Web services are increasingly being deployed on cloud platforms. Due to their interactive nature, Web services need to ensure fast response times to their end users. Unfortunately, the performance of a Web service can suffer due to a sudden surge in incoming traffic. Furthermore, a cloud-based service can also incur performance degradation due to interference, i.e., contention among services in the cloud platform for shared resources. Such issues motivate the need for automated runtime performance management solutions that ensure response time goals are continuously met. This paper explores a control theoretic approach called Model Predictive Control (MPC) for realizing such a solution. MPC is based on an optimization formulation, which lends itself well to expressing multiple constraints related to response time performance and the amount of resources, e.g., number of virtual machines (VMs), available to a Web service. We outline the design and operation of an MPC controller that governs the scale out and scale in of VMs while adhering to operator-specified thresholds for mean response time and the number of VMs available. Using a realistic Web service testbed, we show that the controller is able to satisfy the specified response time constraint even when the service is subjected to workload surges and interference. © 2018 AACC.