Publications [#235794] of Robert Calderbank

Journal articles or Book chapters PUBLISHED
  1. Calderbank, AR; Coffman, EG; Flatto, L, Optimum Head Separation in a Disk System with Two Read/Write Heads, Journal of the Acm, vol. 31 no. 4 (September, 1984), pp. 826-838, Association for Computing Machinery (ACM) [doi] .

    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 left bracket 0,1 right bracket , 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 procesing a request, both heads are moved the same distance in the same direction. Assuming that successive requested locations are independently and uniformly distributed over left bracket 0,1 right bracket , we calculate the invariant measure of a Markov chain representing successive head positions under the nearer-server rule: Requests in left bracket 0,d right bracket are processed by the left head, those in left bracket 1 minus d, 1 right bracket by the right head, and those in left bracket d, 1- minus d right bracket 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) equals 0. 16059 equals min//dE(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.