Performance evaluation of critical software is important but also computationally expensive. It usually involves sophisticated load-testing tools and demands a large amount of computing resources. Analysing different user populations requires even more effort, becoming infeasible in most realistic cases. Therefore, we propose a model-based approach. We apply model-based test-case generation to generate log-data and learn the associated distributions of response times. These distributions are added to the behavioural models on which we perform statistical model checking (SMC) in order to assess the probabilities of the required response times. Then, we apply classical hypothesis testing to evaluate if an implementation of the behavioural model conforms to these timing requirements. This is the first model-based approach for performance evaluation combining automated test-case generation, cost learning and SMC for real applications. We realised this method with a property-based testing tool, extended with SMC functionality, and evaluate it on an industrial web-service application.