It is of great importane to make a recovery action to reconstruct the logical consistency of the databese on the occasion of a system failure. Such a recovery action consists of two operations. One is UNDO operation, which rolls back the effects of all incomplete transactions from the database, and the other is REDO operation, which reflects the results of all complete transactions in the databese. In general, we limit the amount of REDO operation by generating checkpoints, in which the results of a complete transactions(s) are collected in a safe place. In this paper, we discuss evaluation for a database recovery action with periodical checkpoint generations. A new model is proposed to evaluate the recovery action in a case where a failure rate of the system changes with time. The expected recovery time and the availability for one cycle are derived under the assumption of an arbitrary failure-time distribution. In particular, we obtain analytically the optimum checkpoint interval with the maximum availability in the case of an exponential distribution. We numerically calculate the above results by assuming Weibull distributions. We further discuss the numerical results in varying the parameters that we define in our model, and show the impact of these parameters on the recovery action.

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 Huang et al. (1995) and develop the discrete-time stochastic models to estimate the optimal software rejuvenation schedule. More precisely, two software availability models with rejuvenation are formulated via the discrete semi-Markov processes, and the optimal software rejuvenation schedules which maximize the steady-state availabilities are derived analytically. Further, we develop statistically non-parametric 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 the 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.

Software rejuvenation is a preventive and proactive solution that is particularly useful for counteracting the phenomenon of software aging. In this article, we consider periodic software rejuvenation models based on the expected cost per unit time in the steady state under discrete-time operation circumstance. By applying the discrete renewal reward processes, we describe the stochastic behavior of a telecommunication billing application with a degradation mode, and determine the optimal periodic software rejuvenation schedule minimizing the expected cost. Similar to the earlier work by the same authors, we develop a statistically non-parametric algorithm to estimate the optimal software rejuvenation schedule, by applying the discrete total time on test concept. Numerical examples are presented to estimate the optimal software rejuvenation schedules from the simulation data. We discuss the asymptotic behavior of estimators developed in this paper.

This paper considers a probabilistic model for a database recovery action with checkpoint generations when system failures occur according to a renewal process whose renewal density depends on the cumulative operation period since the last checkpoint. Necessary and sufficient conditions on the existence of the optimal checkpoint interval which maximizes the ergodic availability are analytically derived, and solvable examples are given for the well-known failure time distributions. Further, several methods to be needed for numerical calculations are proposed when the information on system failures is not sufficient. We use four analytical/tractable approximation methods to calculate the optimal checkpoint schedule. Finally, it is shown through numerical comparisons that the gamma approximation method is the best to seek the approximate solution precisely.

This paper considers two simulation models for simple unreliable file systems with checkpointing and rollback recovery. In Model 1, the checkpoint is generated at a pre-specified time and the information on the main memory since the last checkpoint is back-uped in a secondary medium. On the other hand, in Model 2, the checkpointing is executed at the time when the number of transactions completed for processing is achieved at a pre-determined level. However, it is difficult to treat such models analytically without employing any approximation method, if queueing effects related with arrival and processing of transactions can not be ignored. We apply the generalized stochastic Petri net (GSPN) to represent the stochastic behaviour of systems under two checkpointing schemes. Throughout GSPN simulation, we evaluate quantitatively the maintainability of checkpoint models under consideration and examine the dependence of model parameters in the optimal checkpoint policies and their associated system availabilities.

This article considers a hybrid data backup model for a file system, which combines both conventional magnetic disk (MD) and write-once, read-many optical disk (OD). Since OD recently is a lower cost medium as well as a longer life medium than the ordinary MD, this kind of backup configuration is just recognized to be important. We mathematically formulate the hybrid data backup model and obtain the closed-form average cost rate when the system failure time and the recovery time follow exponential distributions. Numerical calculations are carried out to obtain the optimal backup policy, which is composed of two kinds of backup sizes from the main memory to MD and from MD to OD and minimizes the average cost rate. In numerical examples, the dependence of the optimal backup policy on the failure and the recovery mechanism is examined.

Checkpointing is one of the most powerful tools to operate a computer system with high reliability. We should execute the optimal checkpointing in some sense. This note shows the optimal checkpoint sequence minimizing the expected loss, Numerical examples are shown for illustration.