Parallel query processing over data streams in cloud computing environments has attracted considerable attention recently in various fields, due to the huge potential value of analyzing massive data or big data in a large number of streaming applications. Nevertheless, existing studies on queries primarily focus on the algorithms for the specific query types with the lack of the general framework for processing various queries. Moreover, existing parallel frameworks in cloud such as MapReduce and its variations are not suitable for many complex queries over complex data streams. In this paper, we extensively discuss the problem of designing the general framework for parallel queries over data streams in cloud. Particularly, we propose and implement a framework called GPS, which can be well adapted to various queries over complex data streams like the uncertain data streams. Furthermore, we further propose a hierarchical and general parallel model for queries over data streams based on the proposed framework, which is more flexible than the MapReduce model. The skyline queries over uncertain data streams based on our proposed framework with real deployment are conducted as an example to verify the performances of our proposals.