In this paper, we propose extensions to UML state diagrams and activity diagrams in order to allow the association of events with exponentially distributed and deterministic delays. We present an efficient algorithm for the state space generation out of these UML diagrams that allows a quantitative analysis by means of an underlying stochastic process. We identify a particular stochastic process, the generalized semi-Markov process (GSMP), as the appropriate vehicle on which quantitative analysis is performed. As innovative feature the algorithm removes vanishing states, i.e. states with no timed events active, and considers branching probabilities within activity diagrams. Furthermore, we introduce a performance evaluation framework that allows a system designer to predict performance measures at several steps in the design process. The applicability of our approach for practical performance and dependability projects is demonstrated by an UML specification of the General Packet Radio Service, a packet switched extension in GSM wireless networks.