Optimum Head Separation in a Disk System with Two Read/Write Heads

Abstract

A mathematical model of computer disk storage devices having two movable read/write heads is studied. Storage addresses are approximated by points in the continuous interval [0, 1], and requests for information on the disk are processed first-come-first-served. We assume that the disk heads are maintained a fixed distance d apart; that is, in processing a request, both heads are moved the same distance in the same direction. Assuming that successive requested locations are independently and uniformly distributed over [0, 1], we calculate the invariant measure of a Markov chain representing successive head positions under the nearer-server rule: Requests in [0, a t] are processed by the left head, those in [1 - d, 1] by the right head, and those in [d, 1 - d] by the nearer of the two heads. Our major objective is the equilibrium expected distance E(d) that the heads are moved in processing a request. For the problem of designing the separation distance d, we show that E (0.44657) ffi 0.16059 ffi mindE(d). Thus, a basic insight of the analysis is that a system with two heads performs more than twice as well as a system with a single head. The results are compared with those for other two-head disk systems. Finally, numerical results are presented that demonstrate that the nearer-server rule is very nearly optimal under the fixed head-separation constraint. © 1984, ACM. All rights reserved.