An interactive application responds to aperiodic user input with computation that can be expressed as activation trees. By bounding the execution time of these trees, we can improve the responsiveness of the application. The application runs in a typical computing environment: a group of uncoordinated but measurable hosts interconnected with a measurable local area network. The environment serves a number of independent users and we do not control it. However, using a remote execution mechanism, we can execute each node (procedure call) of a tree on any host on the network. We want to use this freedom by dynamically mapping nodes to hosts in order to maximize the percentage of trees that execute within their allotted time. My thesis is that this dynamic mapping problem can be solved using history-based prediction. In essence, the idea is to monitor the system and the application and use the measurements to predict how their behaviors will evolve. Each node is then mapped to the host which best serves to match the predicted future application behavior to the predicted future system behavior. We present two strong pieces of evidence that argue that this is an effective approach. The first is an extensive analysis of host load traces on a wide variety of host systems which strongly suggests that load can be predicted from its history. The second is a history-based prediction algorithm that achieves near optimal performance for a simplified variant of the problem. For my thesis, I will extend these results to develop a history-based prediction algorithm for the full dynamic mapping problem. The algorithm will be developed using a realistic trace-driven simulation environment based on host load traces, network traces, and traces of activation trees collected from real applications. Because of its highly realistic nature, I intend to also evaluate the algorithm using the simulator and a set of benchmarks. In addition, I will incorporate my algorithm into a distributed object system to show that it can work in a real system.