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.
In the performance analysis of CSMA networks, a common assumption is the existence of an underlying graph that represents interference between the various nodes in the network. An edge between two nodes means that destructive interference is caused by simultaneous transmission. Both empirical and theoretical support for the notion of an interference graph is provided in @cite_28 @cite_36 .
@cite_28 @cite_36
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A standard assumption in network information theory is that all nodes are informed at all times of the operations carried out (e.g., of the codebooks used) by any other terminal in the network. In this paper, information theoretic limits are sought under the assumption that, instead, some nodes are not informed about the codebooks used by other terminals. Specifically, capacity results are derived for a relay channel in which the relay is oblivious to the codebook used by the source (oblivious relaying), and an interference relay channel with oblivious relaying and in which each destination is possibly unaware of the codebook used by the interfering source (interference-oblivious decoding). Extensions are also discussed for a related scenario with standard codebook-aware relaying but interference-oblivious decoding. The class of channels under study is limited to out-of-band (or “primitive”) relaying: Relay-to-destinations links use orthogonal resources with respect to the transmission from the source encoders. Conclusions are obtained under a rigorous definition of oblivious processing that is related to the idea of randomized encoding. The framework and results discussed in this paper suggest that imperfect codebook information can be included as a source of uncertainty in network design along with, e.g., imperfect channel and topology information. In this paper, we consider CSMA policies for scheduling packet transmissions in multihop wireless networks with one-hop traffic. The main contribution of the paper is to propose a novel CSMA policy, called Unlocking CSMA (U-CSMA), that enables to obtain both high throughput and low packet delays in large wireless networks. More precisely, we show that for torus interference graph topologies with one-hop traffic, U-CSMA is throughput optimal and achieves order-optimal delay. For one-hop traffic, the delay performance is defined to be order-optimal if the delay stays bounded as the network-size increases. Simulations that we conducted suggest that (a) U-CSMA is throughput-optimal and achieves order-optimal delay for general geometric interference graphs and (b) that U-CSMA can be combined with congestion control algorithms to maximize the network-wide utility and obtain order-optimal delay. To the best of our knowledge, this is the first time that a simple distributed scheduling policy has been proposed that is both throughput utility optimal and achieves order-optimal delay. Given a wireless network where some pairs of communication links interfere with each other, we study sufficient conditions for determining whether a given set of minimum bandwidth quality-of-service requirements can be satisfied. We are especially interested in algorithms which have low communication overhead and low processing complexity. The interference in the network is modeled using a conflict graph whose vertices correspond to the communication links in the network. Two links are adjacent in this graph if and only if they interfere with each other due to being in the same vicinity and hence cannot be simultaneously active. The problem of scheduling the transmission of the various links is then essentially a fractional, weighted vertex coloring problem, for which upper bounds on the fractional chromatic number are sought using only localized information. We recall some distributed algorithms for this problem, and then assess their worst-case performance. Our results on this fundamental problem imply that for some well known classes of networks and interference models, the performance of these distributed algorithms is within a bounded factor away from that of an optimal, centralized algorithm. The performance bounds are simple expressions in terms of graph invariants. It is seen that the induced star number of a network plays an important role in the design and performance of such networks. Due to a poor understanding of the interactions among transmitters, wireless networks using carrier sense multiple access with collision avoidance (CSMA CA) have been commonly stigmatized as unpredictable in nature. Even elementary questions regarding the throughput limitations of these networks cannot be answered in general. In this paper, we investigate the behavior of wireless CSMA CA networks to understand how the transmissions of a particular node affect the medium access, and ultimately the throughput, of other nodes in the network. We introduce a theory which accurately models the behavior of these networks and show that, contrary to popular belief, their performance is predictable and can be described by a system of equations. Using the proposed theory, we provide the analytical expressions necessary to fully characterize the capacity region of any wireless CSMA CA network. We show that this region is nonconvex in general and agnostic to the probability distributions of all network parameters, depending only on their expected values. Our theory is also shown to extend naturally to time division multiple access (TDMA) networks and to predict how the network responds to infeasible input rates.