Analysis of disk arm movement for large sequential reads

The common model for analyzing seek distances on a magnetic disk uses a continuous approximation in which the range of motion of the disk arm is the interval [0,1]. In this model, both the current location of the disk arm and the location of the next request are assumed to be points uniformly distributed on the interval [0,1] and therefore the expected seek distance to service the next request is 1/3. In many types of databases including scientific, object oriented, and multimedia database systems, a disk service request may involve fetching very large objects which must be transferred from the disk without interruption. In this paper we show that the common model does not accurately reflect disk arm movement in such cases as both the assumption of uniformity and the range of motion of the disk arm may depend on the size of the objects. We propose a more accurate model that takes into consideration the distribution of the sizes of the objects fetched as well as the disk arm scheduling policy. We provide closed form expressions for the expected seek distance in this model under various assumptions on the distribution of object sizes and the capability of the disk arm to read in both directions and to correct its position before the next read is performed.