RESOURCE ACCESS PROTOCOLS - Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications - page 216

normal execution
critical section

direct blocking
push-through blocking

τ 1

τ 2

τ 3

t 0 t 1 t 2 t 3 t 4 t 5 t 6 t 7

p 3

P 1
P 2
P 3

Figure 7.8 Example of Priority Inheritance Protocol.

From this example, we notice that a high-priority task can experience two kinds of
blocking:

Direct blocking . It occurs when a higher-priority task tries to acquire a resource
already held by a lower-priority task. Direct blocking is necessary to ensure the
consistency of the shared resources.
Push-through blocking . It occurs when a medium-priority task is blocked by a
low-priority task that has inherited a higher priority from a task it directly blocks.
Push-through blocking is necessary to avoid unbounded priority inversion.

Note that in most situations when a task exits a critical section, it resumes the priority
it had when it entered. This, however, is not always true. Consider the example
illustrated in Figure 7.9. Here, task τ 1 uses a resource R a guarded by a semaphore
S a , task τ 2 uses a resource R b guarded by a semaphore S b , and task τ 3 uses both
resources in a nested fashion ( S a is locked first). At time t 1 , τ 2 preempts τ 3 within its
nested critical section; hence, at time t 2 , when τ 2 attempts to lock S b , τ 3 inherits its
priority, P 2 . Similarly, at time t 3 , τ 1 preempts τ 3 within the same critical section, and
at time t 4 , when τ 1 attempts to lock S a , τ 3 inherits the priority P 1 . At time t 5 , when τ 3
unlocks semaphore S b , task τ 2 is awakened but τ 1 is still blocked; hence, τ 3 continues
its execution at the priority of τ 1 . At time t 6 , τ 3

unlocks S a and, since no other tasks

are blocked, τ 3 resumes its original priority P 3 .