Delay scaling in poisson networks

The local delay, defined as the mean time it takes a node to connect to its nearest neighbor, is a fundamental performance metric in a wireless network. For a network with Poisson distributed nodes, we find its scaling behavior (as a function of the rate of transmission) for different types of nearest-neighbor and the two extreme cases of mobility (infinite mobility and no mobility). Remarkably, it turns out that the level of mobility has hardly any effect on the scaling behavior of the local delay; it affects the pre-constant only.