Replication in Mirrored Disk Systems Athena Vakali and Yannis Manolopoulos Department of Informatics, Aristotle University 54006 Thessaloniki, Greece {avakali,manolopo}@athena.auth.gr Abstract. In this paper we study data replication in a mirrored disk sy- stem. Free disk space is exploited by keeping replicas of specific cylinders at appropriate disk locations. Assuming an organ-pipe arrangement we calculate the expected seek distance by varying the probability cylinder access under different distributions. Also, analytic formulae are derived for the expected seek distance under replication and comparison with the conventional (without replication) mirrored disk system is performed. 1 Introduction The “access gap”, i.e. the fact that processor and disk speeds differ by three orders of magnitude, has attracted attention towards minimizing this effect by developing efficient storage subsystems. Seeking is the most important factor in disk operations, therefore we focus on this issue in the sequel. A technique to minimize seeking is the organ-pipe arrangement, which places the most frequent data in the central cylinder, whereas the less frequent data are stored alternati- vely in decreasing order to the left and right of the latter cylinder. It has been proven that this scheme is optimal with respect to seeking [12]. Recently, there has been a considerable interest in shadowed/mirrored disks, where all disks are identical and store the same data. In such systems, enhanced fault tolerance and disk performance are achieved at the expense of storage space. In [3,4,8,10] analytic models have been developed to study the performance of seeking. Also, in [6] the average seek time is estimated when multiple data access streams from different disks are merged into a target disk. Disk rearrangement and adaptive block reorganization have been studied for single disks, in order to reduce seeking either by considering request probability distributions [5,11] or by applying data replication in free disk space [1,2]. The rearrangement techniques have been based on trace driven simulations and seek improvement has been reported for conventional disk configurations. In this paper, a mirrored disk system (i.e. with two identical disks) is studied for specific replication schemes. We assume that single requests arrive under a distribution which supports the organ-pipe scheme. The structure of the rema- inder of the paper is as follows. In Section 2 the model and the system variables are described. In Section 3 we perform the analysis for three replication poli- cies in a mirrored disk system, and derive estimates for the expected seek. In Section 4 we present the algorithm for the evaluation of the expected seek, we W. Litwin et al. (Eds.): ADBIS’98, LNCS 1475, pp. 224–235, 1998. c  Springer-Verlag Berlin Heidelberg 1998