Optimal checkpointing intervals for a double modular redundancy with signatures

This paper considers checkpointing intervals for a double modular redundancy (DMR) with signatures: a signature is a mapping of the original space into a much smaller space and represents the state of each processor. An execution time of a task is divided equally into n intervals, and at the end of each interval, a compare-and-store-checkpoint (CSCP) is always placed. Further, each CSCP interval is also divided equally into m intervals, and at the end of each interval, two processors calculate signatures and compare them. If signatures are different, it is judged that an error has occurred. Then, two processors are rolled back to the previous CSCP. We consider two types of checkpointing schemes: one scheme has signatures between CSCPs, and another scheme has signatures and a function of CCP between CSCPs. For each scheme, the mean execution times are obtained. Optimal checkpointing intervals which minimize the mean times are analytically derived. Further, two schemes are compared as numerical examples.