Impact of Selfish Packet Forwarding on Energy-Efficient Topology Control

Wireless topology control attempts to harness the programmability of radios to build efficient network structures. This paper addresses energy minimization in an ad hoc network of selfish nodes by jointly considering packet forwarding and packet sourcing—two main sources of energy consumption in multi-hop networks. Specifically, we examine how energy-efficient topologies can be established through non-cooperative power control taking into account the possibility of selective and partial packet forwarding in the network. The topology control game, where each node is attempting to minimize its energy consumption while maintaining network connectivity, is shown to be a potential game. This establishes the existence of a Nash Equilibrium (NE). Additionally, the NE is shown to be unique and globally energy-efficient—the nodes transmit at just enough power necessary to maintain all the minimum energy routes in the network. From simulations we observe that when nodes forward a small percentage of packets directed through them, the resulting NE topologies that minimize energy are more densely connected and consume more energy than the topologies that emerge when nodes forward a large portion of incoming packets. From the energy viewpoint, this result is particularly interesting as it quantifies the energy efficiency gains obtained by cooperation and corroborates the need for encouraging nodes to forward packets in a decentralized network.