RTOS Task Priority — DOE Use Case

Summary

This experiment investigates rtos task priority. Full factorial of task priority levels, tick rate, stack size, and preemption threshold for latency and utilization.

The design varies 4 factors: task priority levels (levels), ranging from 4 to 16, tick rate hz (Hz), ranging from 100 to 1000, stack size bytes (bytes), ranging from 512 to 4096, and preemption threshold (level), ranging from 1 to 8. The goal is to optimize 2 responses: worst case latency us (us) (minimize) and cpu utilization pct (%) (maximize). Fixed conditions held constant across all runs include rtos = freertos, mcu clock = 240MHz.

A full factorial design was used to explore all 16 possible combinations of the 4 factors at two levels. This guarantees that every main effect and interaction can be estimated independently, at the cost of a larger experiment (16 runs).

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 worst case latency us, the most influential factors were tick rate hz (48.8%), preemption threshold (26.5%), stack size bytes (16.7%). The best observed value was 26.0 (at task priority levels = 4, tick rate hz = 1000, stack size bytes = 512).

For cpu utilization pct, the most influential factors were preemption threshold (34.6%), stack size bytes (32.7%), tick rate hz (29.4%). The best observed value was 90.0 (at task priority levels = 16, tick rate hz = 100, stack size bytes = 512).

Recommended Next Steps

Consider whether any fixed factors should be varied in a future study.

Experimental Setup

Factors

Factor	Low	High	Unit
`task_priority_levels`	4	16	levels
`tick_rate_hz`	100	1000	Hz
`stack_size_bytes`	512	4096	bytes
`preemption_threshold`	1	8	level

Fixed: rtos = freertos, mcu_clock = 240MHz

Responses

Response	Direction	Unit
`worst_case_latency_us`	↓ minimize	us
`cpu_utilization_pct`	↑ maximize	%

Configuration

use_cases/69_rtos_task_priority/config.json

{
  "metadata": {
    "name": "RTOS Task Priority",
    "description": "Full factorial of task priority levels, tick rate, stack size, and preemption threshold for latency and utilization"
  },
  "factors": [
    {
      "name": "task_priority_levels",
      "levels": [
        "4",
        "16"
      ],
      "type": "continuous",
      "unit": "levels"
    },
    {
      "name": "tick_rate_hz",
      "levels": [
        "100",
        "1000"
      ],
      "type": "continuous",
      "unit": "Hz"
    },
    {
      "name": "stack_size_bytes",
      "levels": [
        "512",
        "4096"
      ],
      "type": "continuous",
      "unit": "bytes"
    },
    {
      "name": "preemption_threshold",
      "levels": [
        "1",
        "8"
      ],
      "type": "continuous",
      "unit": "level"
    }
  ],
  "fixed_factors": {
    "rtos": "freertos",
    "mcu_clock": "240MHz"
  },
  "responses": [
    {
      "name": "worst_case_latency_us",
      "optimize": "minimize",
      "unit": "us"
    },
    {
      "name": "cpu_utilization_pct",
      "optimize": "maximize",
      "unit": "%"
    }
  ],
  "settings": {
    "operation": "full_factorial",
    "test_script": "use_cases/69_rtos_task_priority/sim.sh"
  }
}

Experimental Matrix

The Full Factorial Design produces 16 runs. Each row is one experiment with specific factor settings.

Run	`task_priority_levels`	`tick_rate_hz`	`stack_size_bytes`	`preemption_threshold`
1	4	1000	4096	8
2	16	100	512	8
3	4	1000	512	8
4	4	1000	4096	1
5	16	1000	4096	1
6	16	100	4096	1
7	16	1000	512	1
8	16	100	512	1
9	4	100	512	8
10	4	100	4096	1
11	16	1000	512	8
12	16	1000	4096	8
13	4	1000	512	1
14	16	100	4096	8
15	4	100	512	1
16	4	100	4096	8

Step-by-Step Workflow

1

Preview the design

Terminal

$ doe info --config use_cases/69_rtos_task_priority/config.json

2

Generate the runner script

Terminal

$ doe generate --config use_cases/69_rtos_task_priority/config.json \
    --output use_cases/69_rtos_task_priority/results/run.sh --seed 42

3

Execute the experiments

Terminal

$ bash use_cases/69_rtos_task_priority/results/run.sh

4

Analyze results

Terminal

$ doe analyze --config use_cases/69_rtos_task_priority/config.json

5

Get optimization recommendations

Terminal

$ doe optimize --config use_cases/69_rtos_task_priority/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/69_rtos_task_priority/config.json --multi

7

Generate the HTML report

Terminal

$ doe report --config use_cases/69_rtos_task_priority/config.json \
    --output use_cases/69_rtos_task_priority/results/report.html

Features Exercised

Feature	Value
Design type	`full_factorial`
Factor types	`continuous` (all 4)
Arg style	`double-dash`
Responses	2 (worst_case_latency_us ↓, cpu_utilization_pct ↑)
Total runs	16

Analysis Results

Generated from actual experiment runs using the DOE Helper Tool.

Response: worst_case_latency_us

Top factors: tick_rate_hz (48.8%), preemption_threshold (26.5%), stack_size_bytes (16.7%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
task_priority_levels	1	10.5625	10.5625	0.010	0.9235
tick_rate_hz	1	390.0625	390.0625	0.376	0.5663
stack_size_bytes	1	45.5625	45.5625	0.044	0.8422
preemption_threshold	1	115.5625	115.5625	0.112	0.7520
task_priority_levels*tick_rate_hz	1	370.5625	370.5625	0.358	0.5759
task_priority_levels*stack_size_bytes	1	855.5625	855.5625	0.826	0.4052
task_priority_levels*preemption_threshold	1	45.5625	45.5625	0.044	0.8422
tick_rate_hz*stack_size_bytes	1	473.0625	473.0625	0.457	0.5292
tick_rate_hz*preemption_threshold	1	175.5625	175.5625	0.169	0.6977
stack_size_bytes*preemption_threshold	1	1580.0625	1580.0625	1.525	0.2717
Error	5	5180.8125	1036.1625
Total	15	9242.9375	616.1958

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Normal probability plot for worst_case_latency_us

Half-Normal Plot of Effects

Half-normal plot for worst_case_latency_us

Model Diagnostics

Response: cpu_utilization_pct

Top factors: preemption_threshold (34.6%), stack_size_bytes (32.7%), tick_rate_hz (29.4%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
task_priority_levels	1	0.2500	0.2500	0.001	0.9814
tick_rate_hz	1	20.2500	20.2500	0.049	0.8341
stack_size_bytes	1	25.0000	25.0000	0.060	0.8160
preemption_threshold	1	28.0900	28.0900	0.068	0.8053
task_priority_levels*tick_rate_hz	1	41.6025	41.6025	0.100	0.7645
task_priority_levels*stack_size_bytes	1	678.6025	678.6025	1.632	0.2575
task_priority_levels*preemption_threshold	1	63.2025	63.2025	0.152	0.7127
tick_rate_hz*stack_size_bytes	1	172.9225	172.9225	0.416	0.5474
tick_rate_hz*preemption_threshold	1	22.5625	22.5625	0.054	0.8250
stack_size_bytes*preemption_threshold	1	460.1025	460.1025	1.107	0.3410
Error	5	2078.6325	415.7265
Total	15	3591.2175	239.4145

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Normal probability plot for cpu_utilization_pct

Half-Normal Plot of Effects

Half-normal plot for cpu_utilization_pct

Model Diagnostics

Response Surface Plots

3D surfaces fitted with quadratic RSM. Red dots are observed data points.

cpu utilization pct stack size bytes vs preemption threshold

cpu utilization pct task priority levels vs preemption threshold

cpu utilization pct task priority levels vs stack size bytes

cpu utilization pct task priority levels vs tick rate hz

cpu utilization pct tick rate hz vs preemption threshold

cpu utilization pct tick rate hz vs stack size bytes

worst case latency us stack size bytes vs preemption threshold

worst case latency us task priority levels vs preemption threshold

worst case latency us task priority levels vs stack size bytes

worst case latency us task priority levels vs tick rate hz

worst case latency us tick rate hz vs preemption threshold

worst case latency us tick rate hz vs stack size bytes

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 = 0.9166

Per-Response Desirability

Response	Weight	Desirability	Predicted	Dir
`worst_case_latency_us`	1.0	0.8625	34.00 0.8625 34.00 us	↓
`cpu_utilization_pct`	1.5	0.9545	90.00 0.9545 90.00 %	↑

Recommended Settings

Factor	Value
`task_priority_levels`	16 levels
`tick_rate_hz`	100 Hz
`stack_size_bytes`	4096 bytes
`preemption_threshold`	8 level

Source: from observed run #11

Trade-off Summary

Sacrifice = how much worse than single-objective best.

Response	Predicted	Best Observed	Sacrifice
`cpu_utilization_pct`	90.00	90.00	+0.00

Top 3 Runs by Desirability

Run	D	Factor Settings
#12	0.8217	task_priority_levels=4, tick_rate_hz=100, stack_size_bytes=512, preemption_threshold=1
#7	0.7018	task_priority_levels=4, tick_rate_hz=1000, stack_size_bytes=512, preemption_threshold=8

Model Quality

Response	R²	Type
`cpu_utilization_pct`	0.3362	linear

Full Multi-Objective Output

doe optimize --multi
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================

Overall desirability: D = 0.9166

Response                  Weight Desirability    Predicted  Direction
---------------------------------------------------------------------
worst_case_latency_us        1.0       0.8625       34.00 us   ↓
cpu_utilization_pct          1.5       0.9545       90.00 %   ↑

Recommended settings:
  task_priority_levels = 16 levels
  tick_rate_hz = 100 Hz
  stack_size_bytes = 4096 bytes
  preemption_threshold = 8 level
  (from observed run #11)

Trade-off summary:
  worst_case_latency_us: 34.00 (best observed: 26.00, sacrifice: +8.00)
  cpu_utilization_pct: 90.00 (best observed: 90.00, sacrifice: +0.00)

Model quality:
  worst_case_latency_us: R² = 0.1531 (linear)
  cpu_utilization_pct: R² = 0.3362 (linear)

Top 3 observed runs by overall desirability:
  1. Run #11 (D=0.9166): task_priority_levels=16, tick_rate_hz=100, stack_size_bytes=4096, preemption_threshold=8
  2. Run #12 (D=0.8217): task_priority_levels=4, tick_rate_hz=100, stack_size_bytes=512, preemption_threshold=1
  3. Run #7 (D=0.7018): task_priority_levels=4, tick_rate_hz=1000, stack_size_bytes=512, preemption_threshold=8

Full Analysis Output

doe analyze
=== Main Effects: worst_case_latency_us ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
tick_rate_hz             9.8750       6.2058            48.8%
preemption_threshold    -5.3750       6.2058            26.5%
stack_size_bytes         3.3750       6.2058            16.7%
task_priority_levels    -1.6250       6.2058             8.0%

=== ANOVA Table: worst_case_latency_us ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
task_priority_levels         1      10.5625      10.5625      0.010     0.9235
tick_rate_hz                 1     390.0625     390.0625      0.376     0.5663
stack_size_bytes             1      45.5625      45.5625      0.044     0.8422
preemption_threshold         1     115.5625     115.5625      0.112     0.7520
task_priority_levels*tick_rate_hz    1     370.5625     370.5625      0.358     0.5759
task_priority_levels*stack_size_bytes    1     855.5625     855.5625      0.826     0.4052
task_priority_levels*preemption_threshold    1      45.5625      45.5625      0.044     0.8422
tick_rate_hz*stack_size_bytes    1     473.0625     473.0625      0.457     0.5292
tick_rate_hz*preemption_threshold    1     175.5625     175.5625      0.169     0.6977
stack_size_bytes*preemption_threshold    1    1580.0625    1580.0625      1.525     0.2717
Error                        5    5180.8125    1036.1625
Total                       15    9242.9375     616.1958

=== Interaction Effects: worst_case_latency_us ===
Factor A             Factor B              Interaction   % Contribution
------------------------------------------------------------------------
stack_size_bytes     preemption_threshold     -19.8750            30.6%
task_priority_levels stack_size_bytes         -14.6250            22.5%
tick_rate_hz         stack_size_bytes          10.8750            16.7%
task_priority_levels tick_rate_hz              -9.6250            14.8%
tick_rate_hz         preemption_threshold       6.6250            10.2%
task_priority_levels preemption_threshold      -3.3750             5.2%

=== Summary Statistics: worst_case_latency_us ===

task_priority_levels:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  16                  8    64.7500    29.0898    26.0000   105.0000
  4                   8    63.1250    21.7416    34.0000    94.0000

tick_rate_hz:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  100                 8    59.0000    22.0713    34.0000    94.0000
  1000                8    68.8750    27.8846    26.0000   105.0000

stack_size_bytes:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  4096                8    62.2500    23.8492    26.0000    96.0000
  512                 8    65.6250    27.2970    34.0000   105.0000

preemption_threshold:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  1                   8    66.6250    30.1090    26.0000   105.0000
  8                   8    61.2500    19.9338    34.0000    96.0000

=== Main Effects: cpu_utilization_pct ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
preemption_threshold    -2.6500       3.8683            34.6%
stack_size_bytes         2.5000       3.8683            32.7%
tick_rate_hz            -2.2500       3.8683            29.4%
task_priority_levels    -0.2500       3.8683             3.3%

=== ANOVA Table: cpu_utilization_pct ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
task_priority_levels         1       0.2500       0.2500      0.001     0.9814
tick_rate_hz                 1      20.2500      20.2500      0.049     0.8341
stack_size_bytes             1      25.0000      25.0000      0.060     0.8160
preemption_threshold         1      28.0900      28.0900      0.068     0.8053
task_priority_levels*tick_rate_hz    1      41.6025      41.6025      0.100     0.7645
task_priority_levels*stack_size_bytes    1     678.6025     678.6025      1.632     0.2575
task_priority_levels*preemption_threshold    1      63.2025      63.2025      0.152     0.7127
tick_rate_hz*stack_size_bytes    1     172.9225     172.9225      0.416     0.5474
tick_rate_hz*preemption_threshold    1      22.5625      22.5625      0.054     0.8250
stack_size_bytes*preemption_threshold    1     460.1025     460.1025      1.107     0.3410
Error                        5    2078.6325     415.7265
Total                       15    3591.2175     239.4145

=== Interaction Effects: cpu_utilization_pct ===
Factor A             Factor B              Interaction   % Contribution
------------------------------------------------------------------------
task_priority_levels stack_size_bytes          13.0250            32.6%
stack_size_bytes     preemption_threshold      10.7250            26.9%
tick_rate_hz         stack_size_bytes          -6.5750            16.5%
task_priority_levels preemption_threshold      -3.9750            10.0%
task_priority_levels tick_rate_hz              -3.2250             8.1%
tick_rate_hz         preemption_threshold      -2.3750             6.0%

=== Summary Statistics: cpu_utilization_pct ===

task_priority_levels:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  16                  8    57.9625    15.2656    37.9000    77.1000
  4                   8    57.7125    16.7319    34.4000    90.0000

tick_rate_hz:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  100                 8    58.9625    18.1725    34.4000    90.0000
  1000                8    56.7125    13.4126    40.1000    77.1000

stack_size_bytes:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  4096                8    56.5875    15.1936    34.4000    77.1000
  512                 8    59.0875    16.6917    37.9000    90.0000

preemption_threshold:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  1                   8    59.1625    20.8480    34.4000    90.0000
  8                   8    56.5125     8.6243    43.0000    69.2000

Optimization Recommendations

doe optimize
=== Optimization: worst_case_latency_us ===
Direction: minimize

Best observed run: #12
  task_priority_levels = 4
  tick_rate_hz = 1000
  stack_size_bytes = 512
  preemption_threshold = 8
  Value: 26.0

RSM Model (linear, R² = 0.2412, Adj R² = -0.0347):
  Coefficients:
    intercept                      +63.9375
    task_priority_levels           +0.0625
    tick_rate_hz                   +3.4375
    stack_size_bytes               -7.0625
    preemption_threshold           -8.8125

RSM Model (quadratic, R² = 0.7357, Adj R² = -2.9652):
  Coefficients:
    intercept                      +12.7875
    task_priority_levels           +0.0625
    tick_rate_hz                   +3.4375
    stack_size_bytes               -7.0625
    preemption_threshold           -8.8125
    task_priority_levels*tick_rate_hz +13.3125
    task_priority_levels*stack_size_bytes -4.1875
    task_priority_levels*preemption_threshold -4.9375
    tick_rate_hz*stack_size_bytes  -4.0625
    tick_rate_hz*preemption_threshold -7.0625
    stack_size_bytes*preemption_threshold -0.3125
    task_priority_levels^2         +12.7875
    tick_rate_hz^2                 +12.7875
    stack_size_bytes^2             +12.7875
    preemption_threshold^2         +12.7875

  Curvature analysis:
    tick_rate_hz                   coef=+12.7875  convex (has a minimum)
    stack_size_bytes               coef=+12.7875  convex (has a minimum)
    preemption_threshold           coef=+12.7875  convex (has a minimum)
    task_priority_levels           coef=+12.7875  convex (has a minimum)

  Notable interactions:
    task_priority_levels*tick_rate_hz coef=+13.3125  (synergistic)
    tick_rate_hz*preemption_threshold coef=-7.0625  (antagonistic)
    task_priority_levels*preemption_threshold coef=-4.9375  (antagonistic)
    task_priority_levels*stack_size_bytes coef=-4.1875  (antagonistic)
    tick_rate_hz*stack_size_bytes  coef=-4.0625  (antagonistic)
    stack_size_bytes*preemption_threshold coef=-0.3125  (antagonistic)

  Predicted optimum (from linear model, at observed points):
    task_priority_levels = 16
    tick_rate_hz = 1000
    stack_size_bytes = 512
    preemption_threshold = 1
    Predicted value: 83.3125

  Surface optimum (via L-BFGS-B, linear model):
    task_priority_levels = 4
    tick_rate_hz = 100
    stack_size_bytes = 4096
    preemption_threshold = 8
    Predicted value: 44.5625

  Model quality: Weak fit — consider adding center points or using a different design.

Factor importance:
  1. preemption_threshold  (effect: -17.6, contribution: 45.5%)
  2. stack_size_bytes  (effect: 14.1, contribution: 36.5%)
  3. tick_rate_hz  (effect: 6.9, contribution: 17.7%)
  4. task_priority_levels  (effect: -0.1, contribution: 0.3%)

=== Optimization: cpu_utilization_pct ===
Direction: maximize

Best observed run: #11
  task_priority_levels = 16
  tick_rate_hz = 100
  stack_size_bytes = 512
  preemption_threshold = 8
  Value: 90.0

RSM Model (linear, R² = 0.2708, Adj R² = 0.0057):
  Coefficients:
    intercept                      +57.8375
    task_priority_levels           -1.1875
    tick_rate_hz                   -4.4250
    stack_size_bytes               +0.5125
    preemption_threshold           +6.2875

RSM Model (quadratic, R² = 0.7445, Adj R² = -2.8327):
  Coefficients:
    intercept                      +11.5675
    task_priority_levels           -1.1875
    tick_rate_hz                   -4.4250
    stack_size_bytes               +0.5125
    preemption_threshold           +6.2875
    task_priority_levels*tick_rate_hz -9.8250
    task_priority_levels*stack_size_bytes -0.6125
    task_priority_levels*preemption_threshold -1.6375
    tick_rate_hz*stack_size_bytes  +1.9500
    tick_rate_hz*preemption_threshold +1.0000
    stack_size_bytes*preemption_threshold +1.3875
    task_priority_levels^2         +11.5675
    tick_rate_hz^2                 +11.5675
    stack_size_bytes^2             +11.5675
    preemption_threshold^2         +11.5675

  Curvature analysis:
    preemption_threshold           coef=+11.5675  convex (has a minimum)
    task_priority_levels           coef=+11.5675  convex (has a minimum)
    tick_rate_hz                   coef=+11.5675  convex (has a minimum)
    stack_size_bytes               coef=+11.5675  convex (has a minimum)

  Notable interactions:
    task_priority_levels*tick_rate_hz coef=-9.8250  (antagonistic)
    tick_rate_hz*stack_size_bytes  coef=+1.9500  (synergistic)
    task_priority_levels*preemption_threshold coef=-1.6375  (antagonistic)
    stack_size_bytes*preemption_threshold coef=+1.3875  (synergistic)
    tick_rate_hz*preemption_threshold coef=+1.0000  (synergistic)
    task_priority_levels*stack_size_bytes coef=-0.6125  (antagonistic)

  Predicted optimum (from linear model, at observed points):
    task_priority_levels = 4
    tick_rate_hz = 100
    stack_size_bytes = 4096
    preemption_threshold = 8
    Predicted value: 70.2500

  Surface optimum (via L-BFGS-B, linear model):
    task_priority_levels = 4
    tick_rate_hz = 100
    stack_size_bytes = 4096
    preemption_threshold = 8
    Predicted value: 70.2500

  Model quality: Weak fit — consider adding center points or using a different design.

Factor importance:
  1. preemption_threshold  (effect: 12.6, contribution: 50.7%)
  2. tick_rate_hz  (effect: -8.9, contribution: 35.6%)
  3. task_priority_levels  (effect: 2.4, contribution: 9.6%)
  4. stack_size_bytes  (effect: -1.0, contribution: 4.1%)