The pervasive availability of streaming data from various sources is driving todays’ enterprises to acquire low-latency big data streaming applications (BDSAs) for extracting useful information. In parallel, recent advances in technology have made it easier to collect, process and store these data streams in the cloud. For most enterprises, gaining insights from big data is immensely important for maintaining competitive advantage. However, majority of enterprises have difficulty managing the multitude of BDSAs and the complex issues cloud technologies present, giving rise to the incorporation of cloud service brokers (CSBs). Generally, the main objective of the CSB is to maintain the heterogeneous quality of service (QoS) of BDSAs while minimizing costs. To achieve this goal, the cloud, although with many desirable features, exhibits major challenges — resource prediction and resource allocation — for CSBs. First, most stream processing systems allocate a fixed amount of resources at runtime, which can lead to under- or over-provisioning as BDSA demands vary over time. Thus, obtaining optimal trade-off between QoS violation and cost requires accurate demand prediction methodology to prevent waste, degradation or shutdown of processing. Second, coordinating resource allocation and pricing decisions for self-interested BDSAs to achieve fairness and efficiency can be complex. This complexity is exacerbated with the recent introduction of containers. This dissertation addresses the cloud resource elasticity management issues for CSBs as follows: First, we provide two contributions to the resource prediction challenge; we propose a novel layered multi-dimensional hidden Markov model (LMD-HMM) framework for managing time-bounded BDSAs and a layered multi-dimensional hidden semi-Markov model (LMD-HSMM) to address unbounded BDSAs. Second, we present a container resource allocation mechanism (CRAM) for optimal workload distribution to meet the real-time demands of competing containerized BDSAs. We formulate the problem as an n-player non-cooperative game among a set of heterogeneous containerized BDSAs. Finally, we incorporate a dynamic incentive-compatible pricing scheme that coordinates the decisions of self-interested BDSAs to maximize the CSB’s surplus. Experimental results demonstrate the effectiveness of our approaches.