Non-homogeneous hierarchical Continuous Time Markov Chains

This paper shows a method of calculating the hazard rate of the non-homogeneous Markov chains using different homogeneous probability matrices for several hundreds small time intervals (using default parameters settings — the number of the intervals can be adjusted to balance accuracy/time-consumption ratio). The method is compared to a pessimistic method based on homogeneous Markov chains and used to calculate the hazard rate of the hierarchical Markov chain. The hazard rates of the blocks are calculated independently and the non-homogeneous approach allows us to use them to calculate the hazard rate of the whole system. The independent calculations are significantly faster than the calculation of a single model composed of all models of the blocks.