In this paper, we consider a Cox point process driven by the Manhattan Poisson line process. We calculate the exact cumulative distribution function (CDF) of the path distance (L1 norm) between a randomly selected intersection and the $k$-th nearest node of the Cox process. The CDF is expressed as a sum over the integer partition function $p\!\left(k\right)$, which allows us to numerically evaluate the CDF in a simple manner for practical values of $k$. These distance distributions can be used to study the $k$-coverage of broadcast signals transmitted from a \ac{RSU} located at an intersection in intelligent transport systems (ITS). Also, they can be insightful for network dimensioning in vehicle-to-everything (V2X) systems, because they can yield the exact distribution of network load within a cell, provided that the \ac{RSU} is placed at an intersection. Finally, they can find useful applications in other branches of science like spatial databases, emergency response planning, and districting. We corroborate the applicability of our distance distribution model using the map of an urban area.

翻译：在本文中, 我们考虑由曼哈顿 Poisson 线进程驱动的 Cox 点进程。 我们计算了随机选择的十字路口和 Cox 进程最近节点之间的路径距离( L1 规范) 的准确累积分布函数( CDF ) 。 CDF 表示成整数分割函数$p\\!\\\ left( k\right) 的总计值, 允许我们以简单的方式对 CDF 进行数字评估, 以实际值为 $k$ 。 这些远程分布可用于研究位于智能运输系统交叉点的 \ac{ RSU 传输的广播信号的 $k$- 覆盖值 。 此外, 它们也可以对车辆到 Enveryth( V2X) 系统中的网络维度具有洞察力, 因为它们可以产生一个单元格内网络负荷的精确分布值, 只要 \ ac{RSU 位于一个交叉点。 最后, 它们可以在其他科学分支中找到有用的应用, 如空间数据库、 应急反应规划和区域 。 我们用城市区域地图证实了远程分布模式的可 。