Bicriteria load balancing for online placement in heterogeneous servers with totally-ordered upper bounds

We study the online load balancing problem for two independent criteria in heterogeneous systems. For convenience, we choose a system of distributed file servers located in a cluster as the scenario, although our work is not limited to it. Every server is assigned upper bounds for its load and storage space. We assume that the heterogeneity of servers is eventually reflected by the difference of these assignments among different servers. In this paper, the upper bounds are totally ordered (in the sense that, for any two servers, one must be more capable than another). We propose a solution for balancing their loads and required storage spaces for online document placements, and document reallocation is allowed. The time complexity is O(log NM) plus the reallocation cost incurred, where M is the number of servers, and N is the number of existing documents in the system. This cost is a measure of the price for coping with the heterogeneity of our model.