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Modifying Theorem 2

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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 ... – PowerPoint PPT presentation

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Title: 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.
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