Congestion in randomly deployed wireless ad-hoc and sensor networks

Congestion in wireless ad-hoc sensor networks not only causes packet loss and increases queueing delay, but also leads to unnecessary energy consumption. In these networks, two types of congestion can occur: node-level congestion, which is caused by buffer overflow in the node, or link-level congestion, when wireless channels are shared by several nodes arising in collisions. We study a measure of link-level congestion in static wireless ad-hoc and sensor networks randomly deployed over an area. The measure of congestion considered is the inverse of the greatest eigenvalue of the adjacency matrix of the random graph. This measure gives an approximation of the average quantity of wireless links of a certain length on the network. We review the results to find this measure in Bernoulli random graphs. We use tools from random graph and random matrix theory to extend this measure on Geometric random graphs.