Final answer:
Infrastructure as a Service (IaaS) provides the most control to customers over their cloud environment, offering flexibility and customization of IT resources.
Step-by-step explanation:
The common cloud service model that offers customers the most control over their environment is Infrastructure as a Service (IaaS). Unlike Platform as a Service (PaaS) or Software as a Service (SaaS), IaaS provides the physical or virtual servers, storage, and networking that allows customers to run any software, including operating systems and applications. This model gives customers the flexibility to manage and configure their IT resources as they see fit, allowing for the most customization and control amongst the cloud service models, which also includes Function as a Service (FaaS).