Optimal checkpointing intervals of three error detection schemes by a double modular redundancy

This paper considers three checkpointing schemes which combine a double modular redundancy and three types of checkpoints: compare-and-store-checkpoint (CSCP), store-checkpoint (SCP), and compare-checkpoint (CCP). An execution time of a task is divided equally into n intervals, and at the end of each interval, a CSCP is always placed. Further, each CSCP interval is also divided equally into m intervals, and at the end of each interval, either CCP or SCP is placed except the last one. Introducing the overheads of comparison, storage, and retry, the mean execution times to complete a task for three schemes are obtained, using the theory of probability. Optimal checkpointing intervals, which minimize the mean times, are analytically derived, and are numerically computed. Three schemes are compared as numerical examples and the best checkpointing scheme is chosen.