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Today's networked systems are extensively instrumented for collecting a wealth of monitoring data. In this paper, we propose a framework called System-wide Similarity Query (S2Q) to support a new type of similarity queries on monitoring data for managing complex networked systems. The similarity queries are defined on a novel data model that captures system states, and the implementation includes a streaming algorithm for online state-modeling computation and a companion graph-based indexing technique for fast retrieval of historical system states. S2Q simplifies many systems management tasks through a simple and intuitive query interface available to operators, and two applications are evaluated in the paper: (i) fast diagnosis of repeated failures in enterprise IT systems, and (ii) automated application traffic profiling on computer networks. For the first application, the diagnosis accuracy can reach 95% on a multi-tier web service testbed. For the second application, major network applications were automatically identified in the traffic logs from a large campus wireless network.