Identification and Validation of Markov Models with Continuous Emission Distributions for Execution Times

It has been shown that in some robotic applications, where the execution times cannot be assumed to be independent and identically distributed, a Markov Chain with discrete emission distributions can be an appropriate model. In this paper we investigate whether execution times can be modeled as a Markov Chain with continuous Gaussian emission distributions. The main advantage of this approach is that the concept of distance is naturally incorporated. We propose a framework based on Hidden Markov Model (HMM) methods that 1) identifies the number of states in the Markov Model from observations and fits the Markov Model to observations, and 2) validates the proposed model with respect to observations. Specifically, we apply a tree-based cross-validation approach to automatically find a suitable number of states in the Markov model. The estimated models are validated against observations, using a data consistency approach based on log likelihood distributions under the proposed model. The framework is evaluated using two test cases executed on a Raspberry Pi Model 3B+ single-board computer running Arch Linux ARM patched with PREEMPT_RT. The first is a simple test program where execution times intentionally vary according to a Markov model, and the second is a video decompression using the ffmpeg program. The results show that in these cases the framework identifies Markov Chains with Gaussian emission distributions that are valid models with respect to the observations.