An apparatus in one embodiment comprises a host device that includes at least one processor and an associated memory. The host device is configured to implement a plurality of processes each configured to access a shared region of the memory. The host device is further configured to establish a multi-process control group for the shared region, to maintain state information for the multi-process control group, and to track usage of the shared region by the processes based at least in part on the state information. At least a subset of the processes may comprise respective containers implemented utilizing operating system level virtualization of the processor of the host device. The multi-process control group established for the shared region illustratively comprises a coarse-grained control group having a granularity greater than a single page of the shared region.