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 $iT$ $(i=1,2,\cdots ,N-1$). 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.