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On-line decision making often involves query processing over time-varying data which arrives in the form of data streams from distributed locations. In such environments typically, a user application is interested in the value of some function defined over the data items. For example, the traffic management system can make control decisions based on the observed traffic at major intersections; stock investors can manage their investments based on the value of their portfolios. In this paper we present a system that supports pull based data refresh and query processing techniques where such queries access data from multiple distributed sources. Key challenges in supporting such Continuous Multi-Data Incoherency Bounded Queries lie in minimizing network and source overheads, without loss of fidelity in the query responses provided to users. We address these challenges by using mathematically sound approaches based on Gradient Descent and Constraint Optimization which allow us to adapt the refresh frequencies of the dynamically changing data and adjust the quality of service provided to different users.