Assumptions for scheduling algorithms
Classic literature solves the problem for this situation:
Tasks are periodic
Deadline == next release time
The scheduler is preemptive
Scheduling decisions have not cost
Then, for simplicity of representation:
All times are multiples of a timer tick
Everything is simple and linear
There are mathematical demonstrations for all schedulers
Simplifications can be lifted later
And math becomes more complex
There are a number of interesting schedulers
All of them are mathematically demonstrated