On the scalability of ad hoc networks: a traffic analysis at the center of a network

We investigate the inherent scalability problem of ad hoc networks that originated from the nature of multi-hop 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 hound 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.