A New Approach to O -Line Packet Routing Case Study: 2-Dimensional Meshes

In this paper we present the multistage oo-line routing model, a new and rather natural, way to model oo-line packet routing problems. With this model, the problem of oo-line packet routing reduces to the problem of nding edge disjoint paths on a multistage graph. The multistage oo-line routing model can model any kind of routing pattern on any graph. Furthermore, it incorporates the size of the maximum queue that can be created in any processor. The multistage oo-line routing model accommodates all optimal solutions and can be used to obtain lower bounds that are based not in worst case situations but rather on the actual routing problem under consideration. The paths of the packets are computed by a greedy heuristic method that is based on the distance the packets have to travel. A lot of freedom is left for the user of the model in order to incorporate in the heuristic properties of the underlying interconnection network. We used the multistage oo-line model to study the oo-line permutation packet routing problem on 2-dimensional meshes. We ran millions of experiments based on random generated data and, for all of our experiments, we were able to compute a solution of length equal to the maximum distance a packet had to travel, and thus, match the actual lower bound for each routing pattern.