1. Embedded Systems Exercise 3: Scheduling Real-Time Periodic and Mixed Task Sets
18. May 2005
Alexander Maxiaguine

2. Definitions: RT Periodic Tasks
Arrival Time
Deadline, Di t
Period, Ti
Execution Time, Ci

3. Some Assumptions Tasks are independent
All instances of a periodic task have
same worst-case execution time, Ci
same relative deadline Di<Ti (often Di= Ti)
… see lecture notes for the full list of assumptions

4. Scheduling Problems and Algorithms
Criteria:
Di= Ti vs. Di<Ti
static vs. dynamic priority
preemptive
scheduling
Algorithms for mixed task sets:
Polling Server (static priority)
Total Bandwidth Server (dynamic priority)

5. Rate Monotonic (RM) t t t t Static priority assignment rule:
Assumption:
Di= Ti
Rate Monotonic (RM)
Static priority assignment rule:
Tasks with shorter period get higher priority
High
Low t T1 t T2 t T3 t

6. Deadline Monotonic (DM)
Assumption:
Di< Ti
Deadline Monotonic (DM)
Static priority assignment rule:
Tasks with smaller relative deadline get higher priority
High
Low t T2 t T3 t T1 t

7. Deadline Monotonic (DM)
Static priority assignment rule:
Tasks with smaller relative deadline get higher priority
High
Low t T2 t T3 t T1 t

8. Scheduling Mixed Task Sets
How should aperiodic requests be scheduled?
Solutions:
Polling Server (RM)
Total Bandwidth Server (EDF)

9. RM - Polling Server Basic idea:
Ts determines
priority of
aperiodic tasks
RM - Polling Server
Basic idea:
Introduce an artificial periodic task --- the server for aperiodic requests

10. EDF – Total Bandwidth Server
Basic idea: Dynamically assign deadlines to aperiodic tasks such that the server utilization factor Us (bandwidth) is never exceeded t

11. Schedulability Conditions
Dynamic Priority
EDF (Di= Ti)
TB Server
Static Priority
RM (Di= Ti) DM
Polling Server
sufficient
necessary
& sufficient

12. Necessary and Sufficient Test
Basic Idea:
assume all tasks arrive at the same time (critical instant)
for each task compute the worst-case interference from all higher priority tasks
for each task check
if true for all tasks  the task set is schedulable
Worst-case response time: