Modifying Theorem 2

1
Modifying Theorem 2
Theorem 4 (The synchronous completion time
theorem)
In the above theorem, a task ?i will meet its
completion deadline Di if it satisfies the shown
relation.
2
One Final Example(Taken from Software
Engineering Fundamentals by A. Behforooz)

• Consider the following 3 dependent and periodic
  tasks
• Task 1 C30 T100 D100 E0 B0
• Task 2 C70 T200 D200 E0 B30
• Task 3 C30 T200 D150 E50 B6
• Using theorem 3 ?1 30/100 0.3 ? schedulable
• ?1,?2 (30/100)(7030)/200 0.8 ? schedulable
• ?1,?2,?3 (30/100)(70/200)(30506)/200 1.08
  ? NOT schedulable
• Using theorem 4 W3(t)t03070306 136 ms
• N1,1 1?(136-100)/100? 2
• ? t1 136(2-1)30 166 ms (beyond ?3 deadline)
• Changing task priority from (1-2-3) to (1-3-2)
  results in
• W3(t)t030307030 166 ms

3
Priority Inversion

• Meaning A lower priority task executing before
  one with a higher priority

4
Timeline of previous slide
5
Expanded Portion of Previous Timeline
6
Modified and Augmented Portion from Previous Slide
?1 queued
?1 queued
7
A Solution to Priority Inversion

• Use of Priority Ceiling Protocol (PCP) which is
  made up of 3 rules
• Pre-emption rule
• Regular priority pre-emption
• Inheritance rule
• If a lower priority task blocks a higher
  priority one, the lower inherits the priority of
  the higher priority task
• Priority ceiling rule
• A task cannot get at a shared resource if its
  priority is less than any of the ceilings of the
  shared resources currently locked by other tasks

8
Bad PCP usage Example
Assume tasks A, B, C, and D have priorities as A
highest and D lowest. The tasks use 2 server
tasks as follows S1 used by A and C S2 used by
tasks B and D.
9
McCabes R-T System Analysis

• Uses a modified interpretation of standard DFDs
• Transform ? Markov process state (a probabilistic
  queuing model)
• Data flow ? Transitions
• Therefore the following reasoning may be
  applied
• 0 lt pij 1.0
• (p transitional probability)
• True for each flow path

10
Example of McCabes R-T System Analysis

• Due to the lengthiness of this example it was
  thought better to hand it out as an MS-Word97
  document. Therefore, it is available online and
  in hard-copy form separately. Please refer to it
  while it is explained during lecture sessions.