1 A Pricing Model for Grid Computing Antony Davies Duquesne University April 22, 2005.
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1
A Pricing Model for Grid Computing
Antony Davies
Duquesne University
April 22, 2005
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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.
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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
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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
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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
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$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
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7 Sources: International Data Corporation, Parabon Computation
Market Segmentation 2004
71%
24%
5%
Traditional HPC Clusters Grid Computing
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8 Sources: International Data Corporation, Parabon Computation
Market Segmentation 2007
59%
19%
22%
Traditional HPC Clusters Grid Computing
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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)
![Page 10: 1 A Pricing Model for Grid Computing Antony Davies Duquesne University April 22, 2005.](https://reader038.fdocuments.in/reader038/viewer/2022110322/56649d3f5503460f94a191af/html5/thumbnails/10.jpg)
10 Sources: US Dept. of Commerce, Top500.Org, Parabon Computation
Computing Power Comparison
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
wre
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
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11 Sources: US Dept. of Commerce, Top500.Org, Parabon Computation
Computing Power Comparison
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
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)
20 times #500
![Page 12: 1 A Pricing Model for Grid Computing Antony Davies Duquesne University April 22, 2005.](https://reader038.fdocuments.in/reader038/viewer/2022110322/56649d3f5503460f94a191af/html5/thumbnails/12.jpg)
12 Sources: US Dept. of Commerce, Top500.Org, Parabon Computation
Computing Power Comparison
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
wre
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
![Page 13: 1 A Pricing Model for Grid Computing Antony Davies Duquesne University April 22, 2005.](https://reader038.fdocuments.in/reader038/viewer/2022110322/56649d3f5503460f94a191af/html5/thumbnails/13.jpg)
13 Sources: US Dept. of Commerce, Top500.Org, Parabon Computation
Computing Power Comparison
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
wre
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
![Page 14: 1 A Pricing Model for Grid Computing Antony Davies Duquesne University April 22, 2005.](https://reader038.fdocuments.in/reader038/viewer/2022110322/56649d3f5503460f94a191af/html5/thumbnails/14.jpg)
14 Sources: US Dept. of Commerce, Top500.Org, Parabon Computation
Computing Power Comparison
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
wre
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
![Page 15: 1 A Pricing Model for Grid Computing Antony Davies Duquesne University April 22, 2005.](https://reader038.fdocuments.in/reader038/viewer/2022110322/56649d3f5503460f94a191af/html5/thumbnails/15.jpg)
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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
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0
Subjective value of completed work at time of completion
Subjective discount rate (annual)
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
Market for Computation Generated via a Cluster
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0
Subjective value of completed work at time of completion
Subjective discount rate (annual)
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)
Market for Computation Generated via a Cluster
( ) 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:
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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
Market for Computation Generated via a Cluster
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( )Lambert's W-Function, , satisfies ( )e xx x x
-1/e
0 x
1 x
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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*
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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
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-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
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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
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Present value of benefit of infinite stream of worke 1r
P
Market for Computation Generated via a Grid
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
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Market for Computation Generated via a Grid
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
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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
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Parting comments: Analogies to Electricity
= 0.87 power
= 0.87 power
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A Pricing Model for Grid Computing
Antony Davies
Duquesne University
April 22, 2005