Trends in communication technology and MEMS research point towards a coming age of intelligent systems that will consist of thousands of minature devices -- each capable of a combination of computation, communication, sensing, actuation and motion -- all networked together wirelessly. These large networks will start to resemble thermodynamic particle systems where global properties emerge at a critical level of local interactions.
We will discuss some properties that undergo abrupt "phase transitions" in large-scale wireless networks. At a critical density threshold, the probability that the network obtains these properties changes sharply from nearly zero to nearly one. These thresholds arise in a number of contexts including k-connectivity, token ring formation, probabilistic flooding, channel allocation, and target tracking. By modeling the achievement of some of these properties as constraint satisfaction problems, we show that the critical region also corresponds to a peak in average computational and communication complexity in the network.
We argue that this approach is useful for determining feasible and resource-efficient operating points in both pre-designed and self-configuring wireless networks.