cost of using the cloud. ◭ ◮ • The larger α , the faster the probabilities of the need for computing power x decrease with x . Page 9 of 14 • Thus, the smaller should be the expected cost of using Go Back the cloud. Full Screen • When α increases, indeed C ( x 0 ) − c 0 · x 0 → 0. Close Quit
Cloud Computing: . . . Financial Aspect of . . . 9. Case of Interval Uncertainty: Problem Resulting Questions • In practice, we rarely know the exact costs and proba- Why This Is Important . . . bilities. Case of Complete . . . Resulting Formula for . . . • At best, we know the bounds on these quantities. Optimization: General . . . • So, we know: Case of Interval . . . – the interval [ c 0 , c 0 ] of possible values of c 0 ; When Is It Beneficial . . . – the interval [ c 1 , c 1 ] of possible values of c 1 , and Home Page – the interval [ F ( x ) , F ( x )] of possible values of F ( x ) Title Page (a p-box ). ◭◭ ◮◮ • In this case, we only know that the cost C ( x 0 ) is be- ◭ ◮ tween C ( x 0 ) and C ( x 0 ), where: � ∞ Page 10 of 14 C ( x 0 ) = c 0 · x 0 + c 1 · (1 − F ( x )) dx ; Go Back x 0 � ∞ Full Screen C ( x 0 ) = c 0 · x 0 + c 1 · (1 − F ( x )) dx. x 0 Close Quit
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