Optimal Scheme Models with Imperfect Checkpoint
Abstract
We propose optimal checkpointing models for dual and majority decision structures with imperfect checkpoints. In systems with high reliability, the process returns to the previous checkpoint when errors occur. However, in real-time systems, if the process always returns to the previous checkpoint, its process might not end in time. In this paper, we propose extended checkpoint models in which when errors occur, the process makes forward and backward recoveries, i.e., the process makes the same one again or returns to the first one with some probability. Using dual and majority decision structures as processing modules, these models are applied to constant and random tasks for the processing of objective works. Furthermore, it is shown that processing models are given by the more general forms using a K-out-of-n system. We formulate simultaneous renewal equations for imperfect models and solve them skillfully, using mathematical methods. The mean execution times until the process succeeds are obtained, and optimal policies to minimize them are derived analytically. These results include the former ones and would be useful for some practical checkpoint models.
