Evaluation of the probability of dynamic failure and processor utilization for real-time systems

It is shown how to determine closed-form expressions for task scheduling delay and active task time distributions for any real-time system application, given a scheduling policy and task execution time distributions. The active task time denotes the total time a task is executing or waiting to be executed, including scheduling delays and resource contention delays. The distributions are used to determine the probability of dynamic failure and processor utilization, where the probability of dynamic failure is the probability that any task will not complete before its deadline. The opposing effects of decreasing the probability of dynamic failure and increasing utilization are also addressed. The analysis first addresses workloads where all tasks are periodic, i.e., they are repetitively triggered at constant frequencies. It is then extended to include the arrival of asynchronously triggered tasks. The effects of asynchronous tasks on the probability of dynamic failure and utilization are addressed