A Mean Field Game Analysis of Distributed MAC in Ultra-Dense Multichannel Wireless Networks

This report analyzes the performance of distributed Medium Access Control (MAC) protocols in ultra-dense multichannel wireless networks, whereNfrequency bands (or channels) are shared by$M=mN$devices, and devices make decisions to probe and then transmit over available frequency bands. While such a system can be formulated as anM-player Bayesian game, it is often infeasible to compute the Nash equilibria of a large-scale system due tothe curse of dimensionality. In this report, we exploit the Mean Field Game (MFG) approach and analyze the system in the large population regime (Ntends to∞andmis a constant). We consider a distributed and low complexity MAC protocol where each device probes$d/k$channels by following an exponential clock which ticks with ratekwhen it has a message to transmit, and optimizes the probing strategy to balance throughput and probing cost. We present a comprehensive analysis from the MFG perspective, including the existence and uniqueness of and convergence to the Mean Field Nash Equilibrium and the price of anarchy with respect to the global optimal solution. Our analysis shows that the price of anarchy is at most one half, but is close to zero when the traffic load or the probing cost is low. Our numerical results confirm our analysis and show that the MFNE is a good approximation of theM-player system. Further, this report demonstrates the novelty of MFG analysis, which can be used to study other distributed MAC protocols in ultra-dense wireless networks.