On the scalability of ad hoc networks

We investigate the inherent scalability problem of ad hoc networks originated from the nature of multihop networks. First, the expected packet traffic at the center of a network is analyzed. The result shows that the expected packet traffic at the center of a network is linearly related with the network size, that is, the expected packet traffic at the center of a network is O(k), where k is the radius of a network. From the result, the upper bound of the diameter of a network D=2k, that guarantees the network is scalable, is obtained. The upper bound is given by C/r-1, where C is the channel capacity available to each node and r is the packet arrival rate at each node.