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Selecting Mathematical Software for Dependability Assessment of Computer Systems Described by Stiff Markov Chains

Kharchenko, V. S., Odarushchenko, O., Odarushchenko, V. & Popov, P. T. (2013). Selecting Mathematical Software for Dependability Assessment of Computer Systems Described by Stiff Markov Chains. Paper presented at the 9th International Conference on ICT in Education, Research and Industrial Applications: Integration, Harmonization and Knowledge Transfer, 19-06-2013 - 22-06-2013, Kherson, Ukraine.


Markov and semi-Markov models are widely used in dependability assessment of complex computer-based systems. Model stiffness poses a serious problem both in terms of computational difficulties and in terms of accuracy of the assessment. Selecting an appropriate method and software package for solving stiff Markov models proved to be a non-trivial task. In this paper we provide an empirical comparison of two approaches to dealing with stiffness – stiffness avoidance and stiffness-tolerance. The study includes several well known techniques and software tools used for solving Kolmogorov’s differential equations derived from complex stiff Markov models. In the comparison we used realistic cases studies developed by others in the past: i) a computer system with hardware redundancy and diverse software, and ii) a queuing system with a server break-down and repair. The results indicate that the accuracy of the known methods is significantly affected by the stiffness of the Markov models, which led us to developing a procedure (an algorithm) for selecting the optimal method and tool for solving a given stiff Markov model. The algorithm is, also included in the paper.

Publication Type: Conference or Workshop Item (Paper)
Additional Information: Copyright CEUR Workshop Proceedings 2013
Publisher Keywords: Markov chins, stiffness, stiffness-avoidance, stiffness-tolerance, computer based systems, availability, multi-fragmentation
Subjects: Q Science > QA Mathematics > QA76 Computer software
Departments: School of Science & Technology > Computer Science > Software Reliability
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