1. In a host computer having one or more physical central processing units (CPUs) that support the execution of a plurality of containers, the containers each including one or more processes, wherein the host computer is programmed to perform a method of assigning at least one of the processes to have exclusive affinity to a corresponding physical CPU, the method comprising: determining that a first container is latency sensitive; and responsive to the determining, assigning each of the processes of the first container to have exclusive affinity to one or more corresponding physical CPUs, said assigning comprising: migrating running tasks on the corresponding physical CPUs to the one or more other physical CPUs of the host system; directing queued tasks and interrupt processing for the corresponding physical CPUs to the one or more other physical CPUs; and executing tasks of each of the processes of the first container on the one or more corresponding CPUs to which the process has exclusive affinity.