A Performance Study of a New Grid Protocol and General Grid Structures for Replicated Data

Recently there has been considerable interest in the study of replica-control protocols which are based on organizing several copies of an object into logical structures, such as rectangular grids. In addition to high availability, another objective in exploiting such structures is to improve the degree of load sharing in a system. In this paper, we extend the scope of grid structures to general grids, which allow holes in various positions of a rectangular structure and are useful to consider because they often produce availabilities that are higher than solid grids, where every position must be occupied by a node. We propose an improvement to the existing grid protocol, prove its optimality, and also compare its performance with the existing protocol in terms of availability. In addition, we also o er new insights into the performance of the grids, from both availability and load sharing points of view. Noting that the write availability of square grids tends to 0 for a large number of nodes N, we conduct an asymptotic analysis, and derive the conditions that must be imposed on the dimensions of the grid for the availability to increase asymptotically with increasing N. Algorithms for designing grids to maximize availability independently, and also in conjunction with a load sharing constraint are given.