The 31st Annual IEEE International Conference on Computer Communications: Mini-Conference, 2012

1. Improving Consolidation of Virtual Machines withRisk-Aware Bandwidth Oversubscription inCompute Clouds The 31st Annual IEEE International Conference on Computer Communications: Mini-Conference, 2012 David Breitgand, Amir Epstein Virtualization Technologies, System Technologies & Services IBM Research - Haifa, Israel Presented by Bing Zhang, didclab@UB

2. Motivation (1)clouds & consolidation

3. Motivation (2) • over-subscription (size of VM) • green computing, cost-efficiency & quality of service • smooth-effect (used in lemma 1) “The cost-efficiency of a cloud provider depends on its ability to over-subscribe capacity by leveraging the smoothing effect without degrading the quality of service.”

4. Stochastic Bin Packing problem(SBP) • a set of items S = {X1,...,Xn} where each item is a random variable. • overflow probability p (psla) • Optimized target: the minimum number of unit capacity bins needed in order to pack all the items, such that for each bin, the probability that its capacity is exceeded is at most p. • consider the case where the items independently follow normal distribution N(µi,σi).

5. Stochastic Bin Packing problem(SBP) • SBP is NP-hard.

6. Lemma 1 (observation, smooth-effect, deterministic VM size, classical bin packing)

7. Reduce SBP to Classical Bin Packing • each item i has a deterministic item of size • Because Every feasible solution to the classical bin packing is also feasible for the SBP, since for any bin j, • As shown in [7], the optimal number of bins for the classical bin packing problem when using μi+βσias the size of item i may be much larger than the optimal number of bins for SBP., even if we could optimally solve the classical bin packing problem, which is NP-hard, this optimal number of bins may be much larger than the optimum for SBP. • [7] M. Wang, X. Meng, and L. Zhang, “Consolidating virtual machines with dynamic bandwidth demand in data centers,” in INFOCOM, 2011.

8. classic packing algorithms are often used to achieve practical solutions • First Fit (FF) Animation Demo • First Fit Decreasing (FFD) Animation Demo

9. Approximation Algorithm for SBP

10. Fractional Optimum

11. Proof

12. Proof , reduction between FRAC, OPT, and B

13. Proof , reduction between FRAC, OPT, and B

14. Proof , reduction between FRAC, OPT, and B

15. Online Algorithm

16. Online Algorithm

17. Performance • P is the overflow probability • Evaluate performance using the real data center trace previously reported in [7]. • p = 0.01, actual overflow probability is 5%. • Single VM may deviate from the normal distribution • actual average load per bin in our approach is larger than the theoretically expected effective load and because we use less bins than other algorithms, this increases the overflow probability • P = 0.1. 99% of bins had an overflow probability at most 0.12. • Central Limit theorem, larger hosts/racks are used for consolidating VMs, the actual overflow probability approaches the target one.

18. Online Algorithm, approximation ratio proof. • Goto see [11]