Discrete-time cost analysis for a telecommunication billing application with rejuvenation 1

Software rejuvenation is a proactive fault management technique that has been extensively studied in the recent literature. In this paper, we focus on an example for a telecommunication billing application considered in [1] and develop the discrete-time stochastic models to estimate the optimal software rejuvenation schedules. More precisely, two software cost models with rejuvenation are formulated via the discrete semi-Markov processes, and the optimal software rejuvenation schedules which minimize the expected costs per unit time in the steady state are derived analytically. Further, we develop statistically nonparametric algorithms to estimate the optimal software rejuvenation schedules, provided that the complete sample data of failure times are given. Then, a new statistical device, called discrete total time on test statistics, is introduced. Finally, we examine asymptotic properties for the statistical estimation algorithms proposed in this paper through a simulation experiment.