Paradox 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. The traffic pattern determines where the hot spot is created in the network, and straight line routing itself can balance the relay load in certain cases. In the asymptotic regime, each node's probability that the node serves a packet arriving to the network can be approximated as the multiplication of a half length of its Voronoi cell perimeter and the probability density function that a packet goes through the node's location. Both simulations and analysis confirm that this approximation converges to the exact value. The scaling order of network performance in our analysis is independent of traffic patterns generated by source-destination pair randomness, but for a given node the performance of each node is strongly related to the source-destination pair randomness.