Rotating Escalators upon Deletions for Improving Online Bicriteria Load Balancing

We study the online load balancing problem for two independent criteria upon deletion in this paper. For convenience, we choose a system of distributed homogeneous file servers located in a cluster as the scenario, and propose a solution for balancing their loads and required storage spaces for any sequence of document placements and deletions. The upper bounds of load and storage space are extremely close to the best existing online result for sole placements which do not allow reallocation and replication. Upon deleting a document from a server, other servers experience relative increases in both criteria. However, our upper bound result can tolerate a certain number of deletions. Based on this buffer, for each criterion, we construct an escalator to model the numbers of deletions that the servers can withstand before violating the upper bound. The escalator moves down upon deletion, and the servers of the lowest group, which have the least tolerance, will go through reallocation and rotate back to the highest point. As long as the escalators are valid, the upper bounds are intact.