1 a pricing model for grid computing antony davies duquesne university april 22, 2005

1

A Pricing Model for Grid Computing

Antony Davies

Duquesne University

April 22, 2005

2

Topics

1. Uses for high-performance computation.

2. Methods for generating HPC.

3. Spending on and growth of HPC market.

4. Measuring computational power.

5. Pricing model for computation.

6. Comparison to electricity.

3

Some Uses of High Performance Computation

Rendering Render The Incredibles: 36 years on a single computer

Gene sequence comparison Compare two DNA strands: 2 months on a single computer

Protein folding Fold a single amino acid chain: 1 week on a single computer

Drug discovery Screen all compounds in a single drug database: 60 years

Biological systems analysis Model dynamics of host-parasite relationship: 1 month

4

Other Uses of High Performance Computation

Oil/gas exploration Data mine a typical geophysical data set: 2 months

Inventory management Optimize product storage: 6 months

Traffic management Optimal timing/location for amusement park rides: 12 years

Portfolio analysis Risk/return for all portfolios from 50 stocks: 3,000 years

5

Methods for Generating High Performance Computation

Traditional HPC (“heavy iron”) (~ $50,000 per GF annually)E.g. Cray Supercomputer

Cluster computers (~ $5,000 per GF annually)Dedicated off-the-shelf PC’s wired together

Enterprise grid computersLike a cluster, but captures idle computation on existing in-house computers

Internet grid computersLike a cluster, but captures idle computation from others’ computers

6

$0

$10

$20

$30

$40

$50

$60

$70

2004 2005 2006 2007

An

nu

al S

pe

nd

ing

(b

illio

ns

)

Traditional HPC Clusters Grid Computation

Sources: International Data Corporation, Parabon Computation

Total est. annual spending on HPC: $40 billion in 2004

7 Sources: International Data Corporation, Parabon Computation

Market Segmentation 2004

71%

24%

5%

Traditional HPC Clusters Grid Computing

8 Sources: International Data Corporation, Parabon Computation

Market Segmentation 2007

59%

19%

22%

Traditional HPC Clusters Grid Computing

9 Sources: US Dept. of Commerce, Top500.Org, Parabon Computation

Computing Power Comparison

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

Idle

Com

puta

tion

Top

500

Com

bine

d

Blu

eGen

e(D

OE

/IB

M)

Col

umbi

a(N

AS

A/A

mes

)

Ear

th S

imul

ator

Mar

eNos

trum

Thu

nder

(La

wre

nce

Live

rmor

e) #500

Top

of L

ine

PC

TF

(tr

illi

on

s o

per

atio

ns

per

sec

on

d)



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Idle

Com

puta

tion

Top

500

Com

bine

d

Blu

eGen

e(D

OE

/IB

M)

Col

umbi

a(N

AS

A/A

mes

)

Ear

th S

imul

ator

Mar

eNos

trum

Thu

nder

(La

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nce

Live

rmor

e) #500

Top

of L

ine

PC

TF

(tr

illi

on

s o

per

atio

ns

per

sec

on

d)

1,000 times TOL PC



0

5

10

15

20

25

Idle

Com

puta

tion

Top

500

Com

bine

d

Blu

eGen

e(D

OE

/IB

M)

Col

umbi

a(N

AS

A/A

mes

)

Ear

th S

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ator

Mar

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trum

Thu

nder

(La

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nce

Live

rmor

e) #500

Top

of L

ine

PC

TF

(tr

illi

on

s o

per

atio

ns

per

sec

on

d)

20 times #500



0

10

20

30

40

50

60

70

80

Idle

Com

puta

tion

Top

500

Com

bine

d

Blu

eGen

e(D

OE

/IB

M)

Col

umbi

a(N

AS

A/A

mes

)

Ear

th S

imul

ator

Mar

eNos

trum

Thu

nder

(La

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nce

Live

rmor

e) #500

Top

of L

ine

PC

TF

(tr

illi

on

s o

per

atio

ns

per

sec

on

d)

3 times Thunder



0

200

400

600

800

1000

1200

Idle

Com

puta

tion

Top

500

Com

bine

d

Blu

eGen

e(D

OE

/IB

M)

Col

umbi

a(N

AS

A/A

mes

)

Ear

th S

imul

ator

Mar

eNos

trum

Thu

nder

(La

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nce

Live

rmor

e) #500

Top

of L

ine

PC

TF

(tr

illi

on

s o

per

atio

ns

per

sec

on

d)

15 times BlueGene



0

20000

40000

60000

80000

100000

120000

140000

160000

180000

Idle

Com

puta

tion

Top

500

Com

bine

d

Blu

eGen

e(D

OE

/IB

M)

Col

umbi

a(N

AS

A/A

mes

)

Ear

th S

imul

ator

Mar

eNos

trum

Thu

nder

(La

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nce

Live

rmor

e) #500

Top

of L

ine

PC

TF

(tr

illi

on

s o

per

atio

ns

per

sec

on

d)

150 times Top 500

15

Subjective value of completed work at time of completion

Subjective discount rate (annual)

Work (GFY)

Power (GF)

r

W

P

/PV(completed work) e rW P

Market for Computation Generated via a Cluster

16

0



Work (GFY)

Power (GF)

Useful life of a node (years)

Cost-per-GF of a node today

Annual growth

r

W

P

n

k

rate of price-power ratio ("Moore's rate" 0.35)

0et

tk k

( ) 2( ) ( / )( )0 0 0 0 0PV (cost-per-GF) e e er n r n W P rk k k k


17

0



Work (GFY)

Power (GF)

Useful life of a node (years)

Cost-per-GF of a node today

Annual growth

r

W

P

n

k

rate of price-power ratio ("Moore's rate" 0.35)


( ) 2( ) 00 0 0 0 ( )

PV (cost of power cluster) e e1 e

r n r nr n

PkP P k k k

Simplification assumes that cluster has infinite life:

18

2 /Marginal Benefit of Additional Power

erW P

rW

P

*

0( )

24 1 e r n

rWP

k rW

0( )

Marginal Cost of Additional Power1 e r n

k

1

01

( )

!

ii

i

ix x

i


19

( )Lambert's W-Function, , satisfies ( )e xx x x

-1/e

0 x

1 x

20

P* satisfies first and second order conditions for optimization.

P* satisfies first, but not second, order condition for optimization.

P* is negative.

P* is imaginary.

*

00 ( )

24 1 e r n

rWP

k rW

*

01 ( )

24 1 e r n

rWP

k rW

*

00 ( )

24 1 e r n

rWP

k rW

*

01 ( )

24 1 e r n

rWP

k rW

Four possible solutions for P*

21

Ω = $250,000, k = $12,800, W = 20 GFY, r = 15%, n = 3, δ = 0.7

$0

$5,000

$10,000

$15,000

$20,000

$25,000

$30,000

$35,000

$40,000

$45,000

$50,000

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

Power (GF)

Marginal Benefit of Additional Power Marginal Cost of Additional Power

rW/2

-0.35

002

4

rW

k rW

22

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

- 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Power (GF)

Gro

wth

Rat

e

$0

$5,000

$10,000

$15,000

$20,000

$25,000

$30,000

$35,000

$40,000

$45,000

$50,000

Mar

gin

al B

enef

it o

f P

ower

rW /2

Marginal Benefit of Power

Growth in Marginal Benefit of Time

Growth in Marginal Time of Power

Benefit Benefit Time

Power Time Power

23

Via a grid, the computer and the computation are separated and computation can be priced like electricity.

To simplify, assume that:

1. A consumer’s job continually throws off solutions, in perpetuity, that have a value of per unit work.

2. The grid firm charges a per unit time price of

3. The value of the work is realized and the charges are incurred at the end of each time interval.

4. Discount rate per unit time is r.

baP c

Market for Computation Generated via a Grid

24

Present value of benefit of infinite stream of worke 1r

P


Present value of cost of infinite stream of chargese 1

b

r

aP c

Marginal benefit of additional powere 1r

1

Marginal cost of additional powere 1

b

r

abP

25


Marginal benefit of additional powere 1r

1

Marginal cost of additional powere 1

b

r

abP

1

1*Customer's optimal power

bP

ab

1*Customer's revealed value of workb

ab P

26

Parting comments: Analogies to Electricity

Computation

Power

Work Power Time

GF

GFH

Electricity

Power

Work Power Time

kW

kWH

Computation

Power Reliability Cycles

R C

Electricity

Power Voltage Current

E I

27

Parting comments: Analogies to Electricity

= 0.87 power

= 0.87 power

28

A Pricing Model for Grid Computing

Antony Davies

Duquesne University

April 22, 2005

1 a pricing model for grid computing antony davies duquesne university april 22, 2005

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