Large-scale distributed computing systems often contain thousands of distributed nodes (machines). Monitoring the conditions of these nodes is important for system management purposes, which, however, can be extremely resource demanding as this requires collecting local measurements of each individual node and constantly sending those measurements to a central controller. Meanwhile, it is often useful to forecast the future system conditions for various purposes such as resource planning/allocation and anomaly detection, but it is usually too resource-consuming to have one forecasting model running for each node, which may also neglect correlations in observed metrics across different nodes. In this paper, we propose a mechanism for collecting and forecasting the resource utilization of machines in a distributed computing system in a scalable manner. We present an algorithm that allows each local node to decide when to transmit its most recent measurement to the central node, so that the transmission frequency is kept below a given constraint value. Based on the measurements received from local nodes, the central node summarizes the received data into a small number of clusters. Since the cluster partitioning can change over time, we also present a method to capture the evolution of clusters and their centroids. As an effective way to reduce the amount of computation, time-series forecasting models are trained on the time-varying centroids of each cluster, to forecast the future resource utilizations of a group of local nodes. The effectiveness of our proposed approach is confirmed by extensive experiments using multiple real-world datasets.