On the Cost of Knowledge of Mobility in Dynamic Networks: An Information-Theoretic Approach

In this paper, we extend an information-theoretic approach for characterizing the minimum cost of tracking the motion state information, such as locations and velocities, of nodes in dynamic networks. A rate-distortion formulation is proposed to solve this minimum-cost motion-tracking problem, where the minimum cost is the minimum information rate required to identify the network state at a sequence of tracking time instants within a certain distortion bound. The formulation is applicable to various mobility models, distortion criteria, and stochastic sequences of tracking time instants and hence is general. Under Brownian motion and Gauss-Markov mobility models, we evaluate lower bounds on the information rate of tracking the motion state information of nodes, where the motion state of a node is 1) the node´s locations only, or 2) both its locations and velocities. We apply the obtained results to analyze the geographic routing overhead in mobile ad hoc networks. We present the minimum overhead incurred by maintaining the geographic information of nodes in terms of node mobility, packet arrival process, and distortion bounds. This leads to precise characterizations of the observation that given certain state-distortion allowance, protocols aimed at tracking motion state information may not scale beyond a certain level of node mobility.