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In a stream data analytics system, input data arrive continuously and trigger the processing and updating of analytics results. We focus on applications with real-time constraints, in which, any data unit must be completely processed within a given time duration. To handle fast data, it is common to place the stream data analytics system on top of a cloud infrastructure. Because stream properties, such as arrival rates can fluctuate unpredictably, cloud resources must be dynamically provisioned and scheduled accordingly to ensure real-time responses. It is essential, for existing systems or future developments, to possess the ability of scaling resources dynamically according to the instantaneous workload, in order to avoid wasting resources or failing in delivering the correct analytics results on time. Motivated by this, we propose DRS, a dynamic resource scaling framework for cloud-based stream data analytics systems. DRS overcomes three fundamental challenges: 1) how to model the relationship between the provisioned resources and the application performance, 2) where to best place resources, and 3) how to measure the system load with minimal overhead. In particular, DRS includes an accurate performance model based on the theory of Jackson open queueing networks and is capable of handling arbitrary operator topologies, possibly with loops, splits, and joins. Extensive experiments with real data show that DRS is capable of detecting sub-optimal resource allocation and making quick and effective resource adjustment.