Tandem queueing networks with neighbor blocking and back-offs

We introduce a novel class of tandem queueing networks which arise in modeling the congestion behavior of wireless multi-hop networks with distributed medium access control. These models provide valuable insight in how the network performance in terms of throughput depends on the back-off mechanism that governs the competition among neighboring nodes for access to the medium. The models fall at the interface between classical queueing networks and interacting particle systems, and give rise to high-dimensional stochastic processes that challenge existing methodologies. We present various open problems and conjectures, which are supported by partial results for special cases and limit regimes as well as simulation experiments

Optimal Tradeoff Between Exposed and Hidden Nodes in Large Wireless Networks

Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range we investigate the tradeoff between collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensing range that maximizes throughput critically depends on the activation rate of nodes. For infinite line networks, we prove the existence of a threshold: When the activation rate is below this threshold the optimal sensing range is small (to maximize spatial reuse). When the activation rate is above the threshold the optimal sensing range is just large enough to preclude all collisions. Simulations suggest that this threshold policy extends to more complex linear and non-linear topologies

Delay Performance and Mixing Times in Random-Access Networks

We explore the achievable delay performance in wireless random-access networks. While relatively simple and inherently distributed in nature, suitably designed queue-based random-access schemes provide the striking capability to match the optimal throughput performance of centralized scheduling mechanisms in a wide range of scenarios. The specific type of activation rules for which throughput optimality has been established, may however yield excessive queues and delays. Motivated by that issue, we examine whether the poor delay performance is inherent to the basic operation of these schemes, or caused by the specific kind of activation rules. We derive delay lower bounds for queue-based activation rules, which offer fundamental insight in the cause of the excessive delays. For fixed activation rates we obtain lower bounds indicating that delays and mixing times can grow dramatically with the load in certain topologies as well

Delay performance in random-access grid networks

We examine the impact of torpid mixing and meta-stability issues on the delay performance in wireless random-access networks. Focusing on regular meshes as prototypical scenarios, we show that the mean delays in an $L\times L$ toric grid with normalized load $\rho$ are of the order $(\frac{1}{1-\rho})^L$. This superlinear delay scaling is to be contrasted with the usual linear growth of the order $\frac{1}{1-\rho}$ in conventional queueing networks. The intuitive explanation for the poor delay characteristics is that (i) high load requires a high activity factor, (ii) a high activity factor implies extremely slow transitions between dominant activity states, and (iii) slow transitions cause starvation and hence excessively long queues and delays. Our proof method combines both renewal and conductance arguments. A critical ingredient in quantifying the long transition times is the derivation of the communication height of the uniformized Markov chain associated with the activity process. We also discuss connections with Glauber dynamics, conductance and mixing times. Our proof framework can be applied to other topologies as well, and is also relevant for the hard-core model in statistical physics and the sampling from independent sets using single-site update Markov chains

Balancing exposed and hidden nodes in linear wireless networks

Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range, we investigate the tradeoff between collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensing range that maximizes throughput critically depends on the activation rate of nodes. For infinite line networks, we prove the existence of a threshold: When the activation rate is below this threshold, the optimal sensing range is small (to maximize spatial reuse). When the activation rate is above the threshold, the optimal sensing range is just large enough to preclude all collisions. Simulations suggest that this threshold policy extends to more complex linear and nonlinear topologies. Keywords: Carrier-sensing range; Markov processes; collisions; exposed nodes; hidden nodes; random-access; throughput; wireless network

Learning Wi-Fi Performance

Accurate prediction of wireless network performance is important when performing link adaptation or resource allocation. However, the complexity of interference interactions at MAC and PHY layers, as well as the vast variety of possible wireless configurations make it notoriously hard to design explicit performance models. In this paper, we advocate an approach of “learning by observation” that can remove the need for designing explicit and complex performance models. We use machine-learning techniques to learn implicit performance models, from a limited number of real-world measurements. These models do not require to know the internal mechanics of interfering Wi-Fi links. Yet, our results show that they improve accuracy by at least 49% compared to measurement-seeded models based on SINR. To demonstrate that learned models can be useful in practice, we build a new algorithm that uses such a model as an oracle to jointly allocate spectrum and transmit power. Our algorithm is utility-optimal, distributed, and it produces efficient allocations that significantly improve performance and fairness