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Distributed computing systems often consist of hundreds of nodes, executing tasks with different resource requirements. Efficient resource provisioning and task scheduling in such systems are non-trivial and require close monitoring and accurate forecasting of the state of the system, specifically resource utilisation at its constituent machines. Two challenges present themselves towards these objectives. First, collecting monitoring data entails substantial communication overhead. This overhead can be prohibitively high, especially in networks where bandwidth is limited. Second, forecasting models to predict resource utilisation should be accurate and need to exhibit high inference speed. Mission critical scheduling and resource allocation algorithms use these predictions and rely on their immediate availability. To address the first challenge, we present a communication-efficient data collection mechanism. Resource utilisation data is collected at the individual machines in the system and transmitted to a central controller in batches. Each batch is processed by an adaptive data-reduction algorithm based on Fourier transforms and truncation in the frequency domain. We show that the proposed mechanism leads to a significant reduction in communication overhead while incurring only minimal error and adhering to accuracy guarantees. To address the second challenge, we propose a deep learning architecture using complex Gated Recurrent Units to forecast resource utilisation. This architecture is directly integrated with the above data collection mechanism to improve inference speed of our forecasting model. Using two real-world datasets, we demonstrate the effectiveness of our approach, both in terms of forecasting accuracy and inference speed. Our approach resolves challenges encountered in resource provisioning frameworks and can be applied to other forecasting problems.