Optimal backup policy for a database system with incremental and full backups

The fundamental recovery technique for some medium failures in a database system is regularly carried out by executing a full backup that takes all copies of updated files. However, the overhead of such full backup becomes sometimes very large in a massive database system. To lessen the overhead of backups, an incremental backup with small overhead, which takes only copies of newly updated files, is usually adopted in most database systems. However, the overhead of an incremental backup increases in proportion to the total amount of updated files. It would be necessary to determine when to make full backups. This paper proposes a stochastic model with incremental and full backups: the expected costs incurred for two backups are obtained, and an optimal full backup interval which minimizes them is discussed. It is shown that an optimal interval is given by a finite and unique solution of an equation under suitable conditions. Finally, a numerical example is given and some useful discussions are made.