On-line load balancing in a hierarchical server topology

In a hierarchical server environment, jobs must be assigned in an online fashion to a collection of servers forming a hierarchy of capability. Each job requests a specific server meeting its needs but the system is free to assign it either to that server or to any other server higher in the hierarchy. Each job carries a certain load, which it imparts to the server to which it is assigned. The goal is to minimize the maximum total load on a server. We consider the linear hierarchy, where the servers are totally ordered in terms of capability, and the tree hierarchy, where ancestors are more powerful than their descendants. We investigate several variants of the problem, differing from one another by whether jobs are weighted or unweighted; whether they are permanent or temporary; and whether assignments are fractional or integral. We derive upper and lower bounds on the competitive ratio.