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

Temporal starvation in multi-channel CSMA networks: an analytical framework

In this paper we consider a stochastic model for a frequency-agile CSMA protocol for wireless networks where multiple orthogonal frequency channels are available. Even when the possible interference on the different channels is described by different conflict graphs, we show that the network dynamics can be equivalently described as that of a single-channel CSMA algorithm on an appropriate virtual network. Our focus is on the asymptotic regime in which the network nodes try to activate aggressively in order to achieve maximum throughput. Of particular interest is the scenario where the number of available channels is not sufficient for all nodes of the network to be simultaneously active and the well-studied temporal starvation issues of the single-channel CSMA dynamics persist. For most networks we expect that a larger number of available channels should alleviate these temporal starvation issues. However, we prove that the aggregate throughput is a non-increasing function of the number of available channels. To investigate this trade-off that emerges between aggregate throughput and temporal starvation phenomena, we propose an analytical framework to study the transient dynamics of multi-channel CSMA networks by means of first hitting times. Our analysis further reveals that the mixing time of the activity process does not always correctly characterize the temporal starvation in the multi-channel scenario and often leads to pessimistic performance estimates.Comment: 15 pages, 4 figures. Accepted for publication at IFIP Performance Conference 201

Queue-Based Random-Access Algorithms: Fluid Limits and Stability Issues

We use fluid limits to explore the (in)stability properties of wireless networks with queue-based random-access algorithms. Queue-based random-access schemes are simple and inherently distributed in nature, yet provide the capability to match the optimal throughput performance of centralized scheduling mechanisms in a wide range of scenarios. Unfortunately, the type of activation rules for which throughput optimality has been established, may result in excessive queue lengths and delays. The use of more aggressive/persistent access schemes can improve the delay performance, but does not offer any universal maximum-stability guarantees. In order to gain qualitative insight and investigate the (in)stability properties of more aggressive/persistent activation rules, we examine fluid limits where the dynamics are scaled in space and time. In some situations, the fluid limits have smooth deterministic features and maximum stability is maintained, while in other scenarios they exhibit random oscillatory characteristics, giving rise to major technical challenges. In the latter regime, more aggressive access schemes continue to provide maximum stability in some networks, but may cause instability in others. Simulation experiments are conducted to illustrate and validate the analytical results

Fair Coexistence of Scheduled and Random Access Wireless Networks: Unlicensed LTE/WiFi

We study the fair coexistence of scheduled and random access transmitters sharing the same frequency channel. Interest in coexistence is topical due to the need for emerging unlicensed LTE technologies to coexist fairly with WiFi. However, this interest is not confined to LTE/WiFi as coexistence is likely to become increasingly commonplace in IoT networks and beyond 5G. In this article we show that mixing scheduled and random access incurs and inherent throughput/delay cost, the cost of heterogeneity. We derive the joint proportional fair rate allocation, which casts useful light on current LTE/WiFi discussions. We present experimental results on inter-technology detection and consider the impact of imperfect carrier sensing.Comment: 14 pages, 8 figures, journa

A critical look at power law modelling of the Internet

This paper takes a critical look at the usefulness of power law models of the Internet. The twin focuses of the paper are Internet traffic and topology generation. The aim of the paper is twofold. Firstly it summarises the state of the art in power law modelling particularly giving attention to existing open research questions. Secondly it provides insight into the failings of such models and where progress needs to be made for power law research to feed through to actual improvements in network performance.Comment: To appear Computer Communication