Optimal directory placement on disk storage devices.

We analyze two mathematical models dealing with optimal placement of directories on disk devices. Storage addresses on the disk are approximated by points in the interval [0,1]. Requests for information on the disk are represented by a sequence of file names. To process a request a read-write head is first moved to a directory kept on the disk which specifies the address of the file, and then a head is moved to the specified address. The obtained addresses are assumed to be independent and to be independent and uniform on [0.1].