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Erschienen in:
Warehouse-Scale Computing in the Post-Moore Era Kapitel lesen Erstes Kapitel lesen

2018 | OriginalPaper | Buchkapitel

Risk Aware Stochastic Placement of Cloud Services: The Case of Two Data Centers

verfasst von : Galia Shabtai, Danny Raz, Yuval Shavitt

Erschienen in: Algorithmic Aspects of Cloud Computing

Verlag: Springer International Publishing

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Abstract

Allocating the right amount of resources to each service in any of the data centers in a cloud environment is a very difficult task. This task becomes much harder due to the dynamic nature of the workload and the fact that while long term statistics about the demand may be known, it is impossible to predict the exact demand in each point in time. As a result, service providers either over allocate resources and hurt the service cost efficiency, or run into situation where the allocated local resources are insufficient to support the current demand. In these cases, the service providers deploy overflow mechanisms such as redirecting traffic to a remote data center or temporarily leasing additional resources (at a higher price) from the cloud infrastructure owner. The additional cost is in many cases proportional to the amount of overflow demand.
In this paper we propose a stochastic based placement algorithm to find a solution that minimizes the expected total cost of ownership in case of two data centers. Stochastic combinatorial optimization was studied in several different scenarios. In this paper we extend and generalize two seemingly different lines of work and arrive at a general approximation algorithm for stochastic service placement that works well for a very large family of overflow cost functions. In addition to the theoretical study and the rigorous correctness proof, we also show using simulation based on real data that the approximation algorithm performs very well on realistic service workloads.

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Vorheriges Kapitel Tight Approximability of the Server Allocation Problem for Real-Time Applications
Nächstes Kapitel Towards an Algebraic Cost Model for Graph Operators
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Fußnoten
1
In this case, the goal is to find an integral solution, in which services cannot be split between bins. Later on, we also consider fractional solutions, which allow splitting a service between several bins.
 
2
While we present the results only for SP-MED, we try to keep the discussion in this section as general as possible, so that it is clear what properties are required from a cost function to fall into our framework.
 
3
For example, for SP-MED, \(\epsilon (S)=C_1 \sum _{j=1}^k \sigma _j \psi _0^j(S_j) (\frac{\pi }{2} - \arctan (\varDelta _j))\).
 
4
A similar (simpler and easier to state) result also holds for the other two cost functions we have examined. See Appendix D.
 
5
At first, we also wanted to compare our algorithm with variants of the algorithms considered in [3, 4] for the SBP problem. In both papers, the authors consider the algorithms First Fit and First Fit Decreasing [12] with item size equal to the effective size, which is the mean value of the item plus an extra value that guarantees an overflow probability is at most some given value p. Their algorithm chooses an existing bin when possible, and otherwise opens a new bin. However, when the number of bins is fixed in advance, taking effective size rather than size does not change much. For a new item (regardless of its size or effective size) we keep choosing the bin that is less occupied, but this time we measure occupancy with respect to effective size rather than size. Thus, if elements come in a random order, the net outcome of this is that the two bins are almost balanced and a new item is placed in each bin with almost equal probability.
 
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Breitgand, D., Epstein, A.: Improving consolidation of virtual machines with risk-aware bandwidth oversubscription in compute clouds. In: IEEE INFOCOM 2012, pp. 2861–2865 (2012)
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Nikolova, E.: Approximation algorithms for offline risk-averse combinatorial optimization. Approximation, Randomization, and Combinatorial Optimization, pp. 338–351. Algorithms and Techniques (2010)
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Shabtai, G., Raz, D., Shavitt, Y.: Risk aware stochastic placement of cloud services: the multiple data center case. In: ALGOCLOUD 2017 (2017)
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Ibragimov, I.A., Linnik, Y.V.: Independent and Stationary Sequences of Random Variables. Wolters-Noordhoff, Groningen (1971)MATH
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O’Donnell, R.: Analysis of Boolean Functions. Cambridge University Press, Cambridge (2014)CrossRefMATH
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Michael, R.G., David, S.J.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)MATH
Metadaten
Titel
Risk Aware Stochastic Placement of Cloud Services: The Case of Two Data Centers
verfasst von
Galia Shabtai
Danny Raz
Yuval Shavitt
Copyright-Jahr
2018
Buch
Algorithmic Aspects of Cloud Computing

Print ISBN: 978-3-319-74874-0

Electronic ISBN: 978-3-319-74875-7

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-74875-7_5