Optimal placement of high-probability randomly retrieved blocks on CLV optical discs

Abstract

Optimal data placement on a CLV (Constant Linear Velocity) format optical discs has an objective the minimization of the expected access cost of data retrievals from the disc when the probabilities of access of data items may be different. The problem of optimal data placement for optical discs is both important and more difficult than the corresponding problem on magnetic discs. A good data placement on optical discs is more important because data sets on optical discs such as WORM and CD ROM cannot be modified or moved once they are placed on disc. Currently, even rewritable optical discs are best suited for applications that are archival in nature. The problem of optimal data placement on CLV format optical discs is more difficult, mainly because the useful storage space is not uniformly distributed across the disc surface (along the radius). This leads to a complicated positional performance trade-off not present for magnetic disks. We present a model that encompasses all the important aspects of the placement problem on CLV format optical discs. The model takes into account the nonuniform distribution of useful storage, the dependency of the rotational delay on disc position, a parameterized seek cost function for optical discs, and the varying access probabilities of data items. We show that the optimal placement of high-probability blocks satisfies a unimodality property. Based on this observation, we solve the optimal placement problem. We then study the impact of the relative weights of the problem parameters and show that the optimal data placement may be very different from the optimal data placement on magnetic disks. We also validate our model and analysis and give an algorithm for computing the placement of disc sectors.