Mean-Field Limits for Large-Scale Random-Access Networks

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