Queuing behavior of queue-backlog-based random access scheduling in the many-channel regime

Efficient and distributed scheduling algorithms are essential to garner the full potential of wireless systems with multiple channels, e.g., OFDM systems. Recently, a group of random access scheduling algorithms have been proposed to achieve throughput optimality with a single non-fading channel. While these distributed algorithms can readily be extended to a multi-channel setting, the analysis of their queuing behavior and delay performance is non-trivial in the many-channel regime, since the state space of schedules grows exponentially with the number of channels. In this paper, we first generalize these distributed random access algorithms from a single-channel setting to a multi-channel setting for fully connected networks. In an attempt to characterize the delay performance of this new algorithm, we introduce a novel equivalent deterministic single-queue system and show that the queuing behavior of individual communication links under our algorithm converges to the equivalent queue system as the number of channels grows. By studying this equivalent queue system, we derive a closed-form approximation for the data queue backlogs/delays at the steady state in the many-channel regime.