Optimal positioning of read/write heads in mirrored disks

This work is concerned with finding the expected-travel-distance-minimizing anticipatory positions of disk arms in mirrored disk systems. In such systems, data is duplicated across two or more disk drives. A ‘read’ request may choose to read from any copy, and thus do so from the disk whose arm is closest to the request location. Since a ‘write’ must update all copies, the response time for such a request will depend on the distance of the arm which is furthest away from the request’s location. Some problems of optimally positioning emergency service units on a line and of positioning idle elevators can be viewed mathematically as a special case of the mirrored disks scenario in which there are ‘read’ requests only. This paper shows that, for any request location distribution, if there are more write than read requests then both arms should be located as if read requests did not exist-both at the medium of the distribution. For situations where most requests are of ‘read’ type, the paper derives necessary conditions for optimal locations.