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 favors trajecto...

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Bibliographic Details
Published in:IEEE transactions on information theory 2019-11, Vol.65 (11), p.6875-6897
Main Authors: Konig, Wolfgang, Tobias, Andras
Format: Article
Language:English
Subjects:
Ad hoc networks
Area measurement
Base stations
Entropy
expected number of hops
Gibbs distribution
high-density limit
Interference
message routeing
Multihop ad-hoc network
point processes
Probabilistic models
Probability theory
Qualitative analysis
Radio equipment
Relays
Routeing
selfish routeing
signal-to-interference ratio
Spread spectrum communication
Trajectory
Trajectory measurement
variational analysis
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Summary: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 favors trajectories with low interference, measured in terms of signal-to-interference ratio. This model was introduced in our earlier paper, 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 this paper, we derive its qualitative properties. We analytically identify the emerging typical scenarios 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, regime 1 in the limit of a large communication area and large distances and regime 2 in the limit of a strong interference weight. In both the regimes, the typical trajectory approaches a straight line quickly, in regime 1 with equal hop lengths. Interestingly, in regime 2, the typical length of a hop diverges logarithmically in the distance of the transmitter to the base station. We further analyze (regime 3) local and global repulsive effects of a densely populated subarea on the trajectories.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2019.2924187