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In the recent years we have witnessed a proliferation of distributed stream processing systems that need to operate under bursty workloads. Examples include road traffic control, processing of financial feeds, network monitoring and real-time sensor data analysis systems. Meeting the QoS requirements of the stream processing systems under burstiness is a challenging process. In this paper we present our approach for adaptive rate allocation within the distributed stream processing system to meet the end-to-end execution time and rate demands of the applications. Our algorithm determines the rates of the application components at runtime, with respect to the QoS constraints, to compensate for delays experienced by the components or to react to sudden bursts of load. Our technique is distributed and low-cost. Our detailed experimental results over our Synergy middleware illustrate that our approach is practical, depicts good performance and has low resource overhead.