1. Priority Inheritance and Priority Ceiling Protocols
L. Sha, R. Rajkumar, and J. P. Lehoczky, "Priority Inheritance Protocols: An Approach to Real-Time Synchronization", IEEE Transactions on Computers, Vol. 39, No. 9, Sept

2. Priority Inversion
A high priority task is blocked due to a low priority task
How can it happen?
Mutex for shared resource access
Non-preemptive subsystem access
Network
System bus
Secondary storage

3. Mutual Exclusion via Semaphores
Ensure only one task/process is in the critical section
wait(S) to get access to semaphore S
signal(S) to release S
Example: producer consumer
Producer() { .
wait(S)
critical section /* create data & increment pointer */
signal(S) }

4. Priority Inversion
Source of the figure: Chenyang Lu, Washington University Saint Louis

5. Unbounded Priority Inversion

6. What really happened on Mars?
Repeated resets in the Mars Pathfinder
The Mars Pathfinder mission was widely proclaimed as "flawless" in the early days after its July 4th, 1997 landing on the Martian surface.... But a few days into the mission, not long after Pathfinder started gathering meteorological data, the spacecraft began experiencing total system resets, each resulting in losses of data. The press reported these failures in terms such as "software glitches" and "the computer was trying to do too many things at once"....
For a full story, visit

7. Pathfinder Incident
Classical priority inversion problem due to shared system bus!
Source of the figure: Damir Isovic, Malardaren University, Sweden

8. Priority Inheritance
Inherit the priority of the blocked high priority task

9. Priority Inheritance Protocol (PIP)
If TL blocks a higher proirity task TH, priority(TL) ← priority(TH)
When TL releases a semaphore:
Return to its normal priority if it doesn’t block any task
Otherwise, set priority(PL) ← highest priority of the tasks blocking on a semaphore held by TL
Transitive
T1 blocked by T2: priority(T2) ← priority(T1)
T2 blocked by T3: priority(T3) ← priority(T1)

10. Chained Blocking: Problem of PIP
In the worst case, the highest priority task T1 can be blocked by N lower
priority tasks in the system when T1 has to access N semaphores to finish
the execution!
Source of the figure: Damir Isovic, Malardaren University, Sweden

11. Response Time Analysis of RMS with PIP
For RMS schedulability test, ensure that:
∑ i=1, N (Ci/Ti + Bi/Ti) ≤ n(21/n - 1) , 1 ≤ i ≤ n
Bi is the the longest priority inversion time that could be experienced by Ti
Bi= CSi + CSi CSk where CSi, CSi+1, ..., CSk are the critical sections by which lower priority tasks could block Ti
Sufficient but not necessary because the priority due to contention for CS may not happen in reality

12. Priority Ceiling Protocol (PCP)
Avoid chained blocking
Guarantee a task is blocked by at most one lower priority task
No deadlock
Assumptions
Each task is associated with a fixed priority

13. PCP Each semaphore has the fixed priority ceiling How it works:
ceiling(S) = highest priority among all the tasks that will request S
How it works:
Ti can access a semaphore S if
S is not already allocated to any other task; and
Priority of Ti is higher than the current processor ceiling = max(priority ceilings of all the semaphores allocated to tasks other than Ti)

14. PCP No chained blocking! Ceiling(S1) = 1 (high)
Ceiling(S2) = 2 (medium)
Ceiling(S3) = 2 (medium)
No chained blocking!
Source of the figure: Damir Isovic, Malardaren University, Sweden

15. Schedulability of RMS with PCP
Consider blocking time:
∑ i=1, N (Ci/Ti + Bi/Ti) ≤ n(21/n - 1) , 1 ≤ i ≤ n
Bi = max(CSi, CSi+1, ..., CSk) where CSi, CSi+1, ..., CSk are the critical sections that can block Ti

16. Scheduling Aperiodic + Periodic Tasks

17. Task Arrival Patterns Periodic Sporadic Aperiodic
Aperiodic but minimum interarrival time is known
Worst case
Every sporadic job always arrives at its minimum interarrival time
Treat as periodic tasks
Utilization bound or response time analysis
If schedulable for the worst case, schedulable for all the other cases
Aperiodic
No limitations on interarrival times
Scheduling algorithms we have seen so far do not apply

18. Aperiodic Deadlines Soft: Not much to do in terms of scheduling Firm
Deadline & WCET are given
Start a firm deadline task only if it will finish by the deadline
Let’s discuss several hybrid scheduling algorithms that use RMS for periodic task scheduling
Several approaches to scheduling aperiodic tasks

19. Background Scheduling
Schedule periodic tasks first
Schedule aperiodic tasks only if there’s no periodic task
Periodic tasks
RMS
CPU
High priority queue
Aperiodic tasks
FCFS, EDF, etc.
Low priority queue

20. Background Scheduling with RMS
Task set: T1(2, 6), T2(4,10) where Ti=(Ci, Pi)
Schedulable since 2/6 + 4/10 = 0.73 < 2(21/2-1) = 0.82 T1
T1,1
T1,2
Idle
Schedule aperiodic tasks here 2 4 6
T2,1 T2 2 4 6 8 10

21. Polling Server Use a periodic task to serve aperiodic tasks Algorithm
Period: Ps
Capacity: Cs
Algorithm
Release the server at every period Ps
Serve any pending aperiodic task
Suspend itself, i.e., capacity = 0, if
It consumed Cs; or
There no pending aperiodic request
Replenish capacity, i.e., capacity = Cs, at the next period

22. Schedulability of Polling Server
Aperiodic tasks have no impact on periodic ones
There can be multiple servers
n periodic tasks & m polling servers are schedulable if Up + Us ≤ U(m+n)
Problem: If an aperiodic request arrives right after the server period, it has to wait until the next period → Long response time
Response time of an aperiodic request with execution time Ca is Ps + Ca/Cs Ps

23. Deferrable Server (DS)
Preserve the unused capacity until the end of the current period
Reduce response time to aperiodic requests
DS affects the schedulability of periodic tasks
DS schedulability ≠ RM

24. Priority Exchange Server
Server has the highest priority at the beginning
If there’s no aperiodic request to serve right now, preserve capacity for lower priority task’s execution time
Replenish the capacity at the next period

25. Optimal? No optimal algorithm exists to minimize the response time!
Other servers with RMS
Sporadic server: Replinish capacity only after aperiodic request execution
Slack stealing: No periodic server, but slack stealer tries to steal time from periodic tasks