A host computer has one or more physical central processing units (CPUs) that support the execution of a plurality of containers, where the containers each include one or more processes. Each process of a container is assigned to execute exclusively on a corresponding physical CPU when the corresponding container is determined to be latency sensitive. The assignment of a process to execute exclusively on a corresponding physical CPU includes the migration of tasks from the corresponding physical CPU to one or more other physical CPUs of the host system, and the directing of task and interrupt processing to the one or more other physical CPUs. Tasks of the process corresponding to the container are then executed on the corresponding physical CPU.