1 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Embedded Systems Exercise 2: Scheduling Real-Time Aperiodic Tasks Alexander Maxiaguine 4. May 2005

2 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Definitions: RT Tasks T t Arrival Time Execution Time t Response Time Deadline Lateness

3 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Overview Scheduling aperiodic tasks with real-time constraints Some known algorithms:

4 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Earliest Due Date (EDD) Optimization goal: –minimize the maximum lateness Assumptions on the task set: –independent tasks –synchronous arrival times EDD is non preemptive

5 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Earliest Due Date (EDD) T1 t T2 t T3 t t Jackson’s rule: execute tasks in order of non decreasing deadlines T2 T1 T3

6 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Earliest Deadline First (EDF) Optimization goal: –minimize the maximum lateness Assumptions on the task set: –independent tasks –arbitrary arrival times (dynamic arrivals) EDF is preemptive

7 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Earliest Deadline First (EDF) T1 t T2 t T3 t t Horn’s rule: at any instant execute the task with the earliest absolute deadline T2 T1 T3 T1

8 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Latest Deadline First (LDF) Optimization goal: –minimize the maximum lateness Assumptions on the task set: –tasks with precedence relations –synchronous arrival times LDF is non preemptive

9 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Latest Deadline First (LDF) Main Idea [Lawler]: build the scheduling queue, at run time execute tasks from that queue Building the scheduling queue: –proceed from tail to head –among the tasks without successors or whose successors have been all scheduled, select the task with the latest deadline to be scheduled last –repeat the procedure until all tasks in the set are selected T2 T3T1

10 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Latest Deadline First (LDF) Building the scheduling queue (example): A B C D E ABCDE didi deadlinesDAG Scheduling Queue: A E D C B runt-time scheduler

11 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Ealiest Deadline First (EDF*) Optimization goal: –minimize the maximum lateness Assumptions on the task set: –tasks with precedence relations –arbitrary arrival times EDF* is preemptive

12 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Earliest Deadline First (EDF*) Main idea: modify deadlines and arrival times to satisfy the precedence constraints and then use EDF T2 T3T1 Modifying deadlines: Task must finish the execution within its deadline Task must not finish the execution later than the maximum start time of its successor T1 t T2 t T3 t

13 Swiss Federal Institute of Technology Computer Engineering and Networks Laboratory Earliest Deadline First (EDF*) Main idea: modify deadlines and arrival times to satisfy the precedence constraints and then use EDF T2 T3T1 Modifying arrival times: Task must start the execution not earlier than its release time. Task must not start the execution earlier than the minimum finishing time of its predecessors. T1 t T2 t t T3