Throughput equalization in mean-field hard-core models for CSMA-based wireless networks

In this paper we consider the problem of equalizing throughput of nodes in CSMA-based wireless networks. We model interference in a network using conflict graph, where edges represent hard-core interaction, meaning that the two nodes an edge connects cannot be simultaneously active, or transmitting. In practice, the degrees of nodes in a conflict graph are not constant. In such cases, using CSMA leads to lack of fairness since nodes with larger degree have the potential of getting hold of the medium for smaller fraction of time than the nodes with smaller degree. We present a distributed strategy for throughput equalization. The proposed strategy is based on a mean-field hard-core model of interference, and it equalizes the throughput of the nodes with different degrees. We also show that the mean-field hard-core model exhibits a certain phase transition. We present results of Monte-Carlo simulations to evaluate the the proposed strategy in square grid networks and Poisson networks, in addition to mean-field networks.