Phase transition phenomena in wireless ad hoc networks

There are many contexts in distributed wireless networks where there is a critical threshold, corresponding to a minimum amount of the communication effort or power expenditure by individual nodes, above which a desirable global property exists with high probability. When this individual node effort is below the threshold the desired global property exists with a low probability. This "phase transition" is typically seen to become sharper as the number of nodes in the network increases. We discuss some examples of properties that exhibit such critical behavior: node reachability with probabilistic flooding, ad-hoc network connectivity, and sensor network coordination. We discuss the connections between these phenomena and the phase transitions that have been shown to arise in random graphs. We argue that a good understanding of these phase transition phenomena can provide useful design principles for engineering distributed wireless networks