Summary
This experiment investigates container resource limits. Central Composite design optimizing CPU/memory requests and limits for utilization and stability.
The design varies 3 factors: cpu request m (millicores), ranging from 100 to 1000, cpu limit m (millicores), ranging from 500 to 2000, and memory request mb (MB), ranging from 128 to 1024. The goal is to optimize 2 responses: utilization pct (%) (maximize) and oom kills per day (count) (minimize). Fixed conditions held constant across all runs include memory limit mb = 2048, qos class = burstable.
A Central Composite Design (CCD) was selected to fit a full quadratic response surface model, including curvature and interaction effects. With 3 factors this produces 22 runs including center points and axial (star) points that extend beyond the factorial range.
Quadratic response surface models were fitted to capture potential curvature and factor interactions. The RSM contour plots below visualize how pairs of factors jointly affect each response.
Key Findings
For utilization pct, the most influential factors were cpu limit m (39.9%), memory request mb (30.1%), cpu request m (29.9%). The best observed value was 84.7 (at cpu request m = 550, cpu limit m = 1250, memory request mb = 576).
For oom kills per day, the most influential factors were cpu request m (45.1%), cpu limit m (28.4%), memory request mb (26.5%). The best observed value was 2.5 (at cpu request m = 550, cpu limit m = 1250, memory request mb = 576).
Recommended Next Steps
- Run confirmation experiments at the predicted optimal settings to validate the model.
- Consider whether any fixed factors should be varied in a future study.
Experimental Setup
Factors
| Factor | Low | High | Unit |
|---|---|---|---|
cpu_request_m | 100 | 1000 | millicores |
cpu_limit_m | 500 | 2000 | millicores |
memory_request_mb | 128 | 1024 | MB |
Fixed: memory_limit_mb = 2048, qos_class = burstable
Responses
| Response | Direction | Unit |
|---|---|---|
utilization_pct | ↑ maximize | % |
oom_kills_per_day | ↓ minimize | count |
Configuration
use_cases/34_container_resource_limits/config.json
{
"metadata": {
"name": "Container Resource Limits",
"description": "Central Composite design optimizing CPU/memory requests and limits for utilization and stability"
},
"factors": [
{
"name": "cpu_request_m",
"levels": [
"100",
"1000"
],
"type": "continuous",
"unit": "millicores"
},
{
"name": "cpu_limit_m",
"levels": [
"500",
"2000"
],
"type": "continuous",
"unit": "millicores"
},
{
"name": "memory_request_mb",
"levels": [
"128",
"1024"
],
"type": "continuous",
"unit": "MB"
}
],
"fixed_factors": {
"memory_limit_mb": "2048",
"qos_class": "burstable"
},
"responses": [
{
"name": "utilization_pct",
"optimize": "maximize",
"unit": "%"
},
{
"name": "oom_kills_per_day",
"optimize": "minimize",
"unit": "count"
}
],
"settings": {
"operation": "central_composite",
"test_script": "use_cases/34_container_resource_limits/sim.sh"
}
}
Experimental Matrix
The Central Composite Design produces 22 runs. Each row is one experiment with specific factor settings.
| Run | cpu_request_m | cpu_limit_m | memory_request_mb |
|---|---|---|---|
| 1 | 550 | 1250 | 576 |
| 2 | 1000 | 500 | 1024 |
| 3 | 100 | 2000 | 128 |
| 4 | 550 | 2619.31 | 576 |
| 5 | 550 | 1250 | 576 |
| 6 | -271.584 | 1250 | 576 |
| 7 | 550 | 1250 | -241.932 |
| 8 | 550 | 1250 | 576 |
| 9 | 1000 | 2000 | 128 |
| 10 | 1371.58 | 1250 | 576 |
| 11 | 550 | 1250 | 576 |
| 12 | 550 | -119.306 | 576 |
| 13 | 550 | 1250 | 576 |
| 14 | 100 | 500 | 1024 |
| 15 | 550 | 1250 | 576 |
| 16 | 1000 | 500 | 128 |
| 17 | 550 | 1250 | 1393.93 |
| 18 | 1000 | 2000 | 1024 |
| 19 | 550 | 1250 | 576 |
| 20 | 100 | 500 | 128 |
| 21 | 100 | 2000 | 1024 |
| 22 | 550 | 1250 | 576 |
Step-by-Step Workflow
1
Preview the design
Terminal
$ doe info --config use_cases/34_container_resource_limits/config.json
2
Generate the runner script
Terminal
$ doe generate --config use_cases/34_container_resource_limits/config.json \
--output use_cases/34_container_resource_limits/results/run.sh --seed 42
3
Execute the experiments
Terminal
$ bash use_cases/34_container_resource_limits/results/run.sh
4
Analyze results
Terminal
$ doe analyze --config use_cases/34_container_resource_limits/config.json
5
Get optimization recommendations
Terminal
$ doe optimize --config use_cases/34_container_resource_limits/config.json
6
Multi-objective optimization
With 2 competing responses, use --multi to find the best compromise via Derringer–Suich desirability.
Terminal
$ doe optimize --config use_cases/34_container_resource_limits/config.json --multi
7
Generate the HTML report
Terminal
$ doe report --config use_cases/34_container_resource_limits/config.json \
--output use_cases/34_container_resource_limits/results/report.html
Features Exercised
| Feature | Value |
|---|---|
| Design type | central_composite |
| Factor types | continuous (all 3) |
| Arg style | double-dash |
| Responses | 2 (utilization_pct ↑, oom_kills_per_day ↓) |
| Total runs | 22 |
Analysis Results
Generated from actual experiment runs using the DOE Helper Tool.
Response: utilization_pct
Top factors: cpu_limit_m (39.9%), memory_request_mb (30.1%), cpu_request_m (29.9%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|---|---|---|---|---|
| Source | DF | SS | MS | F | p-value |
| cpu_request_m | 4 | 3161.3336 | 790.3334 | 61.670 | 0.0000 |
| cpu_limit_m | 4 | 2163.5436 | 540.8859 | 42.205 | 0.0000 |
| memory_request_mb | 4 | 2076.3677 | 519.0919 | 40.505 | 0.0000 |
| Lack | of | Fit | 2 | 0.0000 | 0.0000 |
| Pure | Error | 7 | 89.7088 | ||
| Error | 9 | 0.0000 | 12.8155 | ||
| Total | 21 | 6793.3277 | 323.4918 |
Pareto Chart
Main Effects Plot
Normal Probability Plot of Effects
Half-Normal Plot of Effects
Model Diagnostics
Response: oom_kills_per_day
Top factors: cpu_request_m (45.1%), cpu_limit_m (28.4%), memory_request_mb (26.5%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|---|---|---|---|---|
| Source | DF | SS | MS | F | p-value |
| cpu_request_m | 4 | 130.1409 | 32.5352 | 6.009 | 0.0123 |
| cpu_limit_m | 4 | 52.1442 | 13.0361 | 2.408 | 0.1259 |
| memory_request_mb | 4 | 48.2809 | 12.0702 | 2.229 | 0.1462 |
| Lack | of | Fit | 2 | 66.7261 | 33.3630 |
| Pure | Error | 7 | 37.8987 | ||
| Error | 9 | 104.6248 | 5.4141 | ||
| Total | 21 | 335.1909 | 15.9615 |
Pareto Chart
Main Effects Plot
Normal Probability Plot of Effects
Half-Normal Plot of Effects
Model Diagnostics
Response Surface Plots
3D surfaces fitted with quadratic RSM. Red dots are observed data points.
oom kills per day cpu limit m vs memory request mb
oom kills per day cpu request m vs cpu limit m
oom kills per day cpu request m vs memory request mb
utilization pct cpu limit m vs memory request mb
utilization pct cpu request m vs cpu limit m
utilization pct cpu request m vs memory request mb
Multi-Objective Optimization
When responses compete, Derringer–Suich desirability finds the best compromise. Each response is scaled to a 0–1 desirability, then combined via a weighted geometric mean.
Overall Desirability
D = 0.9545
Per-Response Desirability
| Response | Weight | Desirability | Predicted | Dir |
|---|---|---|---|---|
utilization_pct |
1.5 |
0.9545
|
84.70 0.9545 84.70 % | ↑ |
oom_kills_per_day |
1.0 |
0.9545
|
2.50 0.9545 2.50 count | ↓ |
Recommended Settings
| Factor | Value |
|---|---|
cpu_request_m | 1000 millicores |
cpu_limit_m | 2000 millicores |
memory_request_mb | 1024 MB |
Source: from observed run #17
Trade-off Summary
Sacrifice = how much worse than single-objective best.
| Response | Predicted | Best Observed | Sacrifice |
|---|---|---|---|
oom_kills_per_day | 2.50 | 2.50 | +0.00 |
Top 3 Runs by Desirability
| Run | D | Factor Settings |
|---|---|---|
| #2 | 0.9072 | cpu_request_m=-271.584, cpu_limit_m=1250, memory_request_mb=576 |
| #18 | 0.8788 | cpu_request_m=1371.58, cpu_limit_m=1250, memory_request_mb=576 |
Model Quality
| Response | R² | Type |
|---|---|---|
oom_kills_per_day | 0.0935 | linear |
Full Multi-Objective Output
doe optimize --multi
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================
Overall desirability: D = 0.9545
Response Weight Desirability Predicted Direction
---------------------------------------------------------------------
utilization_pct 1.5 0.9545 84.70 % ↑
oom_kills_per_day 1.0 0.9545 2.50 count ↓
Recommended settings:
cpu_request_m = 1000 millicores
cpu_limit_m = 2000 millicores
memory_request_mb = 1024 MB
(from observed run #17)
Trade-off summary:
utilization_pct: 84.70 (best observed: 84.70, sacrifice: +0.00)
oom_kills_per_day: 2.50 (best observed: 2.50, sacrifice: +0.00)
Model quality:
utilization_pct: R² = 0.4125 (quadratic)
oom_kills_per_day: R² = 0.0935 (linear)
Top 3 observed runs by overall desirability:
1. Run #17 (D=0.9545): cpu_request_m=1000, cpu_limit_m=2000, memory_request_mb=1024
2. Run #2 (D=0.9072): cpu_request_m=-271.584, cpu_limit_m=1250, memory_request_mb=576
3. Run #18 (D=0.8788): cpu_request_m=1371.58, cpu_limit_m=1250, memory_request_mb=576
Full Analysis Output
doe analyze
=== Main Effects: utilization_pct ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
cpu_limit_m 41.4500 3.8346 39.9%
memory_request_mb 31.3000 3.8346 30.1%
cpu_request_m 31.0750 3.8346 29.9%
=== ANOVA Table: utilization_pct ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
cpu_request_m 4 3161.3336 790.3334 61.670 0.0000
cpu_limit_m 4 2163.5436 540.8859 42.205 0.0000
memory_request_mb 4 2076.3677 519.0919 40.505 0.0000
Lack of Fit 2 0.0000 0.0000 0.000 1.0000
Pure Error 7 89.7088 12.8155
Error 9 0.0000 12.8155
Total 21 6793.3277 323.4918
=== Summary Statistics: utilization_pct ===
cpu_request_m:
Level N Mean Std Min Max
------------------------------------------------------------
-271.584 1 65.7000 0.0000 65.7000 65.7000
100 4 63.2000 16.0813 47.2000 84.3000
1000 4 34.6250 21.0616 15.7000 63.2000
1371.58 1 45.9000 0.0000 45.9000 45.9000
550 12 65.4667 11.7760 35.6000 84.7000
cpu_limit_m:
Level N Mean Std Min Max
------------------------------------------------------------
-119.306 1 78.5000 0.0000 78.5000 78.5000
1250 12 61.1667 10.2098 35.6000 71.5000
2000 4 43.2500 18.3814 22.4000 66.2000
2619.31 1 84.7000 0.0000 84.7000 84.7000
500 4 54.5750 28.6909 15.7000 84.3000
memory_request_mb:
Level N Mean Std Min Max
------------------------------------------------------------
-241.932 1 35.6000 0.0000 35.6000 35.6000
1024 4 46.9750 17.6375 22.4000 63.2000
128 4 50.8500 30.4213 15.7000 84.3000
1393.93 1 66.9000 0.0000 66.9000 66.9000
576 12 66.2250 9.5696 45.9000 84.7000
=== Main Effects: oom_kills_per_day ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
cpu_request_m 10.2250 0.8518 45.1%
cpu_limit_m 6.4500 0.8518 28.4%
memory_request_mb 6.0000 0.8518 26.5%
=== ANOVA Table: oom_kills_per_day ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
cpu_request_m 4 130.1409 32.5352 6.009 0.0123
cpu_limit_m 4 52.1442 13.0361 2.408 0.1259
memory_request_mb 4 48.2809 12.0702 2.229 0.1462
Lack of Fit 2 66.7261 33.3630 6.162 0.0286
Pure Error 7 37.8987 5.4141
Error 9 104.6248 5.4141
Total 21 335.1909 15.9615
=== Summary Statistics: oom_kills_per_day ===
cpu_request_m:
Level N Mean Std Min Max
------------------------------------------------------------
-271.584 1 10.1000 0.0000 10.1000 10.1000
100 4 7.6750 4.2602 4.1000 12.9000
1000 4 9.6000 4.7735 4.9000 14.9000
1371.58 1 16.1000 0.0000 16.1000 16.1000
550 12 5.8750 2.7343 2.5000 11.0000
cpu_limit_m:
Level N Mean Std Min Max
------------------------------------------------------------
-119.306 1 3.5000 0.0000 3.5000 3.5000
1250 12 7.5583 3.7369 4.2000 16.1000
2000 4 8.9500 4.3000 4.3000 12.9000
2619.31 1 2.5000 0.0000 2.5000 2.5000
500 4 8.3250 4.9655 4.1000 14.9000
memory_request_mb:
Level N Mean Std Min Max
------------------------------------------------------------
-241.932 1 5.0000 0.0000 5.0000 5.0000
1024 4 9.8750 3.6518 4.9000 12.9000
128 4 7.4000 5.0977 4.1000 14.9000
1393.93 1 11.0000 0.0000 11.0000 11.0000
576 12 6.7250 3.9190 2.5000 16.1000
Optimization Recommendations
doe optimize
=== Optimization: utilization_pct ===
Direction: maximize
Best observed run: #17
cpu_request_m = 550
cpu_limit_m = 1250
memory_request_mb = 576
Value: 84.7
RSM Model (linear, R² = 0.2621, Adj R² = 0.1391):
Coefficients:
intercept +58.5682
cpu_request_m +4.7827
cpu_limit_m +9.7689
memory_request_mb +1.7553
RSM Model (quadratic, R² = 0.5502, Adj R² = 0.2129):
Coefficients:
intercept +63.2997
cpu_request_m +4.7827
cpu_limit_m +9.7690
memory_request_mb +1.7553
cpu_request_m*cpu_limit_m -10.2750
cpu_request_m*memory_request_mb -7.3750
cpu_limit_m*memory_request_mb -5.0500
cpu_request_m^2 -1.5908
cpu_limit_m^2 -4.7108
memory_request_mb^2 -0.7958
Curvature analysis:
cpu_limit_m coef=-4.7108 concave (has a maximum)
cpu_request_m coef=-1.5908 concave (has a maximum)
memory_request_mb coef=-0.7958 concave (has a maximum)
Notable interactions:
cpu_request_m*cpu_limit_m coef=-10.2750 (antagonistic)
cpu_request_m*memory_request_mb coef=-7.3750 (antagonistic)
cpu_limit_m*memory_request_mb coef=-5.0500 (antagonistic)
Predicted optimum (from quadratic model, at observed points):
cpu_request_m = 100
cpu_limit_m = 2000
memory_request_mb = 1024
Predicted value: 75.5440
Surface optimum (via L-BFGS-B, quadratic model):
cpu_request_m = 100
cpu_limit_m = 2000
memory_request_mb = 1024
Predicted value: 75.5440
Model quality: Moderate fit — use predictions directionally, not precisely.
Factor importance:
1. cpu_limit_m (effect: 52.0, contribution: 50.2%)
2. cpu_request_m (effect: 29.0, contribution: 28.0%)
3. memory_request_mb (effect: 22.6, contribution: 21.8%)
=== Optimization: oom_kills_per_day ===
Direction: minimize
Best observed run: #17
cpu_request_m = 550
cpu_limit_m = 1250
memory_request_mb = 576
Value: 2.5
RSM Model (linear, R² = 0.1199, Adj R² = -0.0267):
Coefficients:
intercept +7.5364
cpu_request_m -0.1399
cpu_limit_m -0.9218
memory_request_mb +1.3681
RSM Model (quadratic, R² = 0.4887, Adj R² = 0.1053):
Coefficients:
intercept +6.5811
cpu_request_m -0.1399
cpu_limit_m -0.9218
memory_request_mb +1.3681
cpu_request_m*cpu_limit_m +1.1750
cpu_request_m*memory_request_mb +2.1000
cpu_limit_m*memory_request_mb +0.7500
cpu_request_m^2 -0.8124
cpu_limit_m^2 +1.4826
memory_request_mb^2 +0.7626
Curvature analysis:
cpu_limit_m coef=+1.4826 convex (has a minimum)
cpu_request_m coef=-0.8124 concave (has a maximum)
memory_request_mb coef=+0.7626 convex (has a minimum)
Notable interactions:
cpu_request_m*memory_request_mb coef=+2.1000 (synergistic)
cpu_request_m*cpu_limit_m coef=+1.1750 (synergistic)
cpu_limit_m*memory_request_mb coef=+0.7500 (synergistic)
Predicted optimum (from quadratic model, at observed points):
cpu_request_m = 550
cpu_limit_m = -119.306
memory_request_mb = 576
Predicted value: 13.2063
Surface optimum (via L-BFGS-B, quadratic model):
cpu_request_m = 1000
cpu_limit_m = 1375.67
memory_request_mb = 128
Predicted value: 2.8817
Model quality: Weak fit — consider adding center points or using a different design.
Factor importance:
1. memory_request_mb (effect: 11.1, contribution: 46.1%)
2. cpu_limit_m (effect: 8.9, contribution: 36.9%)
3. cpu_request_m (effect: 4.1, contribution: 17.0%)