Effective VM Sizing in Virtualized Data Centers

Ming Chen1, Hui Zhang2, Ya-Yunn Su3, Xiaorui Wang1, Guofei Jiang2, Kenji Yoshihira2

1. University of Tennessee2. NEC Laboratories America3. National Taiwan University

04/19/23 2

Virtualized data centers: server consolidation and green IT

Resource Pool

• Server consolidation - virtualization facilitates consolidation of several physical servers onto a single high end system

— Reduces management costs/overheads — Increases overall utilization

• Green IT - computing more, consume less— Improving infrastructure efficiency —Increasing IT productivity

Today Future

DCiE =IT load power

Total data centerInput power

DCpW =

Data center useful work

Total facility power

DCiE: Data center infrastructure efficiency DCpW: Data center performance per Watt

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In virtualized data centers…

• Server utilization based performance and power management mechanisms– VMware DPM, NEC SSC, IBM Tivoli…

CP

U u

tiliz

atio

n

CPUlow

Overload threshold

CPUhigh

Power-savingmode

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VM sizing – a resource management primitive in virtualized data centers

time

CPU utilization

VM

How much resource allocated to this VM?How much resource allocated to this VM?

Sizing over the maximal load? Low resource utilization!!!Sizing over the maximal load? Low resource utilization!!!

Sizing over the average load? High performance violations!!!Sizing over the average load? High performance violations!!!

Cumulative Distribution Function ofServer Normalized -percentile Loads(5,415 servers of 10 IT systems)

Maximal load is much larger than the average load• 90% of the servers have the maximal load at least 2.2 times larger than their average load; • 50% of the servers have the maximal load at least 7.2 times larger than their average load.

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Effective VM sizing

• Effective size, a new VM sizing concept under probabilistic SLAs – A probabilistic SLA example [Bobroff2007]

– Prob[server x’s CPU utilization at any time > 90%] < 5%

• A VM’s effective size is decided by four factors1. its own workload 2. performance constraint defined as probabilistic SLAs 3. the resource capacity of the server4. the VMs co-hosted in the server

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Stochastic bin packing problem

• Given – a set of items, whose size is described by independent random

variables S = {X1,X2, … ,Xn},– and an overflow probability p,

• Partition – the set S into the smallest number of set (bins) S1 ,… , Sk such

that •

– for all 1 ≤ j ≤ k.

• Effective sizing is the basis of a family of O(1)-approximation algorithms for the stochastic bin packing problem.

VMs workload

machines

SLA

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Effective Sizing – intrinsic demand

• Let a random variable Xi represent a VM i's resource demand, and Cj is the resource capacity of server j.

• The intrinsic demand of VM i on server j is defined as

and Nij is the maximal value of N satisfying the following constraint

where Uk are independent and identically distributed (i.i.d.) random variables with the same distribution as Xi.

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Intrinsic demand – one example

Effective sizing example: i.i.d random variables with normal distribution (server overload probability = 2.5%)

Statistical multiplexing rocks!

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Intrinsic demand – analysis

• Theorem 1. For items with independent Poisson distributions, the First Fit Decreasing (FFD) deterministic bin packing algorithm with effective sizing (intrinsic demand) finds a solution to the stochastic bin packing problem with at most (1.22B*+1) bins of size 1, where B* is the minimum possible number of bins.

• Theorem 2. For items with independent normal distributions, the First Fit Decreasing deterministic bin packing algorithm with effective sizing (intrinsic demand) finds a solution to the stochastic bin packing problem with at most (1.22B*+1) bins of size 1+rc, where B* is the minimum possible number of bins, and rc ≤ 0.496.

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Intrinsic demand may not be enough

• Workload independence assumption might not hold in practice

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Effective Sizing – correlation-aware demand

• Let a random variable Xi represent a VM i's resource demand, and another random variable Xj represent a server j's existing aggregate resource demand from the VMS already allocated to it.

• The correlation-aware demand of VM i on server j is defined as

where σ2i and σ2

j are the variances of the random variables X i and Xj; ρ is the correlation coefficient between Xi and Xj; Zα denotes the α-percentile for the unit normal distribution (α= 1-p).

• For example, if we want the overflow probability p = 0.25%, then α= 99.75%, and Zα = 3.

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Applying effective sizing in production systems

• Practical issues in many dimensions– Product implementation– VM migration cost

• History and correlation aware (HCA) VM placement algorithm in the paper.

– Workload distribution modeling– Workload stationarity– Application-layer SLAs

• Please see discussions in the paper.

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Data center workload traces• Traces on 2525 servers from 10 IT

systems– Each is regarded as a VM in the

simulations.

• Monitoring data: CPU utilization. • 1 week length, 15 minute monitoring

frequency – 672 time points

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Simulation methodology • All physical servers have homogenous hardware specs.

– CPU resource: 3GHZ X 4 (Quadra-core) (the most common CPU model in the traces)

– Memory constraint: the maximal number of VMs allowable if the server is memory bounded (4, 8, 16, …)

• At the beginning of each time window, provoke the server consolidation scheme

– Using the monitoring information in the previous window to make decision

• During each time window, measure the placement scheme by– The number of active servers– Server overflowing probability

• p=5% in the evaluation.

• Five server consolidation schemes– B1: FFD + average load– B2: FFD + maximal load– B3: FFD + VMware DPM VM sizing (μ+2σ, μ - mean, σ – standard deviation) – B4: FFD + 95-percentile load– ES-CA: FFD + effective sizing

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Simulation results

46% less servers than max-load sizing

23% less servers than VMware DPM

10% less servers than 95-percentile

Effective sizing

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Simulation results

34% less servers than max-load sizing

16% less servers than VMware DPM

11% less servers than 95-percentile

Effective sizing

ES-CA

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Conclusions & Future Work

• Effective sizing, a new VM sizing method in server consolidation.– O(1)-approxmiation algorithms for stochastic

bin packing problem.– Migration-cost and workload-correlation aware

VM placement algorithms.

• Future work– Server consolidation in multiple dimensions.

• CPU, memory, disk, network.