Modeling of Latency and Saturation Phenomena in Interconnection Networks

A multiprocessor networks modeled as a ring and as a 2D toroidal lattice of nodes are considered. Each node generates messages with probability lambda per clock cycle per output port. Once an output buffer is not empty, the output port sends out exactly one message every clock cycle. We derive analytical expressions for the queue length distribution, the average number of messages in buffers, and the latency. The network experiences a phase transition from equilibrium to the saturation regime, and the critical exponent is equal to 1. Simulations demonstrate an excellent agreement with theoretical predictions and validate the assumption of independent queues. A model of a ring network where the message generating rate depends on the intensity of the incoming messages is studied by simulation. The results show the emergence of dependences between queues in closely located nodes, and changes in the values of the critical load and critical exponent.