Response Times Reconstructor Based on Mathematical Expectation Quotient for a High Priority Task over RT-Linux

Every computer task generates response times depending on the computer hardware and software. The response times of tasks executed in real-time operating systems such as RT-Linux can vary as their instances evolve even though they always execute the same algorithm. This variation decreases as the priority of the tasks increases; however, the minimum and maximum response times are still present in the same task, and this complicates its monitoring, decreasing its level of predictability in case of contingency or overload, as well as making resource sizing difficult. Therefore, the need arises to propose a model capable of reconstructing the dynamics of response times for the instances of a task with high priority in order to analyze their offline behavior under specific working conditions. For this purpose, we develop the necessary theory to build the response time reconstruction model. Then, to test the proposed model, we set up a workbench consisting of a single board computer, PREEMPT_RT, and a high priority task generated by the execution of a matrix inversion algorithm. This work demonstrates the application of the theory in an experimental process, presenting a way to model and reconstruct the dynamics of response times by a high-priority task on RT-Linux.