1. Effective VM Sizing in Virtualized Data Centers
Ming Chen1, Hui Zhang2, Ya-Yunn Su3,
Xiaorui Wang1, Guofei Jiang2, Kenji Yoshihira2
1. University of Tennessee
2. NEC Laboratories America
3. National Taiwan University

2. Virtualized data centers: server consolidation and green IT
Server consolidation - virtualization facilitates consolidation of several physical servers onto a single high end system
— Reduces management costs/overheads — Increases overall utilization
Resource Pool
Green IT - computing more, consume less
— Improving infrastructure efficiency —Increasing IT productivity
Organizations are constantly faced with the challenge of accommodating increasing amounts of data, increasing numbers of devices and users, and increasingly powerful servers to support critical applications—all while controlling data center costs for power, cooling, and other operations.
improving infrastructure efficiency - strategies that can have a significant effect on overall data center performance per watt, such as using energy-efficient equipment, optimizing data center temperature (77 degree), and utilizing best-practices data center design.
increasing IT productivity - increasing the actual amount of computing work completed in the data center relative to the amount of power used.
Although these two options are key tactics in controlling energy use, they generally represent only an incremental savings. Substantially reducing energy use typically requires adopting a more strategic approach to managing the IT infrastructure than these approaches can provide.
Today
Future
Data center useful work
IT load power
DCiE =
DCpW =
Total data center
Input power
Total facility power
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DCiE: Data center infrastructure efficiency
DCpW: Data center performance per Watt 2 2

3. In virtualized data centers…
Server utilization based performance and power management mechanisms
VMware DPM, NEC SSC, IBM Tivoli…
Overload threshold
CPUhigh
CPU utilization
CPUlow
Power-saving
mode
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4. VM sizing – a resource management primitive in virtualized data centers
How much resource allocated to this VM?
CPU utilization
Sizing over the maximal load? Low resource utilization!!!
Sizing over the average load? High performance violations!!!
time
Cumulative Distribution Function of
Server 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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5. 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 factors
its own workload
performance constraint defined as probabilistic SLAs
the resource capacity of the server
the VMs co-hosted in the server
Check the NOMS06 paper for a reference
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6. 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.
VMs
workload
machines
SLA
Effective sizing is the basis of a family of O(1)-approximation algorithms for the stochastic bin packing problem.
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7. 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
Intuitively, Nij is the maximal number of VMs that can
be packed into server j without breaking the probabilistic
SLA when all the VMs have the same workload pattern
as VM i.
where Uk are independent and identically distributed (i.i.d.) random variables with the same distribution as Xi.
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8. Intrinsic demand – one example
Statistical multiplexing rocks!
Overflowing prob
Effective sizing example: i.i.d random variables with normal distribution (server overload probability = 2.5%)
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9. 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 ≤
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10. Intrinsic demand may not be enough
Workload independence assumption might not hold in practice
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11. 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 σ2j are the variances of the random variables Xi 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.
Intuitively, Nij is the maximal number of VMs that can
be packed into server j without breaking the probabilistic
SLA when all the VMs have the same workload pattern
as VM i.
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12. 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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13. 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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14. 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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15. Simulation results Effective sizing 11/27/2018
46% less servers than max-load sizing
23% less servers than VMware DPM
10% less servers than 95-percentile
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16. Simulation results Effective sizing 11/27/2018
34% less servers than max-load sizing
16% less servers than VMware DPM
11% less servers than 95-percentile
ES-CA
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17. 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.
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