A system that supports multiple contact centers includes a communications network that is coupled between a private network (e.g. MPLS network) and a remote computing environment (e.g. cloud environment). A server system in the remote computing environment monitors health of different network segments (e.g. bandwidth of the connection between the communications network and the remote computing environment, bandwidth of a link used by a tenant to access the private network, etc.). When it is determined that quality of service for voice conversations for one or more contact centers is at risk due to a health status parameter of a network segment reaching a threshold, an appropriate system reaction is triggered. The system reaction may be to offload future calls to a peer remote computing environment to service future calls. The system reaction may also be to cancel outbound campaigns, provide pre-determined “sorry” messages, and the like.