Supporting Web-based services through geographical distributed clusters of servers is a common solution to the increasing volume and variability of modern traffic. These architectures pose interesting challenges to request management strategies where the most important goal is not to achieve maximum performance, but to guarantee stable and robust results. In this paper, we propose novel request management algorithms that are based on autonomic principles that is, on loose collaboration among the closest nodes and no knowledge about the global system state. Experimental evaluation shows that our autonomic-enhanced algorithms can guarantee robust performance in a variety of settings and reduce standard deviations of the response times with respect to existing request management algorithms.