Network services, e.g., video streaming services, are increasingly being deployed on public cloud platforms. Such services often employ horizontal scaling where a group of resource instances, e.g., virtual machines (VMs), handle incoming workload. The response time of such services is often affected by interference, i.e., contention among resource instances belonging to multiple cloud subscribers for shared cloud resources. Most commercial cloud platforms do not support built-in mechanisms to detect interference and mitigate its impact. Consequently, subscribers of such platforms, i.e., network service providers, need to deploy their own mechanisms to ensure a specified end user response time target is continuously met even in the face of fluctuations in workload and interference. This paper describes PRIMA, our implementation of such a mechanism. PRIMA uses automated and controlled performance tests to build models that capture the joint impact of workload and interference on the response time of each resource instance employed by a service. It adapts the system to changing workload and interference conditions by using these models at runtime to control the number of instances in the system and the distribution of load among these instances. Unlike existing subscriber-oriented interference mitigation techniques in literature, PRIMA guarantees that a subscriber-specified response time threshold is satisfied at every resource instance assigned to a service. Furthermore, in contrast to these approaches PRIMA can help a subscriber avoid using more instances than necessary by automatically selecting at runtime the least number of instances required for handling the observed workload and interference. We experimentally validate the effectiveness of PRIMA in both private and public cloud environments. Results show that PRIMA outperforms competing approaches proposed by us and others, including those that are commonly used in practice. They also reveal that PRIMA can automatically calibrate its models at runtime to account for any model prediction errors.