11 research outputs found
Large deviations in relay-augmented wireless networks
We analyze a model of relay-augmented cellular wireless networks. The network
users, who move according to a general mobility model based on a Poisson point
process of continuous trajectories in a bounded domain, try to communicate with
a base station located at the origin. Messages can be sent either directly or
indirectly by relaying over a second user. We show that in a scenario of an
increasing number of users, the probability that an atypically high number of
users experiences bad quality of service over a certain amount of time, decays
at an exponential speed. This speed is characterized via a constrained entropy
minimization problem. Further, we provide simulation results indicating that
solutions of this problem are potentially non-unique due to symmetry breaking.
Also two general sources for bad quality of service can be detected, which we
refer to as isolation and screening.Comment: 28 pages, 5 figures; corrected several misprint
Disruptive events in high-density cellular networks
Stochastic geometry models are used to study wireless networks, particularly
cellular phone networks, but most of the research focuses on the typical user,
often ignoring atypical events, which can be highly disruptive and of interest
to network operators. We examine atypical events when a unexpected large
proportion of users are disconnected or connected by proposing a hybrid
approach based on ray launching simulation and point process theory. This work
is motivated by recent results using large deviations theory applied to the
signal-to-interference ratio. This theory provides a tool for the stochastic
analysis of atypical but disruptive events, particularly when the density of
transmitters is high. For a section of a European city, we introduce a new
stochastic model of a single network cell that uses ray launching data
generated with the open source RaLaNS package, giving deterministic path loss
values. We collect statistics on the fraction of (dis)connected users in the
uplink, and observe that the probability of an unexpected large proportion of
disconnected users decreases exponentially when the transmitter density
increases. This observation implies that denser networks become more stable in
the sense that the probability of the fraction of (dis)connected users
deviating from its mean, is exponentially small. We also empirically obtain and
illustrate the density of users for network configurations in the disruptive
event, which highlights the fact that such bottleneck behaviour not only stems
from too many users at the cell boundary, but also from the near-far effect of
many users in the immediate vicinity of the base station. We discuss the
implications of these findings and outline possible future research directions.Comment: 8 pages, 11 figure
Disruptive events in high-density cellular networks
Stochastic geometry models are used to study wireless networks, particularly cellular phone networks, but most of the research focuses on the typical user, often ignoring atypical events, which can be highly disruptive and of interest to network operators. We examine atypical events when a unexpected large proportion of users are disconnected or connected by proposing a hybrid approach based on ray launching simulation and point process theory. This work is motivated by recent results [12] using large deviations theory applied to the signal-to-interference ratio. This theory provides a tool for the stochastic analysis of atypical but disruptive events, particularly when the density of transmitters is high. For a section of a European city, we introduce a new stochastic model of a single network cell that uses ray launching data generated with the open source RaLaNS package, giving deterministic path loss values. We collect statistics on the fraction of (dis)connected users in the uplink, and observe that the probability of an unexpected large proportion of disconnected users decreases exponentially when the transmitter density increases. This observation implies that denser networks become more stable in the sense that the probability of the fraction of (dis)connected users deviating from its mean, is exponentially small. We also empirically obtain and illustrate the density of users for network configurations in the disruptive event, which highlights the fact that such bottleneck behaviour not only stems from too many users at the cell boundary, but also from the near-far effect of many users in the immediate vicinity of the base station. We discuss the implications of these findings and outline possible future research directions
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
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