Capacity of a wireless ad hoc network with infrastructure

In this paper we study the capacity of wireless ad hoc networks with infrastructure support of an overlay of wired base stations. Such a network architecture is often referred to as hybrid wireless network or multihop cellular network. Previous studies on this topic are all focused on the two-dimensional disk model proposed by Gupta and Kumarin their original work on the capacity of wireless ad hoc networks. We further consider a one-dimensional network model and a two-dimensional strip model to investigate the impact of network dimensionality and geometry on the capacity of such networks. Our results show that different network dimensions lead to significantly different capacity scaling laws. Specifically, for a one-dimensional network of n nodes and b base stations, even with a small number of base stations, the gain in capacity is substantial, increasing linearly with the number of base stations as long as b log b ≤ n. However, a two-dimensional square (or disk) network requires a large number of base stations b = Ω(√n) before we see such a capacity increase. For a 2-dimensional strip network, if the width of the strip is at least on the order of the logarithmic of its length, the capacity follows the same scaling law as in the 2-dimensional square case. Otherwise the capacity exhibits the same scaling behavior as in the 1-dimensional network. We find that the different capacity scaling behaviors are attributed to the percolation properties of the respective network models.