Skip to main content

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

Publication ,  Journal Article
Calderbank, AR; Coffman, EG; Flatto, L
Published in: Journal of the ACM (JACM)
September 20, 1984

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.

Duke Scholars

Published In

Journal of the ACM (JACM)

DOI

EISSN

1557-735X

ISSN

0004-5411

Publication Date

September 20, 1984

Volume

31

Issue

4

Start / End Page

826 / 838

Related Subject Headings

  • Computation Theory & Mathematics
  • 08 Information and Computing Sciences
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Calderbank, A. R., Coffman, E. G., & Flatto, L. (1984). Optimum Head Separation in a Disk System with Two Read/Write Heads. Journal of the ACM (JACM), 31(4), 826–838. https://doi.org/10.1145/1634.1638
Calderbank, A. R., E. G. Coffman, and L. Flatto. “Optimum Head Separation in a Disk System with Two Read/Write Heads.” Journal of the ACM (JACM) 31, no. 4 (September 20, 1984): 826–38. https://doi.org/10.1145/1634.1638.
Calderbank AR, Coffman EG, Flatto L. Optimum Head Separation in a Disk System with Two Read/Write Heads. Journal of the ACM (JACM). 1984 Sep 20;31(4):826–38.
Calderbank, A. R., et al. “Optimum Head Separation in a Disk System with Two Read/Write Heads.” Journal of the ACM (JACM), vol. 31, no. 4, Sept. 1984, pp. 826–38. Scopus, doi:10.1145/1634.1638.
Calderbank AR, Coffman EG, Flatto L. Optimum Head Separation in a Disk System with Two Read/Write Heads. Journal of the ACM (JACM). 1984 Sep 20;31(4):826–838.

Published In

Journal of the ACM (JACM)

DOI

EISSN

1557-735X

ISSN

0004-5411

Publication Date

September 20, 1984

Volume

31

Issue

4

Start / End Page

826 / 838

Related Subject Headings

  • Computation Theory & Mathematics
  • 08 Information and Computing Sciences