The Turn Model for Adaptive Routing

We present a model for designing wormhole routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive. A unique feature of this model is that it is not based on adding physical or virtual channels to network topologies (though it can be applied to networks with extra channels). Instead, the model is based on analyzing the directions in which packets can turn in a network and the cycles that the turns can form. Prohibiting just enough turns to break all of the cycles produces routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive for the network. In this paper, we focus on the two most common network topologies for wormhole routing, n-dimensional meshes and k-ary n-cubes, without extra channels. In an n-dimensional mesh, just a quarter of the turns must be prohibited to prevent deadlock. The remaining three quarters of the turns permit partial adaptiveness in routing. Partially adaptive routing algorithms are described for 2D meshes, n-dimensional meshes, k-ary n-cubes, and hypercubes. Simulations of partially adaptive and nonadaptive routing algorithms for 2D meshes and hypercubes show that which algorithm has the lowest latencies and highest sustainable throughput depends on the pattern of message traffic. For nonuniform traffic, partially adaptive routing algorithms perform better than nonadaptive ones.