1. Deterministic Scheduling
Aperiodic Scheduling
Earliest Deadline Due,
Earliest Deadline First,
Latest Deadline First,
Spring Algorithm
Periodic Scheduling
References: Shaw – Chap 6
Buttazo – Chap 3 & 4

2. Introduction Priority & Round Robin Periodic Scheduling (Feasible Solution)
Example 1:

3. More Round Robin Periodic Scheduling (Non-feasible Solution)
Example 2:

4. APERIODIC TASK SCHEDULING
Notation:

5. Earliest Due Date (EDD) - Jackson’s Rule
Set of tasks:
Problem:
Algorithm:

6. Earliest Due Date (EDD) - Jackson’s Rule

7. Earliest Due Date (EDD) – Example 1

8. Earliest Due Date (EDD) – Example 2

9. Earliest Due Date (EDD) – Guaranteed Feasibility
Order tasks by increasing deadlines. Then:

10. Earliest Deadline First (EDF) – Horn’s Algorithm

11. Earliest Deadline First (EDF) – Example

12. Earliest Deadline First (EDF) – Guarantee of Schedualability
Dynamic Scheduling:
Assume Schedulable
Need to Guarantee that
Assuming all tasks are ordered by increasing deadlines:
Worst case finishing time:
For Guaranteed Schedulability:

13. EDF - Non-Preemptive Scheduling
The scheduling problem for non-preemptive EDF is NP hard

14. Non-Acyclic Search Tree Scheduling

15. Bratley’s Algorithm

16. Scheduling with Precedence Constraints Latest Deadline First (or last
Scheduling with Precedence Constraints Latest Deadline First (or last?)- Optimizes max Lateness

17. Latest Deadline First

18. EDF with Precedence Constraints
The problem of scheduling a set of n tasks with precedent constraints and dynamic activations can be solved if the tasks are preemptable.
The basic ideas is transform a set of dependent tasks into a set of independent tasks by adequate modification of timing parameters. Then, tasks are scheduled by the Earliest Deadline First (EDF) algorithm, iff is schedulable. Basically, all release times and deadlines are modified so that each task cannot start before its predecessors and cannot preempt their successors.

19. EDF with Precedence Constraints
Modifying the release time:

20. EDF with Precedence Constraints
Modifying the Deadlines:

21. Example

22. Jack Stankovic’s Spring Algorithm very powerful and actually has been applied in Jack’s real-time operating system
This does not yield an optimal schedule, but the general problem is NP hard. This does lend itself to artificial intelligence and learning. We are interested here in the concept, rather in any implementation.
The objective is to find a feasible schedule when tasks are have different types of constraints, such as
precedence relations,
resource constraints,
arbitrary arrivals,
non-preemptive properties, and
importance levels.
A heuristic function H is used to drive the scheduling toward a plausible path.
At each level of the search, function H is applied to each of the remaining tasks. The task with the smallest value determined by the heuristic function H is selected to extend the current schedule. If a schedule is not looking strongly feasible, a minimal amount of backtracking is used.

23. Jack Stankovic’s Spring Algorithm
Precedence constraints can be handled by adding a term E =1 if the task is eligible and E = infinity if it is not.

24. Jack Stankovic’s Spring Algorithm

25. Summary

26. Homework #3 (due 5/3/07) : Lecture 4/241) 2) 3)