An empirical study of off-line permutation packet routing on two-dimensional meshes based on the multistage routing method

In this paper we present the multistage off-line method, a new and rather natural way to model off-line packet routing problems, which reduces the problem of off-line packet routing to that of finding edge disjoint paths on a multistage graph. The multistage off-line method can model any kind of routing pattern on any graph and can incorporate the size of the maximum queue allowed in any processor. The paths for the packets are computed by a greedy heuristic method. Based on the multistage off-line method, we study the permutation packet routing problem on two-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.