Creating a schedule for an example task set with non-preemptive Deadline Monotonic (fixed priority) scheduling

Question

In the effort of trying to understand a fixed priority scheduling scheme, such as Deadline Monotonic schedulers, amidst the horribly written definitions online -- I'm trying to schedule an example task set with that policy, in which I require that the execution of tasks is non-preemptive. This means that I have the following assumptions:

1. When a task begins executing, it cannot be stopped by any other task, so the former must finish
2. The tasks in the task set are released periodically (according to period Ti)
3. All tasks are first released at time t=0
4. Each task task_i has a fixed computation time Ci
5. Each task task_i has a relative deadline Di, which is relative to the time in which the task came in (was released)

Assume I have this task set:

• Task 1: C1 = 1, D1 = 2, T1 = 3
• Task 2: C2 = 1, D2 = 5, T2 = 5
• Task 3: C3 = 2, D3 = 5, T3 = 5

According to the exact schedulability test based on worst case response time analysis from Theorem 15 by George et al., the task set is in fact schedulable.

To create the schedule for a supposed interval of time [0, 10], this means that:

• Task 1 becomes available at the instances: 0, 3, 6, 9
• Task 2 becomes available at the instances: 0, 5, 10
• Task 3 becomes available at the instances: 0, 5, 10

With deadline monotonic scheduling, we already know that task_1 >= task_2 >= task_3 according to priority, since the deadline of task_1 <= that of task_2 <= that of task_3.

I will first try to formulate the schedule for each discrete interval, and then ask a follow-up question on the problematic interval:

# interval  ->  executing task
[0, 1] -> task_1
[1, 2] -> task_2
[2, 3] -> task_3
[3, 4] -> task_3
[4, 5] -> task_1
[5, 6] -> task_2
[6, 7] -> I THINK, task_1

So at instance t=6, two tasks are ready: task_1 and task_3. Is it correct that task_1 should get the priority and execute between instances 6 and 7 -- or should task_3 execute since we always do: task_1 then task_2 then task_3?

If it is the case that the higher priority task would execute, then wouldn't this imply that we HAVE to re-sort a queue of pending tasks every time a new task arrives?

If so, doesn't that defy the purpose and then a fixed priority scheduler would actually be dynamic in nature?