Routeing Properties in a Gibbsian Model for Highly Dense Multihop Networks

DOI10.1109/TIT.2019.2924187zbMATH Open1433.94028arXiv1801.04985WikidataQ127680446 ScholiaQ127680446MaRDI QIDQ5211482

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Publication date: 28 January 2020

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1801.04985

zbMATH Keywords

Gibbs distribution signal-to-interference ratio messages travel in hops multihop ad hoc communication network probabilistic model for routing trajectories are chosen at random trajectories with low interference user sends a message to the base station

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Large deviations (60F10) Convergence of probability measures (60B10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)