Capacity-Delay Scaling in Arbitrary Wireless Networks

We establish capacity and delay scaling laws for a general network topology, interference model, and traffic model. There are two main contributions of this paper. Our first contribution is the derivation of capacity-delay scaling laws in terms of spectral properties of the wireless network using results of Diaconis and Stroock (1991) and Sinclair (1992). By representing a wireless network in terms of an appropriate capacitated graph, we determine precise (i.e. upper and lower bound) capacity scaling in terms of the maximal min-cut capacity over a class of graphs. Next, we establish delay scaling using very simple techniques. Our methods apply to general fixed and mobile network models. As a special case, we recover the results of Gupta and Kumar (2000), El Gamal, Mammen, Prabhakar and Shah (2004), Grossglauser and Tse (2002) and Diggavi, Grossglauser and Tse (2003). The second contribution is the derivation of capacity scaling laws for Gaussian channels. In particular, we provide upper and lower bounds on capacity scaling for an arbitrary wireless network with AWGN channels and non-cooperative transmissions. We characterize the capacity scaling for non-cooperative transmissions in terms of the cut-properties of the underlying network graph. We also provide information theoretic upper bounds for general fading AWGN channels. Finally, we evaluate our bounds for grid graph and geometric random graph.