Let's assume a setting where we have one or more operators connected to a keyed stream, and where we expect numerous keys and significant partitioned state (in terms of size) per key.
Is it possible to influence on which Task Managers Flink would schedule each of these operator instances? In a setting with n Task Managers and m operator instances, the worst case would be that multiple (if not all) of these m instances end up sitting on only a few of the n Task Managers, therefore exhausting the available resources.