Verification of Calculations of Non-Homogeneous Markov Chains Using Monte Carlo Simulation
Autoři
Rok
2022
Publikováno
Proceedings of the 2022 25th Euromicro Conference on Digital System Design. Los Alamitos: IEEE Computer Society, 2022. p. 689-695. ISBN 978-1-6654-7404-7.
Typ
Stať ve sborníku
Pracoviště
Anotace
Dependability models allow calculating the rate of
events leading to a hazard state – a situation, where the safety of
the modeled dependable system is violated, thus the system may
cause material loss, serious injuries, or casualties. The calculation
of the hazard rate of the complex non-homogeneous Markov
chains is time-consuming and the accuracy of the results is
questionable. We have presented two methods able to calculate
the hazard rate of the complex non-homogeneous Markov chains
in previous papers. Both methods achieved very accurate results,
thus we compare four Monte-Carlo based simulation methods
(both accuracy and time-consumption) with our methods in
this paper. A simple Triple Modular Redundancy (TMR) model
is used in this paper since its hazard rate can be calculated
analytically.
Non-Homogeneous Continuous Time Markov Chains Calculations
Autoři
Rok
2020
Publikováno
Proceedings of the 23rd Euromicro Conference on Digital Systems Design. Los Alamitos, CA: IEEE Computer Soc., 2020. p. 664-671. ISBN 978-1-7281-9535-3.
Typ
Stať ve sborníku
Pracoviště
Anotace
Dependability models allow calculating the rate of events leading to a hazard state - a situation, where safety of the modeled dependable system is violated, thus the system may cause material loss, serious injuries or casualties. This paper shows a method of calculating the hazard rate of the non-homogeneous Markov chains using different sets of homogeneous differential equations 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 previous version based on probability matrices and used to calculate the hazard rate of the hierarchical Markov chain. The hierarchical Markov chain allows us to calculate the hazard rates of the blocks independently and the non-homogeneous approach allows us to use them to calculate the hazard rate of the whole system. This method will allow us to calculate the hazard rate of the non-homogeneous Markov chain very accurately compared to methods based on homogeneous Markov chains.
Non-homogeneous hierarchical Continuous Time Markov Chains
Autoři
Rok
2020
Publikováno
Microprocessors and Microsystems. 2020, 2020(78), ISSN 0141-9331.
Typ
Článek
Pracoviště
Anotace
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.
Accurate Inexact Calculations of Non-Homogeneous Markov Chains
Autoři
Rok
2019
Publikováno
Proceedings of the 22nd Euromicro Conference on Digital Systems Design. Los Alamitos, CA: IEEE Computer Soc., 2019. p. 470-477. ISBN 978-1-7281-2861-0.
Typ
Stať ve sborníku
Pracoviště
Anotace
Dependability models allow calculating the rate of events leading to a hazard state - a situation, where safety of the modeled dependable system is violated, thus the system may cause material loss, serious injuries or casualties. Hierarchical dependability models allow expressing multiple redundancies made at multiple levels of a system consisting of multiple cooperating blocks. The hazard rates of the blocks are calculated independently and, when combined, they are used 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. The 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. This method will allow us to calculate the hazard rate of the non-homogeneous Markov chain very accurately compared to methods based on homogeneous Markov chains.
Hierarchical Dependability Models based on Non-Homogeneous Continuous Time Markov Chains
Autoři
Rok
2019
Publikováno
2019 14th International Conference on Design & Technology of Integrated Systems In Nanoscale Era (DTIS). IEEE, 2019. ISBN 978-1-7281-3424-6.
Typ
Stať ve sborníku
Pracoviště
Anotace
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. The proposed method is applied on hierarchical dependability models allowing independent calculations of the hazard rates of multiple cooperating blocks of the system. The independent calculations are significantly faster than the calculation of a single model composed of all models of the blocks and the proposed method is very accurate compared to methods based on homogeneous Markov chains.