[CT420]: Add borrowed notes
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year4/semester2/CT420/message.md
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year4/semester2/CT420/message.md
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#### Scheduling Algorithms
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- A schedule is feasible if all the tasks start after their release time and complete before their deadlines
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- Rate-Monotonic Scheduling (RM)
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- A model for optimal static priority scheduling algorithm
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- Not straight-forward when it comes to guarantee the feasibility of a task schedule
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- Use this algorithm if task priorities **do not** change
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- The scheduling decision is made when the current task execution is complete and a new task is released
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- The task utilisation is execution time divided by period
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- The CPU utilisation for the schedule is just the sum of all of these
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- The smallest period is the highest priority for all released tasks
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- Tasks are pre-empted if a higher-priority task is released
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- A general schedulability test for RM is $$
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U \leq n \left( 2^{\frac{1}{n}} - 1 \right)
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$$
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where $n$ is the number of tasks
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- If this is true, a feasible schedule is guaranteed, no need for further analysis
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- Otherwise, you need to actually check feasibility
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- This can be done by checking $$
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W_{i}(t) = \sum_{j = 1}^{i} e_{j} \left( \frac{t}{p_{j}} \right) \leq t
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$$
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for task interval $t$ and number of tasks $i$
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- $\frac{t}{p_{j}}$ is always **rounded up**
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- Check each of the points to see which tasks cause infeasibility which may include repeats of periods
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- In other words, you can check whether 2 tasks will work in the period for
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- The schedule is feasible if this is true
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- Earliest Deadline First (EDF)
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- Use this algorithm if task priorities **do** change over time
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- Also preemptable
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- The tasks with the earliest absolute deadline are given highest priority
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- Priorities are re-evaluated when tasks are released or completed
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- This is an optimal single-processor scheduling algorithm
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- If $U \leq 1$ then the task set is schedulable
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#### Scheduling Example from Paper
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| t | e | p |
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| --- | --- | --- |
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| 1 | 10 | 50 |
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| 2 | 20 | 100 |
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| 3 | 30 | 150 |
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| 4 | 40 | 200 |
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**CE**
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Must execute tasks every 50 ms
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1 + 4 = 50 so we need these to be on their own every time
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2 + 3 = 50 so these also need to be on their own
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is this even possible?
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it will have overruns - 4 has to be split into 2 subtasks
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| t | e | p |
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| --- | --- | --- |
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| 1 | 10 | 50 |
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| 2 | 20 | 100 |
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| 3 | 30 | 150 |
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| 4a | 20 | 200 |
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| 4b | 20 | 200 |
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1 has to be called every time since the period is 50
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| time | tasks | |
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| ---- | -------- | --- |
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| 0 | 1, 2, 4a | |
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| 50 | 1, 4b | |
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| 100 | 1, 2 | |
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| 150 | 1, 3 | |
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| 200 | 1, 2, 4a | |
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| 250 | 1, 4b | |
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| 300 | 1, 2 | |
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| 350 | 1, 3 | |
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**RM**
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Total Utilisation: $$
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\sum_{i = 1}^{n} u_{i}:u_{i} = \frac{e_{i}}{p_{i}}
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$$
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$$
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0.2 + 0.2 + 0.2 + 0.2 = 0.8
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$$
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$$
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0.8 \leq n(2^{1/n} - 1)
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$$
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$$
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0.8 > 0.76
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$$
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$$
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W_{4} = \{50, 100, 150, 200\}
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$$
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$$
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W_{4}(t) = \sum_{j = 1}^{4} e_{j} \left( \frac{t}{p_{j}} \right)
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$$
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$$
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= 10(4) + 20(2) + 30(2) + 40(1)
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$$
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$$
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= 180 < 200
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$$
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this is feasible
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| time | task running | tasks available | |
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| ---- | ------------ | --------------- | --- |
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| 0 | 1 | 1, 2, 3, 4 | |
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| 10 | 2 | 2, 3, 4 | |
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| 20 | 2 | 2, 3, 4 | |
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| 30 | 3 | 3, 4 | |
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| 40 | 3 | 3, 4 | |
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| 50 | 1 | 1, 3, 4 | |
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| 60 | 3 | 3, 4 | |
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| 70 | 4 | 4 | |
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| 80 | 4 | 4 | |
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| 90 | 4 | 4 | |
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| 100 | 1 | 1, 2, 4 | |
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| 110 | 2 | 2, 4 | |
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| 120 | 2 | 2, 4 | |
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| 130 | 4 | 4 | |
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| 140 | | | |
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| 150 | 1 | 1, 3 | |
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| 160 | 3 | 3 | |
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| 170 | 3 | 3 | |
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| 180 | 3 | 3 | |
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| 190 | | | |
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| 200 | 1 | 1, 2, 4 | |
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| 210 | 2 | 2, 4 | |
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| 220 | 2 | 2, 4 | |
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| 230 | 4 | 4 | |
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| 240 | 4 | 4 | |
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| 250 | 1 | 1, 4 | |
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| 260 | 4 | 4 | |
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| 270 | 4 | 4 | |
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| 280 | | | |
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| 290 | | | |
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| 300 | 1 | 1, 3 | |
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**EDF**
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$$
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0.8 < 1
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$$
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this is feasible
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| time | task running | tasks available | |
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| ---- | ------------ | --------------- | --- |
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| 0 | 1 | 1, 2, 3, 4 | |
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| 10 | 2 | 2, 3, 4 | |
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| 20 | 2 | 2, 3, 4 | |
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| 30 | 3 | 3, 4 | |
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| 40 | 3 | 3, 4 | |
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| 50 | 1 | 1, 3, 4 | |
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| 60 | 3 | 3, 4 | |
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| 70 | 4 | 4 | |
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| 80 | 4 | 4 | |
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| 90 | 4 | 4 | |
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| 100 | 1 | 1, 2, 4 | |
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| 110 | 2 | 2, 4 | |
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| 120 | 2 | 2, 4 | |
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| 130 | 4 | 4 | |
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| 140 | | | |
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| 150 | 1 | 1, 3 | |
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| 160 | 3 | 3 | |
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| 170 | 3 | 3 | |
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| 180 | 3 | 3 | |
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| 190 | | | |
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| 200 | 1 | 1, 2, 4 | |
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| 210 | 2 | 2, 4 | |
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| 220 | 2 | 2, 4 | |
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| 230 | 4 | 4 | |
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| 240 | 4 | 4 | |
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| 250 | 1 | 1, 4 | |
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| 260 | 4 | 4 | |
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| 270 | 4 | 4 | |
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| 280 | | | |
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| 290 | | | |
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| 300 | 1 | 1, 3 | |
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