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author | Joel Sherrill <joel@rtems.org> | 2017-03-10 15:26:35 -0600 |
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committer | Joel Sherrill <joel@rtems.org> | 2017-04-25 12:33:18 -0500 |
commit | c8b674582502994299a3a47ad0962c6d46986f36 (patch) | |
tree | 4c7ad6ee613c7f595aee2127016cb315f89dfb4a | |
parent | POSIX Users: Add posix_devctl() (diff) | |
download | rtems-docs-c8b674582502994299a3a47ad0962c6d46986f36.tar.bz2 |
c-user/rate_monotonic_manager.rst: Use Latex math for utilization formulas
Diffstat (limited to '')
-rw-r--r-- | c-user/rate_monotonic_manager.rst | 17 |
1 files changed, 8 insertions, 9 deletions
diff --git a/c-user/rate_monotonic_manager.rst b/c-user/rate_monotonic_manager.rst index 05eb59f..96539ed 100644 --- a/c-user/rate_monotonic_manager.rst +++ b/c-user/rate_monotonic_manager.rst @@ -266,22 +266,21 @@ Processor Utilization Rule .. index:: RMS Processor Utilization Rule The Processor Utilization Rule requires that processor utilization be -calculated based upon the period and execution time of each task. The fraction -of processor time spent executing task index is ``Time(index) / -Period(index)``. The processor utilization can be calculated as follows: +calculated based upon the period and execution time of each task. +The fraction of processor time spent executing task index is ``Time(i) +/ Period(i)``. The processor utilization can be calculated as follows +where n is the number of tasks in the set being analyzed: -.. code-block:: c +.. math:: - Utilization = 0 - for index = 1 to maximum_tasks - Utilization = Utilization + (Time(index)/Period(index)) + Utilization = \sum_{i=1}^{n} Time_i/Period_i To ensure schedulability even under transient overload, the processor utilization must adhere to the following rule: -.. code-block:: c +.. math:: - Utilization = maximum_tasks * (2**(1/maximum_tasks) - 1) + maximumUtilization = n * (2^{\frac{1}{n}} - 1) As the number of tasks increases, the above formula approaches ln(2) for a worst-case utilization factor of approximately 0.693. Many tasks sets can be |