From c8b674582502994299a3a47ad0962c6d46986f36 Mon Sep 17 00:00:00 2001 From: Joel Sherrill Date: Fri, 10 Mar 2017 15:26:35 -0600 Subject: c-user/rate_monotonic_manager.rst: Use Latex math for utilization formulas --- c-user/rate_monotonic_manager.rst | 17 ++++++++--------- 1 file changed, 8 insertions(+), 9 deletions(-) (limited to 'c-user') 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 -- cgit v1.2.3