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c-user/rate_monotonic_manager.rst: Use Latex math for utilization formulas

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Joel Sherrill 2017-03-10 15:26:35 -06:00
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c-user/rate_monotonic_manager.rst
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@ -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