Distributed stream processing systems must function efficiently for data streams that fluctuate in their arrival rates and data distributions. Yet repeated and prohibitively expensive load reallocation across machines may make these systems ineffective, potentially resulting in data loss or even system failure. To overcome this problem, we propose a comprehensive solution, called the Robust Load Distribution (RLD) strategy, that is resilient under data fluctuations. RLD provides ϵ-optimal query performance under an expected range of load fluctuations without suffering from the performance penalty caused by load migration. RLD is based on three key strategies. First, we model robust distributed stream processing as a parametric query optimization problem in a parameter space that captures the stream fluctuations. The notions of both robust logical and robust physical plans that work together to proactively handle all ranges of expected fluctuations in parameters are abstracted as overlays of this parameter space. Second, our Early-terminated Robust Partitioning ( ERP ) finds a combination of robust logical plans that together cover the parameter space, while minimizing the number of prohibitively expensive optimizer calls with a probabilistic bound on the space coverage. Third, we design a family of algorithms for physical plan generation. Our GreedyPhy exploits a probabilistic model to efficiently find a robust physical plan that sustains most frequently used robust logical plans at runtime. Our CorPhy algorithm exploits operator correlations for the robust physical plan optimization. The resulting physical plan smooths the workload on each node under all expected fluctuations. Our OptPrune algorithm, using CorPhy as baseline, is guaranteed to find the optimal physical plan that maximizes the parameter space coverage with a practical increase in optimization time. Lastly, we further expand the capabilities of our proposed RLD framework to also appropriately react under so-called “space drifts”, that is, a space drift is a change of the parameter space where the observed runtime statistics deviate from the expected optimization-time statistics. Our RLD solution is capable of adjusting itself to the unexpected yet significant data fluctuations beyond those planned for via covering the parameter space. Our experimental study using stock market and sensor network streams demonstrates that our RLD methodology consistently outperforms state-of-the-art solutions in terms of efficiency and effectiveness in highly fluctuating data stream environments.