ABSTRACT
We present theoretical models and simulation results for performance of a multiprocessor network modeled as a ring and as a 2D wraparound square lattice of nodes with local processors that generate messages with constant rate per time slot. The buffers can hold a limited number of messages. Explicit theoretical results based on rst-order (independent queues) and second-order approximation of the queue distributions are obtained for small buffer sizes (1 and 2). For larger buffers, the problem appears analytically intractable and has been studied by simulations. The average queue lengths and average latency are obtained. The results show that the model of independent queues, which is valid for networks with innite buffers, is still applicable for small generation rates but breaks down for larger loads, which violates Jackson’s theorem.
