Software development nowadays involves several levels of abstraction: starting from the programming of single objects, to their combination into components, to their publication as services and the overall architecture linking elements at each level. As a result, software engineering is dealing with a wider range of artifacts and concepts (i.e., in the context of this paper: services and business processes) than ever before. In this paper we explore the importance of having an adequate engine for executing business processes written as compositions of Web services. The paper shows that, independently of the composition language used, the overall scalability of the system is determined by how the run-time engine treats the process execution. This is particularly relevant at the service level because publishing a process through a Web service interface makes it accessible to an unpredictable and potentially very large number of clients. As a consequence, the process developer is confronted with the difficult question of resource provisioning. Determining the optimal configuration of the distributed engine that runs the process becomes sensitive both to the actual number of clients and to the kinds of processes to be executed. The main contribution of the paper is to show how resource provisioning for software business processes can be solved using autonomic computing techniques. The engine separates execution in two stages (navigation and dispatching) and uses a controller to allocate the node of a cluster of computers to each one of those stages as the workload changes. The controller can be configured with different policies that define how to reconfigure the system. To prove the feasibility of the concept, we have implemented the autonomic controller and evaluated its performance with an extensive set of experiments.