# Mobile wireless networks

This dramatic result relied on a strong assumption on node mobility: the trajectory of each node is an independent, stationary and ergodic random process with a uniform stationary distribution on the unit disk. Intuitively, the sample path of each node “fills the space over time”, which is unrealistic in many practical settings. A natural question is then how strongly the achievable throughput depends on the assumptions on node mobility.

We therefore consider a model in which the nodes follow a much more limited mobility pattern: all the nodes are on a unit sphere, but each node is constrained to move on a great circle. These great circles are random, but remain fixed over time. Each node moves randomly along its own circle. The mobility process is therefore not symmetric in all the users. Our main result is that if the locations of the great circles are chosen randomly and independently, then for almost all configurations of such great circles, the average long-term throughput per node can be kept constant as the number of nodes increase. Thus, although each node is restricted to move in its own one-dimensional space, the same asymptotic performance is achieved as in the case when they can move in the entire 2-D region. We focus on the unit sphere instead of the unit disk to avoid edge effects, but the results should also be valid for nodes moving along line segments within the unit disk.