Markov chain models and applications
Modeling is a fundamental aspect of the design process of a complex system, as it allows the designer to compare different architectural choices as well as predict the behavior of the system under varying input traffic, service, fault and prevention parameters. For instance, in operational software systems, the phenomenon of software aging in which the state of the software gradually degrades with time and, if untreated, eventually leads to a crash/hang failure has been well recognized. As software is a critical business and a main component of high-technology corporations, this problem has inflated significantly in recent times. To counteract the phenomenon of software aging Markov chain modeling is used in preventive maintenance of operational software systems. The contribution of this chapter is the introduction and analysis of Markov modeling techniques for the preventive maintenance of operational software systems. We have developed a Markov chain formulation for major and minimal maintenance problems given some threshold. Steady-state analysis for inspection-based systems as well as noninspection-based systems is presented. Finally, we have also exploited the features of the Markov regenerative process for preventive maintenance analysis of systems.
