A method performed in a host computer having one or more physical central processing units, CPUs, (145 1, 145 2, 145 3) that support the execution of a plurality of containers, the containers each including one or more processes, 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 (145 1) to one or more other physical CPUs (145 2, 145 3) of the host system; directing queued tasks and interrupt processing for the corresponding physical CPUs (145 1) to the one or more other physical CPUs (145 2, 145 3); and executing tasks of each of the processes of the first container on the one or more corresponding CPUs (145 1) to which the process has exclusive affinity; wherein the first container is a first virtual machine (110 1) and each of the one or more processes included in the first container is a virtual CPU (125 1), and at least one said virtual CPU (125 1) is assigned to have exclusive affinity to a corresponding physical CPU (145 1); wherein determining that the first virtual machine (110 1) is latency sensitive comprises: reading a latency sensitivity indicator for the first virtual machine (110 1); reading a CPU entitlement value for the first virtual machine (110 1); determining that the latency sensitivity indicator is a predetermined value; and determining that the CPU entitlement value is a maximum value; and wherein the maximum value for the CPU entitlement value indicates that each virtual CPU of the first virtual machine is permitted to consume the full processing capacity of one of the physical CPUs. 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 (145 1) to one or more other physical CPUs (145 2, 145 3) of the host system; directing queued tasks and interrupt processing for the corresponding physical CPUs (145 1) to the one or more other physical CPUs (145 2, 145 3); and executing tasks of each of the processes of the first container on the one or more corresponding CPUs (145 1) to which the process has exclusive affinity; migrating running tasks on the corresponding physical CPUs (145 1) to one or more other physical CPUs (145 2, 145 3) of the host system; directing queued tasks and interrupt processing for the corresponding physical CPUs (145 1) to the one or more other physical CPUs (145 2, 145 3); and executing tasks of each of the processes of the first container on the one or more corresponding CPUs (145 1) to which the process has exclusive affinity; wherein the first container is a first virtual machine (110 1) and each of the one or more processes included in the first container is a virtual CPU (125 1), and at least one said virtual CPU (125 1) is assigned to have exclusive affinity to a corresponding physical CPU (145 1); wherein determining that the first virtual machine (110 1) is latency sensitive comprises: reading a latency sensitivity indicator for the first virtual machine (110 1); reading a CPU entitlement value for the first virtual machine (110 1); determining that the latency sensitivity indicator is a predetermined value; and determining that the CPU entitlement value is a maximum value; and reading a latency sensitivity indicator for the first virtual machine (110 1); reading a CPU entitlement value for the first virtual machine (110 1); determining that the latency sensitivity indicator is a predetermined value; and determining that the CPU entitlement value is a maximum value; and wherein the maximum value for the CPU entitlement value indicates that each virtual CPU of the first virtual machine is permitted to consume the full processing capacity of one of the physical CPUs.