A DTMC Model for Performance Evaluation of Irregular Interconnection Networks with Asymmetric Spatial Traffic Distributions

Abstract

Several mathematical models have been proposed to evaluate the performance of interconnection networks used for high-speed connections for supercomputers, switches and routers for local and wide area networks, as well as networks on a chip. Often these models are based on state space reduction by exploiting symmetries of the network and requiring uniform traffic patterns. If an interconnection network is built for a specific application with non-uniform spatial traffic distribution, models that are more general are needed. This paper proposes a mathematical model for performance evaluation of application-specific interconnection networks based on inhomogeneous discrete time Markov chains (DTMC). It supports store and forward routing, irregular network topologies, and asymmetric spatial traffic distributions. The model is described in a generalized way so that it can support arbitrary switching element sizes within the network and its input buffers.