Markov Chains as a Real-time System Monitoring Service : Numerical Repair Rate Optimization (RRO)

Abstract: The expansion and increased complexity of technology is undoubtedly consistent and one can intuitively suppose that this trajectory will not deviate from this course in the years to come. On a continuous basis, concepts that started of as some hypothetical or abstract notions without practical relevance gets transferred to the modern state of our current technology. During these times, where a subset of our technology has the responsibility of handling the safety of our being, research within dependability theory must keep up the pace with technology. One cannot emphasize enough the importance of ensuring the validity of system dependability attributes prior and posterior to development. With the objective of aggregating findings to the research field and potentially derive new propositions this paper assesses the stochastic modeling concepts used within dependability theory. In particular, discrete-time-and continuous-time-Markov chains are outlined in detail, searching for possibilities to extend these processes in the context of real-time system monitoring. As an outcome, numerical 'repair rate optimization' (RRO) through CTMC uniformization is introduced. A technique which deduces a proposed allocation of repair rate adjustment based on the models parametric sensitivities (gradient ascent). The theoretical aspects are verified by development of an algorithm in Matlab that utilizes the above. Additionally, an approach of combining dependability attributes into a unified measure is proposed. Where the (bounded) transient probabilities are regarded as vectors in the L2(R, B(R), λ) Hilbert Space. For which a normalized dependability norm can be obtained by using the induced norm and triangle inequality. This serves as a metric to compare distinct architectures in terms of several, quantitative attributes. The results imply that under the hypothesis that the system/company can adapt to an increased demand on maintenance periodicity, reliability/availability can be significantly improved. Mitigating risk of failure while optimally preserving resources in terms of e.g. core capacity, maintenance personnel, budget and/or required redundancy while conditioning on the actual system behaviour.