An optimal backup policy considering jobs for a hard disk

The advent of the present-day low-cost personal computer and work station has seen widespread applications. These personal computers and work stations often are used as a system including the hard computer disk (called the hard disk). Various files are constructed and stored in the hard disks. Often, those files are lost due to the mis-operation of the user or the failure of the hard disk itself. The usual means to cope with such a situation is to back up the content of the hard disk at specified intervals by the floppy disk and other devices. However, time to backup usually is left to the intuition and the experience of each user. This paper considers this situation, and proposes a backup policy where the backup is executed when a certain number of jobs are completed. Then a formulation is presented to determine the optimal number of jobs, in the sense that the expected cost per unit time is minimized. In this paper, it is assumed that only those parts which are modified or updated after the previous backup are backed up at each time. Based on the formulated expression, the existence condition for the optimal solution is derived.