Online Bounds on Balancing Two Independent Criteria with Replication and Reallocation

We study the online bicriteria load balancing problem in this paper. We choose a system of distributed homogeneous file servers located in a cluster as the scenario and propose three online approximate solutions for balancing their loads and required storage spaces upon placements. We first revisit the best existing solution for simple placement (i.e., without replication and reallocation), and rewrite it in our first algorithm by imposing some flexibilities. Our second algorithm is to apply document replication. The upper bound of load is significantly reduced, without sacrificing that of the storage space. This upper bound contains at least one special case which can never be outperformed by any online simple placement algorithms. Lastly, we show that there exists an online algorithm which allows very little document reallocation, but gives an upper bound result on the load and storage space, which is never reachable by any online algorithms for simple placement. The time complexities of the first two algorithms are in O(log M), and the last algorithm runs in O(log MN) time, where M is the number of servers, and N is the number of existing documents.