A software package tool for Markovian computing models and its applications

Abstract

It is important to operate a computing system with high reliability and performance. To evaluate such a system, it is necessary to derive analytically and/or numerically reliability/performance measures by formulating a stochastic model of the system. A continuous-time Markov process is one of the most powerful stochastic processes for analyzing such a system. A software package tool is developed for calculating the transient state probabilities for a continuous-time Markov process with many states. A randomization technique is adopted for calculating the transient state probabilities, as well as the steady-state probabilities. For the software package tool, the authors specify the initial state probability vector pi (0). Once the initial state probability vector pi (0) is specified, it is possible to calculate the transient state probability vector pi (t) at time t. The authors propose a new idea for calculating the convergence time t/sub s/ of the steady-state probability in advance from knowledge of the randomization technique. They also present two examples of maintenance policies for a computing system and show how their software package tool is useful. >