Achievable Performance in Product-Form Networks

We characterize the achievable range of performance measures in product-form networks where one or more system parameters can be freely set by a network operator. Given a product-form network and a set of configurable parameters, we identify which performance measures can be controlled and which target values can be attained. We also discuss an online optimization algorithm, which allows a network operator to set the system parameters so as to achieve target performance metrics. In some cases, the algorithm can be implemented in a distributed fashion, of which we give several examples. Finally, we give conditions that guarantee convergence of the algorithm, under the assumption that the target performance metrics are within the achievable range.Comment: 50th Annual Allerton Conference on Communication, Control and Computing - 201

Mixing Properties of CSMA Networks on Partite Graphs

We consider a stylized stochastic model for a wireless CSMA network. Experimental results in prior studies indicate that the model provides remarkably accurate throughput estimates for IEEE 802.11 systems. In particular, the model offers an explanation for the severe spatial unfairness in throughputs observed in such networks with asymmetric interference conditions. Even in symmetric scenarios, however, it may take a long time for the activity process to move between dominant states, giving rise to potential starvation issues. In order to gain insight in the transient throughput characteristics and associated starvation effects, we examine in the present paper the behavior of the transition time between dominant activity states. We focus on partite interference graphs, and establish how the magnitude of the transition time scales with the activation rate and the sizes of the various network components. We also prove that in several cases the scaled transition time has an asymptotically exponential distribution as the activation rate grows large, and point out interesting connections with related exponentiality results for rare events and meta-stability phenomena in statistical physics. In addition, we investigate the convergence rate to equilibrium of the activity process in terms of mixing times.Comment: Valuetools, 6th International Conference on Performance Evaluation Methodologies and Tools, October 9-12, 2012, Carg\`ese, Franc

Slow transitions, slow mixing and starvation in dense random-access networks

We consider dense wireless random-access networks, modeled as systems of particles with hard-core interaction. The particles represent the network users that try to become active after an exponential back-off time, and stay active for an exponential transmission time. Due to wireless interference, active users prevent other nearby users from simultaneous activity, which we describe as hard-core interaction on a conflict graph. We show that dense networks with aggressive back-off schemes lead to extremely slow transitions between dominant states, and inevitably cause long mixing times and starvation effects.Comment: 29 pages, 5 figure

A mass spectrometer observation of NO in an auroral arc

NO measurement in auroral arc by mass spectrometer onboard Aerobee rocke

Data Dissemination Performance in Large-Scale Sensor Networks

As the use of wireless sensor networks increases, the need for (energy-)efficient and reliable broadcasting algorithms grows. Ideally, a broadcasting algorithm should have the ability to quickly disseminate data, while keeping the number of transmissions low. In this paper we develop a model describing the message count in large-scale wireless sensor networks. We focus our attention on the popular Trickle algorithm, which has been proposed as a suitable communication protocol for code maintenance and propagation in wireless sensor networks. Besides providing a mathematical analysis of the algorithm, we propose a generalized version of Trickle, with an additional parameter defining the length of a listen-only period. This generalization proves to be useful for optimizing the design and usage of the algorithm. For single-cell networks we show how the message count increases with the size of the network and how this depends on the Trickle parameters. Furthermore, we derive distributions of inter-broadcasting times and investigate their asymptotic behavior. Our results prove conjectures made in the literature concerning the effect of a listen-only period. Additionally, we develop an approximation for the expected number of transmissions in multi-cell networks. All results are validated by simulations

The impact of a network split on cascading failure processes

Cascading failure models are typically used to capture the phenomenon where failures possibly trigger further failures in succession, causing knock-on effects. In many networks this ultimately leads to a disintegrated network where the failure propagation continues independently across the various components. In order to gain insight in the impact of network splitting on cascading failure processes, we extend a well-established cascading failure model for which the number of failures obeys a power-law distribution. We assume that a single line failure immediately splits the network in two components, and examine its effect on the power-law exponent. The results provide valuable qualitative insights that are crucial first steps towards understanding more complex network splitting scenarios

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