Calderbank, AR; Jr, EGC; Flatto, L, *OPTIMAL DIRECTORY PLACEMENT ON DISK STORAGE DEVICES.*,
Journal of the ACM, vol. 35 no. 2
(1988),
pp. 433-446 [doi] .
**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 left bracket 0, 1 right bracket . 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 left bracket 0, 1 right bracket . In the first model we consider a system of two heads separated by a fixed distance d and a directory situated at 0 less than equivalent to x less than equivalent to 1. In the second model we consider a system consisting of one head and n greater than equivalent to 2 directories at 0 less than equivalent to x//1 less than x//2 less than . . . less than x//n less than equivalent to 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.*