Analysis of Shortest Path Routing for Large Multi-Hop Wireless Networks

In this paper, we analyze the impact of straight line routing in large homogeneous multi-hop wireless networks. We estimate the nodal load, which is defined as the number of packets served at a node, induced by straight line routing. For a given total offered load on the network, our analysis shows that the nodal load at each node is a function of the node´s Voronoi cell, the node´s location in the network, and the traffic pattern specified by the source and destination randomness and straight line routing. In the asymptotic regime, we show that each node´s probability that the node serves a packet arriving to the network approaches the products of half the length of the Voronoi cell perimeter and the load density function that a packet goes through the node´s location. The density function depends on the traffic pattern generation by straight line routing, and determines where the hot spot is created in the network. Hence, contrary to conventional wisdom, straight line routing can balance the load over the network, depending on the traffic patterns.