Service Level Agreements (SLAs) are defining the quality of the services delivered from the Cloud Services Providers (CSPs) to the cloud customers. The services are delivered on a pay-per-use model. The quality of the provided services is not guaranteed by the SLA because it is just a contract. The developments around mobile cloud computing and the advent of edge computing technologies are contributing to the diffusion of the cloud services and the multiplication of offers. Although the cloud services market is growing for the coming years, unfortunately, there is no standard mechanism which exists to verify and assure that delivered services satisfy the signed SLA agreement in an automatic way. The accurate monitoring and modelling of the provided Quality of Service (QoS) is also missing. In this context, we aim at offering an automatic framework named PRESENCE, to evaluate the QoS and SLA compliance of Web Services (WSs) offered across several CSPs. Yet unlike other approaches, PRESENCE aims at quantifying in a fair and by stealth way the performance and scalability of the delivered WS. This article focuses on the first experimental results obtained on the accurate modelisation of each individual performance metrics. Indeed, 19 generated models are provided, out of which 78.9% accurately represent the WS performance metrics for two representative SaaS web services used for the validation of the PRESENCE approach. This opens novel perspectives for assessing the SLA compliance of Cloud providers using the PRESENCE framework.