The storage system exports logical storage volumes that are provisioned as storage objects. These storage objects are accessed on demand by connected computer systems using standard protocols, such as SCSI and NFS, through logical endpoints for the protocol traffic that are configured in the storage system. When traffic through a particular protocol endpoint is busy, the logical storage volume undergoes a rebind process pursuant to which the logical storage volume is bound to a new protocol endpoint, and the binding to the old protocol endpoint is removed upon completion of all pending input-output commands issued through the old protocol endpoint.