Lattice-Based Turn Model for Adaptive Routing

Abstract

This paper presents a model for designing partially adaptive logic-based distributed routing algorithms. Unlike the previous methods, the Lattice-based Turn Model associates turn prohibitions with the points of different full-rank integer lattices. Due to the generality of the proposed model, existing approaches can be considered a subset of the solution space identified by this work. Morover, we propose three theorems that are instrumental to the design of lattice-based routing algorithms. In particular, the second theorem gives a necessary and sufficient condition to prove that a lattice-based routing algorithm is deadlock-free as long as the lattice basis meets certain requirements. Based on the proposed model, a novel routing algorithm, called lattice-based routing algorithm (LBRA), is presented. Simulation results exhibit encouraging performance improvements over state-of-the-art approaches when considering real and synthetic benchmarks. For instance, average 71 and 18 percent latency reductions are observed under transpose1 traffic compared to, respectively, Odd-Even and Repetitive Turn Model routing algorithms. Furthermore, LBRA achieves up to 38 and 17 percent performance improvement under real traffic as compared to Odd-Even and Repetitive Turn Model routing algorithms.