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A key requirement for autonomic (i.e., self-*) management systems is a short adaptation time to changes in the networking conditions. In this paper, we show that the adaptation time of a distributed monitoring protocol can be controlled. We show this for A-GAP, a protocol for continuous monitoring of global metrics with controllable accuracy. We demonstrate through simulations that, for the case of A-GAP, the choice of the topology of the aggregation tree controls the trade-off between adaptation time and protocol overhead in steady-state. Generally, allowing a larger adaptation time permits reducing the protocol overhead. Our results suggest that the adaptation time primarily depends on the height of the aggregation tree and that the protocol overhead is strongly influenced by the number of internal nodes. We outline how A-GAP can be extended to dynamically self-configure and to continuously adapt its configuration to changing conditions, in order to meet a set of performance objectives, including adaptation time, protocol overhead, and estimation accuracy.