Cloud computing is a vibrant and dynamic technology. Cloud users can subscribe to various types of cloud services like Infrastructure as a Service (IaaS), Platform as a Service (PaaS), and Software as a Service (SaaS) etc. offered to clients by various cloud service providers like Amazon, Microsoft, Google, IBM, Facebook, Twitter, and WhatsApp etc. SaaS service model is the most popular service model of the cloud. In this service model, cloud user downloads the Application (App) of the cloud service provider (CSP) and interacts with the resources of the CSP by using the App. The App execution engine is placed at various data centers located at different locations by the CSP to optimize the performance of the App. The placement of Cloud App execution engine at various data centers by the CSP plays a vital role in overall performance of SaaS cloud environment. In this paper, we address this issue and propose a performance model of SaaS cloud environment to aid the CSP to optimally place the App execution engine at various locations to improve the overall performance of the Cloud App. The proposed performance model is named as PI3(π3) Cloud performance model, SaaS, Performance model of SaaS cloud, Performance parameters of the cloud. (Prodigal, Ideal, Impoverished, and Inefficient) uses two important performance metrics response time of user request and cost of providing services and it classifies the performance of the SaaS cloud environment into four types: Prodigal, Ideal, Impoverished and Inefficient. Finally, we use the proposed model to analyze and optimize the performance of a SaaS cloud environment.