Abstract
Maximizing network lifetime and optimizing aggregate system utility are important but usually conflict goals in wireless multi-hop networks. For the trade-off, we present a matrix game-theoretic cross-layer optimization formulation to jointly maximize the diverse objectives in such networks with network coding. To this end, we introduce a cross-layer formulation of general network utility maximization (NUM) that accommodates routing, scheduling, and stream control from different layers in the coded networks. Specifically, for the scheduling problem and then the objective function involved, we develop a matrix game with the strategy sets of the players corresponding to hyperlink and transmission mode, and design multiple payoffs specific to lifetime and system utility, respectively. In particular, with the inherit merit that matrix game can be solved with mathematical programming, our cross-layer programming formulation actually benefits from both game-based and NUM-based approaches at the same time by cooperating the programming model for the matrix game with that for the other layers in a consistent framework. Finally, our numerical experiments quantitatively exemplify the possible performance trad-offs with respect to the two variants developed on the multiple objectives in question while qualitatively exhibiting the differences between the framework and the other related works.
