5 Conclusions and Future Work

20 and topologies. As in the case of 2D meshes with double y channels, the turn model may reveal more adaptive routing algorithms than were previously known. For example, 24 of the 32 turns in a double-xy network can be allowed and still prevent deadlock, while the double-xy routing algorithm allows only 8 (Figure 2). Finally, we limited our exploration of routers with six bidirectional network channels to 2D mesh topologies. Perhaps, a diierent topology using the six channels would ooer better performance. \An adaptive and fault tolerant wormhole routing strategy for k-ary n-cubes," IEEE Transactions on Computers, hand, select channels based on local, short-term information. These selections tend to beneet just the routed packet, and only for the immediate future, and tend to interfere with other packets. In so doing, the selections often produce zigzag paths, which disturb the global, long-term evenness of uniform and center-reeection traac in a mesh. The result is increased contention and decreased performance. For the matrix-transpose and bit-reversal traac patterns, the situation is diierent. The xy algorithm embodies the wrong global, long-term information for these patterns and spreads the traac very unevenly. The adaptive algorithms, especially the more adaptive mad-y algorithm, spread the traac fairly evenly by avoiding local, short-term hotspots. They do not spread the traac as evenly as an algorithm would that embodied the correct global and long-term information, but they come reasonably close. The maximum sustainable throughputs for the xy algorithm under uniform and center-reeection traac are 29% and 30%; for the adaptive algorithms under matrix-transpose and bit-reversal traac, they are 26% and 20%. Our goal in this paper has been to examine fully adaptive routing in 2D meshes, and in so doing, to illustrate the utility of our turn model for designing maximally adaptive routing algorithms. Applying the turn model to diierent interconnection networks for 2D meshes shows those with double y channels to be the simplest that support fully adaptive routing. Applying the turn model to 2D meshes with double y channels produces a new routing algorithm that is even more adaptive than the previously known routing algorithms. Simulations of these algorithms show that their relative performances depend on the pattern of message traac. If the network traac is already uniformly distributed, the xy routing algorithm can spread the traac evenly across the channels of the mesh, it performs the best, despite being nonadaptive. Otherwise, the mad-y algorithm performs …