Interconnection networks with heterogeneous activity or finite buffers: beyond Jackson's theorem

We present theoretical models and numerical results for performance of a multiprocessor network modeled as a ring and as a 2-dim wraparound square lattice of nodes with local processors that generate messages with rate λ per clock cycle and two or, respectively, four output ports/buffers. Two different models are considered. One assumes that the generation rate of a node depends on the intensity of the flow of arriving messages. The other model considers networks with limited buffers. The average queue lengths and average latency are obtained. The results show that the model of independent queues, which is valid for networks with homogeneous activity and infinite buffers, is not applicable, which violates the Jackson theorem.