An Efficient Sensitivity Analysis Method 

for Large Cloud Simulations

July 8, 2011 IEEE Cloud 2011

image generated with http://www.wordle.net/ applied to source code for Koala Cloud Simulator created by Mills and Dabrowski 

K. Mills, J. Filliben and C. Dabrowski

NIST
Develop 

Reduced 

Parameter 

Model Identify Most 

Influential Model 

Parameters & 

Significant 

Behaviors Select Parameter 

Combinations under 

which to Compare 

Algorithms

Apply Techniques 

for Analyzing 

Multidimensional 

Result Datasets

Koala simulator

We Developed a 4-Step Method* to Compare Resource 

Allocation Algorithms in Large Distributed Systems

2

July 8, 2011 IEEE Cloud 2011

THIS TALK

*Previously, we applied this method to compare

congestion-control algorithms proposed for the Internet
Problem: Simulations of large cloud systems typically require hundreds of 

parameters that can take on billions of values and that can also report 

hundreds of response variables.

How can one identify the most significant parameters to simulate and 

responses to analyze?

3

Talk Synopsis

Use experiment design theory to reduce

parameter combinations to 256

Use sensitivity analysis

results to identity six most

significant parameters

(2

32)

82

2

11

2

11-5

Fix parameters not considered germane – reduce by 12 parameters

O(10789)

[ 1080 = atoms in visible universe]

(2

32)

23 O(10221)

(2

32)

11 O(10105)

2048

64

Model 

Reduction

Experiment

Design Theory

2

6-1 32

Group related remaining parameters– reduce by 59 parameters

Select only 2 values for each parameter

Use experiment design theory again to reduce

parameter combinations to 32

Level 

Reduction

Sensitivity

Analysis

July 8, 2011 IEEE Cloud 2011

We base our study on the 

Koala infrastructure

cloud simulator

y1, ..., yz = f(x1|[1,...,l] ..., xp|[1,...,l])

Response State-Space Stimulus State-Space
Outline

• Overview of Koala Infrastructure Cloud Simulator

• Sensitivity Analysis Experiment Design

• Reduction of Response Dimensionality

• Identification of Significant Parameters

• Findings and Ongoing Work
Overview of Koala

Infrastructure Cloud Simulator

5

July 8, 2011 IEEE Cloud 2011
Schematic of Koala IaaS Cloud Computing Model

 INTERNET

DEMAND LAYER

SUPPLY 

LAYER

VM 

BEHAVIOR

 LAYER

RESOURCE 

ALLOCATION

 LAYER

User 

#1

User 

#2

User 

#n

User 

#3

User 

#4

User 

#5

User 

#6

User 

#n-3

User 

#n-2

User 

#n-1

CLOUD CONTROLLER

Cluster 

Controller #1

Cluster 

Controller #c

NODE CONTROLLER #k

NODE RESOURCES NODE CONTROLLER #k-1

NODE RESOURCES NODE CONTROLLER #k-2

NODE RESOURCES

NODE CONTROLLER #3

NODE RESOURCES NODE CONTROLLER #2

NODE RESOURCES NODE CONTROLLER #1

NODE RESOURCES

NODE CONTROLLER #p

NODE RESOURCES NODE CONTROLLER #p-1

NODE RESOURCES NODE CONTROLLER #p-2

NODE RESOURCES

NODE CONTROLLER #3

NODE RESOURCES NODE CONTROLLER #2

NODE RESOURCES NODE CONTROLLER #1

NODE RESOURCES

NODE CONTROLLER #q

NODE RESOURCES NODE CONTROLLER #q-1

NODE RESOURCES NODE CONTROLLER #q-2

NODE RESOURCES

NODE CONTROLLER #3

NODE RESOURCES NODE CONTROLLER #2

NODE RESOURCES NODE CONTROLLER #1

NODE RESOURCES

INTRANETINTRANETINTRANET

VMs 

Shown for

One Node Only

VMs 

Shown for

One Node Only

VMs 

Shown for

One Node Only

VM1

VM1

VM1

VM1

VM1

VM1

VM1

VM1

VM1

VM1

VM1

VM1

VM1

VM1

VM1

Cluster 

Controller #cm

(1)

(4)

(4) (3)

(2)

(4) (4)

(5)

6

July 8, 2011 IEEE Cloud 2011
Virtual Machine (VM) Types* Simulated in Koala

7

VM Type

Virtual 

Cores

Virtual Block 

Devices # Virtual 

Network 

Interfaces

Memory 

(GB)

Instruct.

Arch. #

Speed 

(GHz) #

Size (GB) 

of Each

M1 small 1 1.7 1 160 1 2 32-bit

M1 large 2 2 2 420 2 8 64-bit

M1 xlarge 4 2 4 420 2 16 64-bit

C1 medium 2 2.4 1 340 1 2 32-bit

C1 xlarge 8 2.4 4 420 2 8 64-bit

M2 xlarge 8 3 1 840 2 32 64-bit

M4 xlarge 8 3 2 850 2 64 64-bit

*Inspired by Amazon Elastic Compute Cloud VM Types 

VM Types are offered by the Cloud provider and requested by Cloud users

July 8, 2011 IEEE Cloud 2011
Description of User Types Simulated in Koala

8

We created different classes of demand, such as processing users (PU), distributed 

simulation users (MS), peer-to-peer users (PS), Web service users (WS) and 

data search users (DS)

User

Type

VM 

Type(s)

MaxMin

VMs

MaxMax 

VMs

User

Type

VM 

Type(s)

MaxMin

VMs

MaxMax 

VMs

PU1

M1 small

10 100 PS1 C1 

medium

3 10

PS2 10 50

PU3 100 500 PS3 50 100

PU5 500 1000 WS1

M1 large

M2 xlarge

C1 xlarge

1 3

PU2

M1 large

10 100 WS2

M1 large

M2 xlarge

C1 xlarge

3 9

PU4 100 500 WS3

M1 large

M2 xlarge

C1 xlarge

9 12

PU6 500 1000 DS1

M4 xlarge

10 100

MS1 M1 xlarge 10 100 DS2 100 500

MS3 M1 xlarge 100 500 DS3 500 1000

July 8, 2011 IEEE Cloud 2011
Finite-State Machine of Simulated User Behavior in Koala

9

REFLECTING

REQUESTING

RETRYING

RESTING TERMINATING

USER START TIME ARRIVES SELECT USER TYPE, SELECT GEOLOCATION, SELECT # OF REST PERIODS, SELECT THINK PERIOD

FULLY OR PARTIALLY LAUNCHED SEND TERMINATE INSTANCES REQUEST [RETRIES != 0] NERA

THINK PERIOD ENDS SELECT # OF RETRIES, SELECT MIN & MAX VMs, SEND RUN INSTANCE REQUEST

DECREMENT # OF RETRIES, SELECT THINK PERIOD

THINK PERIOD EXPIRES SEND RUN INSTANCE REQUEST

[RETRIES == 0 && REST PERIODS != 0] NERA

HOLDING PERIOD ENDS SELECT HOLDING PERIOD

TERMINATE INSTANCES RESPONSE SELECT USER TYPE, SELECT GEOLOCATION, SELECT # OF REST PERIODS, SELECT THINK PERIOD

SELECT USER TYPE, GEOLOCATION SELECT # OF REST PERIODS, SELECT THINK PERIOD [RETRIES == 0 && REST PERIODS == 0] NERA SELECT REST PERIOD HOLDING

DECREMENT # OF REST PERIODS SELECT # OF RETRIES, SELECT THINK PERIOD REST PERIOD EXPIRES

While Holding Randomly describe, reboot and terminate VM instances

RETRY, REST & FAILURE PATHS

SUCCESS PATH

July 8, 2011 IEEE Cloud 2011
Description of Selected Platform Types Simulated in Koala

10

We created 22 platform classes, inspired by 

a visit to an Amazon EC2 data center

Platform

Type

Physical 

Cores Memory

(GB)

# Physical Disks by Size # 

Network

Interfaces

Instruct.

Arch. #

Speed

(GHz)

250 

GB

500 

GB

750 

GB

1000 

GB

C2 1 1.7 16 3 0 0 0 1 32-bit

C4 1 2 16 3 0 0 0 1 32-bit

C6 2 2.4 16 0 3 0 0 1 32-bit

C8 2 2.4 32 0 3 0 0 1 64-bit

C10 4 2.4 32 0 4 0 3 1 64-bit

C12 4 2 64 0 4 0 3 2 64-bit

C14 4 3 64 0 4 0 3 2 64-bit

C16 8 3 64 0 0 4 3 2 64-bit

C18 8 3 128 0 0 4 3 4 64-bit

C20 16 3 128 0 0 0 7 4 64-bit

C22 16 3 256 0 0 0 7 4 64-bit

July 8, 2011 IEEE Cloud 2011
Sensitivity Analysis Experiment 

Design

11 July 8, 2011 IEEE Cloud 2011
Input Parameters used for Sensitivity Analysis of Koala

12

We identified 11 parameters we expected to significantly influence Koala behavior

Category ID Parameter Name

Duration x1 Simulation duration in hours

Demand Layer

x2 Number of users

x3 Probability of user’s type

x4 Average (and shape of) user holding time

Supply

Layer

x5 Number of clusters

x6 Number of nodes per cluster

x7 Probability of platform configuration type

Resource 

Control Layer

x8 Algorithm for selecting cluster

x9 Algorithm for selecting node

Internet/

Intranet Layer

x10 Number of sites for cloud components

x11 Probability range of packet losses

July 8, 2011 IEEE Cloud 2011
Response Variables used for Sensitivity Analysis of Koala

13

We selected 40 variables that we expected to represent significant Koala dynamics

Category ID Response Name (Definition)

User-Level

Responses

y1 User Request Rate (Requests by All Users / # User Cycles)

y2 NERA Rate (NERAs / Requests by All Users)

y3 Full Grant Rate (Full Grants / (Full Grants + Partial Grants))

y4 User Arrival Rate (# User Cycles / Simulated Hours)

y5 User Give-up Rate (# Users that Gave Up / # User Cycles)

y6 Grant Latency (Weighted Avg. Delay in Granting VMs to Users that Got VMs)

CloudLevel 

Responses

y7 Reallocation Rate (# Times Alternate Cluster Chosen / Requests Granted)

y8 Full Grant Proportion (Avg. Fraction Clusters Offering Full Grants)

y9 NERA Proportion (Avg. Fraction Clusters Reporting NERA)

y10 vCore Utilization (Avg. Fraction of Virtual Cores Used in Cloud)

y11 Memory Utilization (Avg. Fraction of Memory in Use in Cloud)

y12 Disk Space Utilization (Avg. Fraction of Disk Space in Use in Cloud)

y13 pCore Load (Avg. Virtual Cores Allocated / Physical Cores in Cloud)

y14 Disk Count Load (Avg. Virtual Disks Allocated / Physical Disks in Cloud)

y15 NIC Count Load (Avg. Virtual NICs Allocated / Physical NICs in Cloud)

ClusterLevel 

Responses

y16 vCore Util. Var. (Avg. Variance in vCore Utilization across Clusters)

y17 Memory Util. Var. (Avg. Variance in Memory Utilization across Clusters)

y18 Disk Space Util. Var. (Avg. Variance in Disk Space Utilization across Clusters)

y19 pCore Load Var. (Avg. Variance in pCore Load across Clusters)

y20 Disk Count Var. (Avg. Variance in Disk Count Load across Clusters)

y21 NIC Count Var. (Avg. Variance in NIC Count Load across Clusters)

y22 Node Reallocation Rate (# Times Alternate Node Chosen / VMs Allocated)

y23 Cluster NERA Rate (# NERAs / # Responses Avg. across Clusters)

y24 Cluster Full-Grant Rate (# Full Grants / # Responses Avg. across Clusters)

y25 Allocation Rate (Times Cluster chosen / Cluster offered Avg. across Clusters)

y26 SD-NERA (Stand. Dev. in Avg. NERA Rate across Clusters)

y27 SD-Full-Grant (Stand. Dev. in Avg. Full-Grant Rate across Clusters)

y28 SD-Allocation-Rate (Stand. Dev. in Allocation Rate across Clusters)

VM-Level 

Responses

y29 Current Instances (Avg. # VM Instances Extant in Cloud)

y30 M1small Instances (Fraction of Current Instances that are M1 small VMs)

y31 M1large Instances (Fraction of Current Instances that are M1 large VMs)

y32 M1xlarge Instances (Fraction of Current Instances that are M1 xlarge VMs)

y33 C1medium Instances (Fraction of Current Instances that are C1 medium VMs)

y34 C1xlarge Instances (Fraction of Current Instances that are C1 xlarge VMs)

y35 M2xlarge Instances (Fraction of Current Instances that are M2 xlarge VMs)

y36 M4xlarge Instances (Fraction of Current Instances that are M4 xlarge VMs)

MessageLevel 

Responses

y37 WS Message Rate (Avg. # WS Messages Send Per Simulated Hour)

y38 Intra-Site Messages (# WS Messages Sent with Sites / # WS Messages Sent) 

y39 Inter-Site Loss Rate (Avg. Fraction of Inter-Site WS Messages Undelivered)

y40 Intra-Site Loss Rate (Avg. Fraction of Intra-Site WS Messages Undelivered)

July 8, 2011 IEEE Cloud 2011
2-Level OFF Experiment Designs Reduce # of Parameter Combinations, While 

Improving Global Coverage and Minimizing Error in Effect Estimates in comparison 

with comparable Factor-at-a-Time (FAT) Designs

14

We selected two pairs of level settings (SA1 & SA2) and two system sizes (small & large)

Adopted 2-Level

(211-5) “Resolution IV”

OFF experiment design,

requiring 64 simulations

per experiment

Instantiated 4

designs, and simulated

6 repetitions (different

random number seeds) 

with the 2 smaller designs

Required 

(6 x 2 + 2) x 64 = 896 

simulations

SA1-small and SA1-large SA2-small and SA2-large

Parameter Plus Level Minus Level Plus Level Minus Level

x1 1200 hours 600 hours 1600 hours 200 hours

x2 500 (SA1-small)

5000 (SA1-large)

250 (SA1-small)

2500 (SA1-large)

750 (SA2-small)

7500 (SA2-large)

125 (SA2-small)

1250 (SA2-large)

x3

PU1 = 0.2

PU2 = 0.2

PU3 = 0.1

PU4 = 0.1

WS1 = 0.15

WS2 = 0.07

WS3 = 0.03

PS1 = 0.1

PS2 = 0.01

MS1 = 0.1

MS3 =0.01

DS1 = 0.10

DS2 = 0.01

PU1 = 1/6

PU2 = 1/6,

WS1 = 1/6

MS1 = 1/6

PS1 = 1/6

DS1 = 1/6

PU1 = 0.4

PU2 = 0.4

PU3 = 0.1

PU4 = 0.05

PU5 = 0.025

PU6 = 0.025

WS1 = 0.25

WS2 = 0.15

WS3 = 0.1

PS1 = 0.35

PS2 = 0.04

PS3 = 0.01

DS1 = 0.08

DS2 = 0.015

DS3 = 0.005

x4 8 hours (= 1.2) 4 hours (= 1.2) 12 hours (= 1.2) 2 hours (= 1.2)

x5 20 (SA1-small)

40 (SA1-large)

10 (SA1-small)

20 (SA1-large)

30 (SA2-small)

40 (SA2-large)

5 (SA2-small)

10 (SA2-large)

x6 200 (SA1-small)

1000 (SA1-large)

100 (SA1-small)

500 (SA1-large)

400 (SA2-small)

1500 (SA2-large)

50 (SA2-small)

250 (SA2-large)

x7 C22 = 1.0

C8 = 0.25

C14 = 0.25

C18 = 0.25

C22 = 0.25

C14 = 0.2

C16 = 0.2

C18 = 0.2

C20 = 0.2

C22 = 0.2

C2 = 0.1

C4 = 0.1

C6 = 0.1

C8 = 0.1

C10 = 0.1

C12 = 0.1

C16 = 0.1

C22 = 0.3

x8 Percent 

Allocated

Least-Full First Percent 

Allocated

Least-Full First

x9 Next-Fit First-Fit Next-Fit First-Fit

x10 4 1 8 1

x11 10-3

to 10-8 10-4to 10-9 10-2to 10-7 10-5to 10-10

July 8, 2011 IEEE Cloud 2011
Reduction of Response 

Dimensionality

15 July 8, 2011 IEEE Cloud 2011
Correlation Analysis & Clustering (CAC) Reduces Dimensionality

16

We identified an 8-dimensional response space within the 40 responses

Response 

Dimension

SA1-small

(9 dimensions)

SA1-large

(8 dimensions)

SA2-small

(10 dimensions)

SA2-large

(9 dimensions)

Cloud-wide 

Demand/Supply 

Ratio

y1, y2, y3, y5, 

y6, y8, y9, y10, 

y13, y23, y24, 

y25, y29, y30, 

y32, y34, y36, 

y38

y1, y2, y3, y5, 

y6, y7, y8, y9, 

y10, y13, y23, 

y34, y25, y29, 

y30, y32, y33, 

y34, y36, y38

y1, y2, y3, y5, 

y6, y8, y9, y10, 

y11, y13, y14,

y15, y23, y24, 

y25, y38

y1, y2, y3, y5, 

y6, y8, y9, 

y23, y24, 

y25, y38

Cloud-wide 

Resource 

Usage

y10, y11, y12, 

y13, y14, y15

y10, y11, y12, 

y13, y14, y15 y10, y11, y12, 

y13, y14, y15

y10, y11, 

y12, y13, y14, 

y15

Variance in 

Cluster Load

y16, y17, y18, 

y19,y20, y21, 

y26, y27

y16, y17, y18, 

y19,y20, y21, 

y26, y27

y16, y18, y19,

y20, y21, y26, 

y27

y16, y17, y18, 

y19,y20, y21, 

y17 (Mem. y26, y27

Util)

Mix of VM 

Types

y34, y35 (WS) y31 (MS)

y12, y14, y15, 

y30, y31, y33, 

y34, y35, y36

y14, y15, y30, 

y31, y33, 

y34, y35

y31 (MS) y15, y36 (DS)

Number of VMs y29, y37 y37 y29, y37 y29

User Arrival 

Rate y4 y4 y4 y4, y37

Reallocation 

Rate y7, y22 y7, y22 y7 (cluster)

y7, y22 y22 (node)

Variance in 

Choice of 

Cluster

y28 y28 y28 y28

Compute correlation coefficient 

(r) for all response pairs

Examine frequency distribution 

for all |r| to determine 

threshold for correlation pairs 

to retain; |r| > 0.65, here

Create clusters of mutually 

correlated pairs; each cluster 

represents one dimension

Select one response from each 

cluster to represent the 

dimension; we selected 

response with largest mean 

correlation that was not in 

another cluster*

*Not possible for cloud-wide resource usage in SA2-small, so we selected response with highest mean correlation.

July 8, 2011 IEEE Cloud 2011
Analysis of Correlation Directionality Aids Model Verification

17

We checked positive and inverse correlations for reasonableness

Correlation Half-Matrix from

SA1-small, which had largest

number (126) of correlation pairs

with |r| > 0.65

P = positive correlation N = negative correlation

July 8, 2011 IEEE Cloud 2011
Identification of Significant 

Parameters

18 July 8, 2011 IEEE Cloud 2011
** = p < 0.01

* = p < 0.05

more 

users

fewer

clusters

fewer

nodes/

cluster

larger

platforms

Higher NIC Count Load arises from :

Main Effects Analysis (MEA) Identifies Significant Influence of Input 

Parameters on Response Variables

19

We applied MEA to response variables selected using CAC –

this example is y15 (NIC Count Load) for experiment SA1-small

July 8, 2011 IEEE Cloud 2011
Most significant parameters determined through MEA 

of the responses selected using CAC

20

We computed percent of responses influenced (Y) for each parameter, 

weighting p < 0.05 at 1⁄2 and p < 0.01 at 1:

Y = (|{y | p < 0.01}| + 1⁄2 |{y | p < 0.05}|) / |{y}| x 100

green = major influence; yellow = modest influence; orange = minor influence; gray = no influence

Computed average Y for each parameter, weighting experiment Y by number of repetitions

Most significant parameters: x2 (# users), x5 (# clusters), and x6 (# nodes/cluster)

Moderately influential parameters: x3 (user types) and x7 (platform types)

Somewhat influential parameters: x4 (user hold time) and x8 (cluster-selection algorithm)

No influence : x1 (measurement interval), x9 (node-selection algorithm), 

x10 (geo-distribution of cloud components), and x11 (packet loss prob.) Input Parameter

Experiment Weight x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11

SA1 small 6/14 1 57 22 11 44 29 30 12 0 1 0

SA1 large 1/14 0 69 13 25 44 56 31 25 0 13 0

SA2 small 6/14 2 73 38 10 45 62 10 17 1 0 0

SA2 large 1/14 0 56 50 11 39 56 6 11 0 0 0

Avg. Y Est. 1 65 30 12 44 47 20 15 0 1 0

July 8, 2011 IEEE Cloud 2011
Checking Relative Effects from MEAs aids Model Verification

21

We averaged relative effect (D) over all experiment repetitions to determine how 

parameter increase influences direction and magnitude of effect for 8 dimensions

green = D > 50; yellow = D > 30 & D < 50; orange = D > 10 & D < 30; gray = D < 10 Selected

Response

Input Parameter

Dimension x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11

Cloud-wide 

Demand/

Supply Ratio

y3 1 -38 -21 -5 37 40 25 -2 1 5 -1

Cloud-wide

Resource 

Usage

y15 1 23 53 1 -22 -18 19 -1 1 -1 1

Variance in 

Cluster Load y26 0 -101 28 -5 96 59 66 42 0 50 0

Mix of VM 

Types y31 -1 -9 43 -3 7 9 -1 8 2 -4 0

Number of 

VMs y37 -5 48 11 -23 79 53 -5 8 -1 4 -2

User Arrival 

Rate y4 -17 87 2 -80 29 31 15 -4 -1 -3 -5

Reallocation 

Rate y7 0 0 0 0 0 0 0 0 0 0 0

Variance in 

Cluster 

Choice

y28 6 -12 -42 7 -35 32 18 97 2 4 6

July 8, 2011 IEEE Cloud 2011
Findings and Ongoing Work

22 July 8, 2011 IEEE Cloud 2011
Sensitivity Analysis Findings

• Koala cloud simulator exhibits 8 behavioral dimensions

• 6 input parameters significantly influence Koala behaviors

• Using a 2-level experiment design, comparison of resource allocation 

heuristics will require no more than (26 =) 64 parameter combinations, 

fewer (e.g., 25-1 = 32) with 2nd application of 2-level OFF experiment design

• Analysis of direction in response correlations and of direction and 

magnitude in parameter effects suggests Koala behaviors are sensible

• Koala resource requirements permit simulation of moderately-sized cloud 

configurations O(105) nodes

• Koala implementation and our computing infrastructure appear robust 

enough for maximum simulation durations lasting months

23 July 8, 2011 IEEE Cloud 2011
Ongoing Work

24

Currently conducting an experiment to compare 18 resource

allocation heuristics for on-demand IaaS Clouds

Cluster 

Selection

Node 

Selection

Least Full 

First

First Fit

Next Fit

Percent 

Allocated

Tag & Pack

Random

Random

Least Full 

First

Most Full 

First

3 X 6 = 18

Experiment design is “Resolution VI”

2

5-1 OFF, requiring simulating each of the

18 heuristics under 32 conditions (i.e., 576 

total simulations)

Simulations are completed, data collected

and analyzed. Paper in preparation.

July 8, 2011 IEEE Cloud 2011
Backup Slides

25 July 8, 2011 IEEE Cloud 2011
Koala Information Visualizations by Sandy Ressler

(see http://math.nist.gov/~SRessler/cloudviz.html for animations and more)

26

y10 y11 y12 y13 y14 y15

July 8, 2011 IEEE Cloud 2011
Koala Performance Characteristics for Sensitivity Analysis Experiments

27

Resource Usage: Time & Space

Time (minutes) Memory (Megabytes)

Experiment m s min max m s min max

SA1-small

(avg. over 6 reps.)

17 13 2 69.3 54 12 37 73

SA2-small

(avg. over 6 reps.) 56 148 <1 1019 70 44 27 187

SA1-large 2389 2723 211 12,645 266 91 134 467

SA2-large 4173 7659 29 38,057 235 179 53 764

Simulated Time 

(Hours) Number of Users Number of Nodes

Experiment MINUS 

level

PLUS 

level

MINUS 

level

PLUS 

level

MINUS 

level

PLUS 

level

SA1-small 600 1200 250 500 1000 4000

SA2-small 200 1600 125 750 250 12,000

SA1-large 600 1200 2500 5000 10,000 40,000

SA2-large 200 1600 1250 7500 2500 60,000

Simulated Configurations: Time & Space

July 8, 2011 IEEE Cloud 2011