On backup policies for hard computer disks

Abstract

Abstract The present study discusses backup policies for the files stored in a hard computer disk or hard computer disks. Two periodical backup policies are proposed both of which make a backup copy of files in a hard disk at age T , where ‘age’ refers to the elapsed time since the previous operation of making a backup copy or recovering from the hard disk failure. Under Policy I, all the files in the hard disk(s) are copied to the floppy disks or the magnetic tapes at every backup time. Under Policy II, a copy of the files created and/or updated since the previous backup time is added to the backup floppy disks or the magnetic tapes at the current backup time. For each policy, the expected cost per unit time over an infinite time span is formulated as an objective function. The existence of an optimal value of T minimizing the expected cost is examined. Numerical examples are also shown to illustrate the proposed backup policies. It is shown under Policy I that there always exists a positive finite optimal backup time, while the conditions under which an optimal backup time exists are clarified for Policy II.