Acknowledgments 7 Conclusions and Future Work

\An adaptive and fault tolerant wormhole routing strategy for k-ary n-cubes," IEEE Transactions on Computers, 22 addition of channels. In such topologies, the turns are not necessarily 90-degrees and the abstract cycles are not necessarily formed by four turns. A nal important task is the identiication of realistic workload distributions, so that the results of future simulations can be more meaningful. 21 traac has been used in many previous simulation studies, but we know of no real applications that generate uniform traac. A traac pattern is determined by the application and how its processes are mapped to the nodes of the network. For most applications, each node will communicate with some nodes much more than others. Nonuniform traac presents a problem for the xy and e-cube algorithms because they are nonadaptive. Just as they maintain the evenness of uniform traac, they blindly maintain the unevenness of nonuniform traac. The result, as the gures illustrate, is often poor performance. Our goal has been to make the best use of the channels in wormhole-routed interconnection networks. Analyzing the directions in which packets can turn in a network and prohibiting the minimum number of turns that break all of the cycles produces routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive. Deadlock freedom and livelock freedom are essential for routing algorithms. Adaptiveness increases the chances that packets can avoid hot spots and faulty hardware and decreases the chances of indeenite postponement and livelock. Nonminimal routing allows even greater hot-spot avoidance and fault tolerance. The turn model, unlike other approaches to designing adaptive routing algorithms, is applicable to networks with only the channels required by the network topologies (as well as to networks with extra physical or virtual channels). Applied to n-dimensional meshes and k-ary n-cubes without extra channels, the turn model produces several new, partially adaptive routing algorithms. Simulations of these partially adaptive routing algorithms indicate that they can perform better than nonadaptive algorithms for nonuniform patterns of message traac. While the turn model has many advantages, it also has some disadvantages. Adaptive routing can require more complex control logic for route selection than does nonadaptive routing, and this may increase node delay. Part of the complexity is due to the need for a router to decide between multiple output channels, all of which lead to the destination. Another part of the complexity is due to the need …