Modelling composed behaviour
1
PDF and CDF for a normally distributed variable (mu=0, sigma=1)
1
Normal(0, 1)
0.35
0.8
Density at value
0.3
0.25
0.6
0.2
0.4
0.15
0.1
0.2
0.05
0
0
-4
-3
-2
-1
0
Value
2
1
2
3
4
Probability that variable takes values less than value
0.4
A normally distributed variable and its 11-piece approximation (error 0.004148)
1
PUNormal(0, 1)
Normal(0, 1)
0.35
0.8
0.3
Density at value
0.25
0.6
0.2
0.4
0.15
0.1
0.2
0.05
0
0
-4
-2
0
Value
3
2
4
Probability that variable takes values less than value
0.4
PDF and CDF of a bimodal distribution
1
Bimodal
0.5
0.8
Density at value
0.4
0.6
0.3
0.4
0.2
0.2
0.1
0
0
0
1
2
3
4
Value
4
5
6
7
Probability that variable takes values less than value
0.6
PDF and CDF of a less simple distribution
1
Cutoff
0.35
0.8
Density at value
0.3
0.25
0.6
0.2
0.4
0.15
0.1
0.2
0.05
0
0
-5
-4
-3
-2
-1
Value
5
0
1
Probability that variable takes values less than value
0.4
1800
6000
Distribution of Google response times
Distribution of Google ping times
1600
5000
1200
4000
1000
3000
800
600
2000
400
1000
200
0
0
0.2
0.4
0.6
Response time (s)
6
0.8
1
1.2
0
Number of pings
Number of responses
1400
Two Normal variables and their sum
0.35
1
Normal(4, 2.5)
Normal(21, 1)
PUNormal(4, 2.5)+PUNormal(21, 1)
0.8
Density at value
0.3
0.25
0.6
0.2
0.4
0.15
0.1
0.2
0.05
0
0
0
10
20
Value
7
30
40
Probability that variable takes values less than value
0.4
Two Normal variables and their maximum
0.35
1
Normal(8, 2.5)
Normal(9, 1)
Maximum of PUNormal(8, 2.5), PUNormal(9, 1)
0.8
0.3
Density at value
0.25
0.6
0.2
0.4
0.15
0.1
0.2
0.05
0
0
0
5
10
Value
8
15
20
Probability that variable takes values less than value
0.4
Definition of time
my $time = Agrajag::Property->new("time", "seconds", # Names
"Agrajag::Values::Distributions::PiecewiseUniform", # Base type
series
=> "add", # Numerical behaviour in series
parallel_all
=> "max", # Numerical behaviour in parallel-all
parallel_first => "min", # Numerical behaviour in parallel-first
);
9
Definition of cost
my $cost = Agrajag::Property->new("cost", "pence",
# Names
"Agrajag::Values::Distributions::PiecewiseUniform", # Base type
series
=> "add", # Numerical behaviour in series
parallel_all
=> "add", # Numerical behaviour in parallel-all
parallel_first => "add", # Numerical behaviour in parallel-first
);
10
Definition of failure rate
my $failed = Agrajag::Property->new("failed", "per",
"Agrajag::Values::Distributions::PiecewiseUniform",
series
=> "complement_multiply",
parallel_all
=> "complement_multiply",
parallel_first => "multiply",
);
11
Effect on various metrics of combining redundant services
1
If first fails, try second
Parallel, grab first result
Original population
0.01
1e-04
failed
1e-06
1e-08
1e-10
1e-12
1e-14
1e-16
0
0.5
1
1.5
cost
12
2
2.5
Effect on various metrics of combining redundant services
1
If first fails, try second
Parallel, grab first result
Original population
0.01
1e-04
failed
1e-06
1e-08
1e-10
1e-12
1e-14
1e-16
0
20
40
60
time
13
80
100
120
Effect on various metrics of combining redundant services
110
If first fails, try second
Parallel, grab first result
Original population
100
90
80
time
70
60
50
40
30
20
10
0
0
0.5
1
1.5
cost
14
2
2.5
Lowest and highest costs
Process "merge(0.963420737013613 * series(sample 5, nothing),
0.0365792629863866 * series(sample 5, sample 12))":
cost: 0.912921336687748+/-0.168953806141398 pence
failed: 0.00141813147151815+/-0.037631374870547 per
time: 11.0147572693062+/-6.77101498117215 seconds
(conditional)
Process "parallel_first(sample 7, sample 3)":
cost: 2.3 pence
failed: 5.82485889377704e-06+/-0.00241346741531679 per
time: 24.2532671224301+/-13.405833396648 seconds
(parallel)
15
Lowest and highest values for cost
1
Lowest
Highest
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
1
1.2
1.4
1.6
Value
16
1.8
2
2.2
Probability that variable takes values less than value
Density at value
1
Lowest and highest times
Process "parallel_first(sample 22, sample 6)":
cost: 2.08 pence
failed: 4.46342962590052e-12+/-2.11268303961588e-06 per
time: 5.1738590825544+/-1.22048099490178 seconds
(parallel)
Process "merge(0.999515637891236 * series(sample 3, nothing),
0.000484362108764458 * series(sample 3, sample 11))":
cost: 1.19045045676115+/-0.0204626947535409 pence
failed: 1.33872660588175e-05+/-0.00365883681515382 per
time: 109.097014736137+/-63.7990881680071 seconds
(conditional)
17
Lowest and highest values for time
0.4
0.8
0.35
Density at value
0.3
0.6
0.25
0.2
0.4
0.15
0.1
0.2
0.05
0
0
0
100
200
300
400
Value
18
500
600
700
Probability that variable takes values less than value
1
Lowest
Highest
0.45
Lowest and highest failure rates
Process "parallel_first(sample 22, sample 16)":
cost: 2.07 pence
failed: 0 per
time: 5.25660344792234+/-1.27088093492597 seconds
(parallel)
Process "parallel_first(sample 13, sample 12)":
cost: 1.9 pence
failed: 0.00219570724011997+/-0.0468069023738557 per
time: 17.4037570609171+/-6.25604265053334 seconds
(parallel)
19
Effect on various metrics of combining redundant services
(better services cost more)
1
If first fails, try second
Parallel, grab first result
Original population
0.01
1e-04
failed
1e-06
1e-08
1e-10
1e-12
1e-14
1e-16
0
0.5
1
1.5
cost
20
2
2.5
Effect on various metrics of combining redundant services
(better services cost more)
1
If first fails, try second
Parallel, grab first result
Original population
0.01
1e-04
failed
1e-06
1e-08
1e-10
1e-12
1e-14
1e-16
0
20
40
60
time
21
80
100
120
Effect on various metrics of combining redundant services
(better services cost more)
110
If first fails, try second
Parallel, grab first result
Original population
100
90
80
time
70
60
50
40
30
20
10
0
0
0.5
1
1.5
cost
22
2
2.5
Lowest and highest costs
Process "merge(0.972361037709955 * series(sample 0, nothing), 0.027638
cost: 0.904875066061041+/-0.147542504192504 pence
failed: 0.000765704113656396+/-0.0276607630203276 per
time: 98.5800379789004+/-56.9295426092033 seconds
(conditional)
Process "parallel_first(sample 24, sample 23)":
cost: 2.3 pence
failed: 0 per
time: 8.34086497044595+/-2.08869234868699 seconds
(parallel)
23
Lowest and highest times
Process "parallel_first(sample 22, sample 19)":
cost: 2.19 pence
failed: 4.46342962590052e-12+/-2.11268303961588e-06 per
time: 5.1738590825544+/-1.22048099490178 seconds
(parallel)
Process "merge(0.999515637891236 * series(sample 13, nothing), 0.00048
cost: 1.06042623865571+/-0.0193625498743187 pence
failed: 1.33872660588175e-05+/-0.00365883681515382 per
time: 109.097014736137+/-63.7990881680071 seconds
(conditional)
24
Lowest and highest failure rates
Process "parallel_first(sample 24, sample 23)":
cost: 2.3 pence
failed: 0 per
time: 8.34086497044595+/-2.08869234868699 seconds
(parallel)
Process "parallel_first(sample 4, sample 3)":
cost: 1.97 pence
failed: 0.00219570724011997+/-0.0468069023738557 per
time: 17.4037570609171+/-6.25604265053334 seconds
(parallel)
25
Our experience with GT3
26
GT3 “One Point Oh”
• 3α, 3β, 3.0, 3.0.2β(?), 3.0.2, not 3.2 (released end 2003).
• Used service data, notification, dynamic invocation, registry,
lifecycle management, service proxying.
• Moved to pure web services in 2004:
– More stable.
– More widely used (problem solving easier).
– Better documented.
– FUD WRT grid vs WS models (subsequently → WSRF).
• So lots of “one point oh” issues during those twelve months.
• Anachronism, except possibly relevant to new release of GT4?
27
GT3 as product
• Transparency — what’s really working, what’s getting priority
now ?
• Stability — interfaces changed substantially across every
release — catch-up. . .
• Documentation and examples — too basic, no help for common
problems (assumes everything works).
• Comments and code — obfuscated.
• Testing — test-first philosophy would have improved release
quality and provided code examples.
28
GT3 as development environment
• Open source good — if not for fixing at least for understanding
and work-arounds.
• “Google debugging” depends on a good developer community:
tick.
• GT3/Axis borderline hazy — difficult to tell where your
problem is.
• Errors usually meaningless.
• Debug logs too difficult to obtain.
• GT3 container a mistake — no dynamic redeployment.
29
GT3 technologies and choices
• Why GAR? — .deb or .rpm solve the same problem with
much greater maturity.
• MDS and alternatives — more vapourware than FUD — COF
(confidence-optimism-faith)?
• Potentially hugely useful range of interfaces, but with a
performance hit.
• GWSDL — necessary but made it difficult to support both
Grid and WS in the same application.
30