The Business Process Execution Language for Web Services (BPEL) provides a common standard for modeling and sharing business processes across enterprises via Web services. Business applications that handle different operations within a business process usually share computational capacity. In this paper, we provide a method to allocate computational capacity across these applications. Our method takes the follow factors into consideration: random arrivals of business process instances, service time fluctuations of business applications, Quality of Service (QoS) requirements, and the composition structure of the business process specified by BPEL. Using heavy traffic approximations, we formulate and solve the capacity allocation problem as a nonlinear optimization problem with QoS constraints; our method also gives a pessimistic bound on the maximum sustainable request rate the system can support.