On the k Nearest-Neighbor Path Distance from the Typical Intersection in the Manhattan Poisson Line Cox Process

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