Optimal Distribution of Nonperiodic Full and Incremental Backups

Data backups play an important role in effective recovery of system operations, especially, those in computing and Information Technology-related applications. By saving copies of information associated with the completed part of a mission task, a failed system, upon being repaired, can resume its operation from the latest backup point instead of having to repeat the entire work from scratch. This paper considers a repairable, real-time system performing a sequence of nonperiodic full backup (FB) and incremental backup (IB) procedures during its mission. The mission succeeds if a specified amount of work can be accomplished by the system within a deadline. New contributions of this paper are twofold. First, a numerical recursive method is proposed to model effects of the nonperiodic, mixed backup strategy in assessing mission success probability, and expected completion time of the considered system. The method is applicable to any distribution of FBs and IBs and has no limitation on system time-to-failure distributions. Second, the optimal backup policy problem is formulated and solved, which finds the distribution of FBs and IBs maximizing the mission success probability. Examples are provided to illustrate the proposed methodology as well as influence of different parameters on the optimal solution. Advantages of adopting nonperiodic backups over periodic ones are also illustrated.