Air Navigation Service Providers (ANSP) worldwide have been making a considerable effort for the development of a better method to measure and predict aircraft counts within a particular airspace, also referred to as airspace density. An accurate measurement and prediction of airspace density is crucial for a better managed airspace, both strategically and tactically, yielding a higher level of automation and thereby reducing the air traffic controller's workload. Although the prior approaches have been able to address the problem to some extent, data management and query processing of ever-increasing vast volume of air traffic data at high rates, for various analytics purposes such as predicting aircraft counts, still remains a challenge especially when only linear prediction models are used. In this paper, we present a novel data management and prediction system that accurately predicts aircraft counts for a particular airspace sector within the National Airspace System (NAS). The incoming Traffic Flow Management (TFM) data is streaming, big, uncorrelated and noisy. In the preprocessing step, the system continuously processes the incoming raw data, reduces it to a compact size, and stores it in a NoSQL database, where it makes the data available for efficient query processing. In the prediction step, the system learns from historical trajectories and uses their segments to collect key features such as sector boundary crossings, weather parameters, and other air traffic data. The features are fed into various regression models, including linear, non-linear and ensemble models, and the best performing model is used for prediction. Evaluation on an extensive set of real track, weather, and air traffic data including boundary crossings in the U.S. verify that our system efficiently and accurately predicts aircraft counts in each airspace sector.