This dissertation researches the mathematical translation of resource provisioning policy into mathematical terms and parameters to solve the on-line service placement problem. A norm called the Provisioning Norm is introduced. Theorems presented in the work show the Provisioning Norm utility function and greedy, random, local search effectively and efficiently solve the on-line problem. Caching of placements is shown to reduce the cost of change but does not improve response time performance. The use of feedback control theory is shown to be effective at significantly improving performance but increases the cost of change. The theoretical results are verified using a decentralized, self-organizing testbed of web servers. The testbed places services on servers on-line using feedback control by profiling the service and node resources. Web servers share service profiles and find new service placement solutions using parallel searches based on the Provisioning Norm.