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authorJoel Sherrill <joel@rtems.org>2017-03-10 15:26:35 -0600
committerJoel Sherrill <joel@rtems.org>2017-04-25 12:33:18 -0500
commitc8b674582502994299a3a47ad0962c6d46986f36 (patch)
tree4c7ad6ee613c7f595aee2127016cb315f89dfb4a /c-user
parentPOSIX Users: Add posix_devctl() (diff)
downloadrtems-docs-c8b674582502994299a3a47ad0962c6d46986f36.tar.bz2
c-user/rate_monotonic_manager.rst: Use Latex math for utilization formulas
Diffstat (limited to 'c-user')
-rw-r--r--c-user/rate_monotonic_manager.rst17
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