[PATCH 3/3] c-user/rate_monotonic_manager.rst: Use Latex math for utilization formulas
Joel Sherrill
joel at rtems.org
Thu Mar 23 15:56:17 UTC 2017
---
c-user/rate_monotonic_manager.rst | 17 ++++++++---------
1 file 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
--
1.8.3.1
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