Analytic performance models are being increasingly used to support system runtime optimization. This paper considers the modelling features needed to predict the response time behaviour of an industrial enterprise resource planning (ERP) application, SAP ERP. A number of studies have reported modelling success with the application of basic product-form Queueing Network Models (QNMs) to multitier systems. Such QNMs are often preferred in the context of optimization studies due to the low computational costs of their solution. However, we show that these simple models do not support many important features required to accurately characterize industrial applications such as ERP systems. Specifically, our results indicate that software threading levels, asynchronous database calls, priority scheduling, multiple phases of processing, and the parallelism offered by multi-core processors all have a significant impact on response time that cannot be neglected. Starting from these observations, the paper shows that Layered Queueing Models (LQMs) are a robust alternative to basic QNMs, while still enjoying analytical solution algorithms that facilitate their integration in optimization studies. A case study for a sales and distribution workload demonstrates that many of the features supported by LQMs are critical for achieving good prediction accuracy. Results show that, remarkably, all of the features we considered that are not captured by basic product-form QNMs are needed to predict mean response times to within 15% of measured values for a wide range of load levels. If any key feature is absent, the mean response time estimates could differ by 36% to 117% compared to the measured values, thus making the case that such non-product-form modelling features are needed for complex real-world applications.