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Fuzzy Control meets Software Engineering 
Pooyan Jamshidi 
IC4-Irish Centre for Cloud Computing and Commerce 
School of Computing,Dublin City University 
Pooyan.jamshidi@computing.dcu.ie 
DagstuhlSeminar 
Control Theory meets Software Engineering 
September, 2014
Naeem Esfahani and Sam Malek, 
“Uncertainty in Self-Adaptive 
Software Systems” 
Knowledge 
Specification 
Uncertainty 
2
3
Application #1: 
Auto-scaling
~50% = wasted hardwareActual trafficTypical weekly traffic to Web-based applications (e.g., Amazon.com) 
5
Problem 1: ~75% wasted capacityActual demandProblem 2: customer lostTraffic in an unexpected burst in requests (e.g. end of year traffic to Amazon.com) 
6
Really like this?? Auto-scaling enables you to realize this ideal on-demand provisioning 
Time 
Demand 
? Enacting change in the Cloud resources are notreal-time 
7
Capacity we can provision with Auto-ScalingA realistic figure of dynamic provisioning 
8
9
0 50 100 
0 
500 
1000 
1500 
0 50 100 
100 
200 
300 
400 
500 
0 50 100 
0 
1000 
2000 
0 50 100 
0 
200 
400 
600 
10
11
These quantitative values are required to be determined by the user requires deep knowledge of application (CPU, memory, thresholds) requires performance modeling expertise (when and how to scale) A unified opinion of user(s) is required 
Amazon auto scaling 
Microsoft Azure Watch 
12 
Microsoft Azure Auto- scaling Application Block 
12
13
Uncertainty related to enactment latency: 
The same scaling action (adding/removing 
a VM with precisely the same size) took 
different time to be enacted on the 
cloud platform (here is Microsoft Azure) 
at different points and 
this difference were significant 
(up to couple of minutes). 
The enactment latency would be also different 
on different cloud platforms. 14
Offline benchmarking 
Trial-and-error 
Expert knowledge 
Costly and 
not systematic 
A. Gandhi, P. Dube, A. Karve, A. Kochut, L. Zhang, Adaptive, “Model-driven Autoscalingfor Cloud Applications”, ICAC’14 
arrival rate (req/s) 
95% Resp. time (ms) 
400 ms 
60 req/s 15
RobusT2Scale Initial setting + 
elasticity rules + 
response-time SLA 
environment 
monitoring 
application 
monitoring 
scaling 
actions 
Fuzzy Reasoning 
Users 
Prediction/ 
Smoothing 
16
0 0.5 1 1.5 2 2.5 3 
0 
0.2 
0.4 
0.6 
0.8 
1 
1.2 
1.4 
1.6 
1.8 
2 
Region of 
definite 
satisfaction 
Region of 
definite 
Region of dissatisfaction 
uncertain 
satisfaction 
Performance Index 
Possibility 
Performance Index 
Possibility 
words can mean different 
things to different people 
Different users often 
recommend 
different elasticity policies 
0 0.5 1 1.5 2 2.5 3 
0 
0.2 
0.4 
0.6 
0.8 
1 
1.2 
1.4 
1.6 
1.8 
2 
Type-2 MF 
Type-1 MF 
17
18
Workload 
Response time 
0 10 20 30 40 50 60 70 80 90 100 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1 
x 
2 
Membershuip grade 
0 10 20 30 40 50 60 70 80 90 100 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1 
Membersuhip grade 
=> 
=> 
mean 
sd 
19
Rule 
(풍) 
Antecedents Consequent 
풄풂풗품 
풍 
Workload 
Response-time 
Normal 
(-2) 
Effort 
(-1) 
Medium 
Effort 
(0) 
High 
Effort 
(+1) 
Maximum 
Effort (+2) 
1 Very low Instantaneous 7 2 1 0 0 -1.6 
2 Very low Fast 5 4 1 0 0 -1.4 
3 Very low Medium 0 2 6 2 0 0 
4 Very low Slow 0 0 4 6 0 0.6 
5 Very low Very slow 0 0 0 6 4 1.4 
6 Low Instantaneous 5 3 2 0 0 -1.3 
7 Low Fast 2 7 1 0 0 -1.1 
8 Low Medium 0 1 5 3 1 0.4 
9 Low Slow 0 0 1 8 1 1 
10 Low Very slow 0 0 0 4 6 1.6 
11 Medium Instantaneous 6 4 0 0 0 -1.6 
12 Medium Fast 2 5 3 0 0 -0.9 
13 Medium Medium 0 0 5 4 1 0.6 
14 Medium Slow 0 0 1 7 2 1.1 
15 Medium Very slow 0 0 1 3 6 1.5 
16 High Instantaneous 8 2 0 0 0 -1.8 
17 High Fast 4 6 0 0 0 -1.4 
18 High Medium 0 1 5 3 1 0.4 
19 High Slow 0 0 1 7 2 1.1 
20 High Very slow 0 0 0 6 4 1.4 
21 Very high Instantaneous 9 1 0 0 0 -1.9 
22 Very high Fast 3 6 1 0 0 -1.2 
23 Very high Medium 0 1 4 4 1 0.5 
24 Very high Slow 0 0 1 8 1 1 
25 Very high Very slow 0 0 0 4 6 1.6 
Rule 
(퐥) 
Antecedents Consequent 
풄풂풗품 
Work 풍 
load 
Response 
-time 
-2 -1 0 +1 +2 
12 Medium Fast 2 5 3 0 0 -0.9 
10 experts’ responses 
푅푙 : IF (the workload (푥1) is 퐹 푖1, AND the response-time 
(푥2) is 퐺 푖2), THEN (add/remove 푐푎푣푔 
푙 instances). 
푐푎푣푔 
푙 = 
푢=1 
푁푙 푤푢푙 
× 퐶 
푢=1 
푁푙 푤푢푙 
Goal: pre-computations of costly calculations 
to make a runtime efficient elasticity 
reasoning based on fuzzy inference 20
Liang, Q., Mendel, J. M. (2000). Interval type-2 fuzzy 
logic systems: theory and design. Fuzzy Systems, IEEE 
Transactions on, 8(5), 535-550. 
Scaling Actions 
Monitoring Data 
21
0 10 20 30 40 50 60 70 80 90 100 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1 
0.5954 
0.3797 
푀 
0 10 20 30 40 50 60 70 80 90 100 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1 
0.2212 
0.0000 
0 10 20 30 40 50 60 70 80 90 100 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1 
x 
2 
u 
0 10 20 30 40 50 60 70 80 90 100 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1 
x 
2 
u 
Monitoring data 
Workload 
Response time 
22
010203040506070809010000.10.20.30.40.50.60.70.80.910.59540.3797 010203040506070809010000.10.20.30.40.50.60.70.80.910.95680.9377 
23
24
푦푙 , 푦푟 
25
26
050100050010001500050100100200300400500 0501000100020000501000200400600 0501000500100005010005001000 
27
28
0 10 20 30 40 50 60 70 80 90 100 
-500 
0 
500 
1000 
1500 
2000 
Time (seconds) 
Number of hits 
Original data 
betta=0.10, gamma=0.94, rmse=308.1565, rrse=0.79703 
betta=0.27, gamma=0.94, rmse=209.7852, rrse=0.54504 
betta=0.80, gamma=0.94, rmse=272.6285, rrse=0.70858 
0 
0.2 
0.4 
0.6 
0.8 
1 
1.2 
1.4 
Big spike Dual phase Large variations Quickly varying Slowly varying Steep tri phase 
0 50 100 
0 
500 
1000 
1500 
0 50 100 
100 
200 
300 
400 
500 
0 50 100 
0 
1000 
2000 
0 50 100 
0 
200 
400 
600 
0 50 100 
0 
500 
1000 
0 50 100 
0 
500 
1000 
Root Relative Squared Error 
29
SUT 
Criteria 
Big spike 
Dual phase 
Large variations 
Quickly varying 
Slowly varying 
Steep tri phase 
RobusT2Scale 
푟푡95% 
973ms 
537ms 
509ms 
451ms 
423ms 
498ms 푣푚 
3.2 
3.8 
5.1 
5.3 
3.7 
3.9 
Overprovisioning 
푟푡95% 
354ms 
411ms 
395ms 
446ms 
371ms 
491ms 푣푚 
6 
6 
6 
6 
6 
6 
Under provisioning 
푟푡95% 
1465ms 
1832ms 
1789ms 
1594ms 
1898ms 
2194ms 푣푚 
2 
2 
2 
2 
2 
2 
SLA: 풓풕ퟗퟓ≤ퟔퟎퟎ풎풔 
For every 10s control interval•RobusT2Scale is superior to under-provisioning in terms of guaranteeing the SLA and does not require excessive resources•RobusT2Scale is superior to over-provisioning in terms of guaranteeing required resources while guaranteeing the SLA 30
0 
0.02 
0.04 
0.06 
0.08 
0.1 
alpha=0.1 alpha=0.5 alpha=0.9 alpha=1.0 
Root Mean Square Error 
Noise level: 10% 31
Application #2: Self-Adaptive Software Connectors
⊭푅 
Environment=D 
Environment=D’ 
Environment=D’ 
⊨푅 
⊨푅 Adapted to satisfy requirements while it is running Reliable RuntimeEfficient 
33
0 
0.5 
1 
1.5 
2 
2.5 
3 
3.5 
4 
4.5 
5 
0 
0.5 
1 
1.5 
2 
2.5 
3 
3.5 
4 
4.5 
5 
1.5 
2 
2.5 
3 
3.5 
4 
output1 
34
35
0 
1 
2 
3 
4 
5 
x 10 
-3 
1 2 3 4 5 6 7 8 
0 
0.05 
0.1 
0.15 
0.2 
0.25 
1 2 3 4 5 
36
0.05 
0.1 
0.15 
0.2 
0.25 
0.3 
0.35 
Type-1 FLS Type-2 FLS 
RMSE 
• The rule reduction reduced the rules 
quite considerably. 
• IT2 FLCs are more robust due to less 
mean error and less variation in the 
estimation error. 
• T1 FLCs in some realization drop more 
rules in comparison with the IT2 FLCs. 
• IT2 FLC original designs can be designed 
with less rules. 
37
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 
0 
0.2 
0.4 
0.6 
0.8 
1 
1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 
Noise Amplitude (α=0.5) 
RMSE 
α=0.7 α=0.95 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1 
1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 
IT2 FLC T1 FLC 
38
Future Directions
Current Solution 
(my PhD Thesis 
+ IC4 work on 
auto-scaling) 
Future Plan 
Updating K 
in MAPE-K 
Design-time @ Runtime 
Assistance 
Multi-cloud
41
42
Challenge 1: ~75% wasted capacity 
Actual 
demand 
Challenge 2: 
customer lost 
⊭ 푅 
Environment=D 
Environment=D’ 
Environment=D’ 
⊨ 푅 
⊨ 푅 
Adapted to satisfy 
requirements 
while it is running 
 Reliable 
 Run-time Efficient 
Current Solution 
(my PhD Thesis 
+ IC4 work on 
auto-scaling) 
Future Plan 
Updating K 
in MAPE-K 
Design-time @ Runtime 
Assistance 
Multi-cloud 
RobusT2Scale Initial setting + 
elasticity rules + 
response-time SLA 
environment 
monitoring 
application 
monitoring 
scaling 
actions 
Fuzzy Reasoning 
Users 
Prediction/ 
Smoothing 
43
http://computing.dcu.ie/~pjamshidi/PDF/SEAMS2014.pdf 
More 
Details? 
=> 
http://www.slideshare.net/pooyanjamshidi/ 
Slides? 
=> 
44 
Thank you! 
=> 
Aakash Ahmad 
Claus Pahl 
SoodehFarokhi
Requirement: R 
0 50 100 
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0 50 100 
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0 50 100 
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0 50 100 
0 
500 
1000 
0 50 100 
0 
500 
1000 
Environment: D 
Model: S 
Implementation Monitoring 
Execution 
Runtime 
Design-time 
Reasoning 
Self-adaptation 
Specification 
S,D⊨R 
S,D⊭R 
46
Looking for references? 
http://computing.dcu.ie/~pjamshidi/PDF/SEAMS2014.pdf 
47
48
49
50
푦푟 − 푦푙 
51
52

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Fuzzy Control meets Software Engineering

  • 1. Fuzzy Control meets Software Engineering Pooyan Jamshidi IC4-Irish Centre for Cloud Computing and Commerce School of Computing,Dublin City University Pooyan.jamshidi@computing.dcu.ie DagstuhlSeminar Control Theory meets Software Engineering September, 2014
  • 2. Naeem Esfahani and Sam Malek, “Uncertainty in Self-Adaptive Software Systems” Knowledge Specification Uncertainty 2
  • 3. 3
  • 5. ~50% = wasted hardwareActual trafficTypical weekly traffic to Web-based applications (e.g., Amazon.com) 5
  • 6. Problem 1: ~75% wasted capacityActual demandProblem 2: customer lostTraffic in an unexpected burst in requests (e.g. end of year traffic to Amazon.com) 6
  • 7. Really like this?? Auto-scaling enables you to realize this ideal on-demand provisioning Time Demand ? Enacting change in the Cloud resources are notreal-time 7
  • 8. Capacity we can provision with Auto-ScalingA realistic figure of dynamic provisioning 8
  • 9. 9
  • 10. 0 50 100 0 500 1000 1500 0 50 100 100 200 300 400 500 0 50 100 0 1000 2000 0 50 100 0 200 400 600 10
  • 11. 11
  • 12. These quantitative values are required to be determined by the user requires deep knowledge of application (CPU, memory, thresholds) requires performance modeling expertise (when and how to scale) A unified opinion of user(s) is required Amazon auto scaling Microsoft Azure Watch 12 Microsoft Azure Auto- scaling Application Block 12
  • 13. 13
  • 14. Uncertainty related to enactment latency: The same scaling action (adding/removing a VM with precisely the same size) took different time to be enacted on the cloud platform (here is Microsoft Azure) at different points and this difference were significant (up to couple of minutes). The enactment latency would be also different on different cloud platforms. 14
  • 15. Offline benchmarking Trial-and-error Expert knowledge Costly and not systematic A. Gandhi, P. Dube, A. Karve, A. Kochut, L. Zhang, Adaptive, “Model-driven Autoscalingfor Cloud Applications”, ICAC’14 arrival rate (req/s) 95% Resp. time (ms) 400 ms 60 req/s 15
  • 16. RobusT2Scale Initial setting + elasticity rules + response-time SLA environment monitoring application monitoring scaling actions Fuzzy Reasoning Users Prediction/ Smoothing 16
  • 17. 0 0.5 1 1.5 2 2.5 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Region of definite satisfaction Region of definite Region of dissatisfaction uncertain satisfaction Performance Index Possibility Performance Index Possibility words can mean different things to different people Different users often recommend different elasticity policies 0 0.5 1 1.5 2 2.5 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Type-2 MF Type-1 MF 17
  • 18. 18
  • 19. Workload Response time 0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 2 Membershuip grade 0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Membersuhip grade => => mean sd 19
  • 20. Rule (풍) Antecedents Consequent 풄풂풗품 풍 Workload Response-time Normal (-2) Effort (-1) Medium Effort (0) High Effort (+1) Maximum Effort (+2) 1 Very low Instantaneous 7 2 1 0 0 -1.6 2 Very low Fast 5 4 1 0 0 -1.4 3 Very low Medium 0 2 6 2 0 0 4 Very low Slow 0 0 4 6 0 0.6 5 Very low Very slow 0 0 0 6 4 1.4 6 Low Instantaneous 5 3 2 0 0 -1.3 7 Low Fast 2 7 1 0 0 -1.1 8 Low Medium 0 1 5 3 1 0.4 9 Low Slow 0 0 1 8 1 1 10 Low Very slow 0 0 0 4 6 1.6 11 Medium Instantaneous 6 4 0 0 0 -1.6 12 Medium Fast 2 5 3 0 0 -0.9 13 Medium Medium 0 0 5 4 1 0.6 14 Medium Slow 0 0 1 7 2 1.1 15 Medium Very slow 0 0 1 3 6 1.5 16 High Instantaneous 8 2 0 0 0 -1.8 17 High Fast 4 6 0 0 0 -1.4 18 High Medium 0 1 5 3 1 0.4 19 High Slow 0 0 1 7 2 1.1 20 High Very slow 0 0 0 6 4 1.4 21 Very high Instantaneous 9 1 0 0 0 -1.9 22 Very high Fast 3 6 1 0 0 -1.2 23 Very high Medium 0 1 4 4 1 0.5 24 Very high Slow 0 0 1 8 1 1 25 Very high Very slow 0 0 0 4 6 1.6 Rule (퐥) Antecedents Consequent 풄풂풗품 Work 풍 load Response -time -2 -1 0 +1 +2 12 Medium Fast 2 5 3 0 0 -0.9 10 experts’ responses 푅푙 : IF (the workload (푥1) is 퐹 푖1, AND the response-time (푥2) is 퐺 푖2), THEN (add/remove 푐푎푣푔 푙 instances). 푐푎푣푔 푙 = 푢=1 푁푙 푤푢푙 × 퐶 푢=1 푁푙 푤푢푙 Goal: pre-computations of costly calculations to make a runtime efficient elasticity reasoning based on fuzzy inference 20
  • 21. Liang, Q., Mendel, J. M. (2000). Interval type-2 fuzzy logic systems: theory and design. Fuzzy Systems, IEEE Transactions on, 8(5), 535-550. Scaling Actions Monitoring Data 21
  • 22. 0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5954 0.3797 푀 0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.2212 0.0000 0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 2 u 0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 2 u Monitoring data Workload Response time 22
  • 24. 24
  • 26. 26
  • 28. 28
  • 29. 0 10 20 30 40 50 60 70 80 90 100 -500 0 500 1000 1500 2000 Time (seconds) Number of hits Original data betta=0.10, gamma=0.94, rmse=308.1565, rrse=0.79703 betta=0.27, gamma=0.94, rmse=209.7852, rrse=0.54504 betta=0.80, gamma=0.94, rmse=272.6285, rrse=0.70858 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Big spike Dual phase Large variations Quickly varying Slowly varying Steep tri phase 0 50 100 0 500 1000 1500 0 50 100 100 200 300 400 500 0 50 100 0 1000 2000 0 50 100 0 200 400 600 0 50 100 0 500 1000 0 50 100 0 500 1000 Root Relative Squared Error 29
  • 30. SUT Criteria Big spike Dual phase Large variations Quickly varying Slowly varying Steep tri phase RobusT2Scale 푟푡95% 973ms 537ms 509ms 451ms 423ms 498ms 푣푚 3.2 3.8 5.1 5.3 3.7 3.9 Overprovisioning 푟푡95% 354ms 411ms 395ms 446ms 371ms 491ms 푣푚 6 6 6 6 6 6 Under provisioning 푟푡95% 1465ms 1832ms 1789ms 1594ms 1898ms 2194ms 푣푚 2 2 2 2 2 2 SLA: 풓풕ퟗퟓ≤ퟔퟎퟎ풎풔 For every 10s control interval•RobusT2Scale is superior to under-provisioning in terms of guaranteeing the SLA and does not require excessive resources•RobusT2Scale is superior to over-provisioning in terms of guaranteeing required resources while guaranteeing the SLA 30
  • 31. 0 0.02 0.04 0.06 0.08 0.1 alpha=0.1 alpha=0.5 alpha=0.9 alpha=1.0 Root Mean Square Error Noise level: 10% 31
  • 32. Application #2: Self-Adaptive Software Connectors
  • 33. ⊭푅 Environment=D Environment=D’ Environment=D’ ⊨푅 ⊨푅 Adapted to satisfy requirements while it is running Reliable RuntimeEfficient 33
  • 34. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1.5 2 2.5 3 3.5 4 output1 34
  • 35. 35
  • 36. 0 1 2 3 4 5 x 10 -3 1 2 3 4 5 6 7 8 0 0.05 0.1 0.15 0.2 0.25 1 2 3 4 5 36
  • 37. 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Type-1 FLS Type-2 FLS RMSE • The rule reduction reduced the rules quite considerably. • IT2 FLCs are more robust due to less mean error and less variation in the estimation error. • T1 FLCs in some realization drop more rules in comparison with the IT2 FLCs. • IT2 FLC original designs can be designed with less rules. 37
  • 38. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 0 0.2 0.4 0.6 0.8 1 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% Noise Amplitude (α=0.5) RMSE α=0.7 α=0.95 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% IT2 FLC T1 FLC 38
  • 40. Current Solution (my PhD Thesis + IC4 work on auto-scaling) Future Plan Updating K in MAPE-K Design-time @ Runtime Assistance Multi-cloud
  • 41. 41
  • 42. 42
  • 43. Challenge 1: ~75% wasted capacity Actual demand Challenge 2: customer lost ⊭ 푅 Environment=D Environment=D’ Environment=D’ ⊨ 푅 ⊨ 푅 Adapted to satisfy requirements while it is running  Reliable  Run-time Efficient Current Solution (my PhD Thesis + IC4 work on auto-scaling) Future Plan Updating K in MAPE-K Design-time @ Runtime Assistance Multi-cloud RobusT2Scale Initial setting + elasticity rules + response-time SLA environment monitoring application monitoring scaling actions Fuzzy Reasoning Users Prediction/ Smoothing 43
  • 44. http://computing.dcu.ie/~pjamshidi/PDF/SEAMS2014.pdf More Details? => http://www.slideshare.net/pooyanjamshidi/ Slides? => 44 Thank you! => Aakash Ahmad Claus Pahl SoodehFarokhi
  • 45.
  • 46. Requirement: R 0 50 100 0 500 1000 1500 0 50 100 100 200 300 400 500 0 50 100 0 1000 2000 0 50 100 0 200 400 600 0 50 100 0 500 1000 0 50 100 0 500 1000 Environment: D Model: S Implementation Monitoring Execution Runtime Design-time Reasoning Self-adaptation Specification S,D⊨R S,D⊭R 46
  • 47. Looking for references? http://computing.dcu.ie/~pjamshidi/PDF/SEAMS2014.pdf 47
  • 48. 48
  • 49. 49
  • 50. 50
  • 52. 52