the 31st annual ieee international conference on computer communications: mini-conference, 2012

Improving Consolidation of Virtual Machines with

Risk-Aware Bandwidth Oversubscription in

Compute CloudsThe 31st Annual IEEE International Conference on Computer Communications:

Mini-Conference, 2012

David Breitgand, Amir EpsteinVirtualization Technologies, System Technologies & Services

IBM Research - Haifa, Israel

Presented by Bing Zhang, didclab@UB

Motivation (1)clouds & consolidation

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.”

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).

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

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

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 +βσi as 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.

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

Approximation Algorithm for SBP

Fractional Optimum

Proof

Proof , reduction between FRAC, OPT, and B

Proof , reduction between FRAC, OPT, and B

Proof , reduction between FRAC, OPT, and B

Online Algorithm

Online Algorithm

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.

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