Orderly broadcasting in a 2D torus

We describe an ordering of the vertices of a 2-dimensional torus and study the upper bound on the orderly broadcast time. Along with messy broadcasting, orderly broadcasting is another model where the nodes of the network have limited knowledge about their local neighborhood. However, while messy broadcasting explores the worst-case performance of broadcast schemes, orderly broadcasting, like the classical broadcast model, is concerned with finding a fixed ordering of the vertices of a graph that will minimize the overall broadcast time.