Backlog-based random access in wireless networks : fluid limits and delay issues

We explore the spatio-temporal congestion dynamics of wireless networks with backlog-based random-access mechanisms. While relatively simple and inherently distributed in nature, suitably designed backlog-based access schemes provide the striking capability to match the optimal throughput performance of centralized scheduling algorithms in a wide range of scenarios. In the present paper, we show that the specific activity functions for which maximum stability has been established, may however yield excessive queue lengths and delays. The results reveal that more aggressive/persistent access schemes can improve the delay performance, while retaining the maximum stability guarantees in a rich set of scenarios. In order to gain qualitative insights and examine stability properties we will investigate fluid limits where the system dynamics are scaled in space and time. As it turns out, several distinct types of fluid limits can arise, exhibiting various degrees of randomness, depending on the structure of the network, in conjunction with the form of the activity functions. We further demonstrate that, counter to intuition, additional interference may improve the delay performance in certain cases. Simulation experiments are conducted to illustrate and validate the analytical findings

Wireless data performance in multi-cell scenarios

The performance of wireless data systems has been extensively studied in the context of a single base station. In the present paper we investigate the flow-level performance in networks with multiple base stations. We specifically examine the complex, dynamic interaction introduced by the strong impact of interference from neighboring base stations. We derive two types of lower and upper bounds for the number of active flows, transfer delays and flow throughputs in the various cells. While the first type of bounds are rather rough and simple to compute, the second type of bounds are sharper, but harder to calculate. In order to obtain closed-form estimates for the latter bounds, we introduce two limit regimes, termed fluid and quasi-stationary regime, where the system dynamics evolve on a very fast and a very slow time scale, respectively. Importantly, the performance in both limit regimes is insensitive, thus yielding simple, explicit estimates that render the detailed statistical characteristics of the system largely irrelevant. Numerical experiments show that the upper bounds evaluated in the quasi-stationary regime provide conservative and extremely tight approximations

Consistent expressions of refraction, polarization, light scattering and electric birefringence deduced from improved evaluations of local field effects and light scattered intensity - Applications to liquids

Classical orientation theories of rigid molecules in electro-optic fields are reexamined and significantly improved. Firstly a more consistent evaluation of local field effects is made within the practical spherical model by introducing approximations at the end of theoretical calculations only. This modification does not change classical formulae for refraction (Lorentz-Lorenz) and light scattering (depolarized Rayleigh intensity), but polarization and electric birefringence formulae are modified. Secondly a more correct derivation allows us to obtain a general expression of the light scattered intensity applicable both to dense fluids and to the perfect gas. Thirdly a more rigourous expression of the density fluctuation term is deduced without any approximation about the local field. The four electro-optic formulae are applied successfully to several liquids

Flow-level Stability of Utility-Based Allocations for Non-Convex Rate Regions

We investigate the stability of utility-maximizing allocations in networks with arbitrary rate regions. We consider a dynamic setting where users randomly generate data flows according to some exogenous traffic processes. Network stability is then defined as the ergodicity of the process describing the number of active flows. When the rate region is convex, the stability region is known to coincide with the rate region, independently of the considered utility function. We show that for non-convex rate regions, the choice of the utility function is crucial to ensure maximum stability. The results are illustrated on the simple case of a wireless network consisting of two interacting base stations

Insensitive bandwidth sharing in data networks

We represent a data network as a set of links shared by a dynamic number of competing flows. These flows are generated within sessions and correspond to the transfer of a random volume of data on a pre-defined network route. The evolution of the stochastic process describing the number of flows on all routes, which determines the performance of the data transfers, depends on how link capacity is allocated between competing flows. We use some key properties of Whittle queueing networks to characterize the class of allocations which are insensitive in the sense that the stationary distribution of this stochastic process does not depend on any traffic characteristics (session structure, data volume distribution) except the traffic intensity on each route. We show in particular that this insensitivity property does not hold in general for well-known allocations such as max-min fairness or proportional fairness. These results are ilustrated by several examples on a number of network topologies

How mobility impacts the flow-level performance of wireless data networks

The potential for exploiting rate variations to improve the performance of wireless data networks by opportunistic scheduling has been extensively studied at the packet level. In the present paper, we examine how slower, mobility-induced rate variations impact the performance at the flow level, accounting for the dynamic number of users sharing the transmission resource. We identify two limit regimes, termed fluid regime and quasi-stationary regime, where the rate variations occur on an infinitely fast and an infinitely slow time scale, respectively. Using stochastic comparison techniques, we show that these limit regimes provide simple, insensitive performance bounds that only depend on easily calculated load factors. Additionally, we prove that for a broad class of Markov-type fading processes, the performance varies monotonically with the time scale of the rate variations. The results are illustrated through numerical experiments, showing that the fluid and quasi-stationary bounds are remarkably sharp in certain typical cases