二项线过程：距离分布

摘要：

我们介绍了二项线过程（BLP），一种新的空间随机模型的表征街道的无线和车载网络的统计评估。现有的街道随机几何模型，例如，泊松线过程（PLP）和曼哈顿线过程（MLP）缺乏城市街道网络的一个重要方面：城市中心的街道密集，郊区附近的街道稀疏。与这些模型相反，BLP将街道的生成点限制在以欧几里得平面的原点为中心的固定半径，从而捕获街道相对于与中心的距离的不均匀性。我们推导出一个封闭形式的表达式的接触分布的BLP从一个随机的位置上的平面。利用这一点，我们引入了新的二项式线考克斯过程（BLCP）来模拟点的BLP的各条线，并推导出分布到最近的BLCP点从任意位置。使用数值结果，我们强调，从城市中心用户的角度来看，郊区用户的街道的空间配置是显着不同的。在本文中开发的框架可以与现有的模型线过程更准确地描述城市和郊区环境中的街道。

英文摘要：

We introduce the binomial line process (BLP), a novel spatial stochastic model for the characterization of streets in the statistical evaluation of wireless and vehicular networks. Existing stochastic geometry models for streets, e.g., Poisson line processes (PLP) and Manhattan line processes (MLP) lack an important aspect of city-wide street networks: streets are denser in the city center and sparse near the suburbs. Contrary to these models, the BLP restricts the generating points of the streets to a fixed radius centered at the origin of the Euclidian plane, thereby capturing the inhomogeneity of the streets with respect to the distance from the center. We derive a closed-form expression for the contact distribution of the BLP from a random location on the plane. Leveraging this, we introduce the novel Binomial line Cox process (BLCP) to emulate points on individual lines of the BLP and derive the distribution to the nearest BLCP point from an arbitrary location. Using numerical results, we highlight that the spatial configuration of the streets is remarkably distinct from the perspective of a city center user to that of a suburban user. The framework developed in this paper can be integrated with the existing models of line processes for more accurate characterization of streets in urban and suburban environments.

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