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Service-oriented systems are complex systems, often extending and integrating existing enterprise systems. The fast development pace that SOA enables and the inherent complexity of such systems makes it difficult to maintain an up-to-date overview of the different system components, often plagued by unexpected and difficult to predict and locate performance problems. When dealing with such systems the issue of properly describing the system and the interaction between system components, in a way that allows to perform a fast preliminary approximation of the systempsilas performance, has to be addressed. The present paper addresses these issues by proposing FMC-QE (fundamental modeling concepts for quantitative evaluation) - a hierarchical modeling methodology, as basis for quantitative system modeling and performance evaluation. A service provider using Axis2, an advanced framework for web services developed by the Apache Foundation, is modeled as a test study. Axis2 is presented to familiarize the reader with the framework and to capture the complexity of the system. Using FMC-QE, a model of the system is built, as well as detailed representations of the the input and output processing flows. An FMC-QE Tableau corresponding to the model is presented as basis for the mathematical support used for performance estimation and evaluation.