Dynamic mathematical model for resource management and scheduling in cloud computing environments

The object of the research is resource management and scheduling in Kubernetes clusters, in particular, data centers. It was determined that in many publications dedicated to optimization models of scheduling for Kubernetes, mathematical models either do not include constraints at all, or only have the constraints determined on the high level only. The purpose of the research is the creation of a dynamic low-level mathematical optimization model for resource management and scheduling in cloud computing environments that utilize Kubernetes. Examples of such environments include the data centers where the customers can rent both dedicated servers and resources of shared hosting servers that are allocated on demand. The suggested model was created using the principles of creation of mathematical models of discrete (combinatorial) optimization, and was given the name “dynamic” because it takes the time parameter into account. The model receives data about individual servers in the cluster and individual pods that should be launched as an input. The model aims to regulate not only individual assignments of pods to nodes, but also turning on and off the servers. The model has objectives of: minimization of the average number of shared hosting servers running; maximization of the average resource utilization coefficient on such servers; minimization of the number of occasions when the servers are turned on and off; minimization of resource utilization by the pods that are running on shared hosting servers but created by the customers renting the dedicated servers. The model considers resource constraints, among other limitations.