Core Capacity Region of Energy-Limited, Delay-Tolerant Wireless Networks

We model energy-limited, delay-tolerant wireless networks as non-transferable-utility (NTU) cooperative network flow games. We model the utility of each node as a positive linear function of the number of bits that the node sends as a source and the number of bits that it receives as a destination. Based on the core of a cooperative game, we define the "core capacity region" of these networks as the set of utility vectors that cannot be collapsed by any coalition. We show that the core capacity region is non-empty. This implies that even if the nodes have perfect side information on all of the Joules-per-bit link costs in the entire network, there still exists a network solution such that no subset of the nodes can improve the utilities of all of its members over those in this network solution. We present an algorithm to compute the core capacity region. We show that the only core solution under the many-to-one traffic model with a single sink and stationary nodes is the direct transmission strategy; however, when virtual prices are allowed as signals, cooperative solutions emerge within the core capacity region. We show that the core capacity region is non-empty under pricing. The core capacity region serves as a useful concept in the analysis of cooperative, energy-limited, delay-tolerant networks