Optimal directory placement on disk storage devices

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Abstract
Two mathematical models dealing with optimal placement of directories on disk devices are analyzed. 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 that specifies the address of the file, and then a head is moved to the specified address. The addresses are assumed to be independent and uniform on [0,1]. In the first model we consider a system of two heads separated by a fixed distance d and a directory situated at 0 ≤ x ≤ 1. In the second model we consider a system consisting of one head and n ≥ 2 directories at 0 ≤ x 1 < x 2 < … < x n ≤ 1. For both models we study the problem of finding those values of the parameters that minimize the expected head motion to process a request in statistical equilibrium.

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