Availability Assessment of Computer Systems Described by Stiff Markov Chains: Case Study

Abstract

Markov models are widely used in dependability assessment of complex computer-based systems. Model stiffness poses a serious problem in terms of both computational difficulties and 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- stiffness avoidance and stiffness-tolerance. The study includes several well-known techniques and software tools used for solving differential equations derived from stiff Markov models. In the comparison, we used realistic case studies developed by others in the past. 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 an algorithm for selecting the optimal method and tool to solve a given stiff Markov model. The proposed algorithm was used to assess the availability of a redundant FPGA-based safety controller. © Springer International Publishing Switzerland 2013.