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+#### 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            |     |