A Comparison Between Discrete And Continuous Emission Distributions In Hidden Markov Models Of Execution Times.

Tasks performed by real-time systems must be executed within precise deadlines. A deadline breachcan have disastrous effects, therefore time predictability is crucial in real-time systems. Thus, it isimportant that real-time systems guarantee the results are obtained within the time restrictions inaddition to being logically valid. The hidden Markov model is a method used to model probability distribution over a series of ob-servations where these observations are probabilistically dependent and the state of the system is hidden. In light of these perspectives, the hidden states will likely follow a sequence corresponding to the observed computation times. PROSITool and MarkovChainET are software tools for proba-bilistic modeling of execution times of real-time applications. For systems whose behavior needs tobe predicted, comparing these two approaches can be beneficial. PROSITool framework uses discrete emission distributions meanwhile MarkovChainET is a framework that uses continuous emissiondistributions. There has been no direct comparison between continuous and discrete emission distributions ofHMM of execution times, or how parameters defined for the generation of these execution timesinfluence them. Thus, this work provides a comparison of the two software tools mentioned. The estimation has been made for a limited number of observations based on the parameters given. Ob-servations made for the computation times have been classified into states by the two approaches.We are able to determine whether the state change event is independent or not by analyzing thecomputation time required by the previous execution. An independent state is one without direct impact on the other. We run some tests to check the ability of the discrete and continuous emis-sion distributions to classify these observations into independent states based on execution timelogs collected from three different Markov Models. The following significant finding was reached:Based on the tests made, the results have shown that for the continuous framework, the percentage of independent states is significantly higher than for the discrete framework. As a more robust framework, the continuous framework appears to be a better choice for adaptive approaches