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.
Abstract Random-access algorithms such as the Carrier-Sense Multiple-Access (CSMA) protocol provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years fairly tractable models have been shown to yield remarkably accurate throughput estimates in scenarios with saturated buffers. In contrast, in non-saturated scenarios, where nodes refrain from competition for the medium when their buffers are empty, a complex two-way interaction arises between the activity states and the buffer contents of the various nodes. As a result, the throughput characteristics in such scenarios have largely remained elusive so far. In the present paper we provide a generic structural characterization of the throughput performance and corresponding stability region in terms of the individual saturation throughputs of the various nodes. While the saturation throughputs are difficult to explicitly determine in general, we identify certain cases where these values can be expressed in closed form. In addition, we demonstrate that various lower-dimensional facets of the stability region can be explicitly calculated as well, depending on the neighborhood structure of the interference graph. Illustrative examples and numerical results are presented to illuminate the main analytical findings. Random-access algorithms such as the Carrier-Sense Multiple-Access (CSMA) protocol provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years, fairly tractable models have been shown to yield remarkably accurate throughput estimates for CSMA networks. These models typically assume that both the transmission durations and the back-off periods are exponentially distributed. We show that the stationary distribution of the system is in fact insensitive with respect to the transmission durations and the back-off times. These models primarily pertain to a saturated scenario where nodes always have packets to transmit. In reality however, the buffers may occasionally be empty as packets are randomly generated and transmitted over time. The resulting interplay between the activity states and the buffer contents gives rise to quite complicated queueing dynamics, and even establishing the stability criteria is usually a serious challenge. We explicitly identify the stability conditions in a few relevant scenarios, and illustrate the difficulties arising in other cases.