Computing bounds on steady state availability of repairable computer systems

Abstract

One of the most important performance measures for computer system designers is system availability. Most often, Markov models are used in representing systems for dependability/availability analysis. Due to complex interactions between components and complex repair policies, the Markov model often has an irregular structure, and closed-form solutions are extremely difficult to obtain. Also, a realistic system model often has an unmanageably large state space and it quickly becomes impractical to even generate the entire transition rate matrix. In this paper, we present a methodology that can (i) bound the system steady state availability and at the same time, (ii) drastically reduce the state space of the model that must be solved. The bounding algorithm is iterative and generates a part of the transition matrix at each step. At each step, tighter bounds on system availability are obtained. The algorithm also allows the size of the submodel, to be solved at each step, to be chosen so as to accommodate memory limitations. This general bounding methodology provides an efficient way to evaluate dependability models with very large state spaces without ever generating the entire transition rate matrix.