1. A method, said method comprising: in response to a request for a proposed additional data transfer from a source storage system to a target storage system, one or more processors of one or more computers estimating utilization of one or more data transfer components of the source storage system and the target storage system that would occur during the proposed additional data transfer combined with other scheduled data transfers involving the source storage system and the target storage system, based in part on (i) an I/O request rate for the source storage system and the target storage system for recent actual data transfers involving the source storage system and the target storage system combined with (ii) an estimated I/O request rate for the source storage system and the target storage system for the proposed additional data transfer; and said one or more processors ascertaining whether the estimated utilization exceeds a corresponding utilization threshold, and if so, said one or more processors postponing execution of the proposed additional data transfer, and if not, said one or more processors initiating execution of the proposed additional data transfer.