An initiating processing tile generates an offload request that may include a processing tile ID, source data needed for the computation, program counter, and destination location where the computation result is stored. The offload processing tile may execute the offloaded computation. Alternatively, the offload processing tile may deny the offload request based on congestion criteria. The congestion criteria may include a processing workload measure, whether a resource needed to perform the computation is available, and an offload request buffer fullness. In an embodiment, the denial message that is returned to the initiating processing tile may include the data needed to perform the computation (read from the local memory of the offload processing tile). Returning the data with the denial message results in the same inter-processing tile traffic that would occur if no attempt to offload the computation were initiated.