文章基本信息

标题：A Gibbsian model for message routeing in highly dense multihop networks
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作者：Wolfgang König ; András Tóbiás
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：1
页码：211-258
DOI：10.30757/ALEA.v16-08
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We investigate a probabilistic model for routeing of messages in relayaugmentedmultihop ad-hoc networks, where each transmitter sends one messageto the origin. Given the (random) transmitter locations, we weight the family ofrandom, uniformly distributed message trajectories by an exponential probabilityweight, favouring trajectories with low interference (measured in terms of signal-tointerferenceratio) and trajectory families with little congestion (measured in termsof the number of pairs of hops using the same relay). Under the resulting Gibbsmeasure, the system targets the best compromise between entropy, interferenceand congestion for a common welfare, instead of an optimization of the individualtrajectories.In the limit of high spatial density of users, we describe the totality of all themessage trajectories in terms of empirical measures. Employing large deviationsarguments, we derive a characteristic variational formula for the limiting free energyand analyse the minimizer(s) of the formula, which describe the most likely shapesof the trajectory ow. The empirical measures of the message trajectories welldescribe the interference, but not the congestion; the latter requires introducingan additional empirical measure. Our results remain valid under replacing the twopenalization terms by more general functionals of these two empirical measures.
关键词：Gibbs distribution of trajectories; high-density limit; large deviations;empirical measure; number of incoming hops; weak topology; variational formula; minimizer;multihop ad-hoc network; message trajectories; signal-to-interference ratio; congestion.