On the Cost of Knowledge of Mobility in Dynamic Networks

In this paper, an information-theoretic framework is developed for characterizing the minimum cost, in bits per second, of tracking the motion state information, such as locations and velocities, of nodes in dynamic networks. The minimum-cost motion-tracking problem is formulated as a rate-distortion problem, where the minimum cost is the minimum rate of information required to identify the network state at a sequence of tracking time instants within a certain distortion bound. The formulation is general in that it can be applied to a variety of mobility models, distortion criteria, and stochastic sequences of tracking time instants. Under the Gauss-Markov mobility model, lower bounds on the information rate of tracking the motion state information of nodes in dynamic networks are derived, where the motion state of a node is 1) the node's locations only, or 2) both its locations and velocities. The results are then used to analyze the protocol overhead of geographic routing protocols in mobile ad hoc networks. The minimum overhead incurred by maintaining the geographic information of the nodes is characterized in terms of node mobility, packet arrival process and distortion bounds. This leads to precise mathematical description of the observation that, given certain state-distortion allowance, protocols aimed at tracking motion state information (such as geographic routing protocols) may not scale beyond a certain level of node mobility.