Response-time analysis

For arbitrarily fixed priorities, including RM, DM and others, the Response Time Analysis is an exact test (i.e., a necessary and sufficient condition) in the following conditions:

• full preemption, synchronous release, independent tasks and D ≤ T.

Worst-case response time (WCRT, Rwc, R,...) = maximum time interval between arrival and finish instants.

• 

Schedulability test based on the WCRT

<=> task set is schedulable.

The WCRT of a given task occurs when the task is activated at the same time as all other high-priority tasks (critical instant).

Ii – interference caused by the execution of higher priority tasks.

Computing Rwci

The equation is solved iteratively. Stop conditions are:

• A deadline is violated.

  • Rwci(m) > Di

• Convergence (two successive iterations yield the same result).

  • Rwc i (m + 1) = Rwc i (m)

Algorithm

Repeat Step 3 until convergence or deadline violation

Example

Restrictions to the schedulability tests previously presented

The previous schedulability tests must be modified in the following cases:

• Non-preemption.

• Tasks not independent.

  • Share mutually exclusive resources.

  • Have precedence constrains.

• It is also necessary to take into account the overhead of the kernel, because the scheduler, dispatcher and interrupts consume CPU time.

Impact of non-preemption