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Prof. Daniel A. MenascéDepartment of Computer ScienceGeorge Mason Universityg ywww.cs.gmu.edu/faculty/menasce.html

1© 2004 D. A. Menascé. All Rights Reserved.

f f fMost of the figures in this set of slides come from the book “Performance by Design:

l b l bcomputer capacity planning by example,” by Menascé, Almeida, and Dowdy, Prentice Hall,

l f b dd2004. It is strictly forbidden to copy, post on a Web site, or distribute electronically, in part

l f h l d h f lor entirely, any of the slides in this file.


A large compan ses an internal Web ser er to A large company uses an internal Web server to allow its programmers, testers, and documentation personnel to download two types of files:

PDF files containing documents and manualsZIP files containing software files.

The server has one CPU and 4 identical disks.4PDF files are stored on disks 1 and 2 (with evenly distributed access)ZIP files are stored in disks 3 and 4 (with evenly ZIP files are stored in disks 3 and 4 (with evenly distributed access)


© 2004 D. A. Menascé. All Rights Reserved. 4

fHow many PDF and ZIP file downloads can be sustained concurrently with given response times?What is the impact of using Secure Sockets

f d l dLayer (SSL) for secure downloads?


Elapsed Time File Type Size (KB) (sec)PDF 303 1.43ZIP 1233 5 81ZIP 1233 5.81ZIP 1077 5.08PDF 315 1.48ZIP 1240 5.84PDF 413 1.95ZIP 1139 5.37ZIP 1139 5.37ZIP 1198 5.64PDF 323 1.52ZIP 1188 5 60

. . . . . . . . . . . . . ZIP 1188 5.60


Cpdf = 43 1 KB / 377 6 KB = 0 114 < 0 25 single class


Cpdf = 43.1 KB / 377.6 KB = 0.114 < 0.25 single class

l d d dKnown population standard deviation.Unknown population standard deviation:

Large samples (≥30): sample standard deviation is a good estimate for population t d d d i ti OK t l standard deviation. OK to use normal distribution: use z distribution

Small samples and original variable is normally Small samples and original variable is normally distributed: use t distribution with n‐1 degrees of freedom.of freedom.


αμ −=≤≤ 1]Pr[ 21 cc

(c1,c2): confidence interval( 1 2)α: significance level (e.g., 0.05)(1 – α): confidence coefficient (e.g., 0.95)) g100(1 – α): confidence level (e.g., 95%)


μ

Sample Interval include μ?1 YES2 YES2 YES3 NO…100 YES100 YES

100 (1 α) of the 100 samples include the population mean μ

10

100 (1 – α) of the 100 samples include the population mean μ.

© 2004 D. A. Menascé. All Rights Reserved.

If th b ti i l i d d t d If the observations in a sample are independent and come from the same population that has mean μand standard deviation σ then the sample mean for plarge samples has a normal distribution with mean μ and standard deviation σ/ .

)/(n

The standard deviation of the sample mean is called

)/,(~ nNx σμp

the standard error.


)/,( nN σμ

μc2=Q(1-α/2)c1=Q(α/2)c2=Q(1-α/2)

Q( /2) )/( nN σμ

μ

1-α

c1 Q(α/2)c1=Q(α/2) )/,( nN σμ

c1 c2

α/2α/20

(1 – α/2)-quantile of standard

x2=z 1-α/2

N(0,1)

(1 α/2) quantile of standardnormal distribution

1-αα/2α/2

2 1 α/2

x1=z α/2 = - z 1-α/2

x1 x20

2/12 ασμ −+= zn

c

12

2/12/1 αασμσμ −−=+= zn

zn

c

• 100 (1-α)% confidence interval for the population mean:

),( 2/12/1n

szx

n

szx αα −− +−

nn

: sample meanx ps: sample standard deviationn: sample size

: (1 α/2) quantile of a unit normal variate (N(0 1))z : (1 – α/2)-quantile of a unit normal variate (N(0,1)).2/1 α−z


• 100 (1-α)% confidence interval for the population mean:

),( ]1;2/1[]1;2/1[n

stx

n

stx nn −−−− +− αα

nn

: sample meanx ps: sample standard deviationn: sample size

: critical value of the t distribution with n 1 degrees of]12/1[t : critical value of the t distribution with n-1 degrees of freedom for an area of α/2 for the upper tail.

]1;2/1[ −− nt α


= (1-α/2)-quantile of a unit normal variate (N(0, 1)):= NORMINV (1-α/2,0,1) = NORMSINV(1- α/2)

H lf i t l CONFIDENCE ( )

2/1 α−z

Half-interval = CONFIDENCE (α, σ, n)

]12/1[t (1 /2) til f t i t ith 1 d f]1;2/1[ −− nt α = (1-α/2)-quantile of t-variate with n-1 degrees of freedom = TINV(α, n-1)


Czip = 85 7 KB / 1155 6 KB = 0 074 < 0 25 single class


Czip = 85.7 KB / 1155.6 KB = 0.074 < 0.25 single class

From our goal of determining the max no. of PDF g gand ZIP concurrent downloads while still meeting a given SLA, a closed multiclass QN model is used.To complete parameterization of the model, To complete parameterization of the model, concurrency level for each class (file type) and service demands at each device are needed.Computing concurrency levels:Computing concurrency levels:

From Section 5.7.4, the average concurrency level, , of class r jobs can be estimated as:

n∑

rN

h i h l d i f j b i f l d

,1

n

i rir

eN

τ== ∑

where ei, r is the elapsed time of job i of class r, andτ is the measurement interval

© 2004 D. A. Menascé. All Rights Reserved.17

hThen,411

,1 731.5

3 7 4i pdf

i

eN == = = ≈

∑

589

,

3.7 4interval duration 200

3207 7

pdf

i zip

N

e

= = = ≈

∑1 3207.7

16.1 16interval duration 200

izipN == = = ≈

Will use a ratio of 1:4 for PDF to ZIP file downloads


dComputing Service Demands

Service demands depend on file sizes

Experiments conducted on a similar Web server machine with 1 CPU and 1 disk

A set of n dummy files with files sizes of 10 KB 100 A set of n dummy files with files sizes of 10 KB, 100 KB, 200 KB, 500 KB, 800 KB, and 1000 KB are used.

For each file size the n files are downloaded while For each file size, the n files are downloaded while measuring the CPU and disk utilization of the test server.

Service demand = utilization/(n / interval)




msec1.77)2919.06.3774078.0(5.0

msec4.390604.06.3771046.0

,2,1

,

=+××==

=−×=

pdfdiskpdfdisk

pdfCPU

DD

D

msec8.1200604.06.11551046.0

0

,

,4,3

=−×=

==

zipCPU

pdfdiskpdfdisk

D

DD

0

msec8.235)2919.06.11554078.0(5.0

21

,4,3

==

=+××==

zipdiskzipdisk

zipdiskzipdisk

p

DD

DD

,2,1 zipdiskzipdisk


Service Demands (sec)CPU 0.0394 0.1208Disk 1 (PDF) 0.0771 0.0000Disk 2 (PDF) 0.0771 0.0000Disk 3 (ZIP) 0.0000 0.2358Disk 4 (ZIP) 0.0000 0.2358

Closed QN:• two classes: PDF and ZIP.

t l ti ti 1 4

23

• customer population ratio: 1:4


Evenly distribute both file types to all 4 disks

Service Demands (sec)CPU 0 0394 0 1208CPU 0.0394 0.1208Disk 1 (PDF) 0.0386 0.1179Disk 2 (PDF) 0.0386 0.1179Disk 3 (ZIP) 0.0386 0.1179Disk 4 (ZIP) 0.0386 0.1179


14

10

12se

c)

8

10

do

wn

load

s/s

4

6

hro

ug

hp

ut

(d

2

Th

0

0 20 40 60 80 100 120 140 160 180

Total Number of Concurrent Users

PDF O i Fil Di t ZIP O i Fil Di t


PDF - Orig. File Distr. ZIP - Orig. File Distr.PDF - Balanced File Distr. ZIP - Balanced File Distrib.

After some point (after 20 users) throughput saturates because After some point (after 20 users), throughput saturates because utilization of one of the Web server devices (disks 3 & 4) approaches 100%Max throughput for PDF in original config is 12 files/sec. however, g g gfor balanced config, max throughput for PDF is reduced to 5 files/sec.Max throughput for ZIP in original config is 4.2 files/sec. however, for balanced config, max throughput for ZIP is increased to 6 6 for balanced config, max throughput for ZIP is increased to 6.6 files/sec.Total throughput measured for both PDF and ZIP is reduced by 28% from 16.2 (=12+4.2) to 11.6 (5+6.6). However, since ZIP files are much larger than PDF files total throughput measured in are much larger than PDF files, total throughput measured in bandwidth (KB/sec) increases by 1.4%, from 9384.72 (=12x377.6+4.2x1155.6) KB/sec to 9514.96 (=5x377.6+6.6x1155.6) KB/sec


40

S f

30

35

sec)

SLA for Response Times:• PDF: 7 seconds• ZIP: 20 seconds

20

25

nlo

ad T

ime

(s

10

15

0

vera

ge

Do

wn

104 customers

164 customers

5

10

Av

0

0 20 40 60 80 100 120 140 160 180

Total Number of Concurrent Customers

PDF O i Fil Di t ZIP O i Fil Di t


PDF - Orig. File Distr. ZIP - Orig. File Distr.PDF - Balanced File Distr. ZIP - Balanced File Distr.

After about 20 concurrent users throughput saturates After about 20 concurrent users, throughput saturates for all classes, and so download times increase linearly with no. of concurrent users.F t d l d ti f For 104 concurrent users, average download times for ZIP at original config reaches its SLA of 20 secs, while download times for PDF is far below its SLA of 7 secs. Th f t d l d t d b Thus, max no. of concurrent downloads supported by original config is 104.For balanced config, average download time for ZIP

h t 6 t hil reaches 20 secs at 164 concurrent users, while download times for PDF is still below 7‐sec SLA. Thus, balanced config supports 58% more users than the i i l original one.


f fUse of Secure Sockets Layer (SSL) for user authentication and data integrity and

f d lconfidentiality.SSL has a handshake phase during which

bl k d hpublic key encryption is used to exchange secrets used to generate a symmetric key.h k h d f dThe symmetric key is then used for data

exchange in the second phase.




fPublic Key (PK) cryptography is order of magnitudes slower than symmetric key

hcryptography.

encrypting a 128‐byte block using a public key of 512 bits takes 3.5 msec on a Pentium‐II 266 MHz while symmetric key encryption using AES would take less than one microsecond on the same take less than one microsecond on the same machine.


Symmetric key cryptography is not scalable to a large number of users: they are required

h kto share a secret key.It is faster to encrypt with a public key than to d h kdecrypt with a secret key.


MessageMessageDigest 101…1010g

FunctionLarge

Small(e g 128 bits)Large (e.g., 128 bits)


A Digest AMessageDigest

g

gFunction

B Digest B

If A B Di t A Di t B35

If A =B => Digest A = Digest B© 2004 D. A. Menascé. All Rights Reserved.

?MessageDigest Digest Ag

Functiong

36

Extremely hard to get A from Digest A!© 2004 D. A. Menascé. All Rights Reserved.

fMessage digest generation is a fast operation. For example, the hash generation

f l k l brate of SHA‐1 is 13 clock cycles per byte on a Pentium machine. So, a digest of a 1‐Mbyte f l ld b d lfile would be generated in approximately 13 msec on a 1 GHz Pentium machine.



HTTP

S SSL H d h k• selection of cryptographicalgorithmS

SSSL Handshake

Protocolalgorithm

• mutual authentication• exchange of secrets

through PKL

SSL RecordProtocol

• compression/decompression• encryption/decryption

through PK

TCP

Protocol • message authentication



(Client random number session id cypher suites)

43

(Client random number, session id, cypher suites)


(X 509 Certificate server random number server session ID cypher suites)

44

(X.509 Certificate, server random number, server session ID, cypher suites)


(master secret key encrypted with server’s public key)

45

(master secret key encrypted with server s public key)


(digest of all messages sent by client encrypted with bulk encryption key)

46

(digest of all messages sent by client encrypted with bulk encryption key)


Handshake CPU Processing Time (msec)

gTime per KB (msec)

Low Security 10.2 0.104Medium Security 23.8 0.268Hi h S it 48 0 0 609High Security 48.0 0.609

Levels of security depend on key lengths and on the strength of the security algorithms usedstrength of the security algorithms used.

Additional Service Demands (sec) for Secure Download

49.5 ms = 10.2 + 0.104 * 377.6

PDF ZIPLow Security 0.0495 0.1304Medium Security 0.1250 0.3333Medium Security 0.1250 0.3333High Security 0.2781 0.7519


No. Concurrent X_PDF X_ZIP R_PDF R_ZIPDownloads (files/sec) (files/sec) sec sec

20 2.25 3.15 1.78 5.09Low Security

40 2.26 3.17 3.55 10.0860 2.25 3.18 5.32 15.1080 2.25 3.18 7.10 20.12

20 1.22 1.75 3.28 9.1340 1.22 1.76 6.56 18.1960 1 22 1 6 9 8 2 2

Medium Security

60 1.22 1.76 9.85 27.27

20 0.63 0.91 6.34 17.49High Security

40 0.63 0.92 12.69 34.93


Factors that affect Factor LevelsFactors that affect performance: processor speed,

Factor Levels

Processor Speed

2.0, 2.4, 2 8 3 1

p p ,number of processors, and main memory.

l l f

Speed (GHz)

2.8, 3.1

No 1 2 4 8Levels: values of a factor.

No. processors

1, 2, 4, 8

Main 1 2 4Main memory (GB)

1, 2, 4

(GB)


Select a representative Elapsed Time (sec)

Elapsed Time Select a representative

workload and apply it to the two servers and

Type Size (KB)

( )Original Server

(sec) New Server

New-Original

PDF 300 1.42 1.39 -0.03PDF 301 1.42 1.38 -0.04PDF 301 1.42 1.38 -0.03

measure the download times in each case.

h

PDF 301 1.42 1.38 0.03PDF 301 1.42 1.38 -0.04PDF 302 1.42 1.41 -0.01PDF 302 1.42 1.42 0.00PDF 302 1.42 1.38 -0.04

Compute the difference between the download times

ZIP 1000 4.71 4.71 -0.01ZIP 1001 4.72 4.58 -0.14ZIP 1002 4.72 4.59 -0.13ZIP 1004 4.73 4.60 -0.13

. . . . . . . . . . . . . .

download times. ZIP 1005 4.73 4.55 -0.18ZIP 1005 4.73 4.71 -0.02ZIP 1005 4.74 4.62 -0.12ZIP 1005 4.74 4.58 -0.15ZIP 1006 4.74 4.58 -0.16ZIP 1007 4.75 4.62 -0.13


Compute the 95% Difference (new-orig) for PDF Files:Mean -0 0357Compute the 95%

confidence interval for the average difference between the download

Mean -0.0357Standard Deviation 0.0235Lower bound 95% CI Difference -0.0380Upper bound 95% CI Difference -0.0334

between the download times.If the 95% confidence

Difference (new-orig) for ZIP Files:Mean -0.1109Standard Deviation 0.0631Lower bound 95% CI Difference -0.1160

interval for the average difference contains zero, then the two servers are

Lower bound 95% CI Difference 0.1160Upper bound 95% CI Difference -0.1058

then the two servers are statistically identical at the 95% confidence level.

The new server outperforms theoriginal server for both PDF andZIP files at the 95% confidence level

51

level.

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