Routing algorithm of minimizing maximum link congestion on grid networks

As regular topology networks, grid networks are widely adopted in network deployment. Link congestion and routing path length are two critical factors that affect the delay and throughput of a network. In this paper, we study the routing problem in grid networks concerning these two factors. The main objective of our routing algorithms is to minimize the maximum link congestion. The shortest path minimum maximum (SPMM) link congestion and non-shortest path minimum maximum (NSPMM) link congestion routing problems are studied. The two problems are first formulated as integer optimization problems. Then, corresponding routing algorithms (SPMM and NSPMM routing algorithms) are proposed. For SPMM routing algorithm, the path length is optimal, while for NSPMM routing algorithm, the path is limited in a submesh. Thus, the path length can be bounded. At last, we compare the proposed routing algorithms under different scenarios with other popular routing algorithms (RowColumn, ZigZag, Greedy, Random routing algorithms). The performances are evaluated through different metrics including link congestion, path length, path congestion, path congestion to path length ratio, delay and throughput.