One or both of read and write accesses to a fabric-attached memory module via a fabric interconnect are monitored. In one or more implementations, offloading of one or more tasks accessing the fabric-attached memory module to a processor of a routing system associated with the fabric-attached memory module is initiated based on the read and write accesses to the fabric-attached memory module. Additionally or alternatively, replicating memory of the fabric-attached memory module to a cache memory of a computing node in the disaggregated memory system executing one or more tasks of a host application is initiated based on the write accesses to the fabric-attached memory module.