A Lower Bound on Network Layer Control Information

Any asymptotic mean stationary mobility model generates, at the network layer, a route process that satisfies the Asymptotic Equipartition Partition Theorem of Information Theory. This permits an information theoretic lower bound for network layer control information. By recasting the mobility problem as a Dynamical System, we provide a unique and rigorous examination of mobility models and routing protocols. In particular, new results on stationary and ergodic properties of common mobility models – via two useful generalizations – are provided. The important concept ‘perfect simulation’ for reliable, and repeatable, results is formalized. A fixed to variable length encoding lemma – of independent interest – for asymptotically mean stationary sources is developed. Finally, a lower bound on network layer control information is presented.