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

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

Improving the Accuracy of Software Reliability Modeling by Predicting the Number of Secondary Software Defects

Reliability assessment and prediction of the number of faults/defects is an important part of the software engineering process. Many software reliability models assume that all detected are removed with certainty and no new faults are introduced. However, the introduction of secondary faults during software updates has become quite common in software development practice, which can be explained by the enormous complexity of modern computer applications. In the paper we consider different scenarios of introducing secondary faults and how to predict number of such faults. Finally, we discuss how different SRGMs like Jelinski-Moranda, Exponential, Schick-Wolverton, Musa and Lipov models can be modified to account secondary faults in order to improve accuracy of software reliability prediction. We use an industrial case study to demonstrate applicability of the proposed approach. Our results show that considering secondary faults helped to considerably improve accuracy of software failure rate prediction

Empirical evaluation of accuracy of mathematical software used for availability assessment of fault-tolerant computer systems

Dependability assessment is typically based on complex probabilistic models. Markov and semi-Markov models are widely used to model dependability of complex hardware/software architectures. Solving such models, especially when they are stiff, is not trivial and is usually done using sophisticated mathematical software packages. We report a practical experience of comparing the accuracy of solutions stiff Markov models obtained using well known commercial and research software packages. The study is conducted on a contrived but realistic cases study of computer system with hardware redundancy and diverse software under the assumptions that the rate of failure of software may vary over time, a realistic assumption. We observe that the disagreement between the solutions obtained with the different packages may be very significant. We discuss these findings and directions for future research