Virtual Selfishness Queue and Its Application

In this letter, we investigate the node's dynamic selfishness and the rate allocation in time-varying selfish wireless networks (SeWNs). We model the dynamics of the node's selfishness by designing a virtual forwarding selfishness queue (v-FSQ) and a virtual receiving selfishness queue (v-RSQ). Specifically, the v-FSQ is constructed with the consideration of the node's residual energy and employed incentives, while the v-RSQ is constructed with the consideration of the node's data queue state information. By virtual of nodes' v-RSQs and v-FSQs, a stochastic optimization problem is formulated to maximize the time-average network utility, which is related to the SeWNs throughput, whilst bounding the nodes' selfishness queues. The dynamic rate allocation is obtained with the aid of the Lyapunov optimization theory. Simulation results verify the theoretical analysis of our proposed scheme.