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This paper considers the novel area of quality-of-information (QoI)-aware network management of multitasking wireless sensor networks (WSNs). Specifically, it provides an investigation of new task admission and resource utilization mechanisms for controlling the individual QoI provided to new and existing tasks using real-time feedback-based monitoring mechanisms. The paper describes three key design elements in support of the above: (a) the QoI satisfaction index of a task, which quantifies the degree to which the required QoI is satisfied by the WSN; (b) the QoI network capacity, which expresses the ability of the WSN to host a new task with specific QoI requirements without sacrificing the attained QoI levels of other existing tasks, and (c) an adaptive, negotiation-based admission control mechanism that reconfigures and optimizes the usage of network resources in order to optimally accommodate the QoI requirements of all tasks. Finally, extensive results are presented for assessing the performance of the proposed solution for the case of an intruder detection application scenario.