Mean-field analysis of CSMA wireless networks

In recent years both the number and the variety of devices that rely on wireless connectivity have shown huge growth. Consequently, wireless networks are going through a tremendous growth in size and complexity, supporting immense numbers of nodes and data volumes. Well-established methodologies have been developed for evaluating the performance in saturated buffer conditions. However, these provide no insight in the performance of networks with intermittent packet arrivals. The occurrence of empty buffers in the latter scenario results in a complex interaction between activity states and packet queues, which severely complicates the performance analysis. Motivated by these challenges, we develop a mean-field approach to analyze buffer contents and packet delays in a many-sources regime. The mean-field behavior simplifies the analysis of a large-scale network with packet arrivals and buffer dynamics to a low-dimensional fixed-point calculation for a network with saturated buffers. In particular, the analysis yields explicit expressions for the buffer content and packet delay distribution in terms of the fixed-point solution. The method we propose can in fact be extended to more complex scenarios, and generalizations to a queue-based protocol and a multi-hop model are briefly outlined.