Virtual machine consolidation is attractive in cloud computing platforms for several reasons including reduced infrastructure costs, lower energy consumption and ease of management. However, the interference between co-resident workloads caused by virtualization can violate the service level objectives (SLOs) that the cloud platform guarantees. Existing solutions to minimize interference between virtual machines (VMs) are mostly based on comprehensive micro-benchmarks or online training which makes them computationally intensive. In this paper, we present CloudScope, a system for diagnosing interference for multi-tenant cloud systems in a lightweight way. CloudScope employs a discrete-time Markov Chain model for the online prediction of performance interference of co-resident VMs. It uses the results to optimally (re)assign VMs to physical machines and to optimize the hypervisor configuration, e.g. the CPU share it can use, for different workloads. We have implemented CloudScope on top of the Xen hypervisor and conducted experiments using a set of CPU, disk, and network intensive workloads and a real system (MapReduce). Our results show that CloudScope interference prediction achieves an average error of 9%. The interference-aware scheduler improves VM performance by up to 10% compared to the default scheduler. In addition, the hypervisor reconfiguration can improve network throughput by up to 30%.