Loosely-coupled distributed systems organized as collections of so-called cloud-native microservices are able to adapt to traffic in very fine-grained and flexible ways. For this purpose, the cloud-native microservices exploit containerization and container management systems such as Kubernetes. This paper presents a formal model of resource consumption and scaling for containerized microservices deployed and managed by Kubernetes. Our aim is that the model, developed in Real-Time ABS, can be used as a framework to explore the behavior of deployed systems under various configurations at design time—before the systems are actually deployed. We further present initial results comparing the observed behavior of instances of our modeling framework to corresponding observations of real systems. These preliminary results suggest that the modeling framework can provide a satisfactory accuracy with respect to the behavior of distributed microservices managed by Kubernetes.