Traffic Analysis in Random Delaunay Tessellations and Other Graphs

In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erd"os-Renyi random graphs, geometric random graphs, expanders and random $k$-regular graphs. Moreover we show that adding a random matching to the original graph can considerably reduced the maximum vertex flow.