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