Tail asymptotics of signal-to-interference ratio distribution in spatial cellular network models

We consider a spatial stochastic model of wireless cellular networks, where the base stations (BSs) are deployed according to a simple and stationary point process on $\mathbb{R}^d$, $d\ge2$. In this model, we investigate tail asymptotics of the distribution of signal-to-interference ratio (SIR), which is a key quantity in wireless communications. In the case where the path-loss function representing signal attenuation is unbounded at the origin, we derive the exact tail asymptotics of the SIR distribution under an appropriate sufficient condition. While we show that widely-used models based on a Poisson point process and on a determinantal point process meet the sufficient condition, we also give a counterexample violating it. In the case of bounded path-loss functions, we derive a logarithmically asymptotic upper bound on the SIR tail distribution for the Poisson-based and $\alpha$-Ginibre-based models. A logarithmically asymptotic lower bound with the same order as the upper bound is also obtained for the Poisson-based model.Comment: Dedicated to Tomasz Rolski on the occasion of his 70th birthda

Routeing properties in a Gibbsian model for highly dense multihop networks

We investigate a probabilistic model for routeing in a multihop ad-hoc communication network, where each user sends a message to the base station. Messages travel in hops via the other users, used as relays. Their trajectories are chosen at random according to a Gibbs distribution that favours trajectories with low interference, measured in terms of sum of the signal-to-interference ratios for all the hops, and collections of trajectories with little total congestion, measured in terms of the number of pairs of hops arriving at each relay. This model was introduced in our earlier paper [KT17], where we expressed, in the high-density limit, the distribution of the optimal trajectories as the minimizer of a characteristic variational formula. In the present work, in the special case in which congestion is not penalized, we derive qualitative properties of this minimizer. We encounter and quantify emerging typical pictures in analytic terms in three extreme regimes. We analyze the typical number of hops and the typical length of a hop, and the deviation of the trajectory from the straight line in two regimes, (1) in the limit of a large communication area and large distances, and (2) in the limit of a strong interference weight. In both regimes, the typical trajectory turns out to quickly approach a straight line, in regime (1) with equally-sized hops. Surprisingly, in regime (1), the typical length of a hop diverges logarithmically as the distance of the transmitter to the base station diverges. We further analyze the local and global repulsive effect of (3) a densely populated area on the trajectories. Our findings are illustrated by numerical examples. We also discuss a game-theoretic relation of our Gibbsian model with a joint optimization of message trajectories opposite to a selfish optimization, in case congestion is also penalize

End-to-end admission control of multiclass traffic in WCDMA mobile network and wireline differentiated services

Master'sMASTER OF ENGINEERIN

A Gibbsian model for message routing in highly dense multi-hop networks

We investigate a probabilistic model for routing in relay-augmented multihop ad-hoc communication networks, where each user sends one message to the base station. Given the (random) user locations, we weigh the family of random, uniformly distributed message trajectories by an exponential probability weight, favouring trajectories with low interference (measured in terms of signal-to-interference ratio) and trajectory families with little congestion (measured by how many pairs of hops use the same relay). Under the resulting Gibbs measure, the system targets the best compromise between entropy, interference and congestion for a common welfare, instead of a selfish optimization. We describe the joint routing strategy in terms of the empirical measure of all message trajectories. In the limit of high spatial density of users, we derive the limiting free energy and analyze the optimal strategy, given as the minimizer(s) of a characteristic variational formula. Interestingly, expressing the congestion term requires introducing an additional empirical measure

Routeing properties in a Gibbsian model for highly dense multihop networks

We investigate a probabilistic model for routeing in a multihop ad-hoc communication network, where each user sends a message to the base station. Messages travel in hops via other users, used as relays. Their trajectories are chosen at random according to a Gibbs distribution, which favours trajectories with low interference, measured in terms of signal-to-interference ratio. This model was introduced in our earlier paper [KT18], where we expressed, in the limit of a high density of users, the typical distribution of the family of trajectories in terms of a law of large numbers. In the present work, we derive its qualitative properties. We analytically identify the emerging typical scenarios in three extreme regimes. We analyse the typical number of hops and the typical length of a hop, and the deviation of the trajectory from the straight line, (1) in the limit of a large communication area and large distances, and (2) in the limit of a strong interference weight. In both regimes, the typical trajectory approaches a straight line quickly, in regime (1) with equal hop lengths. Interestingly, in regime (1), the typical length of a hop diverges logarithmically in the distance of the transmitter to the base station. We further analyse (3) local and global repulsive effects of a densely populated subarea on the trajectories.Comment: 36 pages, 5 figure

Design and Performance Analysis of Next Generation Heterogeneous Cellular Networks for the Internet of Things

The Internet of Things (IoT) is a system of inter-connected computing devices, objects and mechanical and digital machines, and the communications between these devices/objects and other Internet-enabled systems. Scalable, reliable, and energy-efficient IoT connectivity will bring huge benefits to the society, especially in transportation, connected self-driving vehicles, healthcare, education, smart cities, and smart industries. The objective of this dissertation is to model and analyze the performance of large-scale heterogeneous two-tier IoT cellular networks, and offer design insights to maximize their performance. Using stochastic geometry, we develop realistic yet tractable models to study the performance of such networks. In particular, we propose solutions to the following research problems: -We propose a novel analytical model to estimate the mean uplink device data rate utility function under both spectrum allocation schemes, full spectrum reuse (FSR) and orthogonal spectrum partition (OSP), for uplink two-hop IoT networks. We develop constraint gradient ascent optimization algorithms to obtain the optimal aggregator association bias (for the FSR scheme) and the optimal joint spectrum partition ratio and optimal aggregator association bias (for the OSP scheme). -We study the performance of two-tier IoT cellular networks in which one tier operates in the traditional sub-6GHz spectrum and the other, in the millimeter wave (mm-wave) spectrum. In particular, we characterize the meta distributions of the downlink signal-to-interference ratio (sub-6GHz spectrum), the signal-to-noise ratio (mm-wave spectrum) and the data rate of a typical device in such a hybrid spectrum network. Finally, we characterize the meta distributions of the SIR/SNR and data rate of a typical device by substituting the cumulative moment of the CSP of a user device into the Gil-Pelaez inversion theorem. -We propose to split the control plane (C-plane) and user plane (U-plane) as a potential solution to harvest densification gain in heterogeneous two-tier networks while minimizing the handover rate and network control overhead. We develop a tractable mobility-aware model for a two-tier downlink cellular network with high density small cells and a C-plane/U-plane split architecture. The developed model is then used to quantify effect of mobility on the foreseen densification gain with and without C-plane/U-plane splitting