  We establish mean-field limits for large-scale random-access networks with
buffer dynamics and arbitrary interference graphs. While saturated-buffer
scenarios have been widely investigated and yield useful throughput estimates
for persistent sessions, they fail to capture the fluctuations in buffer
contents over time, and provide no insight in the delay performance of flows
with intermittent packet arrivals. Motivated by that issue, we explore in the
present paper random-access networks with buffer dynamics, where flows with
empty buffers refrain from competition for the medium. The occurrence of empty
buffers thus results in a complex dynamic interaction between activity states
and buffer contents, which severely complicates the performance analysis. Hence
we focus on a many-sources regime where the total number of nodes grows large,
which not only offers mathematical tractability but is also highly relevant
with the densification of wireless networks as the Internet of Things emerges.
We exploit time scale separation properties to prove that the properly scaled
buffer occupancy process converges to the solution of a deterministic
initial-value problem, and establish the existence and uniqueness of the
associated fixed point. This approach simplifies the performance analysis of
networks with huge numbers of nodes to a low-dimensional fixed-point
calculation. For the case of a complete interference graph, we demonstrate
asymptotic stability, provide a simple closed-form expression for the fixed
point, and prove interchange of the mean-field and steady-state limits. This
yields asymptotically exact approximations for key performance metrics, in
particular the stationary buffer content and packet delay distributions. The
methodological framework that we develop easily extends to various model
refinements as will be illustrated by several examples.
