Optimal policies for a database system with two backup schemes

This paper considers two backup schemes for a database system: a database is updated at a nonhomogeneous Poisson process and an amount of updated files accumulates additively. To ensure the safety of data, full backups are performed at time NT or when the total updated files have exceeded a threshold level K, and between them, cumulative backups as one of incremental backups are made at periodic times iT (i=1;2;...;N-1). Using the theory of cumulative processes, the expected cost is obtained, and an optimal number N* of cumulative backup and an optimal level K* of updated files which minimize it are analytically discussed. It is shown as examples that optimal number and level are numerically computed when two costs of backup schemes are given.