Software rejuvenation is a preventive maintenance technique that has been extensively studied in recent literature. In this paper, we extend the classical result by Huang et al. (1995), and in addition propose a modified stochastic model to generate the software rejuvenation schedule. More precisely, the software rejuvenation models are formulated via the semi-Markov reward process, and the optimal software rejuvenation schedules are derived analytically in terms of the reward rate. In particular, we consider the two special cases: steady-state availability and expected cost per unit time in the steady state. Further, we develop non-parametric algorithms to estimate the optimal software rejuvenation schedules, provided that the statistically complete (unsensored) sample data of failure time is given. In numerical examples, we compare two models from the viewpoints of system availability and economic justification, and examine asymptotic properties for the statistical estimation algorithms.

This paper addresses a parameter estimation problem of Markovian arrival process (MAP). In network traffic measurement experiments, one often encounters the group data where arrival times for a group are collected as one bin. Although the group data are observed in many situations, nearly all existing estimation methods for MAP are based on nongroup data. This paper proposes a numerical procedure for fitting a MAP and a Markov-modulated Poisson process (MMPP) to group data. The proposed algorithm is based on the expectation-maximization (EM) approach and is a natural but significant extension of the existing EM algorithms to estimate parameters of the MAP and MMPP. Specifically for the MMPP estimation, we provide an efficient approximation based on the proposed EM algorithm. We examine the performance of proposed algorithms via numerical experiments and present an example of traffic analysis with real traffic data.