Critical Phenomena in Interconnection Networks with Heterogeneous Activity

Theoretical models and numerical results for performance of the computer interconnection networks with heterogeneous activity are presented. The networks are modeled as a ring or as 2-dim toroidal square lattice of nodes with local processors with two or, respectively, four output ports/buffers. The processors generate messages with two different rates, λ1 or λ2, per clock cycle and per output buffer, depending on the intensity of the flow of the arriving messages. The average queue lengths and average latencies are obtained. The model of independent queues and the Jackson theorem are not applicable for this type of networks. It is shown that the networks undergo the phase transition of the second order with non-trivial critical exponents.