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In this paper we consider aperiodic checkpoint placement problems with equality constraints over an infinite time horizon and develop both exact and approximate algorithms to determine the optimal checkpoint sequences minimizing the relevant expected costs. More precisely, the problem is to minimize the expected recovery cost (expected checkpointing cost) subject to a given level of the expected checkpointing cost (expected recovery cost). First, we develop exact computation algorithms to derive the optimal aperiodic checkpoint sequence by applying the Lagrange multiplier. Second, we propose approximate algorithms based on the variational calculus approach. Numerical examples are devoted to compare two computation algorithms in terms of both accuracy of the resulting checkpoint sequences and their computation efficiency.

In this paper we consider two kinds of sequential checkpoint placement problems with infinite/finite time horizon. For these problems, we apply the approximation methods based on the variational principle and develop the computation algorithms to derive the optimal checkpoint sequence approximately. Next, we focus on the situation where the knowledge on system failure is incomplete, i.e. the system failure time distribution is unknown. We develop the so-called min-max checkpoint placement methods to determine the optimal checkpoint sequence under the uncertain circumstance in terms of the system failure time distribution. In numerical examples, we investigate quantitatively the min-max checkpoint placement methods, and refer to their potential applicability in practice.

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