An optimal N-job backup policy maximizing availability for a hard computer disk

Personal computers and engineering work stations are generally used with hard computer disks which preserve a variety of files for reference. Some or all of these files are sometimes lost because of human errors and failures of the computer system or the hard disk. Making a backup copy of files on floppy disks or magnetic tapes protects a user from such serious losses. The present study discusses an optimal backup policy for a hard computer disk where a backup copy of files in the hard disk is made when N jobs of updating or creating files are finished. The availability of the proposed backup policy is formulated and the existence of the optimal integer N* which maximizes the availability is examined. It is shown that there always exists an optimal integer N* equal to or greater than 1. A numerical example is presented to illustrate the theoretical model for determining the optimal backup policy using gamma distributions to describe the setup time, the job processing time and the backup time for a system subject to exponential failures.