The recent explosive growth in information networks has driven a huge increase in content. For efficient and flexible information retrieval over such large networks, agent technology has received much attention. We previously proposed an agent execution control method for time-constrained information retrieval that finds better results by terminating an agent that has already acquired results of high-enough quality or one that is unlikely to improve the quality of results with continued retrieval. However, this method assumed that all agents have identical time constraints. This leads to a disparity in the obtained score between users who give individual time constraints. In this paper, we propose a fair and efficient scheduling method based on the expected improvement of the highest score (EIS). The proposed method allocates all CPU resources to the agent that has the highest EIS to decrease the difference between users' scores and to increase the mean highest score of requested results.