Privacy is a major concern in cloud computing since clouds are considered as untrusted environments. In this study, we address the problem of privacy-preserving range query processing on clouds. Several solutions have been proposed in this line of work, however, they become inefficient or impractical for many monitoring applications, including real-time monitoring and predicting the spatial spread of seasonal epidemics (e.g., H1N1 influenza). In this case, a system often confronts a high rate of incoming data. Prior schemes may thus suffer from potential performance issues, e.g., overload or bottleneck. In this paper, we introduce an extension of PINED-RQ to address these limitations. We also demonstrate experimentally that our solution outperforms PINED-RQ.