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Routeing Properties in a Gibbsian Model for Highly Dense Multihop Networks

机译：吉布斯模型中高密度多跳网络的路由属性

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摘要

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.
机译：我们研究了一种概率模型，用于在多跳自组织通信网络中进行路由，其中​​每个用户向基站发送一条消息。邮件通过其他用户作为中继在跃点中传播。它们的轨迹是根据吉布斯分布随机选择的，吉布斯分布有利于以信号干扰比衡量的低干扰的轨迹。该模型是在我们较早的论文中介绍的，我们在此基础上以高用户密度为限，以大数定律表示了轨迹族的典型分布。在本文中，我们推导了其定性性质。我们分析性地确定了三种极端情况下正在出现的典型情况。我们分析了典型的跳数和典型的跳长，以及轨迹与直线的偏离，在大通信区域和大距离的限制下为方案1，在强干扰权重的限制下为方案2。在这两种情况下，典型轨迹都在具有相同跃点长度的情况下快速接近一条直线。有趣的是，在方式2中，典型的跳段长度在发射机到基站的距离上呈对数分叉。我们进一步分析（区域3）人口稠密分区对轨迹的局部和全局排斥作用。

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