1. Real-Time Scheduling David Ferry CSCI 3500 – Operating Systems
Saint Louis University St. Louis, MO 63103

2. Real-Time Problem Domain
“Real-time is not real fast” Some problems require high predictability and reliability, e.g. sense-compute-actuate loop at Hz
Cyber
Physical
Gather Sensor Data
Sensors
Compute Response
Actuators
Send Actuator Commands
CSCI Operating Systems

3. CSCI 3500 - Operating Systems
Real-Time Task Model
Multiple tasks, each with:
Periodic rate, T
Worst-case execution time, C
Deadline relative to release time, D
Note: There is no advantage to completing a job early!
Task
Period, T
WCET, C
Deadline, D A 3 1 B 5 1 3 5 8 13 B 6 4 2 10 A 7 9 11 12 14 15
CSCI Operating Systems

4. Rate Monotonic (RM) Algorithm
Preemptive Rate Monotonic – The task with the shortest period always executes as highest priority. B A A B B A B B A B B A B B A B 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
CSCI Operating Systems

5. Earliest Deadline First (EDF)
Preemptive Earliest Deadline First – The task with the next deadline always executes as highest priority. B A A B B B A B A B B A B B B A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
CSCI Operating Systems

6. Earliest Deadline First (EDF)
Preemptive Earliest Deadline First – The task with the next deadline always executes as highest priority. B A
EDF A B B B A B A B B A B B B A RM A B B A B B A B B A B B A B
CSCI Operating Systems

7. Real-Time Scheduling Problem
Given a set of tasks, does a particular scheduling algorithm guarantee they will all get enough time to complete by their deadline, and how do we prove it? Here we can prove that RM and EDF work for this particular task set with an appeal to the hyperperiod... Is there a better way? What if hyperperiod was large?
Restart
EDF A B B B A B A B B A B B B A RM A B B A B B A B B A B B A B 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
CSCI Operating Systems

8. CSCI 3500 - Operating Systems
Schedulablity Tests
RM and EDF are common names because they have rigorously proven schedulability tests that make it easy to decide whether they can schedule a task set or not. These are usually sufficient but not necessary. If a task set meets the criteria then we know it can be scheduled, but if it doesn’t meet the criteria we don’t know that it can’t be scheduled. For RM and EDF these tests are utilization bounds.
CSCI Operating Systems

9. CSCI 3500 - Operating Systems
Utilization
The utilization of a task is it’s execution requirement divided by its period. I.e. Ui = Ci / Ti so for example: The utilization of a task set is the sum all utilizations in the task set.
Task
Period, T
WCET, C
Deadline, D
Utilization A 3 1
0.333 B 5
0.6
CSCI Operating Systems

10. RM & EDF Utilization Bounds
Liu and Layland (1973) proved that a set of n tasks is schedulable under RM if: U = ∑ Ci / Ti ≤ n(21/n – 1) Or for large n: U ≤ 0.69 Xu and Parnas (1990) proved a set of tasks is schedulable under EDF if: U = ∑ Ci / Ti ≤ 1
CSCI Operating Systems

11. Sufficiency vs. Necesscity
Schedulability tests are only sufficient, not necessary: E.g.: Utilization of this task set is Schedulability bound from last slide for n=2: U ≤ n(21/n – 1) = 2*(√2 - ) = 0.83
Task
Period, T
WCET, C
Deadline, D
Utilization A 3 1
0.333 B 5
0.6 A B RM
CSCI Operating Systems