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Stream processing systems have become important, as applications like media broadcasting, sensor network monitoring and on-line data analysis increasingly rely on real-time stream processing. Such systems are often challenged by the bursty nature of the applications. In this paper, we present BARRE (Burst Accommodation through Rate REconfiguration), a system to address the problem of bursty data streams in distributed stream processing systems. Upon the emergence of a burst, BARRE dynamically reserves resources dispersed across the nodes of a distributed stream processing system, based on the requirements of each application as well as the resources available on the nodes. Our experimental results over our Synergy distributed stream processing system demonstrate the efficiency of our approach.