The Connectivity of Selfish Wireless Networks

The network connectivity of selfish wireless networks (SeWNs) constituted by selfish nodes (SeNs) is investigated. The SeN´s degree of node-selfishness (DeNS) is used for characterizing the effects of its energy resources and the benefits of the incentives provided for enhancing its transmission willingness. Furthermore, the SeNs´ signal to interference plus noise ratios are defined in terms of both their DeNSs and their interference factors. We then continue by quantifying the effect of node-selfishness on the grade of network connectivity and derive both the upper and lower bounds of the critical DeNS. Explicitly, the network is deemed to be connected when the DeNS is below the lower bound and unconnected for a DeNS above the upper bound. This allows us to quantify the asymptotic critical DeNSs for our SeWNs. In addition, we develop an energy-conscious node-selfishness model for characterizing the relationship between the SeN´s residual energy and its DeNS. Based on this model and on the asymptotic critical DeNS derived, the critical amount of residual energy required for maintaining a specific grade of network connectivity is determined, which is verified by our simulation results.